UBC Theses and Dissertations

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UBC Theses and Dissertations

Nuclear magnetic resonance in inhomogeneous magnetic fields Norwood, Timothy John 1985

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NUCLEAR MAGNETIC RESONANCE IN INHOMOGENEOUS MAGNETIC FIELDS  by TIMOTHY JOHN NORWOOD B.Sc.  (Hons.), U n i v e r s i t y  o f L o n d o n , 1983  THESIS SUBMITTED I N PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department  of Chemistry)  We a c c e p t t h i s t h e s i s a s c o n f o r m i n g to the required  standard  THE UNIVERSITY OF B R I T I S H COLUMBIA S e p t e m b e r , 1985 © Timothy  J o h n N o r w o o d , 1985  In p r e s e n t i n g  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of  requirements f o r an advanced degree a t the  the  University  o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make it  f r e e l y a v a i l a b l e f o r reference  and  study.  I further  agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may  be granted by the head o f  department o r by h i s o r her r e p r e s e n t a t i v e s .  my  It i s  understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain  s h a l l not be allowed without my  permission.  Department of  C H E M I S T R Y  The  U n i v e r s i t y o f B r i t i s h Columbia  1956  Main Mall  V6T  1Y3  Van couve r , Canada  Date  19 S E P T E M B E R  1785  written  i i ABSTRACT  The attempt  work d e s c r i b e d i n t h i s  t o overcome the l i m i t a t i o n s  s p e c t r o s c o p y by m a g n e t i c areas: high resolution chemical s h i f t In  t h e s i s was  field  i m p o s e d upon  inhomogeneity  r e s o l v e d NMR  imaging field  i n two  specific  liquids,  in isotropic  inhomogeneity  i n an  NMR  spectroscopy i n i s o t r o p i c  both cases magnetic  the r e s o l u t i o n  initiated  liquids. may  degrade  of s p e c t r a t o s u c h an e x t e n t t h a t no  useful  i n f o r m a t i o n c a n be o b t a i n e d f r o m them. I n h i g h r e s o l u t i o n spectroscopy  i t i s n e c e s s a r y t o be a b l e t o e x t r a c t  the parameters shifts,  present within  the spectrum  imaging experiments  s t r i n g e n t ; and  NMR  accurately  s u c h as c h e m i c a l  c o u p l i n g c o n s t a n t s and peak a r e a s . I n c h e m i c a l  resolved  and  the requirements are  shift  less  i t i s only necessary t h a t the resonances  of  different  c h e m i c a l s p e c i e s be r e s o l v e d . However, e v e n t h e  less  stringent  r e q u i r e m e n t s o f NMR  to  imaging are o f t e n d i f f i c u l t  meet a s t h e s a m p l e v o l u m e s r e q u i r e d a r e o f t e n of  magnitude l a r g e r  r e s o l u t i o n NMR The  use  orders  in conventional high  spectroscopy. of zero-quantum c o h e r e n c e  as a p o t e n t i a l problem  than those r e q u i r e d  several  solution  has been  t o the magnetic  field  investigated inhomogeneity  i n both of these a r e a s . Zero-quantum coherences  independent parameters  of magnetic desired  field  inhomogeneity  i n both c a s e s , though  are  and c o n t a i n t h e  they are d i s p l a y e d i n  a way  w h i c h d i f f e r s f r o m c o n v e n t i o n a l NMR In  this thesis,  existing  zero-quantum  spectra. coherence  e x p e r i m e n t s h a v e been e v a l u a t e d f o r use w i t h magnetic  fields,  purpose.  S e v e r a l c o m p l e t e l y new  a n d , where n e c e s s a r y , a d a p t e d  f o r p r o d u c i n g broad-band  coherence  s p e c t r a and a l s o  decoupled  for  use.  i s as c l o s e  has been e v a l u a t e d a s a  unknown compounds and a l s o  c o m p o n e n t s o f c o m p l e x m i x t u r e s by B o t h d e c o u p l e d and experiments are adapted  "signature"  non-decoupled  zero-quantum  J - r e s o l v e d experiment  fields.  i s a l s o adapted  tool  The  for this  the  recognition. coherence  t o p r o v i d e imaging experiments  i n inhomogeneous m a g n e t i c  ease  for identifying  a l l o w t h e s e p a r a t i o n o f t h e i m a g e s of d i f f e r e n t species  to  s p e c t r a as p o s s i b l e , hence f a c i l i t a t i n g  Zero-quantum coherence  identifying  zero-quantum  for presenting coupling constants  and c h e m i c a l s h i f t s i n a manner w h i c h  of  for this  e x p e r i m e n t s h a v e been  developed  c o n v e n t i o n a l NMR  inhomogeneous  which  chemical two-dimensional purpose.  iv TABLE  OF  CONTENTS  Page ABSTRACT  ii  TABLE OF CONTENTS  iv  L I S T OF TABLES  v i i  L I S T OF FIGURES  viii  CHAPTER I - INTRODUCTION  1  1.1 - M a g n e t i c F i e l d  Inhomogeneity  2  1.2 - M u l t i p l e - Q u a n t u m C o h e r e n c e  4  1.3 - The P r o d u c t O p e r a t o r F o r m a l i s m  10  - References  CHAPTER I I - NUCLEAR MAGNETIC RESONANCE  15  SPECTROSCOPY  IN AN INHOMOGENEOUS MAGNETIC F I E L D 2.1 - Zero-Quantum S p e c t r o s c o p y  i n an  Inhomogeneous M a g n e t i c F i e l d 2.2 - E d i t i n g  Zero-Quantum C o h e r e n c e S p e c t r a  2.3 - N o n - S e l e c t i v e E x c i t a t i o n of  17  18 30  and D e t e c t i o n  Zero-Quantum C o h e r e n c e i n an  Inhomogeneous M a g n e t i c F i e l d  31  2.4 - H o m o n u c l e a r B r o a d - B a n d D e c o u p l e d Zero-Quantum C o h e r e n c e S p e c t r o s c o p y  36  2.5 - S i n g l e - Q u a n t u m J - R e s o l v e d B r o a d Band D e c o u p l e d Zero-Quantum S p e c t r o s c o p y  48  V  2.6 - The R e c o n s t r u c t i o n o f S i n g l e - Q u a n t u m Spectra  i n an Inhomogeneous M a g n e t i c  Field  61  2.7 - The A s s i g n m e n t o f Zero-Quantum Coherence  Spectra  i n Inhomogeneous  Magnetic F i e l d s  66  2.8 - The A n a l y s i s o f M i x t u r e s  i n an  Inhomogeneous M a g n e t i c F i e l d  by t h e  R e c o g n i t i o n o f t h e Zero-Quantum Coherence  Signatures of Their  Constituents  74  2.9 - E x p e r i m e n t a l  82  - References  84  CHAPTER I I I -NUCLEAR MAGNETIC RESONANCE  IMAGING I N  AN INHOMOGENEOUS MAGNETIC F I E L D 3.1 - N u c l e a r M a g n e t i c R e s o n a n c e 3.2 - C h e m i c a l S h i f t  Imaging  R e s o l v e d Imaging  87 88 92  3.3 - Zero-Quantum C o h e r e n c e R e s o l v e d Imaging 3.4 - B r o a d - B a n d  95 Decoupled  Zero-Quantum  Coherence Resolved Imaging  105  3.5 - J - R e s o l v e d I m a g i n g  114  3.6 - E x p e r i m e n t a l  121  - References  CHAPTER I V - CONCLUSION  122  126  vi APPENDIX I - PRODUCT OPERATOR EVOLUTION A1.1 - I n t r o d u c t i o n  130  t o t h e E v o l u t i o n of  Product Operators  131  A1.2 - C h e m i c a l S h i f t E v o l u t i o n  132  A1.3 - S p i n - S p i n  133  Coupling  Evolution  A1.4 - R a d i o - F r e q u e n c y P u l s e  Evolution  A1.5 - Zero-Quantum C o h e r e n c e E v o l u t i o n - References APPENDIX I I - ZERO-QUANTUM SPECTRA OF AMINO ACIDS  133 134 135 137  VI  1  LIST OF TABLES  TABLE I P h a s e c y c l i n g schemes f o r m u l t i p l e - q u a n t u m coherence order s e l e c t i o n TABLE I I E f f e c t s of present at broad-band f o r an A X 2  t h e p u l s e a=90° on t h e p r o d u c t o p e r a t o r s t h e end o f t h e e v o l u t i o n t i m e t ^ o f t h e decoupled zero-quantum experiment spin-system.  TABLE I I I E f f e c t s o f an a r b i t r a r y p u l s e a on t h e p r o d u c t o p e r a t o r s p r e s e n t a t t h e end o f t h e e v o l u t i o n t i m e trj o f t h e b r o a d - b a n d d e c o u p l e d z e r o - q u a n t u m e x p e r i m e n t f o r an A X spin-system. 2  vi ii L I S T OF  FIGURES  Page CHAPTER I F i g u r e 1.1. S p i n v e c t o r a n d r o t a t i n g f r a m e r e p r e s e n t a t i o n s o f an e n s e m b l e o f s p i n s a t t h e r m a l e q u i l i b r i u m and as s i n g l e - q u a n t u m coherence.  6  F i g u r e 1.2. E n e r g y d i a g r a m f o r an AX s p i n - s y s t e m showing t h e phase c o h e r e n c e s which a r e p o s s i b l e .  8  F i g u r e 1.3. P r o d u c t o p e r a t o r s a n d t h e i r c o r r e s p o n d i n g r o t a t i n g frame r e p r e s e n t a t i o n s .  13  CHAPTER I I Figure  2.1. B a s i c z e r o - q u a n t u m e x p e r i m e n t .  F i g u r e 2.2. B a s i c z e r o - q u a n t u m e x p e r i m e n t magnetic f i e l d gradient order s e l e c t i o n . Figure  19 with  2.3. R e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t .  19 23  F i g u r e 2.4. Z e r o - q u a n t u m s p e c t r a o f , A. L - a l a n i n e , B. L - t h r e o n i n e , C. L - v a l i n e , D. L - a s p a r a g i n e , i n d i v i d u a l l y ' i n a homogeneous m a g n e t i c f i e l d , a n d E. t o g e t h e r i n an i n h o m o g e n e o u s m a g n e t i c f i e l d . 28 F i g u r e 2.5. S i n g l e - q u a n t u m s p e c t r a o f a m i x t u r e o f L - a l a n i n e , L - t h r e o n i n e , L - v a l i n e and L - a s p a r a g i n e , A. i n homogeneous a n d B. i n h o m o g e n e o u s m a g n e t i c fields.  29  F i g u r e 2.6. Z e r o - q u a n t u m s p e c t r a o f L - t h r e o n i n e o b t a i n e d w i t h d i f f e r e n t l e n g t h s of p r e p a r a t i o n and r e f o c u s s i n g p e r i o d s w i t h the r e f o c u s s e d zero-quantum experiment. 32 F i g u r e 2.7. R e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t w i t h A. an a c c o r d i o n p r e p a r a t i o n p e r i o d , a n d B. w i t h a c c o r d i o n p r e p a r a t i o n and r e f o c u s s i n g p e r i o d s . 34  ix  F i g u r e 2.8. Z e r o - q u a n t u m s p e c t r a o f L - t h r e o n i n e o b t a i n e d w i t h the r e f o c u s s e d zero-quantum experiment w i t h A. an a c c o r d i o n p r e p a r a t i o n p e r i o d , a n d B. w i t h a c c o r d i o n p r e p a r a t i o n and r e f o c u s s i n g p e r i o d s . " 35 F i g u r e 2.9. B r o a d - b a n d d e c o u p l e d experiment.  zero-quantum  38  F i g u r e 2.10. Z e r o - q u a n t u m s p e c t r a o f a m i x t u r e o f e t h a n o l and 2 - p r o p a n o l , A. u n d e c o u p l e d , B-D. d e c o u p l e d , w i t h a=90°.  43  F i g u r e 2.11. G r a p h o f z e r o - q u a n t u m c o h e r e n c e i n t e n s i t y v s . l e n g t h of e v o l u t i o n time f o r ethanol and 2 - p r o p a n o l w i t h t h e b r o a d - b a n d decoupled zero-quantum experiment.  45  F i g u r e 2.12. B r o a d - b a n d d e c o u p l e d s p e c t r a of e t h a n o l and 2-propanol  48  zero-quantum w i t h a=45°.  F i g u r e 2.13. S i n g l e - q u a n t u m J - r e s o l v e d decoupled zero-quantum experiment.  broad-band  55  F i g u r e 2.14. Z e r o - q u a n t u m s p e c t r a o f L - a l a n i n e , A. u n d e c o u p l e d , B. d e c o u p l e d , C. o b t a i n e d w i t h t h e single-quantum J - r e s o l v e d broad-band decoupled zero-quantum experiment.  58  F i g u r e 2.15 S i n g l e - q u a n t u m J - r e s o l v e d b r o a d decoupled zero-quantum spectrum of e t h a n o l .  58  band  F i g u r e 2.16. S i n g l e - q u a n t u m J - r e s o l v e d b r o a d - b a n d d e c o u p l e d z e r o - q u a n t u m s p e c t r a o f 2 - p r o p a n o l , A. w i t h a=45°, B. w i t h a=22.5°.  59  F i g u r e 2.17. S p e c t r a o f L - t h r e o n i n e , A. single-quantum J - r e s o l v e d broad-band decoupled s p e c t r u m , B. d i a g r a m a t i c r e p r e s e n t a t i o n o f t h e method o f r e c o n s t r u c t i o n o f s i n g l e - q u a n t u m s p e c t r a from t h o s e o b t a i n e d i n t h e s i n g l e - q u a n t u m J - r e s o l v e d b r o a d - b a n d d e c o u p l e d z e r o - q u a n t u m e x p e r i m e n t . C. R e c o n s t r u c t e d single-quantum s p e c t r a of L - t h r e o n i n e f r o m t h e s p e c t r u m i n p a r t A. D. N o r m a l single-quantum spectrum of L - t h r e o n i n e . 64  X  F i g u r e 2.18. S p e c t r a of a m i x t u r e o f L - v a l i n e , L - l e u c i n e , L - a s p a r a g i n e , L - a s p a r j t i c a c i d , and L - i s o l e u c i n e . A. S i n g l e - q u a n t u m s p e c t r u m . B. Z e r o - q u a n t u m s p e c t r u m w i t h T , T ' = 6 0 msec. C. z e r o - q u a n t u m s p e c t r u m w i t h T , T ' = 1 4 0 msec.  77  F i g u r e 2.19. B r o a d - b a n d d e c o u p l e d zero-quantum s p e c t r a o f : A. L - v a l i n e , L - l e u c i n e , L - a s p a r a g i n e , L - a s p a r t i c a c i d and L - i s o l e u c i n e , B. L - v a l i n e , C. L - l e u c i n e , D. L - a s p a r a g i n e , E. L - a s p a r t i c a c i d , F, L-i soleuc ine.  80  CHAPTER I I I F i g u r e 3.1. A. One g r a d i e n t p r o j e c t i o n i m a g i n g e x p e r i m e n t . B. R e p r e s e n t a t i o n o f a w a t e r p h a n t o m . C. R e p r e s e n t a t i o n o f a p r o j e c t i o n o f t h e phantom (B) o b t a i n a b l e w i t h t h e one g r a d i e n t p r o j e c t i o n experiment. 90 F i g u r e 3.2. experiment  Two-dimensional  F i g u r e 3.3. C h e m i c a l experiment. F i g u r e 3.4. experiment.  shift  spin-density  resolved  Zero-quantum coherence  imaging  imaging  resolved  93  93 imaging  98  F i g u r e 3.5. A. Phantom o f 2 - p r o p a n o l , e t h a n o l a n d w a t e r . B. Z e r o - q u a n t u m c o h e r e n c e r e s o l v e d image o f t h e phantom ( A ) . C. Z e r o - q u a n t u m s p e c t r u m o f t h e phantom ( A ) . D. S i n g l e - q u a n t u m s p e c t r u m o f t h e phantom ( A ) .  101  F i g u r e 3.6. D a t a s e t s o f : A. c h e m i c a l s h i f t r e s o l v e d i m a g i n g e x p e r i m e n t , B. Z e r o - q u a n t u m c o h e r e n c e r e s o l v e d imaging experiment.  104  F i g u r e 3.7. B r o a d - b a n d d e c o u p l e d zero-quantum coherence r e s o l v e d imaging experiment.  1 07  Figure  3.8.  Images o f a phantom o f  X 1  e t h a n o l , 2 - p r o p a n o l , and w a t e r : A. u n d e c o u p l e d , B-D. d e c o u p l e d . E. S i n g l e - q u a n t u m s p e c t r a o f p h a n t o m . 109 F i g u r e 3.9. Z e r o - q u a n t u m s p e c t r a c o r r e s p o n d i n g t o t h e i m a g e s i n F i g u r e 3.8. p a r t s A-D. 112 F i g u r e 3.10. A. R e p r e s e n t a t i o n o f t h e phantom u s e d t o o b t a i n t h e images i n F i g u r e 3.8. B-I s l i c e s t a k e n t h r o u g h t h e images i n F i g u r e 3.8 A-D. 113 F i g u r e 3.11. A. H o m o n u c l e a r t w o - d i m e n s i o n a l J - r e s o l v e d e x p e r i m e n t . B. H o m o n u c l e a r two-dimensional J - r e s o l v e d imaging experiment.  116  F i g u r e 3.12. P s p e c t r a : A. J - s p e c t r u m o f ATP. B. J - s p e c t r u m of ADP. C. S i n g l e - q u a n t u m s p e c t r u m o f ATP. D. S i n g l e - q u a n t u m s p e c t r u m o f ADP.  117  3 1  Figure  3.13.  3 1  P  J-resolved  image o f ADP  and ATP.  120  APPENDIX I I Figure  A2.1. Zero-quantum s p e c t r a of L - g l u t a m i n e .  F i g u r e A2.2.  Zero-quantum s p e c t r a of L - m e t h i o n i n e .  F i g u r e A2.3. acid.  Zero-quantum s p e c t r a of L - g l u t a m i c  F i g u r e A2.4.  Zero-quantum s p e c t r a of L - a s p a r a g i n e .  F i g u r e A2.5. alanine.  Zero-quantum s p e c t r a of  F i g u r e A2.6  139 139  140  L-0-phenyl  Zero-quantum s p e c t r a of L - l e u c i n e .  140  141 141  F i g u r e A2.7.  Zero-quantum s p e c t r a of L - t h r e o n i n e .  142  F i g u r e A2.8.  Zero-quantum s p e c t r a of L - i s o l e u c i n e .  142  xii  F i g u r e A2.9. Z e r o - q u a n t u m s p e c t r u m o f L - v a l i n e .  143  F i g u r e A2.10. Z e r o - q u a n t u m s p e c t r a o f L - p r o l i n e .  143  F i g u r e A 2 . 1 1 . Z e r o - q u a n t u m s p e c t r u m of L - c y s t e i n e .  143  F i g u r e A2.12. Z e r o - q u a n t u m s p e c t r a o f L - t r y p t o p h a n . 144 F i g u r e A2.13. Z e r o - q u a n t u m s p e c t r a o f L - s e r i n e .  144  F i g u r e A2.14. Z e r o - q u a n t u m s p e c t r a o f L - a r g i n i n e .  145  F i g u r e A2.15. Z e r o - q u a n t u m s p e c t r u m of L - a l a n i n e .  145  F i g u r e A2.16. Z e r o - q u a n t u m s p e c t r u m o f L - a s p a r t i c acid.  145  XI 1 1  ACKNOWLEDGMENT I would l i k e Hall  f o r the constant  undertaking my  t o a c k n o w l e d g e my  t h e work h e r e i n .  great  I would a l s o l i k e  discussions  and  f o r proof  s p e e d and a t s h o r t  h e l p f u l and e n l i g h t e n i n g t h a n k Mr S t a n l e y  t o Dr.  h e l p and g u i d a n c e he has g i v e n  g r a t i t u d e t o Mr. J a c q u e s B r i a n d  thesis with  deep g r a t i t u d e  assistance.  while  t o acknowledge  reading  this  n o t i c e and a l s o f o r  discussions.  L u c k and Mr L a l i t h  me  I would a l s o l i k e  Talagala  L.D.  for helpful  to  1  CHAPTER I *  INTRODUCTION  2 1.1 M a g n e t i c F i e l d Magnetic  field  p r o b l e m i n NMR. centimeter although  within  i n h o m o g e n e i t y h a s a l w a y s been a m a j o r  Originally  t h e p r o b l e m was c o n f i n e d t o a c u b i c  o r so of sample  d e e p w i t h i n t h e b o w e l s o f a magnet,  i n recent years  increasing The  Inhomogeneity  t h e sample  some a p p l i c a t i o n s h a v e n e c e s s i t a t e d  v o l u m e by s e v e r a l o r d e r s o f m a g n i t u d e .  degree of magnetic  field  homogeneity a t t a i n a b l e  t h e magnet o f a c o n v e n t i o n a l h i g h r e s o l u t i o n  spectrometer  h a s i n c r e a s e d c o n s i d e r a b l y i n r e c e n t t i m e s due t o  b o t h t h e improvement  o f magnet t e c h n o l o g y  implementation  of s o p h i s t i c a t e d shimming  magnetic  inhomogeneity s t i l l  field  p a r t i c u l a r l y at high f i e l d s .  and t h e techniques.  result  F o r example,  a magnetic  field i n 10  s  i n a l i n e w i d t h o f 0.1 Hz a t 10 MHz, b u t a t 100 MHz  t h e same l e v e l  of homogeneity  will  result  Hz, a n d a t 1,000 MHz t h e l i n e w i d t h w i l l higher the magnetic needed  However,  remains a problem,  i n h o m o g e n e i t y over t h e volume of i n t e r e s t o f 1 p a r t will  NMR  field  i n a l i n e w i d t h of 1  be 10 H z . C l e a r l y , t h e  the greater the l e v e l  of  homogeneity  t o o b t a i n t h e same r e s o l u t i o n . T h i s i s , p e r h a p s , t h e  m a j o r p r o b l e m c o n f r o n t e d a s one g o e s t o h i g h e r fields,  counterbalancing  magnetic  t h e i r advantages of i n c r e a s e d  s p e c t r a l d i s p e r s i o n and b e t t e r s i g n a l - t o - n o i s e . The  o t h e r a r e a o f NMR where m a g n e t i c  i s a p r o b l e m , and here even a t low f i e l d imaging.  Here  field  inhomogeneity  s t r e n g t h s , i s NMR  t h e problem eminates from t h e i n h e r e n t l y l a r g e  v o l u m e o f some o f t h e o b j e c t s w h i c h i t i s d e s i r e d t o image,  3 s u c h a s human b e i n g s , a n d i s p a r t i c u l a r l y categories  o f e x p e r i m e n t s : t h o s e w h i c h seek  from w i t h i n a s p e c i f i c those  critical  i n two  to obtain  s m a l l volume w i t h i n t h e sample, and  i m a g i n g e x p e r i m e n t s w h i c h a l l o w one t o e x t r a c t t h e image  of a s p e c i f i c  resonance. In both types of experiment  spectroscopic  r a t h e r than s p a t i a l  fatally  s u s c e p t i b l e t o magnetic  In both conventional where one w o u l d increase would  like  high  information  field  to resolve r e l a t i v e l y  inhomogeneity  i s often  inhomogeneity.  field  s p e c t r a l d i s p e r s i o n , a n d i n NMR  like  which  i t is  r e s o l u t i o n NMR s p e c t r o s c o p y ,  t o go t o h i g h e r  c o m p a r a t i v e l y low f i e l d  strengths to  i m a g i n g , where one  w e l l separated resonances at  s t r e n g t h s , magnetic  field  i s a problem, a problem which cannot c u r r e n t l y  be met due t o e i t h e r t e c h n i c a l o r p r a c t i c a l Given t h i s  reality  o v e r c o m e ? The b a s i c would  spectra  can the l i m i t a t i o n s  limitations. i t i m p o s e s be  requirement f o r a s o l u t i o n to t h i s  seem t o be t o make t h e r e l e v a n t  spectroscopic  p a r a m e t e r s , c h e m i c a l s h i f t s and s c a l a r c o u p l i n g s , o f , o r a t l e a s t l e s s dependent upon, m a g n e t i c i n h o m o g e n e i t y . T h i s may a p p e a r  problem  independent  field  t o be w i s h f u l t h i n k i n g , b u t i t  i s n o t ! I t h a s been known f o r some t i m e t h a t among t h e c l a s s of phenomena known a s m u l t i p l e - q u a n t u m c o h e r e n c e particular  o r d e r of coherence, zero-quantum coherence,  containing chemical s h i f t also  [ 1 - 4 ] one  and s c a l a r c o u p l i n g  independent of magnetic  field  while  information, i s  inhomogeneity.  4 The  o b j e c t of t h i s  overcoming  thesis  the l i m i t a t i o n s  inhomogeneity. zero-quantum  i s t o e x p l o r e ways o f  imposed  F o r t h e most p a r t  coherence  upon NMR  by m a g n e t i c  field  i t i s the p o t e n t i a l i t i e s  which a r e of i n t e r e s t  in this  of  respect,  b o t h i n t h e c o n t e x t o f s p e c t r o s c o p y ( C h a p t e r I I ) , and a l s o i n the  c o n t e x t of i m a g i n g f o r o b t a i n i n g  spin-density III).  images o f d i f f e r e n t c h e m i c a l s p e c i e s . ( C h a p t e r  I n b o t h c a s e s t h e s c o p e and  l i m i t a t i o n s of  e x p e r i m e n t s a r e d i s c u s s e d , and new In it  will  the l i g h t  ones a r e  o f t h e s e o b j e c t i v e s and  existing  developed.  t h e means by  be a t t e m p t e d t o meet them a q u e s t i o n must be  what i s m u l t i p l e - q u a n t u m 1.2  the s e p a r a t e d  Multiple-Quantum  which answered:  coherence?  Coherence  Multiple-quantum coherences are those coherences n o t obey t h e w e l l by  itself  convey  any  coherence  known t r a n s i t i o n  i s not n e c e s s a r i l y  r u l e Am=±1. T h i s  very e n l i g h t e n i n g  as  which  do  definition  i t does n o t  i d e a as t o what, p h y s i c a l l y , a m u l t i p l e - q u a n t u m i s . This problem  has been e x a c e r b a t e d by t h e l a c k  e x p l a n a t i o n p r o v i d e d by t h e w i d e l y u s e d c l a s s i c a l  of  and  s e m i c l a s s i c a l v e c t o r m o d e l s . - O n e o f t h e e a s i e s t ways t o a t t a i n an u n d e r s t a n d i n g o f t h e n a t u r e o f m u l t i p l e - q u a n t u m  coherence  i s t o do so as an e x t e n s i o n o f an u n d e r s t a n d i n g o f  the  normally observed single-quantum coherence. T h i s , widely held b e l i e f s to the c o n t r a r y ,  is itself  m i s u n d e r s t o o d . M i s c o n c e p t i o n s of the n a t u r e of cphererice u s u a l l y a r i s e  despite  often single-quantum  from a l a c k of a p p r e c i a t i o n  of t h e  5 l i m i t a t i o n s of t h e models being  used t o d e s c r i b e  where i t i s t h a t t h e m o d e l d e p a r t s Figure  i t , thati s ,  from p e r c e i v e d  reality.  1.1A i s a r e p r e s e n t a t i o n o f t h e p r e c e s s i o n o f an  e n s e m b l e o f v e c t o r s w i t h random p h a s e w i t h r e s p e c t t o t h e xy-plane  i n a magnetic  field  magnetic d i p o l e of a nucleus.  B . Each v e c t o r represents the Q  T h i s how one m i g h t e x p e c t t o  f i n d an e n s e m b l e o f s p i n s a t e q u i l i b r i u m i n a m a g n e t i c w i t h s l i g h t l y more s p i n s a l i g n e d w i t h t h e f i e l d it.  Figure  1.1B d e p i c t s t h e c o r r e s p o n d i n g  r e p r e s e n t a t i o n . The v e c t o r r e p r e s e n t s magnetization pulse  rotating  through  the net macroscopic  o f t h e e n s e m b l e . When a 90°  radio-frequency  90° o n t o t h e y - a x i s . A common m i s c o n c e p t i o n  i s not the case.  the y - a x i s a c t u a l l y  i s that  The r o t a t i n g  the y-axis.  frame model's v e c t o r  the xy-plane  has  the effect  along  r e p r e s e n t s a phase c o h e r e n c e between t h e  s t a t e s of t h e s p i n , w i t h and a g a i n s t t h e f i e l d ,  in  vector  spin vectors, representing the nuclear  m a g n e t i c d i p o l e moments a r e now a l l a l i g n e d a l o n g  two  i n the  frame model, of t i p p i n g t h e n e t m a g n e t i z a t i o n  the i n d i v i d u a l  This  against  frame  i s a p p l i e d t o t h e ensemble i t h a s t h e e f f e c t ,  rotating  all  than  field,  a s c a n be s e e n f r o m F i g u r e  a a n d |3,  1.1D. The 90° p u l s e  o f e q u a l i z i n g t h e p o p u l a t i o n s o f t h e two s p i n  s t a t e s a a n d j3 a n d c r e a t i n g a p h a s e c o h e r e n c e b e t w e e n them with respect along  t o the xy-plane,  t h e + y - a x i s than  b u t w i t h more s p i n s i n p h a s e  the -y-axis.  6  B  Z -1  Y  X  D  •  Y  X  F i g u r e 1.1. A. P r e c e s s i o n i n a m a g n e t i c f i e l d B o f an e n s e m b l e of v e c t o r s , r e p r e s e n t i n g t h e m a g n e t i c d i p o l e s of s p i n - 1 / 2 n u c l e i , w i t h random p h a s e i n t h e x y - p l a n e , and w i t h n e t m a g n e t i s a t i o n o n l y i n t h e z - d i r e c t i o n , as one m i g h t e x p e c t t o f i n d a t t h e r m a l e q u i l i b r i u m . B. C o r r e s p o n d i n g r o t a t i n g f r a m e r e p r e s e n t a t i o n o f p a r t A, t h e v e c t o r r e p r e s e n t s t h e n e t m a c r o s c o p i c m a g n e t i s a t i o n . C. P h a s e - c o h e r e n c e of an e n s e m b l e o f s p i n s i n t h e x y - p l a n e a l o n g t h e y - a x i s , as w o u l d be p r e s e n t a f t e r t h e a p p l i c a t i o n o f a 90$ r a d i o - f r e q u e n c y p u l s e t o t h e e n s e m b l e a t e q u i l i b r i u m ( p a r t A ) . D. C o r r e s p o n d i n g r o t a t i n g f r a m e r e p r e s e n t a t i o n of p a r t C. c  7 Whereas s i n g l e - q u a n t u m  coherences  b e t w e e n t h e two s t a t e s o f one s p i n multiple-quantum coherences  a r e phase  coherences  i n the xy-plane,  c o n s i s t o f phase  coherences  b e t w e e n t h e a a n d j5 s t a t e s o f a number o f d i f f e r e n t  coupled  spins i n the xy-plane. U n l i k e single-quantum coherences  cannot  be c r e a t e d d i r e c t l y  detected d i r e c t l y coil;  multiple-quantum by a 90° p u l s e o r  [ 5 ] , a s t h e y do n o t c o u p l e w i t h t h e r e c e i v e r  t h e i r c r e a t i o n and d e t e c t i o n w i l l  (section The spin  coherences,  be d i s c u s s e d l a t e r  2.1). simplest multiple-quantum  system,  w h i c h may g i v e r i s e  coherences  o c c u r f o r an AX  t o z e r o - and d o u b l e - as w e l l  as s i n g l e - q u a n t u m c o h e r e n c e s , F i g u r e 1.2. From t h e F i g u r e i t c a n be s e e n t h a t Am=0 f o r t h e z e r o - q u a n t u m c o h e r e n c e . for  t h e A - s p i n Am =1 b e t w e e n e n e r g y A  Although  l e v e l s 2 a n d 3, f o r t h e  X - s p i n Am =-1, g i v i n g , o v e r a l l , Am=0. L i k e w i s e i t c a n be s e e n x  that  f o r t h e double-quantum t r a n s i t i o n The  rotating  actual precessional  Am=2.  frequency of a s p i n  i n the  f r a m e may be e x p r e s s e d a s  co' =CJ + 7 A B ( x , y , z )  (1.1)  where CJ i s t h e p r e c e s s i o n a l absence of magnetic inhomogeneity x, y, a n d z .  field  frequency of the spin  inhomogeneity  i n the  and AB(x,y,z)  i s the  e x p e r i e n c e d by a s p i n a t t h e s p a t i a l c o o r d i n a t e s  8  4  j8 jS A  i  x  01^  SQC = Single-quantum coherence ZQC = Zero-quantum coherence DQC = Double-quantum coherence  F i g u r e 1 . 2 . E n e r g y d i a g r a m f o r an AX s p i n - s y s t e m s h o w i n g t h e the phase coherences which a r e p o s s i b l e .  9  The  general expression  multiple-quantum coherence co  p Q C  =  £Am (to k  k  f o r the chemical s h i f t  of a  i s g i v e n by  +7AB(x,y,z))  (1.2)  where Am=±1 d e p e n d i n g on t h e change o f m a g n e t i c quantum number of  spin  k f o r a P - o r d e r m u l t i p l e - q u a n t u m c o h e r e n c e , where P i s  g i v e n by:  P= £ A m  (1.3)  k  From e q u a t i o n 1.2 i t c a n be s e e n t h a t a c o h e r e n c e between  double-quantum  two c o u p l e d s p i n s A a n d B w i l l  precess at a  frequency g i v e n by:  "DQCT A W  + a J  B 27AB(x,y,z)  C l e a r l y double-quantum magnetic Similarly  (1.4)  +  field  coherence  i s twice as s u s c e p t i b l e t o  inhomogeneity as single-quantum coherence.  the precessional  frequency of zero-quantum  coherence  may be e x p r e s s e d a s  ZQC  U  =  "A  ~B U  which i s the d i f f e r e n c e  (  i seffectively  t h e same f o r s p i n s  t h e same m o l e c u l e t h e t e r m c a n c e l s o u t m a k i n g  zero-quantum  5  i n f r e q u e n c i e s o f s p i n s A a n d B.  Consequently as AB(x,y,z) within  K  coherences independent of magnetic  field  )  10 inhomogeneity. Multiple-quantum coherences s p i n s not a c t i v e w i t h i n i n more d e t a i l  later  the coherence, t h i s w i l l  development  be d i s c u s s e d  ( s e c t i o n s 2.5, A 1 . 5 ) .  1.3 The P r o d u c t O p e r a t o r The  only exhibit couplings to  Formalism  o f m u l t i p u l s e NMR  y e a r s h a s been a c c o m p a n i e d  experiments  by t h e d e v e l o p m e n t  i n recent  of models w i t h  w h i c h t o d e s c r i b e them. T h e s e m o d e l s c a n g e n e r a l l y be c a t e g o r i s e d a s b e i n g o f one o f two t y p e s . One a p p r o a c h h a s been t o u s e c l a s s i c a l adequate  or s e m i c l a s s i c a l v e c t o r models.  f o r d e s c r i b i n g e x p e r i m e n t s such as s p i n - e c h o e s [ 6 ] ,  slow c h e m i c a l exchange are  Although  [ 7 , 8 ] and s p i n  imaging  [9] t h e s e models  i n a d e q u a t e f o r more s o p h i s t i c a t e d e x p e r i m e n t s s u c h a s  t h o s e i n v o l v i n g m u l t i p l e - q u a n t u m c o h e r e n c e . The o t h e r i s d e n s i t y o p e r a t o r t h e o r y [ 1 0 - 1 2 ] , T h i s can cope  with  arbitrarily  complex p u l s e s e q u e n c i e s a l t h o u g h t h i s  the expense  of p h y s i c a l  The  i n t r o d u c e d by  Although o r i g i n a t i n g  r e f e r r e d t o above.  i n density operator theory i t r e t a i n s the  i n t u i t i v e c o n c e p t s and p h y s i c a l s e m i c l a s s i c a l v e c t o r models.  this thesis  Sorensen,  Bodenhausen and E r n s t i s e s s e n t i a l l y a m i d d l e  r o a d b e t w e e n t h e two b a s i c a p p r o a c h e s  definitively  i s often at  intuition.  product o p e r a t o r approach  Eich, Levitt,  approach  i n s i g h t of the c l a s s i c a l or  Product operators are  i n t r o d u c e d i n r e f e r e n c e [13] which the reader of i s strongly  recommended t o r e a d . As c a n be  seen  11 f r o m t h e r e f e r e n c e , an a t t e m p t t o i n t r o d u c e p r o d u c t adequately than  w o u l d t a k e a c o n s i d e r a b l e amount o f s p a c e ,  i s a v a i l a b l e here,  contents  operators  of r e f e r e n c e  section the nature  more  t h e r e f o r e o n l y a summary o f t h e  [13] w i l l  of product  be g i v e n h e r e i n . ' I n t h i s  o p e r a t o r s and t h e i r o r i g i n s  be d i s c u s s e d , a n d t h e r u l e s f o r t h e i r  will  use a r e g i v e n i n  Appendix I . A density operator combination  o c a n be e x p r e s s e d  as a l i n e a r  of base o p e r a t o r s B :  a(t)=p (t)B s  (1.6)  s  T h e s e b a s e o p e r a t o r s may, irreducible  f o r e x a m p l e , be e x p r e s s e d  tensor operators  h e r e i n , as product  [14,15] o r , as w i l l  as  be done  operators: (1.7)  B  where N = t o t a l  number o f s p i n - 1 / 2  nuclei  i n the s p i n  k = i n d e x o f n u c l e u s , v=x, y o r z , q=number o f s i n g l e operators  i n the product,  a=1  system, spin  f o r q n u c l e i and a=0 f o r N-q  nuclei. Although orthogonal  product  operators  f o r spin-1/2  with respect to trace formation  nuclei are  they a r e not  normalised, i . e . Tr{B  r  ,B } =5 s r,s  (1.8)  12 The  s e t of product  generated  o p e r a t o r s f o r a two s p i n s y s t e m  using equation  q=0 q  =  *=  Any  1.7:  (1/2)E  1  T  2  (E=unity  k x ' k y ' kz' :  2 I  :  2 I  ky ly'  2 I  kz iz  2 I  Z  2 I  operator)  lx'  1  kx ly'  2 I  1  kx ix'  1  J  ky lz' I  ly'  1  l z  kx lz' I  2 I  2  kz lx' J  I  2 I  k  : y  ix'  kz ly' I  :  d e n s i t y o p e r a t o r may be e x p r e s s e d  of s u c h a s e t . P r o d u c t  c a n be  as a l i n e a r  operators greatly  c a l c u l a t i o n s of pulse experiments  combination  s i m p l i f y the  a p p l i e d t o weakly  coupled  s y s t e m s b e c a u s e t h e f a t e o f i n d i v i d u a l o p e r a t o r t e r m s c a n be f o l l o w e d and a s s o c i a t e d w i t h c l e a r p h y s i c a l S i n g l e - s p i n product  meaning.  o p e r a t o r s may be d e s c r i b e d a s  follows:  Ij^  J  kz  J  kx  J  ky  longitudinal magnetization  of s p i n k  in-phase  x-magnetization  o f s p i n k,  in-phase  y-magnetization  o f s p i n k,  r e p r e s e n t s magnetization along the z - a x i s of the r o t a t i n g  f r a m e , F i g u r e 1.3.A, a s one m i g h t f i n d when t h e s y s t e m thermal  equilibrium.  of s p i n k w h i c h Figure  a n d 1^  correspond  i sat  t o t h e components  a r e i n phase a l o n g t h e x - a x i s and y - a x i s ,  1.3.B, o f t h e r o t a t i n g  f r a m e . F o r e x a m p l e , a 90°  r a d i o - f r e q u e n c y p u l s e a c t s upon t h e s p i n k a t e q u i l i b r i u m , to give I  k  .  1^  13  F i g u r e 1.3. P r o d u c t o p e r a t o r s and t h e i r c o r r e s p o n d i n g r o t a t i n g frame r e p r e s e n t a t i o n s : A. L o n g i t u d i n a l m a g n e t i z a t i o n o f s p i n k. B. I n - p h a s e y - m a g n e t i z a t i o n of s p i n k. C. x - m a g n e t i z a t i o n of s p i n k a n t i p h a s e w i t h r e s p e c t t o s p i n 1.  14 Two-spin product 2 I  kx lz J  :  a  n  i P  t  to 2 I  ky lz I  :  a  n  kx ix' :  2  i P  t  I  a  s  n  a  s  kz lz I  :  y-magnetization  e  of s p i n k w i t h respect  of s p i n k w i t h  *y ly> l  2  l° 9i n  t u c  1  k x  T  l y  a  n  "kyhx'  d  coherences  ^i l n a  o f s p i n s k and 1,  two-spin  Antiphase magnetization, 2 I ^ ^ x  z  o r d e r o f s p i n s k a n d 1.  f o r example, F i g u r e  r e p r e s e n t s two c o m p o n e n t s o f a m u l t i p l e t w h i c h phases.  As i t s i n t e g r a t e d i n t e n s i t y  p o p u l a t i o n of energy without observable larger  ^ kx lz mz I  I  I  I  I  I  :  t  to spin-correlated  n e t p o l a r i z a t i o n and  magnetization.  x-magnetization  :  coherence.  s p i n systems t h r e e s p i n terms  to ^ kx lx mz  order corresponds l e v e l s without  w  have o p p o s i t e  represent a  s u p e r p o s i t i o n o f z e r o - and d o u b l e - q u a n t u m Longitudinal two-spin  appear:  of s p i n k a n t i p h a s e w i t h respect  s p i n s 1 a n d m, o  s  P*  coherence  n  of s p i n s k and.l  antiphase  w i t h r e s p e c t t o s p i n m, 41, I , I : kx l x mx 4 I  kz lz mz I  I  Antiphase  :  1.3.C,  i s z e r o i t does not c o u p l e  w i t h the r e c e i v e r . Two-spin coherences  In  respect  s p i n 1,  two-spin 2 I  x-magnetization  e  s p i n 1,  to 2 I  n  o p e r a t o r s may be d e s c r i b e d a s f o l l o w s :  three-spin r  coherence,  longitudinal three-spin order.  two-spin  coherence  c o n s i s t s of z e r o - and  1 5  d o u b l e - q u a n t u m c o h e r e n c e w i t h m u l t i p l e t c o m p o n e n t s t h a t have o p p o s i t e p h a s e s d e p e n d i n g upon t h e p o l a r i z a t i o n o f t h e " p a s s i v e " s p i n m. T h r e e - s p i n  coherence c o n s i s t s of a  s u p e r p o s i t i o n of single-quantum and  triple-quantum The  coherence  (combination  lines)  coherence.  e f f e c t s of chemical  shift  e v o l u t i o n and r a d i o - f r e q u e n c y  and s c a l a r  coupling  p u l s e s c a n be d e s c r i b e d by a  s e r i e s of t r a n s f o r m a t i o n s of t h e type: exp{-i*B }B exp{i*B }= r  s  £b  r  where 4>B c a n t a k e t h e f o r m r  precession, and  01^  ( nJ^± ) 21 ^ I  fcs  (r,$)B  (^) ) j T  I  l  (1.9)  fc  f ° chemical r  c z  shift  f o r weak s c a l a r c o u p l i n g e v o l u t i o n  f o r a r a d i o frequency  p u l s e about the v - a x i s a p p l i e d  t o t h e n u c l e u s k'. How one p u t s  this  into practice,  t o calculate the effects  of t h e p u l s e s a n d d e l a y s o f a p u l s e s e q u e n c e on a s p i n s y s t e m , is discussed i n d e t a i l  i n Appendix I .  References 1.  A n d e r s o n , W.A.,  2.  A n d e r s o n , W.A., F r e e m a n , R., a n d R e i l l e y , C.A., J . Chem. Phys.  (1963),  Phys. Rev.  39,  (1956),  Yatsiv,  4.  B a x , A., T w o - D i m e n s i o n a l N u c l e a r  Phys. Rev.  L i q u i d s , Delf Univ. 5.  850.  1518  3.  S.,  104,  (1959),  n_3,  1522  Magnetic  Press, Mijnbouwplein,  Resonance i n (1982),  Wokaun, A., a n d E r n s t , R.R., Chem. P h y s . L e t t .  pp.  (1977),  139 52,  16 407 6.  C a r r , H.Y., a n d P u r c e l l ,  7.  J e e n e r , J . , M e i e r , B.H., Bachmann, P., a n d E r n s t , R.R., J . Chem. P h y s .  8.  R e v . ( 1 9 5 4 ) , 94, 630  ( 1 9 7 9 ) , 7J_, 4546  B o d e n h a u s e n , G., a n d E r n s t , R.R., J . Am. Chem. Soc ( 1 9 8 2 ) , 104,  9.  E.M., P h y s .  1304  M a n s f i e l d , P., a n d M o r r i s , P.G., NMR I m a g i n g i n B i o m e d i c i n e , A c a d e m i c P r e s s , New Y o r k ,  10. F a n o , U., Rev. Mod. P h y s . 11. S l i c h t e r , edition),  (1982)  ( 1 9 5 7 ) , 29, 74  CP., Principles Springer, B e r l i n ,  of Magnetic  Resonance, (2nd  (1978)  12. B l u m , K., D e n s i t y M a t r i x T h e o r y a n d A p p l i c a t i o n s , P r e s s , New Y o r k , 13. S o r e n s e n , and  O.W.,  Plenum  (1981 ) E i c h , G.W.,  L e v i t t , M.H.,  B o d e n h a u s e n , G.,  E r n s t , R.R., P r o g r . N u c l . Magn. R e s o n . S p e c t r o s c .  ( 1 981 ) , J_4, 1 37 14. B a i n , A.D., a n d B r o w s t e i n , J . Magn. R e s o n . 15. S a n c t u a r y , B.C., J . Chem. P h y s .  ( 1 9 8 2 ) , 47, 409  ( 1 9 7 6 ) , 64, 4352  17  CHAPTER I I NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY IN AN INHOMOGENEOUS MAGNETIC F I E L D  18 2.1  Zero-Quantum S p e c t r o s c o p y i n an Inhomogeneous M a g n e t i c  Field Zero-quantum c o h e r e n c e s , u n l i k e coherences, cannot a single  90°  single-quantum  be p r e p a r e d d i r e c t l y  by t h e a p p l i c a t i o n  p u l s e to a s p i n system at e q u i l i b r i u m ,  n e i t h e r c a n t h e y be o b s e r v e d d i r e c t l y . s o p h i s t i c a t e d p u l s e sequence  of  and  C o n s e q u e n t l y a more  i s needed w h i c h c a n g e n e r a l l y  be  b r o k e n down i n t o t h r e e p a r t s [ 1 ] . Firstly coherence,  i t i s necessary to prepare the  s e c o n d l y i t must be a l l o w e d t o e v o l v e , and  i t must be c o n v e r t e d back c a n be d i r e c t l y the  most common p u l s e s e q u e n c e  i s modulated coherence  u s e d t o do t h i s  that  as a  evolution.  i s given i n  2.1.  The coherence  first  90°  pulse c r e a t e s in-phase  i n the r o t a t i n g  preparation period  single-quantum  frame w h i c h e v o l v e s d u r i n g t h e  T under  the i n f l u e n c e of c h e m i c a l s h i f t  s c a l a r c o u p l i n g s i n t o antiphase single-quantum coherence. antiphase single-quantum coherence multiple-quantum coherences e v o l v e d u r i n g t , . Next them back  i s converted  by t h e s e c o n d  the t h i r d  90°  90°  multiple-quantum coherence  and The  into  p u l s e , and  these  pulse p a r t i a l l y converts  i n t o antiphase single-quantum coherences,  a m p l i t u d e s of which are modulated of  which  o b s e r v e d . T h i s must be done i n s u c h a way  observed single-quantum coherence  Figure  thirdly  into single-quantum coherence,  f u n c t i o n o f t h e e x t e n t of z e r o - q u a n t u m The  zero-quantum  the  as a f u n c t i o n of the e x t e n t  e v o l u t i o n . The  invisible  19  90£  90|, ti  Preparation  Acquisition  Zero-quantum evolution  Figure  Table order  2.1 B a s i c z e r o - q u a n t u m  I . Phase c y c l i n g selection.  Pulse  phase $ Receiver phase  0° 0° 0° 0° 0° 0°  90J  experiment.  schemes f o r m u l t i p l e - q u a n t u m  90°  180°  0° 180°  0° 180° 0° 0°  T  270°  Orders  0° 180°  0 0 1 0 2  905  coherence  selected  1 2 3 4 5 6 7 8 2 4 6 8 3 5 7 4 8 6  90S ti  \  I)  f\(\\r  Gradient Z  Preparation  Zero-quantum  Acquisition  evolution  F i g u r e 2.2 B a s i c z e r o - q u a n t u m e x p e r i m e n t ! w i t h m a g n e t i c gradient order s e l e c t i o n .  field  20 antiphase  single-quantum  single-quantum are performed time  coherences rephase i n t o  coherences which are detected. incrementing  a data matrix  S(t  1 f  t , by a c o n s t a n t  t )  will  2  transformation with respect will  yield  the  be  amount, A t , ,  yield  s p e c t r u m w i t h a sweep w i d t h  g i v e n by  the  v a r i o u s o r d e r s of m u l t i p l e - q u a n t u m o r by u s i n g a p u l s e d m a g n e t i c  to t  1  l/2At,  Phase c y c l i n g methods make use  each the  f  Hz.  s e p a r a t i n g out  the  c o h e r e n c e , by p h a s e  field  orders  to  multiple-quantum  p r a c t i c a l m e t h o d s of  s e n s i t i v i t i e s of d i f f e r e n t  matrix,  spectrum corresponding  c o l u m n s of t h e m a t r i x , w i l l  each  Fourier  v a l u e of t , . F o u r i e r t r a n s f o r m a t i o n w i t h r e s p e c t  T h e r e a r e two  experiments  rows o f t h e  2  single-quantum  If n  obtained.  to t , the  visible  cycling  gradient. of t h e  of  differing  multiple-quantum  c o h e r e n c e t o a p h a s e c h a n g e of a r a d i o f r e q u e n c y  pulse[l-3].  a pulse  p-order  i s p h a s e s h i f t e d by an a n g l e  multiple-quantum p</>.  There are  coherence w i l l  <p, t h e n  experience  a  a phase s h i f t  If  of  s e v e r a l d i f f e r e n t methods of s e p a r a t i o n based  on  p h a s e p r o p e r t i e s [ 2 , 4 - 7 ] , I n t h e most w i d e l y u s e d o f t h e s e f o r e a c h v a l u e of t , s e v e r a l e x p e r i m e n t s a r e p e r f o r m e d different excitation combination results For  o r d e t e c t i o n p u l s e p h a s e s and  of the Free  I n d u c t i o n Decays  i n the c a n c e l l a t i o n  of s i g n a l  the b a s i c multiple-quantum  (FIDs)  due  t o unwanted  experiment given  with  linear  taken.  This orders.  in figure  the phase c y c l i n g  scheme u s e d t o s e l e c t  is given  I . T h i s assumes o n l y the a b i l i t y  i n Table  a  [2]  2.1  zero-quantum coherence t o phase  21 shift  by m u l t i p l e s o f 90°  (an u n a v o i d a b l e c o n s t r a i n t on most  NMR  s p e c t r o m e t e r s ) and c o n s e q u e n t l y a l s o l e t s t h r o u g h  and  e i g h t h order multiple-quantum coherence,  isotropic are  solution  usually  the r e l a t i v e  s m a l l . To be most e f f e c t i v e t h e m a g n e t i z a t i o n must  The p u l s e d f i e l d different  g r a d i e n t method o f s e p a r a t i n g o u t t h e  t o magnetic  [ 2 , 8 ] . T h i s h a s t h e same t h e o r e t i c a l sensitivity  inhomogeneity  basic multiple-quantum  field  inhomogeneity  b a s i s as phase  a s pAa>. C o n s e q u e n t l y  dephasing  o c c u r . A f t e r b e i n g c o n v e r t e d back i n t o magnetization resulting  same m a g n e t i c  field  by  magnetic  ifa  magnetic  f o r a time T d u r i n g t , w i t h i n the  experiment  multiple-quantum coherence  from  p r o p o r t i o n a l t o pT single-quantum  p-order  c a n be r e p h a s e d  by a p p l y i n g t h e  g r a d i e n t f o r p times as l o n g . T h i s i s  because single-quantum coherence at  o r d e r s of  i s e x p e r i e n c e d by a p - o r d e r  gradient i s applied  coherence  [ 9 ] makes u s e  d i s c u s s e d a b o v e . An o f f s e t Aw c a u s e d  multiple-quantum coherence  will  coherence  s e n s i t i v i t i e s of d i f f e r e n t  multiple-quantum coherence  field  experiment  f o r each v a l u e of t , .  o r d e r s of m u l t i p l e - q u a n t u m  the d i f f e r i n g  field  each  a n d i t a l s o n e c e s s i t a t e s the. p e r f o r m i n g a minimum  number o f f o u r e x p e r i m e n t s  of  though i n  i n t e n s i t i e s of these o r d e r s  be a l l o w e d t o r e t u r n t o e q u i l i b r i u m a f t e r (>5T,),  fourth  will  o n l y dephase or  rephase  1/p t h e r a t e o f p - o r d e r m u l t i p l e - q u a n t u m c o h e r e n c e .  orders w i l l which  remain  d e p h a s e d . To s e l e c t z e r o - q u a n t u m  i s u n a f f e c t e d by m a g n e t i c  field  inhomogeneity  necessary t o apply the magnetic  field  g r a d i e n t once,  Other  coherence i t i s only during t .  22 to  dephase a l l other o r d e r s p r e s e n t , F i g u r e Due  field  to i t s greater f l e x i b i l i t y  g r a d i e n t method of o r d e r  otherwise In given  i n F i g u r e 2.2  the  will  90°  in-phase  pulse w i l l  the p u l s e  c e n t r e of an a d d i t i o n a l p u l s e , F i g u r e 2.3, experiment.  dephase b e f o r e  180°  i t can  due  to magnetic f i e l d  T h i s sequence i s s i m i l a r  be  into  solved  by  sequence.  one  i n the  the t h i r d  90°  zero-quantum  t o one  introduced  i n t h e c o n t e x t of  by  multiple-quantum  [10]. e f f e c t s of t h e r e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t  a s p i n system can formalism  be d e s c r i b e d i n t e r m s of t h e [ 1 1 ] , F o r an A X  transverse relaxation, this The  and  inhomogeneity,  refocussing period after  Ernst  evolve  p u l s e s i n t o the p u l s e  t o form the r e f o c u s s e d  S o r e n s e n , L e v i t t and  operator  Firstly  single-quanum coherence c r e a t e d  i n t h e c e n t r e of t h e p r e p a r a t i o n p e r i o d and  The  unless  sequence  reasons.  m a g n e t i z a t i o n . T h i s problem can  i n t r o d u c t i o n of two  filtering  pulsed  dephase d u r i n g the p r e p a r a t i o n p e r i o d ,  These r e f o c u s dephasing one  the  i s used h e r e i n  does n o t work f o r two  i n v i s i b l e antiphase  the t h i r d  visible  selection  inhomogeneous m a g n e t i c f i e l d  magnetization  by  efficiency  stated.  an  secondly  and  2.2.  first  90°  i s as  follows:  frame, - ( I . + 2 I Ay  product  s p i n system, n e g l e c t i n g  2  pulse produces magnetization  a x i s of t h e r o t a t i n g  on  V  Ay  ). T h i s  e v o l v e s d u r i n g t h e p r e p a r a t i o n p e r i o d r due  along  the  -y  subsequently  to the  Hamiltonian  9C  80  o V  90 o  90  80 o Y  tl  V2  IP ' 1  Gradient Z  Preparation  Zero-quantum i  Refocussing  Acquisition  evolution  F i g u r e 2.3 R e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t w i t h m a g n e t i c f i e l d g r a d i e n t o r d e r s e l e c t i o n . The 180° p u l s e s i n t h e p r e p a r a t i o n and r e f o c u s s i n g p e r i o d s a r e e s s e n t i a l i n an inhomogeneous m a g n e t i c f i e l d t o r e v e r s e d e p h a s i n g due t o magnetic f i e l d inhomogenieties.  24 27rJ rI.  I  A V  AA  the  , chemical  v  AZ  shift  e v o l u t i o n b e i n g c a n c e l e d o u t by  AZ  180° p u l s e a t T / 2 . - ( l  A  2I  y +  X y  )  2  '  A Z  J  T  l  A ,  Z z  I  -I  ;  A y  cosM,J  A X  r)  .  ^ W x z ^ ^ A X ^ ^ ^ A X ^ +  2  Wxz  s i n ( 7 r J  ^ ^ y ^ z ^ z ^  The  W  A  Z  ^  5  ^  AX 1  A  T ) c 0 s ( 7 r J  "  2  ^ ^ ^  X  ^  AX  T )  -  Xy  2 I  c o s ( 7 r J  2.1 i n t o l o n g i t u d i n a l m a g n e t i s a t i o n  This w i l l  be c o n v e r t e d  back i n t o I .  and 2 I  Ay  p u l s e and w i l l dimension  T )  (  s e c o n d 90° p u l s e c o n v e r t s t h e f i r s t a n d f i f t h  equation  to  AX  I  A  )  and 2 I  z  .  X z  by t h e t h i r d 90°  V t r  Ay  c o n t r i b u t e t o t h e peak a t 0.0 Hz i n t h e F1  t , . The f o u r t h t e r m  i s converted  i n t o t h e term  4I  respect A  z  I  X  y  z e r o - q u a n t u m c o h e r e n c e b e t w e e n t h e two X s p i n s a n t i p h a s e respect t o the passive A spin. This w i l l scalar couplings or chemical  1  f  coherence w i l l  s i x t h terms of t h e e q u a t i o n a r e c o n v e r t e d »  I A x  X y  2 I  Ax Xy' J  a  n  d  2 I  Xx Ay I  r  X  y  ,  with  a n d h e n c e when only  c o n t r i b u t e t o t h e peak a t 0.0 Hz i n F 1 . The s e c o n d ,  2 I  I  n o t e v o l v e due t o  s h i f t during t  back i n t o s i n g l e - q u a n t u m  coherences,  1  terms of  of the data s e t as i t i s not modulated w i t h  converted  '  2  e  into s  P  e  c  t  t h i r d , and  two-spin i  v  e  l  Y  which  c o n t a i n both z e r o - and double-quantum coherence [ 1 1 ] . Pure zero-quantum coherence i s g i v e n by:  (  1  /  2  )  (  2  I  A X  I  X X  +  2 I  Ay Xy I  ) =  { Z  Q  T }  x  ( 2  '  2 )  and  ^^Vxx Therefore  - AxV f Z Q T } 2I  the amplitude  =  y  of zero-quantum coherence  (2.3) present  25 after  t h e s e c o n d 90° p u l s e  i s g i v e n by:  X  2sin(7rJ  A X  r)  -2cos ( 7 T J T ) s i n (7rd" T ) = {ZQT} . A X  Non-zero multiple-quantum the p u l s e d magnetic will  evolve  shift  field  during  n  = n  A  -n  shift  g r a d i e n t . Zero-quantum  eff  AX  = J  extent  (2.5) s c a l a r c o u p l i n g by:  ( 2  of e v o l u t i o n d u r i n g AX 1 t  2 I  -2I  X z  I  R  a third  t  {ZQT} sin(7rJ x  x  X z  t  e f  f  Q  e f f  y  e f f  6 )  X 1 Xz. t  t  I  1  )  t, )cosfi  t , )sin(O  (ZQT} sin(7rJ 90° p u l s e  I  e f f  *  i s g i v e n by:  t , )cos(Q  e f f  -{ZQT} cos(jrJ -2I  t  A z X z .> A 1 A z .  y  1  [11], the  J  7 r J  chemical  i s g i v e n by:  {ZQT} cos(7rJ  t  spins  " XX  {ZQT} « y  After  coherences  x  the e f f e c t i v e  J  The  e f f  be d e p h a s e d by  t , under t h e i n f l u e n c e of b o t h  e f f e c t i v e chemical  and  coherences w i l l  and s c a l a r c o u p l i n g s t o p a s s i v e  (2.4)  y  AX  e ff  t,)  e f f  t, )  t, ) s i n ( Q  e f f  t, )  (2.7)  i s applied:  X  {ZQT}  ( 7 r / 2 ) ( I y  V  I  {ZQT}  (ZQT)  / U  X  /  2 ) < 4 I  2  >  (  I  A  z  I  X  x  )  ( 2  (TT/2)(I ( ,  ( 1/2) ( 2 I  + I  Ax Xz  + 2 I  2I  Ax X x \  A X  XyWxx  Ax  +  I  Xx'  -H +  ;  X X  '  8 )  )  "xyWxz' <1/2)<2I  ( 2  A x  I x X  +  'Az'xz'  -  9 )  26  (2.10)  21  { ZQT}  v  (TT/2)(I  -H  A X  ^ / ^ " x y W x x  The t e r m s on t h e r i g h t single-quantum into  directly  Zy Ax Xz  4 I  I  I  which w i l l  single-quantum  side of equation  "  )  side of equation  coherences  in-phase  X X  t e r m s on t h e r i g h t  of equation  During  by  l  )  which i s not  either  as ^  coherence. = X  X  0 .  The  2.10are unaffected two-spin  of equation  order 2.11 are  coherence.  the refocussing period T' the antiphase c o h e r e n c e f o r m e d by t h e t h i r d 9 0 ° p u l s e  of equation  scalar  1  upon e v o l v i n g  single-quantum  The terms' on t h e r i g h t  single-quantum right  '  The terms, on t h e r i g h t  zero-quantum coherence and l o n g i t u d i n a l  zero-quantum  2  2.8 are antiphase  2.9 a r e t h r e e - s p i n coherence,  The l a t t e r d o e s n o t become o b s e r v a b l e  antiphase  (  be o b s e r v e d  coherence.  observable, and antiphase  respectively.  )  (on t h e  2 . 8 ) w i l l e v o l v e under t h e i n f l u e n c e o f  couplings, chemical  s h i f t e v o l u t i o n being canceled out  the 180° pulse a t T ' / 2 , thus:  </ 1  2  )  <  2 I  A« XxI  /  ( l  -  2 I  2 I  Ax Xz>  ' ^ A z ^ z ,  I  2 ) [ 2 I  Az Xx I  Ax Xz :  + C O s ( 7 r J  C O s 2 ( , r J  AX  + I  Consequently  A  y  sin(7rJ  Ax Xz I  A  X  s i n 2 (  7  the amplitude  J  ) + I  Xy  ' >sin(7TJ  T ' )cos(7rJ  * AX  T  s i n U j  AX^  )  r , )  - ^ A y W x z ^ ^ A X -I  AX '  r , ) 1  A X  A X  r' )  r' ) (  2  of i n - p l i a s e , and hence v i s i b l e ,  '  1  2  )  27 single-quantum coherence present at time T' o r i g i n a t i n g the  zero-quantum  coherence c o n s i s t i n g  from  of t h e s p i n s A and X i s  g i v e n by: I  It  Xy  + I  Ay  =  ( /2) t s i n ( 7 r J T ' . ) - s i n ( T T J ^ T ' ) cos ( T T J ^ T ' ) ]  (2.13)  1  A X  s h o u l d be n o t e d t h a t  t h i s h a s t h e same f o r m a s e q u a t i o n  2.4. The  r e f o c u s s e d zero-quantum  used t o o b t a i n t h e zero-quantum  experiment  ( f i g u r e 2.3) was  s p e c t r a o f t h e amino a c i d s  L - a l a n i n e , L - v a l i n e , L - t h r e o n i n e , and L - a s p a r a g i n e i n a homogeneous m a g n e t i c the  magnetic  zero-quantum  field  field,  F i g u r e 2.4 A-D. The h o m o g e n e i t y o f  was t h e n d e g r a d e d , F i g u r e  2.5, and t h e  spectrum of a m i x t u r e of t h e amino a c i d s  w i t h t h e same p u l s e s e q u e n c e 2.4 E. The z e r o - q u a n t u m  obtained  a n d t h e same p a r a m e t e r s , F i g u r e  coherences of t h e i n d i v i d u a l  components of t h e m i x t u r e a r e c l e a r l y  d i s c e r n i b l e whereas t h e  corresponding single-quantum spectrum  i s of l i t t l e use.  Consequently the data s e t , s ( t , t ) , 1  2  was o n l y  Fourier  t r a n s f o r m e d w i t h r e s p e c t t o t , . As t h e F I D i n t r a p i d l y as a consequence o n l y the t , FIDs w i t h i n be c o - a d d e d extreme  of t h e magnetic the f i r s t  field  2  decayed very  inhomogeneity  2-3 m i l l i s e c o n d s o f t  t o b u i l d up s i g n a l - t o - n o i s e  could  2  (S/N). I n t h e c a s e of  inhomogeneity only the f i r s t p o i n t  of the t  2  FID,  c o l l e c t e d a t t h e t o p o f t h e s p i n - e c h o , may be o f u s e . E a c h zero-quantum  spectrum took under  15 m i n u t e s t o a c q u i r e ,  which  i s by no means p r o h i b i t i v e when one c o n s i d e r s t h e l a c k o f alternatives  i n an i n h e r e n t l y  inhomogeneous magnetic  D  to  CD  ~1  800  I  I  600  I  I  400  I  I  200  1  I  0.0  1  1  -200  "1  1  1  -400  I  -600  F i g u r e 2.4 Zero-quantum s p e c t r a o b t a i n e d a t 270 MHz w i t h t h e r e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t . I n a homogeneous m a g n e t i c f i e l d : A. L - a l a n i n e , B. L - t h r e o n i n e , C. L - v a l i n e , D. L - a s p a r a g i n e . I n an inhomogeneous m a g n e t i c f i e l d : E. A m i x t u r e of t h e a b o v e . A l l c o n c e n t r a t i o n s were 0.1 m o l a r i n D 0 ; T,T'=60 msec, At,=600 /usee, t o t a l a c q u i s i t i o n t i m e was 15 minutes i n each case. 2  1  ' X~  Hz  i  i  1  600  1 400  1  1 200  1  1 0.0  1  1 -200  1  1 -400  1  1 -600  F i g u r e 2.5 S i n g l e quantum s p e c t r a a t 270 MHz o f a s o l u t i o n i n D 0 of L - a l a n i n e , L - t h r e o n i n e , L - v a l i n e and L - a s p a r a g i n e , a l l c o n c e n t r a t i o n s 0.1 m o l a r . A. I n a homogeneous m a g n e t i c f i e l d , B. I n an inhomogeneous m a g n e t i c f i e l d c o r r e s p o n d i n g t o F i g u r e 2.4 E. 2  r Hz  30 environment  s u c h as one m i g h t  find  i n the c o n t e x t of  NMR  imaging. 2.2  Editing  Zero-Quantum C o h e r e n c e S p e c t r a  Up u n t i l zero-quantum  t h e p r e s e n t t i m e most p r a c t i t i o n e r s NMR  of  h a v e been more c o n c e r n e d w i t h e n s u r i n g  they o b t a i n the whole  of the zero-quantum  spectrum  t h a n o n l y p a r t o f i t , a l t h o u g h t h e r e have been  that  [12]  rather  qualified  exceptions [13]. From e q u a t i o n 2.4 excitation  i t c a n be s e e n t h a t t h e e f f i c i e n c y  of zero-quantum  coherence  i s dependent  of  upon t h e  s c a l a r c o u p l i n g s o f t h e s p i n s and t h e l e n g t h o f t h e preparation period  T . C o n s e q u e n t l y t h e a b s o l u t e and  i n t e n s i t i e s of t h e z e r o - q u a n t u m for  relative  coherences observed w i l l  vary  a g i v e n s p i n s y s t e m f r o m one v a l u e o f T t o a n o t h e r . A t  c e r t a i n v a l u e s , w h e n e v e r e q u a t i o n 2.4 c a s e o f an A X  2  i s equal t o z e r o i n the  s p i n system, the zero-quantum  coherence w i l l  absent from the spectrum e n t i r e l y .  The d e p e n d e n c y  c o u p l i n g s and r w i l l  s p i n system t o a n o t h e r ,  although  i t will  v a r y f r o m one  the e f f e c t i v e data a c q u i s i t i o n  field  inhomogeneity  t i m e t o 2-3  d u r i n g which time the s p i n system w i l l e v o l u t i o n due  undergo  t o s c a l a r c o u p l i n g s , assuming  magnetization detected originating  from  may  milliseconds negligible  the c o u p l i n g  c o n s t a n t s concerned a r e not l a r g e . C o n s e q u e n t l y the of  scalar  be g e n e r a l l y e a s y t o c a l c u l a t e [ 1 1 ] .  As has been n o t e d a b o v e , m a g n e t i c limit  upon  be  intensity  zero-quantum  31 c o h e r e n c e , and  hence the  intensity  coherence observed  i n the  d e p e n d e n t upon t h e  relevant  the of  refocussing period  of  that  zero-quantum  r e s u l t a n t spectrum, w i l l scalar couplings  r'. This  and  the  i s analogous to the  z e r o - q u a n t u m e x c i t a t i o n upon s c a l a r c o u p l i n g s  discussed  above. For  2.13,  can  and  an A X  be  be e a s i l y c a l c u l a t e d f o r o t h e r  spin  of  dependency r  and  spin system t h i s given  2  length  in  equation  systems  [11]. Both p r e p a r a t i o n opportunity  p r o b l e m of for  refocussing periods  to e d i t the observed s i g n a l .  this ability, appreciated  and  particularly  when one  The  at lower f i e l d s ,  considers  resonance o v e r l a p  that  provide  an  importance  of  is readily  i n zero-quantum space  the  i n a s p e c t r u m i s o f t e n worse  i t s single-quantum counterpart.  This  than  i s because  zero-quantum coherences o n l y occur at the d i f f e r e n c e i n resonance frequencies usually  of two  coupled  s p i n s and  therefore  o c c u r w i t h i n a n a r r o w e r f r e q u e n c y r a n g e . The  e f f e c t s of v a r y i n g  the p r e p a r a t i o n  and  refocussing  upon a zero-quantum s p e c t r u m a r e d e m o n s t r a t e d for  L-threonine.  2.3  Non-Selective  C o h e r e n c e i n an  E x c i t a t i o n and  Detection  Inhomogeneous M a g n e t i c  of  editing periods  in Figure  Zero-Quantum  Field  G i v e n t h e c o n s t r a i n t s i m p o s e d upon t h e d e t e c t i o n z e r o - q u a n t u m c o h e r e n c e i n inhomogeneous magnetic preparation reasonably  and  refocussing  uniform  times,  e x c i t a t i o n and  how  2.6  can  one  d e t e c t i o n of  be  of  fields  by  c e r t a i n of  zero-quantum  a  32 A  I  300  i i i r—|—i—i—i—i—|—i—1-71—1—j—1—1—1—1  200  100  0.0  [ 1—1—1—1—j—1—1—1—1—j  -100  -200  Hz  F i g u r e 2.6 Z e r o - q u a n t u m s p e c t r a o b t a i n e d a t 80 MHz i n a n inhomogeneous magnetic f i e l d w i t h t h e r e f o c u s s e d zero-quantum e x p e r i m e n t o f 0.1 m o l a r L - t h r e o n i n e i n D 0 w i t h : A. T,T'=60 msec, B. T,T'=100 msec, C. T , T ' = 1 4 0 msec, D. T=100 msec, T'=60 msec. I n e a c h c a s e At,=1.67 msec, 256 b l o c k s were c o l l e c t e d w i t h 4 a c q u i s i t i o n s p e r b l o c k . A c q u i s i t i o n t i m e s 15-16 minutes. 2  33 coherences? One p o s s i b i l i t y w o u l d be t o r e p e a t several different spectra together the  spectra  values  the experiment f o r  o f T a n d r ' and a d d t h e r e s u l t i n g  [ 1 3 ] . One m i g h t , f o r e x a m p l e , a d d  i n Figure  2.6 A a n d C t o o b t a i n  zero-quantum spectrum of L - t h r e o n i n e .  together  complete  The m a j o r  of t h i s method i s t h e e x t r a t i m e i t i n v o l v e s .  disadvantage  Alternatively,  E r n s t a n d c o - w o r k e r s [ 1 2 ] h a v e p r o p o s e d t h e u s e o f an "accordion" is  preparation period  period  i n c r e m e n t e d by n A t , b e c o m i n g r + n t , . U s u a l l y n i s s e t t o  SO.25 s o t h a t t h e J - e n c o d i n g on  i n which the p r e p a r a t i o n  i tw i l l  c a u s e t o be s u p e r i m p o s e d  t o p of the zero-quantum spectrum w i l l  sufficiently  so as n o t t o d i s t o r t  be s c a l e d down  i t s i g n i f i c a n t l y . I t works  because t h e l e n g t h of t h e p r e p a r a t i o n p e r i o d w i l l t o t h a t needed t o e x c i t e least  correspond  each zero-quantum coherence f o r a t  p a r t of t h e e x p e r i m e n t , assuming t h a t t h e t i m e range i s  adequate. In Figure refocussed  2.7A t h e p r e p a r a t i o n  sub-sequence of the  z e r o - q u a n t u m e x p e r i m e n t h a s been r e p l a c e d w i t h t h e  "accordion"  preparation period. Despite  ensuring  e x c i t a t i o n of  all  zero-quantum c o h e r e n c e , t h i s sequence does n o t ensure  all  will  be d e t e c t e d .  acquisition invisible  This  antiphase  magnetization  s p e c t r u m by c h o o s i n g  effective  i s b e c a u s e i t assumes t h e e f f e c t i v e  t i m e t o be l o n g e n o u g h f o r a l l c o m p o n e n t s o f  in-phase magnetization  T h i s would  that  indeed  to evolve  through v i s i b l e  a n d h e n c e n o t t o be e d i t e d o u t o f t h e  a certain  value  of t h e r e f o c u s s i n g  be t h e c a s e i n a homogeneous f i e l d  acquisition  time..  where t h e  t i m e i s r e l a t i v e l y l o n g , b u t n o t i n an  T+nt,  III  ll  2  T+nt, 2  I  U  T 2  1 1  Gz  1 1  Preparation  j  Zero-quantum  ;  evolution  Refocussing  Acq.  i  B  T+nt, 2  G  T+nt, 2  1 1  2  Preparation  T+nt, 2  ti  j i i i i i  CO  T+nt, 2  ..„  i i i l i i i  i  1  j  Refocussing  i i  F i g u r e 2.7 A. R e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t w i t h " a c c o r d i o n " p r e p a r a t i o n p e r i o d . B. R e f o c u s s e d z e r o - q u a n t u m experiment with "accordion" p r e p a r a t i o n and r e f o c u s s i n g periods.  Acq.  35 A  IJVJ B  I 300  i  i  i—i—|—i—i—i—i—|—i—i—i—i—j—i—i—i—i—|—i—i—i—i—j—i—i—i—i 200  100  0.0  -100  -200  | Hz  F i g u r e 2.8 Z e r o - q u a n t u m s p e c t r a a t 80 MHz o f 0.1 m o l a r L - t h r e o n i n e i n D 0 w i t h : A. The r e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t w i t h an " a c c o r d i o n " p r e p a r a t i o n p e r i o d ( F i g u r e 2 . 7 A ) , B. The r e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t w i t h " a c c o r d i o n " p r e p a r a t i o n and r e f o c u s s i n g p e r i o d s . In b o t h c a s e s T=70 msec, A t , = 1.67 msec, n=.12 . 256 b l o c k s c o l l e c t e d , 8 a c q u i s i t i o n s p e r b l o c k . A c q u i s i t i o n t i m e s 35-37 m i n u t e s . 2  36 inhomogeneous f i e l d only a couple "accordion" still  where t h e e f f e c t i v e a c q u i s i t i o n  of m i l l i s e c o n d s . Consequently d e s p i t e the  preparation period the refocussing period  cause e d i t i n g ,  u s i n g an " a c c o r d i o n " period,Figure spectrum  Figure  Figure  r e f o c u s s i n g as w e l l as p r e p a r a t i o n s e q u e n c e was u s e d t o o b t a i n t h e  2.8B w h i c h i s c l e a r l y more u n i f o r m  obtained  will  2.8A. T h i s p r o b l e m was o v e r c o m e by  2.IB. T h i s p u l s e  i n Figure  counterpart  time i s  with a constant  than i t s  refocussing period i n  2.8A. The p a r a m e t e r s u s e d were t h e same i n b o t h  cases.  B o t h s e q u e n c e s were f o u n d t o p r o d u c e s i g n i f i c a n t l y intense peaks, r e f l e c t e d refocussed  i n the poorer  zero-quantum experiment  as many a c q u i s i t i o n s p e r b l o c k acquisition refocussed inherent  S/N c o m p a r e d t o t h e  ( F i g u r e 2.6) a l t h o u g h  were c o l l e c t e d .  twice  Hence t h e t o t a l  t i m e was t w i c e a s l o n g a s t h a t u s e d f o r t h e zero-quantum experiment  i n accordion  techniques.  i n Figure Varying  p r e p a r a t i o n and r e f o c u s s i n g p e r i o d s and  less  d e t e c t i o n of a given  2.5. T h i s i s  the length of the  results  i n the c r e a t i o n  zero-quantum coherence being  a t an  optimum f o r o n l y p a r t o f t h e e x p e r i m e n t w h e r e a s t h e f i x e d p r e p a r a t i o n and r e f o c u s s i n g i n t e r v a l experiment r e s u l t s zero-quantum coherence chosen being  optimised  i n the  throughout the  whole of t h e e x p e r i m e n t . 2.4 H o m o n u c l e a r B r o a d - B a n d D e c o u p l e d Zero-Quantum C o h e r e n c e Spectroscopy Zero-quantum s p e c t r a have s e v e r a l major over t h e i r  single-quantum counterparts.  disadvantages  Among t h e s e  arethe  37 time they t a k e t o a c q u i r e (each spectrum experiment)  and  corresponding The  latter  the narrow  resonance  f r e q u e n c y range  single-quantum  two-dimensional  relative  s p e c t r a over which  feature i s a direct  zero-quantum coherences  is a  r e s u l t of t h e p r o p e r t y o f  coupled spins. Often t h i s  t o o v e r l a p p i n g , a more c r o w d e d and hence l e s s spectrum.  T h i s problem  m a n i p u l a t i n g t h e p r e p a r a t i o n and  required  i f the type of s p i n  i n c r e a s e d t o t r y and  resonances  by  easily  refocussing times to edit  ( s e c t i o n 2 . 1 ) . Time c o n s u m i n g t r i a l  a r e n o t known. A l t e r n a t i v e l y  s y s t e m and  and  decouple  the r e s o l u t i o n  of t h e  f o r m e r m u l t i p l e t now  possibly  might  T h i s would  requiring  lower  be  to  lead  to  resolution  t i m e . I f a l l the i n t e n s i t i e s of a  went i n t o one  peak f e w e r  be r e q u i r e d t o b u i l d up c o m p a r a b l e A p u l s e s e q u e n c e was  used;  r e f e r r e d t o .above w o u l d  the e n t i r e zero-quantum spectrum.  broad-band  spectrum  r e s o l v e c r o w d e d and o v e r l a p p i n g  b o t h of the problems  and hence l e s s a c q u i s i t i o n  would  error i s  i n c r e a s i n g t h e number o f t , i n c r e m e n t s  a much s i m p l e r s p e c t r u m ,  the  i t s coupling constants  t h i s a l s o takes time. A t h i r d a l t e r n a t i v e which alleviate  leads  can be o v e r c o m e by  spectrum  can be  they occur.  which occur at the d i f f e r e n c e i n  f r e q u e n c i e s o f two  interpretable  to the  acquisitions  S/N.  designed to accomplish  the  d e c o u p l i n g of zero-quantum s p e c t r a w h i c h  i s shown  i n F i g u r e "2.9. I t has  been known f o r some t i m e how  homonuclear broad-band  decoupled  to  produce  single-quantum  spectra.  This  180o  9C»x T/2  1 80 oY  9C>x t,/2  T/2  ao td-tx/2  180o T/2  1 1 1 1  i  Gradient Z  1  Preparation  |  Zero-quantum  evolution  Refocussing  i i i i i  Figure 2.9 Broad band decoupled zero-quantum  experiment.  i Acquisition  39 was  originally  achieved  two-dimensional s e q u e n c e was  by t a k i n g a p r o j e c t i o n t h r o u g h  J - r e s o l v e d spectrum  designed  broad-band decoupled  specifically spectra  adapted to o b t a i n a Jeener  [14]. Later a  a  pulse  t o o b t a i n homonuclear  [ 1 5 ] w h i c h was  subsequently  spectrum decoupled  i n one  dimension  [16]. The and  u n d e r l y i n g p r i n c i p l e s of d e c o u p l i n g  zero-quantum s p e c t r a are  most e a s i l y u n d e r s t o o d information  vary  t h e same. I t i s  by c o n s i d e r i n g what i t t a k e s  i n t o t h e F1  spectrum. For  fundamentally  single-quantum  d i m e n s i o n of a  t h a t the a c q u i r e d  f u n c t i o n of t , due  signal  interest  i s m o d u l a t e d as  such as  t h a t i n F i g u r e 2.3,  v a l u e of t , a g i v e n zero-quantum coherence w i l l extent  m o d u l a t e s the a c q u i r e d corresponding  due  to chemical  signal  e v o l u t i o n due  t h e i r modulating  must  shift,  (equations  at  have  and  each  evolved  this  2.7-2.13). L i k e w i s e  to s c a l a r couplings r e s u l t s  the a c q u i r e d  s i g n a l as w e l l . T h i s g i v e s  in rise  to a zero-quantum spectrum complete w i t h m u l t i p l e t s t r u c t u r e when F o u r i e r t r a n s f o r m e d  with respect  to t , . Therefore,  d e c o u p l e a z e r o - q u a n t u m s p e c t r u m a l l one  has  ensure t h a t w h i l e the extent  shift evolution  v a r i e s w i t h t , , the e x t e n t not.  I t has  of c h e m i c a l  been w e l l d o c u m e n t e d  has  t o do  to  i s to  of s c a l a r c o u p l i n g e v o l u t i o n does [ 1 7 , 1 8 ] t h a t a 180°  a p p l i e d t o a homonuclear s p i n s y s t e m , as experiment,  a  t o t h i s p r o p e r t y . For example, i n a  zero-quantum experiment  to a d i f f e r e n t  put  two-dimensional  e a c h v a l u e o f t , t h e p r o p e r t y of  i n s u c h a way  to  in a  t h e e f f e c t o f r e v e r s i n g the  1  pulse  spin-echo  e v o l u t i o n of  the  a  40 spin  s y s t e m due t o c h e m i c a l  inhomogeneities  shift  and magnetic  field  b u t l e a v e s e v o l u t i o n due t o s c a l a r c o u p l i n g s  u n a f f e c t e d . T h i s a p p l i e s e q u a l l y t o z e r o - and  single-quantum  coherences. In  the decoupled  zero-quantum experiment,  zero-quantum e v o l u t i o n time, extent  t ^ , i s constant. Therefore the  o f e v o l u t i o n due t o s c a l a r c o u p l i n g s o f a z e r o - q u a n t u m  c o h e r e n c e c r e a t e d by t h e s e c o n d 90° p u l s e w i l l being  F i g u r e 2.9, t h e  u n a f f e c t e d by t h e p o s i t i o n  Thus t h e a c q u i r e d couplings extent  signal w i l l  o f t h e 180° p u l s e w i t h i n i t .  n o t be m o d u l a t e d due t o s c a l a r  i n t h e t , dimension of t h e data  of c h e m i c a l  shift  be c o n s t a n t ,  set S ( t  1  evolution at this  completely •results t,  reversed,  point  due t o c h e m i c a l  to t , will  zero-quantum  spectrum.  F o r an A X  . The  being  a t t,/2=t^.  This  evolution. Fourier therefore yield  transformation  the decoupled  s p i n system t h e e v o l u t i o n of a zero-quantum  2  c o h e r e n c e b e t w e e n s p i n s A a n d X d u r i n g t ^ c a n be d e s c r i b e d thus: {2QT}  y  "WV^Wxz, W y J  vary  s i g n a l being modulated w i t h respect t o  shift  with respect  2  chemical  c  i n the experiment  t o a maximum a g a i n  i n the acquired  t )  e v o l u t i o n on t h e o t h e r h a n d w i l l  f r o m a maximum a t t,/2=0 t o z e r o when t / 2 = t j / 2 , shift  1 r  2  )  I  X z  AX d- 1  W V  ( t  2  t  )  I  :  '^Ax +  / 2 ) 2 I  X Z  W  Az Xz, I  ;  2  )  l  A  2  j  W, 0  A yV (  2 )  V  41 {ZQT} COS[fi y  ef  f  *+{ZQT} sin[n x  ( t , - t ) ]cOS(7TJ d  +2I {ZQT} sin[J2  e f f  x  X z  f l  d  e f f  X z  t )  (t , - t ) ]cos(7rJ  e f f  (ZQT} cos[n  -2I  ef f  y  e f f  t )  (t -t ) ]sinUJ 1  d  d  f  t )  e f f  t )  e f  (t , - t ) ] s i n ( i r J d  d  (2.14)  d  C l e a r l y a l l s c a l a r c o u p l i n g e v o l u t i o n i s independent An e x a m p l e o f z e r o - q u a n t u m d e c o u p l i n g  i s given i n Figure  2.10 B f o r a s o l u t i o n o f e t h a n o l a n d 2 - p r o p a n o l the c o r r e s p o n d i n g 2.10  of t , .  i n D 0, 2  undecoupled zero-quantum spectrum  i n Figure  A. From an e x a m i n a t i o n  whether a p a r t i c u l a r in-phase  terms 2 I  antiphase  A x  I  of e q u a t i o n  2.14  i t c a n be s e e n t h a t  zero-quantum coherence i s p r e s e n t as the X x  ,  terms such as  2I 4 I  A y  I  ,  X y  2I  ^y Xy Xz I  I  a t  A  x  t  I *  X  y  i e  , e  and 2 I n  °^  d  fc  A  I  y  d  *  X  f o l l o w s t h a t a c o h e r e n c e may  be c o m p l e t e l y  of t  d  f o r a l l v a l u e s of t , . T h i s has  c o n s e q u e n c e s a s c a n be s e e n f r o m T a b l e  or as  and t  d  .  or  both at the  important  I I . The t a b l e shows t h e  e f f e c t s o f t h e p u l s e a=90° a t t h e e n d o f t o p e r a t o r s present a t t h a t time  ,  in-phase  c o m p l e t e l y a n t i p h a s e , o r , more n o r m a l l y , p a r t i a l l y end  x  s  d e p e n d e n t o n l y upon t h e c o u p l i n g c o n s t a n t s c o n c e r n e d It  and  f o r an A X  2  d  on t h e p r o d u c t  spin  system.  42 T a b l e I I . E f f e c t s o f t h e p u l s e a=90° on t h e p r o d u c t o p e r a t o r s p r e s e n t a t t h e end o f t h e e v o l u t i o n t i m e t ^ o f t h e b r o a d - b a n d d e c o u p l e d z e r o - q u a n t u m e x p e r i m e n t f o r an A X s p i n s y s t e m . 2  Product operators present before pulse a  2 I  Ay Xx  Product operators present a f t e r p u l s e a=90° ( v i s i b l e terms i n bold type)  2 I  J  Az Xx J  "^Ax^y  '"Ax !!  ^Ax^x  2 I  Ax Xx  2 I  Az Xz  2 I  Ay Xy  ~  4 I  1  J  I  " ^ A y V x z 4 I  Ay Xx Xz  ~  4 I  I  4 I  ~  I  Ax Xy Xz I  I  41 I I * Ax Xx Xy  Ax Xx Xz I  :  4 I  I  Az Xz Xy I  4 I  I  Az Xx Xy I  I  Ax Xz Xy I  I  C l e a r l y o n l y the in-phase converted be v i s i b l e  into antiphase after  be o b s e r v e d .  2 I  I A X  Xy  single-quantum  a  n  d  2 I  Ay Xx I  coherence  a  r  e  which  which  Therefore  a zero-quantum coherence  i s in-phase  a t t h e end o f t ^  t ^ c a n be c h o s e n s u c h  that a l l of  i s only present as a n t i p h a s e  m a g n e t i z a t i o n a t t h e end of t h e p e r i o d and hence w i l l e d i t e d out of the observed demonstrated  will  r e p h a s i n g . I n o t h e r words, o n l y t h a t p a r t of  a zero-quantum coherence will  terms  zero-quantum spectrum.  This i s  f o r a s o l u t i o n of e t h a n o l and 2-propanol  i n F i g u r e 2.10 C a n d D where 2 - p r o p a n o l  be  in D 0 2  and e t h a n o l  r e s p e c t i v e l y h a v e been e d i t e d o u t o f t h e s p e c t r u m .  The  graph  i n F i g u r e 2.11 shows how t h e i n t e n s i t i e s o f t h e c o m p o n e n t s o f  F i g u r e 2.10. Z e r o - q u a n t u m s p e c t r a o f e t h a n o l a n d 2 - p r o p a n o l , 1:1 i n D 0 . A. C o n v e n t i o n a l z e r o - q u a n t u m s p e c t r a o b t a i n e d w i t h t h e r e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t ; T,T'=60 msec, At,=1.67 msec. 256 b l o c k s c o l l e c t e d , 4 a c q u i s i t i o n s p e r b l o c k . B-D. B r o a d b a n d d e c o u p l e d z e r o - q u a n t u m s p e c t r a : B. ^ = 4 4 3 msec, C. td=413 msec, D. td=493 msec. I n B-D T=60 msec, At,=1.67 msec, a=90°. 256 b l o c k s c o l l e c t e d , 4 a c q u i s i t i o n s p e r b l o c k . Peak a s s i g n m e n t s : e t h a n o l ±197 Hz, 2 - p r o p a n o l ±225 Hz. 2  44 the above s o l u t i o n i n t e n s i t i e s can  were f o u n d  be e a s i l y p r e d i c t e d by c o n s t r u c t i n g t h e  appropriate product  o p e r a t o r s . The  zero-quantum coherence  of an A X  proportional  to c o s  reflected  2-propanol  For  by  t o v a r y w i t h t ^ f o r a=90°. T h e s e  n  1  T  J  f f  a n  e  d  in Figure  the  was  a which  two  observed an AMX  different  s p i n system  Ay My Xz"  A  4 I  Az Mz Xy'  a  I  I  I  P l u  n  t  iph  to zero i t w i l l  at e d i t i n g .  a  s  s  e  i H  w  convert  evolve  As n e i t h e r J  into observable  a n t i p h a s e a t t h e end  become  4 I  ^  I z  a  I  a  n  t  c a t  i P  n  i° a  s  n  e  o f  a  f o r an A X 90°  i n t o v i s i b l e inphase be  corresponding might  would  m a g n e t i z a t i o n of t h e p a s s i v e s p i n =  will  single-quantum  p u l s e t h i s term  X  hence e d i t i n g  i s equal  M  s p i n system  n  X w i t h r e s p e c t t o t h e s p i n s A and X. As ^ x ^ rephase  X  between s p i n s A  of t h e e v o l u t i o n p e r i o d . A  PPli  Xz Xy'  nor J  A  even i f t ^ i s s e t so t h a t a l l of i t i s  a n t i p h a s e zero-quantum coherence 0 n  including  into  in-phase  be o b s e r v e d  I  be  between s p i n s A  X  and M w i l l  I  pulse  m a g n e t i z a t i o n of the p a s s i v e s p i n X w i t h  e  Hence t h e z e r o - q u a n t u m c o h e r e n c e  ^y Xy Xz*  the  For example, f o r  t h i s term  coherence.  4 I  by  be  hence w i l l  a zero-quantum coherence  r e s p e c t t o t h e s p i n s A and M.  be  will  e v o l v e d u r i n g t ^ i n t o a n t i p h a s e terms  4 I  I  coupled  coherence  be c a p a b l e o f r e f o c u s s i n g and  thus thwarting attempts  and M w i l l  be  i s somewhat d i f f e r e n t . E v e n when a=90°  i n t o antiphase single-quantum  will  to  2.11.  some a n t i p h a s e t e r m s of a z e r o - q u a n t u m c o h e r e n c e converted  found  t h i s dependency i s  s p i n s y s t e m s w i t h more t h a n  s p i n s the s i t u a t i o n  of  s p i n system  n  ( 3 £f )>  intensity  single-quantum  effective.  w  o  u  l d  coherence  never and  Peak intensity  l — i — i — i — i — i — i — i — r — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i 273 313 353 393 433 473 513 t^ (msec)  F i g u r e 2 . 1 1 . G r a p h o f peak i n t e n s i t y v s . t ^ f o r t h e b r o a d d e c o u p l e d z e r o - q u a n t u m e x p e r i m e n t f o r a 1:1 s o l u t i o n o f e t h a n o l and 2 - p r o p a n o l i n D 0 . 2  band  46  T a b l e I I I . E f f e c t s of a p u l s e a on t h e p r o d u c t o p e r a t o r s p r e s e n t a t t h e end of t h e e v o l u t i o n t i m e t ^ o f t h e b r o a d - b a n d d e c o u p l e d z e r o - q u a n t u m e x p e r i m e n t f o r an A X s p i n s y s t e m . 2  Product operators present before pulse a  Vxx  2  '"Ax ** 1  2 I  Ax Xx I  Product operators present a f t e r pulse a ( v i s i b l e terms i n b o l d type)  2 I  Ay Xx  _  I  2  Ax Xx Xz I  I  c o s a  Ax Xy I  c  o  2  s  I  -  a  2  Ay Xy I  Az Xy  I  I  " 4  s  i  n  a  4  A y  I  I  0  c  O  I  S  0  '  8  X z  I  a  I  c  2  1  I  Ax Xy Xz I  I  s  2  a  C  s  O  s  i  4 I  Az Xy Xy  C O S a s i n 2 a  I  I  I  2  n  C O S a s i n 2 a  1  1  i  n  I  a  a  s  I  I  i  I  I  4  I  Az Xx Xy  s  "  4 I  Ax Xy Xz  c o s 2 a  I  -  4  I  I  A x  I  X z  Ax Xz Xy  One p r o b l e m i s how  I  I  i  I  n  s i n a  I  I  2  c  o  s  2  a  s  i  n  a  a  Az Xz Xy I  I  I  I  c  o  s  a  s i n 3 a  s  i  n  a  C O S a s i n a  "  I  a  A y X y X y  I  n  2  -* Ay Xx Xy  Az Xx Xz I  n  a  C O s 2 a  I  i  I  4 I  I  s  Ax Xx Xy  COSasin2a  Ay Xx Xz  4 I  4 I  s  cosasina  X z  4  Ay Xz Xy  4 I  _ 4 I  a  Az Xz  l  1  X z  o  I  4 I  4 I  I  A Y  "  0 0 8  Az Xy Xz  I  U  I  n  X  - Az Xz Xz Ay Xx Xz  i  AK Xz  I  2I  c o s 2 a  - ^ ^ y ^ y ^ z  4 I  s  :  -"AXWXZ  _  Az Xx  I  Ax Xx  2 I  v  _ 4 I  2  2 I  21.Ay I Xy  I  a  X z  4 I  C  O  S  a  s  i  n  Ax Xy Xy I  I  C O S a s i n a  a  s i n 2 a  t o e n s u r e t h a t one o b t a i n s t h e  c o m p l e t e d e c o u p l e d z e r o - q u a n t u m s p e c t r u m . T h e r e a r e two possible solutions:  firstly,  the spectra obtained with  several  47 different  v a l u e s o f t ^ c a n be c o - a d d e d ,  p u l s e a c a n be v a r i e d  o r , a l t e r n a t i v e l y , the  f r o m 90°. The e f f e c t s  o f an a r b i t r a r y  p u l s e a on t h e p r o d u c t o p e r a t o r s p r e s e n t f o r an A X system a f t e r  coherence  t e r m s , none o f w h i c h become  when a=90° o r an i n t e g e r m u l t i p l e o f i t , g i v e  terms which w i l l  become v i s i b l e a f t e r  be o b s e r v e d  rephasing are i n bold type i n Table I I I . S e t t i n g i n a n t i p h a s e zero-quantum  potentially  zero-quantum  a=45°  will  coherence being converted i n  that are involved  i n an a n t i p h a s e  coherence product operator the l e s s e f f i c i e n t  be i t s c o n v e r s i o n i n t o p o t e n t i a l l y The  after  o b s e r v a b l e t e r m s w i t h maximum e f f i c i e n c y .  G e n e r a l l y , t h e more n u c l e i  will  rise to  r e p h a s i n g when a does  n o t meet t h i s c o n d i t i o n . Terms w h i c h w i l l  result  spin  t ^ c a n be e v a l u a t e d f r o m T a b l e I I I . Some o f t h e  a n t i p h a s e zero-quantum visible  2  o b s e r v a b l e terms [ 1 2 ] .  e x p e r i m e n t s i n F i g u r e 2.10 B-D were r e p e a t e d w i t h  a=45° a n d t h e s e r e s u l t s  a r e shown i n F i g u r e 2.12. I n e a c h  both coherences are v i s i b l e , most i n t e n s e  r e s o n a n c e even  and 2-propanol g i v e s r i s e t o t h e when t h e v a l u e o f t ^ was u s e d  w h i c h h a d p r e v i o u s l y , when a=90°, e d i t e d three factors.  Firstly,  a n t i p h a s e zero-qantum which w i l l  case  i tout. This reflects  i t i s d e p e n d e n t upon t h e p r o p o r t i o n o f  coherence  yield potentially  terms  f o r each s p i n  system  o b s e r v a b l e t e r m s when a c t e d upon  by t h e p u l s e a. S e c o n d l y , i t r e f l e c t s t h e r e l a t i v e s i z e o f t h e s e terms, and t h i r d l y , t h e e f f i c i e n c y converted  into potentially  system t h e s i z e  w i t h which they a r e  o b s e r v a b l e t e r m s . F o r an A X  of t h e s e a n t i p h a s e zero-quantum  2  spin  coherence  t e r m s c a n be e v a l u a t e d f r o m e q u a t i o n 2.14, a n d t h e i r  48  PI  F i g u r e 2.12. B r o a d band d e c o u p l e d z e r o - q u a n t u m s p e c t r a o f a 1:1 s o l u t i o n o f e t h a n o l a n d 2 - p r o p a n o l i n D 0 w i t h a=45°: A. t j = 4 l 3 msec, B. t<3=443 msec, C. td=493 msec. T = 60 msec, At!=1.67 msec, 256 b l o c k s c o l l e c t e d , 4 a c q u i s i t i o n s p e r b l o c k . Peak a s s i g n m e n t s : e t h a n o l ±197 H z , 2 - p r o p a n o l ±225 Hz. 2  (  49 conversion e f f i c i e n c y It  s h o u l d be  F i g u r e 2.11,  can  noted  t h a t the coherence  u n l i k e F i g u r e 2.10,  a b o u t 0.0Hz. T h i s i s due positive  a r e no l o n g e r  t o one  later  [  90°.  i n t h e F1  is potentially  spectrum  a limitation  vivo  has  the  t o map  i n a homogeneous m a g n e t i c  recently  i n an e x p e r i m e n t  which  field  t h a t two  [ 2 0 , 2 1 ] , most  g i v e s r i s e to a spectrum  c o u l d be e n h a n c e d  d e c o u p l i n g the zero-quantum coherences, and  hence u s e f u l n e s s .  2.5  Single-Quantum J-Resolved Spectroscopy  dimensional  spin-spin coupling  t o t h a t of t h e SECSCY e x p e r i m e n t  u s e f u l n e s s of these experiments  rule  experiment.  been d e m o n s t r a t e d  networks  Zero-quantum  considers  be t a k e n up by  a p p l i c a t i o n s of t h i s  previously  format  when one  spin-spin  r e f o c u s s i n g p e r i o d s . T h i s w o u l d seem t o  z e r o - q u a n t u m s p e c t r a c a n be u s e d  a similar  the  h e n c e upon t ^ a s t ^ n A t , .  f o r m o l e c u l e s where  m i l l i s e c o n d s more w i l l  p r e p a r a t i o n and  It  induced  be d i s c u s s e d i n  i s d e p e n d e n t upon  r e l a x a t i o n times are short, p a r t i c u l a r l y  o u t most in  the  participating  t o the other  T h i s phenomenon w i l l  number of t , i n c r e m e n t s , n, u s e d and  t h a t up t o 200  symmetrical  12,19].  Resolution  This  of  t r a n s f e r of  of t h e  t h a t of the n e g a t i v e f r e q u e n c y  by v a r y i n g a f r o m  intensities  t o the p r e f e r e n t i a l  zero-quantum frequency  s p i n s and  detail  be e v a l u a t e d f r o m T a b l e I I I .  Broad-Band  improving  Decoupled  with  [21-23].  The  by resolution  50 One o f t h e m a j o r p r o b l e m s f o r d e t e r m i n i n g between  zero-quantum c o h e r e n c e s , and hence  s t r u c t u r e of chemical species s o l e l y lies  in their multiplet  connectivity  i n determining the  from such c o h e r e n c e s ,  structure.  The c o u p l i n g c o n s t a n t s a n d a l s o t h e m u l t i p l e t  structure  of z e r o - q u a n t u m c o h e r e n c e s a r e n o t , on t h e w h o l e , t h e same a s their  single-quantum counterparts.  In general the e f f e c t i v e  c o u p l i n g c o n s t a n t of a m u l t i p l e - q u a n t u m c o h e r e n c e c o n s i s t i n g of s p i n s k c o u p l i n g t o a p a s s i v e s p i n m i s g i v e n b y :  J  eff  =  K  A m  k km J  ( 2  '  1 5 )  where Am^=±1, t h e c h a n g e i n t h e m a g n e t i c quantum number o f s p i n k. C o n s e q u e n t l y n o t o n l y a r e t h e e f f e c t i v e constants d i f f e r e n t  coupling  f r o m t h o s e f o u n d on s i n g l e - q u a n t u m  coherences, but a s p i n which can p a r t i c i p a t e  i n more t h a n one  z e r o - q u a n t u m c o h e r e n c e may e x h i b i t d i f f e r e n t  coupling  c o n s t a n t s i n each case. C l e a r l y  t h i s makes t h e e l u c i d a t i o n o f  s p i n - s p i n c o u p l i n g n e t w o r k s , and hence species, d i f f i c u l t .  identifying  I t w o u l d seem t h e r e f o r e t h a t i f  zero-quantum coherences e x h i b i t e d  single-quantum m u l t i p l e t  s t r u c t u r e and c o u p l i n g c o n s t a n t s t h a t t h e i r g r e a t l y enhanced  in this  problem i s not q u i t e  u s e w o u l d be  r e s p e c t . B u t , i t s h o u l d be n o t e d , t h e  so s i m p l e t o o v e r c o m e . E a c h  c o h e r e n c e i s a c o h e r e n c e between were somehow  chemical  zero-quantum  two s p i n s and h e n c e  t o r e p l a c e the zero-quantum m u l t i p l e t  i f one  structure  one w o u l d be d o i n g so w i t h n o t one b u t two s i n g l e - q u a n t u m ones. T h i s ,  i t w o u l d seem, w o u l d n o t l e a v e one any b e t t e r o f f .  51 T h e r e f o r e n o t o n l y d o e s one single-quantum m u l t i p l e t selectivly.  The  participating  have t o r e p l a c e t h e z e r o - w i t h  s t r u c t u r e but one  single-quantum m u l t i p l e t  s p i n must be  t o do i t  s t r u c t u r e of  found o n l y a t the  z e r o - q u a n t u m f r e q u e n c y and n e g a t i v e zero-quantum  has  positive  t h a t of t h e o t h e r o n l y a t t h e  frequency.  Given these r e q u i r e m e n t s , the s o l u t i o n would present  itself  as f o l l o w s . F i r s t l y  spectrum.  Secondly  coherence  frequency encoding  transfer  decouple  the p o s i t i v e  The  coherences  f r o m 90°  preferential  before  ( s e c t i o n 2 . 4 ) . I t was  of c o h e r e n c e  participating  will  been  noted that  a f r o m 90°  results  [12,19,21],  zero-quantum coherence.  the n e g a t i v e  i n phase i n s t e a d of  from  quadrature-phase  d e t e c t i o n w i t h r e s p e c t t o t , . W i t h phase m o d u l a t i o n ,  e n c o d e d c a n be  distinguished.  because  amplitude  originating  T h i s makes p o s s i b l e  a m p l i t u d e m o d u l a t i o n , p o s i t i v e and  The  preferentially  s p i n and  m o d u l a t i o n of s i n g l e - q u a n t u m c o h e r e n c e  if a is  experiment  occur  be  has  zero-quantum frequency to the o t h e r . T h i s i s p o s s i b l e varying  the  acquisition.  p o s i t i v e zero-quantum frequency w i l l t r a n s f e r e d t o one  s p i n and  resulting  i n the decoupled zero-quantum  transfer  zero-quantum  t o one p a r t i c i p a t i n g  d e c o u p l i n g of z e r o - q u a n t u m c o h e r e n c e s  discussed previously varied  the  seem t o  zero-quantum  n e g a t i v e t o the o t h e r . T h i r d l y J-encode the single-quantum  one  unlike  negative frequencies  52  From T a b l e  I I and e q u a t i o n s  s e e n t h a t f o r an A X  spin  2  antiphase single-quantum a-90° o r i g i n a t i n g  system  +  ( 2 I  d +  observable  present a f t e r  from zero-quantum coherence  the pulse  i n the  i s g i v e n by:  )=  Az Xx  -  X  Clearly 2.15  the p o t e n t i a l l y  coherence  broad-band d e c o u p l i n g experiment oP(r t  2.2, 2.3 a n d 2.14 i t c a n be  2 I  Ax Xz I  ) c o s I ( 0  A-°X  ) ( t  i- d  the antiphase single-quantum  t  ) ] c o s ( i r J  coherence  eff d t  )  ( 2  '  1 5 )  i n equation  i s o n l y a m p l i t u d e m o d u l a t e d . T h e r e f o r e p o s i t i v e and  n e g a t i v e zero-quantum f r e q u e n c i e s a r e i n d i s t i n g u i s h a b l e and will  b o t h be c a r r i e d by b o t h p a r t i c i p a t i n g From T a b l e  I I I and e q u a t i o n s  s e e n t h a t f o r an A X potentially created  (  + t  from  2I  d  +  A z  I  X x  A z  I  +2 I  and  system  2.2, 2.3 a n d 2.14 i t c a n be the general expression f o r  observable antiphase single-quantum  f o r an X s p i n  °X '  spin  2  spins.  zero-quantum coherence  coherence  by an a r b i t r a r y  pulse a  i s g i v e n by:  ) =  c o s [ ( 0 - f l ) (t i - t ) ] c o s U J A  X y  x  d  e f  s i n [ (^ "fi ) (t ,-t^) ]cos(rrJ A  x  f  t )sina d  t^Jsinacosa  e ff  f o r an A s p i n :  -2I  A x  I  X z  c o s [ ( n " ^ ) (t i ~ t ) ]cos(7rJ  e f  +2 I  A y  I  X z  s i n [ (fi fi ) (t ,-t ) ]cos(7rJ  e ff  A  x  d  _  A  x  d  f  t )sina d  t )sinacosa d  (2.16)  53 •41. I I s i n [ (S2 -fl„) ( t , - t , ) ] s i n ( 7 r J , , t J s i n a c o s a Ax Xz Xz A X a err a v  ~  Both  4 I  v  Ay Xz Xz I  I  s p i n s now  c o s  ^  ( n  A~ X f l  have two  single-quantum  will  l  _  t  d  )  ]sin(irJ  (the f i r s t  t )sinacos a d  from  two  i s m o d u l a t e d by c o s [ ( f i  antiphase  in-phase  terms i n e q u a t i o n s -fl )(t,-t^)]  A  and  x  2.16 the  s i n [ ( f l " f l ) ( t , - t ^ ) ] i n e a c h c a s e . Hence e a c h s p i n A  x  be p h a s e m o d u l a t e d a s a f u n c t i o n o f t h e e x t e n t  chemical  (2.17)  2  e f f  components of  coherence o r i g i n a t i n g  2 . 1 7 ) . One  o t h e r by  t  orthogonal  zero-quantum coherence and  ) (  shift  e v o l u t i o n of t h e p a r e n t  of  zero-quantum  coherence  making p o s s i b l e quadrature-phase  detection with respect to t , .  There  between e q u a t i o n s  i s an  important  difference  •2.17, i n t h a t t h e l a t t e r  has  a negative  t h e sense of phase m o d u l a t i o n different;  one  spin w i l l  o f t h e two  the other w i l l  phase m o d u l a t i o n .  The  transformed  direct  This results  spins  result  of t h i s  p o s i t i v e encoded phase w i l l  give rise  in  being  have a c o r r e s p o n d i n g  w i t h r e s p e c t t o t , the  z e r o - q u a n t u m p e a k , and  and  have a p o s i t i v e p h a s e m o d u l a t i o n  r e s p e c t t o t , and  Fourier  term.  2.16  with  negative  i s t h a t when spin with a  t o the  positive  the o t h e r , w i t h a n e g a t i v e  p h a s e , t h e n e g a t i v e z e r o - q u a n t u m p e a k . Hence  encoded  preferential  t r a n s f e r of c o h e r e n c e i s a c h i e v e d as d e s i r e d . U n f o r t u n a t e l y t h e r e a r e c o m p l i c a t i o n s . The and  2.17  s i n a and  show d i f f e r e n t  have e q u a l  result,  but  two  terms of e q u a t i o n s  d e p e n d e n c i e s upon t h e p u l s e a n g l e  sinacosa respectively.  terms w i l l will  first  I f s i n a = s i n a c o s a then  i n t e n s i t i e s and  i f t h e y a r e not- e q u a l  pure phase  2.16 a,  both  modulation  t h e i r modulation  can  be  54 b r o k e n down i n t o two c o m p o n e n t s . One component i s p h a s e modulated  and t h e o t h e r a m p l i t u d e modulated.  modulated  component r e s u l t s  in preferential  coherence as d e s c r i b e d above, magnetization w i l l rise  result  The  t r a n s f e r of  but the amplitude  i n non-preferential  modulated  transfer,  t o b o t h p o s i t i v e and n e g a t i v e zero-quantum  upon F o u r i e r  phase  giving  frequencies  t r a n s f o r m a t i o n . This reduces the o v e r a l l  e f f i c i e n c y of the p r e f e r e n t i a l  transfer process.  As a t e n d s t o z e r o s i n a t e n d s t o s i n a c o s a a n d t h e e f f i c i e n c y of p r e f e r e n t i a l overall  signal  intensity  transfer w i l l  will  elsewhere that the i n t e n s i t y  increase although the  d e c r e a s e . I t h a s been shown r a t i o o f t h e two p e a k s  arising  f r o m t h e F o u r i e r t r a n s f o r m a t i o n o f t h e m o d u l a t i o n o f one k i n d spin  i s proportional The  to tan (a/2)[21]. 2  t h i r d and f o u r t h t e r m s o f e q u a t i o n 2.17 o r i g i n a t e  from a n t i p h a s e zero-quantum  coherence and, as w i t h t h e f i r s t  two  and a m p l i t u d e  t e r m s , c o n s i s t of phase  components. T h i s w i l l the  same e f f i c i e n c y  difference In to  i n phase  more c o m p l e x  give rise to preferential  as t h e f i r s t  consequently  with  two t e r m s , a l t h o u g h w i t h a  spin  systems  c o h e r e n c e may be t r a n s f e r r e d  i n t h e zero-quantum  (page 4 4 ) . The e f f i c i e n c y  significantly  transfer  o f 90°.  s p i n s of a k i n d not i n v o l v e d  concerned  modulated  coherence  of t h i s p r o c e s s i s  r e d u c e d when a i s r e d u c e d f r o m 90° t o 45° a n d i s not a s i g n i f i c a n t  problem.  90;  1  180°, T/2  180°.  90S  T/2  Gradient Z  t:/2  OiJ t -ti/2 d  180° nt,  2  1  nt,  1  Xniiiii,,..  cn cn  1 1  Preparation  ] Zero-quantum  evolution  Refocussing  1 1 1 1 1 I  I F i g u r e 2.13. S i n g l e - q u a n t u m J - r e s o l v e d b r o a d band d e c o u p l e d zero-quantum experiment.  Acquisition  56  T a k i n g t h e above i n t o a c c o u n t c h o i c e of a w i l l  i t c a n be  be a c o m p r o m i s e b e t w e e n  t r a n s f e r , w h i c h becomes more e f f i c i e n t overall  signal  The  third  intensity, requirement  subsequence  which d e c r e a s e s as a tends t o z e r o . i s t o J-encode t h e m a g n e t i z a t i o n ,  which  r e f o c u s s e s and J - e n c o d e s . refocussing  i n t h e same way  the  T h i s i s done by r e p l a c i n g  t i m e r w i t h n t , , and  two-dimensional experiment to  two-dimensional purely  f o l l o w s t h e p u l s e a by one  retaining  c e n t r e o f t h i s p e r i o d , F i g u r e 2.13.  functions  the  as a t e n d s t o z e r o , and  [ 2 4 , 2 5 ] . T h i s i s a c h e i v e d by r e p l a c i n g  refocussing  the  that  preferential  as i s done i n t h e c o n v e n t i o n a l J - r e s o l v e d experiment  seen  as a normal  the  This  which  the  180°  pulse at  subsequence  J-resolved  by i n t r o d u c i n g p h a s e m o d u l a t i o n  due  s c a l a r c o u p l i n g e v o l u t i o n as a f u n c t i o n of t , [ 2 4 , 2 5 ] , n i s  a J-scaling  factor:  the single-quantum m u l t i p l e t  on t o p o f t h e d e c o u p l e d z e r o - q u a n t u m  coherence  s c a l e d - u p r e l a t i v e t o the r e s t of the spectrum n. A v a l u e of n>1  would  will  be  by a f a c t o r  i n c r e a s e the r e s o l u t i o n  single-quantum m u l t i p l e t s , although also  superimposed  of  the  potentially  i n c r e a s i n g the o v e r l a p of a d j a c e n t c o h e r e n c e s . A v a l u e of would  decrease the r e s o l u t i o n of the s i n g l e - q u a n t u m  structure,  c a n c e l l a t i o n of  coherence  n<1  multiplet  u s e f u l where t h e r e i s o v e r l a p p i n g , a l t h o u g h i t  s h o u l d be n o t e d t h a t  The  of  insufficient  r e s o l u t i o n may  lead  to  peaks.  e v o l u t i o n of i n v i s i b l e a n t i p h a s e s i n g l e - q u a n t u m into visible  in-phase single-quantum coherence  and  57 J - e n c o d i n g b o t h depend upon e v o l u t i o n to  s c a l a r c o u p l i n g s . The  multiplet  o f t h e m a g n e t i z a t i o n due  c e n t r a l peak o f an odd  does not e v o l v e d u r i n g the J - e n c o d i n g  Consequently  the c e n t r a l peaks  superimposed  upon d e c o u p l e d z e r o - q u a n t u m  be o b s e r v e d  o f odd  subsequence.  numbered  multiplets  coherences w i l l  not  i n t h i s experiment. T h i s i s because a l l  single-quantum coherence of  numbered  zero-quantum  modulated  coherence  as a f u n c t i o n  evolution  of t h e e x t e n t  is initially  invisible  a n t i p h a s e m a g n e t i s a t i o n a f t e r t h e p u l s e a. C o n s e q u e n t l y t h e y do n o t e v o l v e due of  odd  to s c a l a r c o u p l i n g s the c e n t r a l  numbered m u l t i p l e t s  invisible.  However, t h i s  will  the zero-quantum  r e m a i n a n t i p h a s e and  r e s u l t s i n o n l y minor  as the s i n g l e - q u a n t u m m u l t i p l e t in  coherence  structure  will  s p e c t r u m . As t h e two m u l t i p l e t s  the observed s p l i t t i n g  peak c a n be r e a d i l y d e d u c e d .  peaks  hence  inconvenience  of b o t h s p i n s  active  be p r e s e n t i n t h e r e s u l t i n g  must s h a r e a c o u p l i n g c o n s t a n t  and a s t h e r e must be a s u f f i c i e n t to cause  as  of  spin  of t h e o t h e r t h e a b s e n c e  of a  Any  number of e a c h  kind  r e m a i n i n g a m b i g u i t y may  removed by r e f e r e n c e t o t h e c o n v e n t i o n a l  be  zero-quantum  spectrum. The molar factor  experiment  i s demonstrated  L-alanine in D 0 2  f o r a s o l u t i o n of  i n F i g u r e 2.14  n s e t t o 2 t o improve  C, w i t h t h e  resolution  0.1  J-scaling  of the m u l t i p l e t s .  d o u b l e t and a q u a r t e t a r e p r e s e n t a s e x p e c t e d and e x h i b i t c o u p l i n g c o n s t a n t as would  be e x p e c t e d f o r an A X  The  c o n v e n t i o n a l and b r o a d - b a n d  are  g i v e n i n F i g u r e s 2.14  A one  spin  system.  d e c o u p l e d zero-quantum  spectra  A and B  respectively.  3  58  B  300 F i g u r e 2.14. S p e c t r a o f 0.1 m o l a r L - a l a n i n e i n D 0 . A. C o n v e n t i o n a l zero-quantum spectrum o b t a i n e d w i t h the r e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t . T , T ' = 6 0 msec, At,=1.67 msec. 256 b l o c k s c o l l e c t e d , 4 a c q u i s i t i o n s p e r b l o c k . B. B r o a d band d e c o u p l e d z e r o - q u a n t u m s p e c t r u m . T=60 msec, t j=443 msec, At, = 1.67 msec. 256 b l o c k s c o l l e c t e d , 4 a c q u i s i t i o n s p e r b l o c k . C. S i n g l e - q u a n t u m J - r e s o l v e d b r o a d band d e c o u p l e d z e r o - q u a n t u m s p e c t r u m . a=22.5°, T=60 msec, t^=443 msec, At,=1.67 msec, n=2. 256 b l o c k s c o l l e c t e d , 8 a c q i s i t i o n s p e r b l o c k . 2  (  ~\—r  300  1  I 200  F i g u r e 2.15. zero-quantum msec, t j = 4 l 3 acquisitions (  r  100  -i—i—i—r T  ~i—r  ~i—r  T  -100  0.0  ~i—i—i—r  T  -200  ~i—r  Hz  S i n g l e - q u a n t u m J - r e s o l v e d b r o a d band d e c o u p l e d s p e c t r u m o f e t h a n o l i n D 0 ( 2 : 1 ) . a=45°, T=60 msec, A t , = 1.67 msec, n=2. 256 b l o c k s c o l l e c t e d , 8 per block. 2  1  59  300  200  100  -100  0.0  -200  F i g u r e 2.16. S i n g l e - q u a n t u m J - r e s o l v e d b r o a d band d e c o u p l e d z e r o - q u a n t u m s p e c t r a o f 2 - p r o p a n o l i n D 0 ( 3 : 1 ) . A. a=45°. B. a=22.5°. I n b o t h c a s e s T=60 msec, tqj=493 msec, At,=1.67 msec, n=2. 256 b l o c k s c o l l e c t e d , 8 a c q u i s i t i o n s p e r b l o c k . 2  Hz  60  The 2.15.  corresponding  The  s p e c t r u m of e t h a n o l  c e n t r a l peak o f t h e t r i p l e t  • s t a t e d above t h i s  i s obvious  coupling constant.  in Figure  i s m i s s i n g though  as  g i v e n t h e n e c e s s i t y o f a common  In t h i s case  non-preferential transfer  i s given  i t can  be  seen t h a t  of c o h e r e n c e i s not  significant.  Due  t o t h e o v e r l a p of r e s o n a n c e s i t i s not p o s s i b l e t o a s c e r t a i n the e x t e n t of n o n - p r e f e r e n t i a l t r a n s f e r L-alanine.  I n F i g u r e 2.16  A i s g i v e n the  spectrum f o r 2-propanol. expected doublet  the  As was  preferential  Although  i t due  transfer  due  by  signal  reducing  a f r o m 45°  a. C o h e r e n c e t r a n s f e r  a l s o be  of  t o 22.5° t h i s  B.  t o such  reduced  of  Interference  a v a l u e of t ^ f o r which the  small.  I f t h e optimum v a l u e of t ^ i s not  can  performed with s e v e r a l d i f f e r e n t  by  s p i n s can  terms t h a t g i v e r i s e to i t are e i t h e r absent  be  or  reducing  be f u r t h e r  zero-quantum relatively  known t h e v a l u e s and  experiment the  results  co-added t o o b t a i n the complete spectrum. L i k e w i s e t o ensure that the  initial  c o m p l e t e and  e x c i t a t i o n of zero-quantum c o h e r e n c e s i s  resonably  of  t o s p i n s not of a k i n d i n v o l v e d i n a  given zero-quantum coherence w i l l  by c h o o s i n g  extra  at the c o s t  i n t e n s i t y , F i g u r e 2.16  to coherence t r a n s f e r  reduced  an  as  to non-preferential transfer  be g r e a t l y a l l e v i a t e d , a l t h o u g h  overall  the angle  i s present  i n c r e a s e s as a d e c r e a s e s ( p r o p o r t i o n a l  2  reducing  the d o u b l e t  d i s c u s s e d above, the e f f i c i e n c y  to t a n ( a / 2 ) ) . Therefore problem can  corresponding  s e p t e t , m i n u s i t s c e n t r a l p e a k , has  s t i c k i n g o u t of  coherence.  of c o h e r e n c e f o r  uniform  i t may  be  necessary  s e v e r a l v a l u e s of T . However, the spectrum o b t a i n e d  to  use  from  one  61 experiment w i l l  a l l o w one  t o determine whether or not  z e r o - q u a n t u m c o h e r e n c e s of a r e p r e s e n t e d present  f r o m t h e number of d i f f e r e n t  exhibited 2.6  The  by  the m u l t i p l e t s  Reconstruction  Inhomogeneous M a g n e t i c Nuclear chemistry  scalar  upon t h e a b i l i t y  to  in analytical interpret  of p e a k s , t h e i r and  chemical  [12,20],  multiplet  shifts  zero-quantum s p e c t r a g i v e r i s e  [26-28],  t o none of  T h e i r peak a r e a s  c o m p l e x f u n c t i o n s of c o u p l i n g c o n s t a n t s  and  are  preparation  s t r u c t u r e s are d i f f e r e n t . Their  coupling constants  in  Fields.  information d i r e c t l y  Thesir m u l t i p l e t  couplings  of Single-Quantum S p e c t r a  structures, coupling constants, Conventional  are  present.  s i n g l e - q u a n t u m s p e c t r a , the area  this  s p i n system  M a g n e t i c R e s o n a n c e as a t o o l  i s centred  a l l the  time.  effective  are d i f f e r e n t . A l s o , only the magnitude  t h e d i f f e r e n c e of t h e c h e m i c a l  s h i f t s of two  coupled  of  spins i s  revealed. Although  i t i s conceivable  t h a t new  analytical  m i g h t be d e v e l o p e d t o a l l o w r e a d y e x t r a c t i o n o f f r o m z e r o - q u a n t u m s p e c t r a as  from t h e i r  counterparts,  of  the c o m p l e x i t y  shifts  development  e t c . of t h e two  unlikely.  information  single-quantum  such a t a s k , g i v e n  r e l a t i o n s h i p s between t h e c o u p l i n g c o n s t a n t s , chemical  methods  peak  the  complex  areas,  w o u l d seem t o make s u c h a  62 As NMR  a n a l y s i s has d e v e l o p e d a r o u n d and c e n t e r e d upon  s i n g l e - q u a n t u m s p e c t r a t h e most u s e f u l methods of spectral likely  information  i n inhomogeneous m a g n e t i c  obtaining  fields  are  t o be t h o s e w h i c h p r o v i d e s i n g l e - q u a n t u m p a r a m e t e r s i n  t h e most d i r e c t l y  a c c e s s i b l e way.  J - r e s o l v e d broad-band  The  single-quantum  decoupled zero-quantum  e x p e r i m e n t comes  c o n s i d e r a b l y nearer t o t h i s goal than the c o n v e n t i o n a l zero-quantum  experiment. T h i s i s because  e f f e c t i v e zero-quantum  i t replaces the  c o u p l i n g c o n s t a n t s and  multiplet  s t r u c t u r e s w i t h t h e s i n g l e - q u a n t u m c o u p l i n g c o n s t a n t s and multiplet  s t r u c t u r e s of t h o s e s p i n s a c t i v e  zero-quantum information  coherence. B e s i d e s making a c c e s s i b l e  the  i n h e r e n t w i t h i n t h e s e p a r a m e t e r s i t a l s o means  t h a t s c a l a r c o u p l i n g n e t w o r k s c a n be e a s i l y because a s p i n a c t i v e will  in a given  i n two d i f f e r e n t  g i v e r i s e t o t h e same m u l t i p l e t  traced. This i s  zero-quantum  coherences  s t r u c t u r e on one peak f o r  each coherence. T h i s i s demonstrated f o r L - t h r e o n i n e i n F i g u r e 2.17A. The p r e s e n c e o f t h e o c t e t , t h o u g h  incompletely  r e s o l v e d , on one peak o f e a c h z e r o - q u a n t u m t h e c o n n e c t i v i t y . Hence t h e s p i n s y s t e m may deduced.  The  coherence be  indicates  readily  two d o u b l e t s have d i f f e r e n t c o u p l i n g c o n s t a n t s  and so do n o t r e s u l t  f r o m t h e same s p i n .  A l a r g e p a r t of t h e a n a l y s i s of s i n g l e - q u a n t u m s p e c t r a i s b a s e d upon c h e m i c a l s h i f t s ; m e t h y l e n e p r o t o n s r e s o n a t e i n one r e g i o n of t h e spectrum, a r o m a t i c p r o t o n s i n a n o t h e r , e t c . T h i s i n f o r m a t i o n would  seem t o be l a c k i n g  in a  zero-quantum  s p e c t r u m w h i c h o n l y p r e s e n t s one w i t h t h e d i f f e r e n c e i n  63 chemical s h i f t s . may  A zero-quantum  correspond to a coupling  that  f r e q u e n c y of a g i v e n  b e t w e e n two  their  identity.  I f o n l y one  could t e l l  from t h e  d e c o u p l e d zero-quantum  the  two m u l t i p l e t s on a g i v e n c o h e r e n c e  the  o t h e r i t would  t h i s experiment  a l l o w one  the complete  single-quantum  s a y , d o w n f i e l d of  reassemble  single-quantum spectrum  2.17  i t c a n be s e e n t h a t  t y p e s o f o r t h o g o n a l t e r m . One  by c o s [ ( & ~ & ) ( t i - t ^ ) ] ,  •modulated  A  X  sin[(n ~n )(t,-t^)]. A  magnitude  term,  The  x  of  first  (^ ~^ ) ' ^ A  u t  x  from except  TMS.  p u l s e a t h e a n t i p h a s e s i n g l e quantum c o h e r e n c e  s p i n c o n s i s t s of two  the  and  i d e a as t o  spectrum which of  was,  to accurately  s i n g l e t s and a r e f e r e n c e s u c h a s From e q u a t i o n s 2.16  the  single-quantum  i s g i v e n a much l e s s c e r t a i n  J - r e s o l v e d broad-band  for  s p i n s s e p a r a t e d by  f r e q u e n c y i n any number o f r e g i o n s i n t h e  s p e c t r u m . Hence one  magnitude  and  of  after each  is  t h e o t h e r by  o f t h e s e i s o n l y d e p e n d e n t upon ^  fc  e  s e c o n c  ^'  sine  t n e  modulated  i s a l s o d e p e n d e n t upon t h e s i g n . T h e r e f o r e i t c a n  seen t h a t  i f n >& A  x  the m o d u l a t i o n of s p i n X w i l l  n e g a t i v e p h a s e m o d u l a t i o n w i t h r e s p e c t t o t , and p o s i t i v e phase modulated be t r u e :  spin X w i l l  frequency. I f & <fl A  x  p r e s e n c e o f a 180°  spin A a  h a v e a . p o s i t i v e p h a s e m o d u l a t i o n and  a t the n e g a t i v e zero-quantum  be t h e most u p f i e l d  have a  the r e v e r s e w i l l  A a n e g a t i v e phase m o d u l a t i o n . C o n s e q u e n t l y the multiplet  be  o f t h e two  s i g n s of a l l zero-quantum  single-quantum  frequency w i l l  s p i n s and v i c e v e r s a .  pulse before a c q u i s i t i o n w i l l frequencies.  spin  always The  r e v e r s e the  64  l  300  i  i  i  j—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|  i  200  100  0.0  -100  -200  Hz  B  Z e r o - q u a n t u m coherence connectivity  Reconstructed single-quantum spectrum  11  65  F i g u r e 2.17. A. S i n g l e - q u a n t u m J - r e s o l v e d b r o a d b a n d d e c o u p l e d z e r o - q u a n t u m s p e c t r u m o f 0.5 m o l a r L - t h r e o n i n e i n D 0 r e s u l t i n g f r o m t h e a d d i t o n o f two s p e c t r a o b t a i n e d i n e x p e r i m e n t s i n w h i c h r was s e t t o 60 msec a n d 140 msec. A l l o t h e r p a r a m e t e r s were t h e same: ^ = 4 3 1 msec, At,=1.67 msec, n=2. 256 b l o c k s c o l l e c t e d , 8 a c q u i s i t i o n s p e r b l o c k . B. R e p r e s e n t a t i o n o f t h e method o f r e c o n s t r u c t i o n o f a s i n g l e - q u a n t u m spectrum from t h e spectrum o b t a i n e d i n the s i n g l e - q u a n t u m J - r e s o l v e d b r o a d band d e c o u p l e d z e r o - q u a n t u m experiment f o r L-threonine. F i r s t l y i t i s necessary t o r e c o g n i s e t h e zero-quantum c o n n e c t i v i t i e s which a r e r e v e a l e d by t h e o c c u r a n c e o f t h e same s i n g l e - q u a n t u m m u l t i p l e t on d i f f e r e n t zero-quantum coherences. Connected zero-quantum c o h e r e n c e s a r e t h e n r e a r r a n g e d s o t h a t t h e i r common m u l t i p l e t s a r e s u p e r i m p o s e d upon one a n o t h e r . T h i s g i v e s r i s e t o t h e s i n g l e - q u a n t u m s p e c t r u m e x c e p t f o r s i n g l e t s w h i c h do n o t p a r t i c i p a t e i n z e r o - q u a n t u m c o h e r e n c e s . C. S i n g l e - q u a n t u m spectrum of L - t h r e o n i n e r e c o n s t r u c t e d from the spectrum i n p a r t A a c c o r d i n g t o t h e method d e s c r i b e d a b o v e D. C o n v e n t i o n a l s i n g l e - q u a n t u m s p e c t r u m o f L - t h r e o n i n e o b t a i n e d u n d e r t h e same conditions. 2  66 Consequently, easily  reassemble  w i t h t h i s experiment the single-quantum  inhomogeneous m a g n e t i c single-quantum  field  i t is possible  spectrum  e v e n i n an  where o b t a i n i n g t h e  normal  spectra i s otherwise impossible, except.  e x c e p t i o n s t o t h i s a r e s i n g l e s p i n s ( w h i c h do n o t zero-quantum coherences) demonstrated One  magnetic  field  underneath  This i s  for L-threonine.  t h i s t e c h n i q u e d o e s have o v e r  single-quantum  spectrum  a  b e s i d e s independence  i n h o m o g e n e i t i e s i s t h a t any m u l t i p l e t  a singlet  This experiment  s u c h as HDO has  The  form  and a r e f e r e n c e s u c h as TMS.  i n F i g u r e 2.17  advantage  conventional  to  will  t h r e e major  now  of  hidden  be r e v e a l e d .  disadvantages.  Firstly,  peak a r e a s a r e c o m p l e x f u n c t i o n s o f c o u p l i n g c o n s t a n t and l e n g t h of t h e p r e p a r a t i o n p e r i o d of  T . Secondly, the s m a l l value  the p u l s e a necessary to a c h i e v e e f f i c i e n t  coherence relatively  transfer low  results  intensity  preferential  i n the a c q u i r e d s i g n a l having a  w h i c h may  be r e f l e c t e d  i n poor  T h i r d l y , t h e l e n g t h of t i m e i n v o l v e d : e a c h e x p e r i m e n t minimum t i m e of msec, and  ( r + t ^ ) w h i c h may  in addition,  problem  e a s i l y amount t o 400-500  to J-encoding  The  Assignment  of  (NnAt,). This  times.  o f Zero-Quantum C o h e r e n c e S p e c t r a i n  Inhomogeneous M a g n e t i c  Fields  will  i f t h e c h e m i c a l s p e c i e s of  i n t e r e s t have s h o r t s p i n - s p i n r e l a x a t i o n 2.7  S/N.  takes a  t h e N t h b l o c k of t h e e x p e r i m e n t  c o n t a i n an a d d i t i o n a l d e l a y due i s p o t e n t i a l l y a major  the  67 In  this  spectra w i l l  s e c t i o n t h e assignment of zero-quantum  coherence  be d i s c u s s e d w i t h r e f e r e n c e t o a number o f  r e p r e s e n t a t i v e amino a c i d s f o r w h i c h t h e z e r o - q u a n t u m  spectra  o b t a i n e d under a s t a n d a r d s e t of c o n d i t i o n s a r e g i v e n i n A p p e n d i x 11 . The a s s i g n m e n t o f t h e z e r o - q u a n t u m compound i s p o t e n t i a l l y  trivial  i f a fully  single-quantum spectrum i s a v a i l a b l e . calculate the difference of the  s p e c t r u m o f a known assigned  I t i s only necessary to  i n resonance f r e q u e n c i e s of each  pair  c o u p l e d s p i n s and t o l o o k f o r a peak a t t h a t f r e q u e n c y i n zero-quantum  spectrum. For example,  spectrum of L - t h r e o n i n e i n D 0 2  the single-quantum  has t h r e e resonances [ 2 9 ] , at  288 Hz, 347 H z , a n d 105 H z , c o r r e s p o n d i n g t o t h e a, 0, a n d 7 p r o t o n s . Consequently, assuming  a l l t h e p r o t o n s have m u t u a l l y  r e s o l v e d s c a l a r c o u p l i n g s , one w o u l d e x p e c t t o f i n d t h e zero-quantum and  183 Hz r e s p e c t i v e l y . The f o r m e r two c o h e r e n c e s o c c u r a s  predicted of  c o h e r e n c e s a-/3, £-7, a n d a-7 a t 59 H z , 242 Hz,  ( F i g u r e A2.7). A l t h o u g h i t does occur t h e l a t t e r i s  relatively  low i n t e n s i t y as t h e c o u p l i n g c o n s t a n t  s m a l l . S m a l l v a l u e s o f f and r ' t e n d t o e m p h a s i s e c o h e r e n c e s between whereas  because  c o h e r e n c e s between  be e m p h a s i s e d  t h e zero-quantum  more w e a k l y c o u p l e d  by l a r g e r v a l u e s o f T a n d T ' . T h i s i s c o h e r e n c e o f two s p i n s i s g e n e r a t e d  from t h o s e components of t h e i r are  zero-quantum  spins with a l a r g e mutual c o u p l i n g constant  zero-quantum  spins w i l l  is  single-quantum coherence  which  a n t i p h a s e w i t h r e s p e c t t o e a c h o t h e r . The r a t e a t w h i c h  in-phase single-quantum coherence w i l l  evolve into antiphase  68 single-quantum  coherence w i t h respect t o a given s p i n i s  d e p e n d e n t upon t h e i r m u t u a l c o u p l i n g c o n s t a n t . the c o u p l i n g constant single-quantum small  i s l a r g e the d e s i r e d  coherence w i l l  Consequently i f  antiphase  e v o l v e q u i c k l y , and i f i t i s  slowly. If  two o r more z e r o - q u a n t u m c o h e r e n c e s o v e r l a p a  knowledge of t h e i r  f r e q u e n c i e s may be i n s u f f i c i e n t t o  determine which are p r e s e n t . a l t e r n a t i v e courses Firstly, multiplet  In t h i s case there are three  of a c t i o n .  t h e z e r o - q u a n t u m c o h e r e n c e s may have  s t r u c t u r e s , i n which case,  sufficient,  the coherences present  Secondly,  by u s i n g d i f f e r e n t  different  i f resolution i s  c a n be d e t e r e m i n e d . v a l u e s of r and r ' , t h e  p r e p a r a t i o n a n d r e f o c u s s i n g p e r i o d s , i t may be p o s s i b l e t o edit  o u t some o f t h e o v e r l a p p i n g c o h e r e n c e s t o s i m p l i f y t h e  spectrum. F o r example, t h e zero-quantum spectrum of L-isoleucine obtained  with  of o v e r l a p p i n g c o h e r e n c e s , to  T a n d T'=60 msec c o n t a i n s a number F i g u r e A2.8.A. By c h a n g i n g T a n d r '  100 msec, F i g u r e A2.8.B, o r 140 msec, F i g u r e A2.8.C, t h e  s p e c t r u m i s g r e a t l y s i m p l i f i e d and t h e o v e r l a p of c o h e r e n c e s reduced. T h i r d l y , t h e z e r o - q u a n t u m s p e c t r u m c a n be b r o a d - b a n d decoupled  t o t r y a n d r e s o l v e c o h e r e n c e s whose m u l t i p l e t s  o v e r l a p . F o r e x a m p l e , f r o m an e x a m i n a t i o n single-quantum  of t h e  s p e c t r u m o f L - v a l i n e [ 3 0 ] one m i g h t  expect  69 t h r e e s t r o n g zero-quantum coherences: 107  a-0,  0~7, a n d 0-7' a t  H z , 99 H z , and 94 Hz r e s p e c t i v e l y . The o v e r l a p o f  multiplets  i n t h e z e r o - q u a n t u m s p e c t r u m makes i t i m p o s s i b l e t o  d e t e r m i n e which of these  coherences are present  Upon b r o a d - b a n d d e c o u p l i n g  (Figure A2.9).  t h e zero-quantum spectrum,  Figure  2.19.B, i t c a n be s e e n t h a t o n l y t h e a-0 a n d 0-7  coherences  are present,  resolved.  although  t h e peaks a r e i n c o m p l e t e l y  What d o e s one do i f an a s s i g n e d is  not a v a i l a b l e ? In single-quantum  single-quantum  spectrum  NMR s p e c t r o s c o p y  i t is  o f t e n p o s s i b l e t o a s s i g n a s p e c t r u m , p a r t i a l l y o r w h o l l y , by the use of f o u r types multiplet  of parameters: chemical  shifts,  s t r u c t u r e s , c o u p l i n g c o n s t a n t s , a n d peak  Chemical s h i f t s t e l l w i t h i n a molecule,  areas.  one a b o u t t h e e n v i r o n m e n t o f a s p i n  whether  i t i s aromatic,  adjacent  to a  heteronucleus e t c . The  m u l t i p l e t s t r u c t u r e of a resonance  provides  i n f o r m a t i o n on n e i g h b o u r i n g  s p i n s ; how many s p i n s  coupled  are identical  t o and whether they  i t is  o r d i f f e r e n t and  h e n c e what k i n d o f s p i n s y s t e m i t i s p a r t o f . Coupling of c o u p l e d through  constants  tell  one a b o u t t h e r e l a t i v e l o c a t i o n s  s p i n s , by t h e i r m a g n i t u d e w h e t h e r a c o u p l i n g i s  t w o , t h r e e , o r f i v e b o n d s , a n d t h e y may a l s o  conformational Peak a r e a s particular  provide  information. tell  one how many s p i n s g i v e r i s e t o a  resonance and a r e p a r t i c u l a r l y  u s e f u l when a number  70 of r e s o n a n c e s o v e r l a p , and spin  facilitate  the i d e n t i f i c a t i o n  systems. To what e x t e n t i s t h e i n f o r m a t i o n  a c c e s s i b l e w i t h i n a zero-quantum Zero-quantum  summarized  coherence  above  spectrum?  coherences occur at the d i f f e r e n c e i n  f r e q u e n c i e s o f two c o u p l e d s p i n s and a r e " t h e r e f o r e w i t h i n a narrower f r e q u e n c y range than t h e i r c o u n t e r p a r t s . Zero-quantum  found  single-quantum  frequencies are r e l a t i v e  rather  t h a n a b s o l u t e and c o n s e q u e n t l y t h e i n f o r m a t i o n w h i c h c a n extracted example, is  of  f r o m them i s a l s o r e l a t i v e . One whether  likely  a proton active  cannot t e l l ,  i n a zero-quantum  be  for  coherence  t o be a r o m a t i c o r a d j a c e n t t o a h e t e r o n u c l e u s - f r o m  its position  i n t h e s p e c t r u m . One  can o n l y t e l l  whether i t  a r i s e s f r o m two s p i n s i n a s i m i l a r  e n v i r o n m e n t , hence h a v i n g  s i m i l a r c h e m i c a l s h i f t s and g i v i n g  rise  zero-quantum  two  f r e q u e n c y , o r between  e n v i r o n m e n t s and hence  giving  to a  small  spins in different  rise to a large  zero-quantum  frequency. The m u l t i p l e t  s t r u c t u r e of a zero-quantum  coherence  still  p r o v i d e s i n f o r m a t i o n on t h e s p i n s y s t e m o f w h i c h t h e  spins  active  way  i n the coherence are p a r t , but  s i n g l e - q u a n t u m c o h e r e n c e s . Zero-quantum  in a different coherences  e x h i b i t c o u p l i n g s t o t h o s e s p i n s not a c t i v e and hence  give r i s e to d i f f e r e n t  splitting  from  only  i n the coherence patterns.  71 The  coupling  constants  e x h i b i t e d by  zero-quantum  c o h e r e n c e s o f t e n c o r r e s p o n d t o t h e d i f f e r e n c e of  two  single-quantum coupling constants  m a k i n g them  more d i f f i c u l t constant large  may  coupling  c o r r e s p o n d t o t h e d i f f e r e n c e of two  single-quantum coupling  corresponding may  2.15)  to i n t e r p r e t . A s m a l l zero-quantum  single-quantum coupling  and  (equation  constants.  constants  I f the  are very  zero-quantum c o u p l i n g  s m a l l or relevant  similar  constant  two  may  the  be  even l e a d t o t h e m u t u a l c a n c e l l a t i o n o f  unresolved  unresolved  peaks. The  peak a r e a s of z e r o - q u a n t u m c o h e r e n c e s a r e  f u n c t i o n s of of  single-quantum coupling  the p r e p a r a t i o n  and  constants  refocussing periods  experiment. Consequently they cannot e a s i l y the  number o f  spins giving  Taking these f a c t o r s provided  by  surveyed  of the be  i n t o account the  used to  i t can  be  coherence.  t o o n l y one  be  more  information  From t h e amino  s e e n t h a t t h e a s s i g n m e n t of some w i l l  trivial;  those which  ( F i g u r e A 2 . 1 5 ) , and  ( F i g u r e A2.16). These are  a l l compounds w h i c h h a v e o n l y  t y p e s of c o u p l e d  h e n c e p r o d u c e o n l y one  are  rare  instances  give  L-cysteine  (Figure A2.11), L - a l a n i n e  c o h e r e n c e , and  acids  the  zero-quantum c o h e r e n c e such as  s p i n and  reveal  information  of u s e f u l  single-quantum counterparts.  lengths  zero-quantum  to a zero-quantum  t o have a l o w e r c o n t e n t  zero-quantum s p e c t r a of rise  the  z e r o - q u a n t u m c o h e r e n c e s w o u l d seem t o be  a m b i g u o u s and than t h e i r  rise  and  complex  L-aspartic  of zero-quantum  acid two  zero-quantum spectra  72 being e a s i e r t o a s s i g n than single-quantum ones. compounds o f i n t e r e s t however g i v e r i s e zero-quantum calculate of  t o more t h a n  the f r e q u e n c i e s of zero-quantum  these. Unfortunately chemical s h i f t accuracy which i s degraded i s calculated.  [ 3 1 ] an a c c u r a c y o f ±0.2 frequency thus c a l c u l a t e d ±0.28 ppm, adequate dispersed  still  I n one ppm  t a b l e s have  from  limited zero-quantum  t y p i c a l chemical s h i f t  i s quoted. For a  the accuracy w i l l  table  zero-quantum  be r e d u c e d t o  A l t h o u g h t h i s may  be  s i m p l e r compounds w i t h a few w i d e l y  more c o m p l e x  i t p r o v e s t o be  the amino a c i d s s u r v e y e d over h a l f 22.5  Hz  (0.28 ppm)  L-glutamic acid within  30-50 Hz  the range  10-40  L - i s o l e u c i n e w i t h i n t h e r a n g e 0-100 e x t e n t s u c h a m b i g u i t i e s may  i n a d e q u a t e . Of  have c o h e r e n c e s which a r e  of each o t h e r . For  L - m e t h i o n i n e w i t h i n the range  multiplet  coherences  r e s o n a n c e s s u c h as L - t h r e o n i n e , f o r compounds w h i c h  are only a l i t t l e  within  t a b l e s , and h e n c e t o  f u r t h e r when a  o r 22.5 Hz a t 80.3 MHz.  to assign  to  single-quantum resonance f r e q u e n c i e s  i t s s p i n s by t h e use o f c h e m i c a l s h i f t  frequency  one  c o h e r e n c e . F o r a known compound i t i s p o s s i b l e  the approximate  calculate  Most  example,  (Figure Hz  Hz  A2.2.C),  ( F i g u r e A2.3.B) and  ( F i g u r e A2.8.A).  be removed i f t h e  To  an  calculated  s t r u c t u r e s of t h e s e c o h e r e n c e s a r e d i f f e r e n t . T h i s  has t h e p r e r e q u i s i t e t h a t t h e r e s o l u t i o n of t h e  zero-quantum  s p e c t r u m be h i g h enough t o r e s o l v e t h e s c a l a r c o u p l i n g s c o n c e r n e d . T h i s i s p o t e n t i a l l y a problem as t h e c o u p l i n g c o n s t a n t s of zero-quantum smaller than t h e i r  c o h e r e n c e s may  be  considerably  single-quantum c o u n t e r p a r t s thus leading  to  73 ambiguity  as  to t h e i r perceived  r e d u c e d by  multiplicity  may  be  but  t h i s w o u l d r e q u i r e more t i m e ,  number of  i n c r e a s i n g the  t , i n c r e m e n t s u s e d and  of a c q u i s i t i o n s per As  increases  will  relaxation  particularly  times.  the  spectrum, the  a l s o i n i n c r e a s i n g the  This  is liable  to which  to  i n a p p e n d i x 2) may  refocussing periods p r e v e n t one  be  of t h e  short  spin-spin  e v o l u t i o n time,  although  t h i s p r o b l e m may  lengths  of the p r e p a r a t i o n  described  previously  In the  e x p e r i m e n t . O v e r l a p may  light  the m u l t i p l i c i t y  be a l l e v i a t e d and  (section  several  NMR  the as  i t w o u l d seem t h a t  i n the  i s not  simplest  a b s e n c e of  a  with  single-quantum spectra often  i s an  the  broad-band decoupled  experiment. This experiment produces spectra  any  realistic  compounds,  been d e v e l o p e d h e r e i n :  single-quantum J-resolved  for  also  zero-quantum e x p e r i m e n t s . However, t h e r e  a l t e r n a t i v e w h i c h has  f e a t u r e s of  and  2.2).  information,  o b j e c t i v e , except f o r the very conventional  by c h a n g i n g  of t h e s e c o n s i d e r a t i o n s  spectroscopic  spectra  of a c o h e r e n c e  refocussing periods  the a s s i g n m e n t of zero-quantum s p e c t r a , other  the  be  spent i n the p r e p a r a t i o n  from d e t e r m i n i n g  S/N.  also  h u n d r e d m i l l i s e c o n d s (120-280 msec f o r t h e a m i n o a c i d given  number  same  acquisition  f o r compounds w i t h  In a d d i t i o n t o t h e  the  the e x t e n t  have r e l a x e d b e f o r e S/N.  problem  both i n i n c r e a s i n g  t , , increases  hence d e c r e a s i n g  problematic,  r e s o l u t i o n of  i n c r e m e n t needed t o a t t a i n  the e v o l u t i o n time,  magnetization  . This  zero-quantum  w i t h many of  the  r e g a r d e d as e s s e n t i a l  t h e a s s i g n m e n t of c o h e r e n c e s . E a c h z e r o - q u a n t u m c o h e r e n c e  74 e x h i b i t s t h e s i n g l e - q u a n t u m m u l t i p l e t s o f t h e two c o u p l e d s p i n s which g i v e r i s e  to i t- revealing a single-quantum  spin-spin connectivity. Also, different  zero-quantum  c o h e r e n c e s w h i c h have a s p i n i n common h a v e a m u l t i p l e t i n common. T h i s a l l o w s one t o e x t e n d s p i n - s p i n c o u p l i n g through d i f f e r e n t  zero-quantum  determine the s p e c i f i c  c o h e r e n c e s and hence t o  l o c a t i o n w i t h i n a s p i n system of the  spins active i n a particular it  coherence. With t h i s  may a l s o be p o s s i b l e t o i d e n t i f y  least  experiment  unknown compounds, o r a t  t h e s p i n s y s t e m s t h e y c o n t a i n , by v i r t u e o f t h e f a c t  that their  s i n g l e - q u a n t u m s p e c t r a c a n be l a r g e l y  f r o m t h e one p r o d u c e d  be c o m p e n s a t e d  reassembled  i n t h i s experiment. Although the  s p e c t r a l w i d t h of the experiment  the  networks  f o r . A higher  i s relatively  magnetic  field  narrow  t h i s can  c a n be u s e d , o r  s p e c t r u m c a n be e d i t e d by v a r y i n g t h e l e n g t h o f t h e  p r e p a r a t i o n p e r i o d t o reduce crowding or o v e r l a p p i n g of coherences. A l t e r n a t i v e l y reduced. I t should have s i g n i f i c a n t  t h e J - s c a l i n g f a c t o r n c a n be  n o t be f o r g o t t e n t h a t t h i s e x p e r i m e n t  d i s a d v a n t a g e s w h i c h were d i s c u s s e d  does  above  (sect ion 2.6). 2.8 The A n a l y s i s o f M i x t u r e s Field  by t h e R e c o g n i t i o n  Signatures  of T h e i r  Besides using within  i n an Inhomogeneous M a g n e t i c  o f t h e Zero-Quantum  Coherence  Constituents the spectroscopic parameters  t h e zero-quantum  spectrum  itself  contained  t o deduce t h e i d e n t i t y  o f t h e compound g i v i n g r i s e t o i t i t i s p o s s i b l e t o u s e  75 zero-quantum  spectra  n o t s o much by u s i n g  i n a quite different  a r i s e s under  i s done  t h e p a r a m e t e r s w h i c h c a n be e x t r a c t e d  f r o m them b u t by u s i n g it  way. T h i s  the pattern  a given  of a spectrum a s a whole as  s e t of c o n d i t i o n s as a " s i g n a t u r e " of  t h e compound p r o d u c i n g i t . T h e r e f o r e u s e i s made n o t o n l y t h e coherence do  frequencies  a n d m u l t i p l e t s t r u c t u r e s , a s one m i g h t  i n an a t t e m p t t o a s s i g n  relative which  the spectrum, but a l s o of t h e  i n t e n s i t i e s of coherences as p a r t of t h e s i g n a t u r e  i s n o t p r a c t i c a l when a t t e m p t i n g To make u s e o f z e r o - q u a n t u m  it  i s necessary to acquire  compounds one w i l l  coherence  a catalogue  come a c r o s s ,  to assign  compounds w h i c h one i s s p e c i f i c a l l y  spectra  of s p e c t r a  or a t l e a s t  the spectrum. i n t h i s way f o r the  f o r those  looking f o r , i n a  similar  manner t o t h o s e p r e v i o u s l y c o m p i l e d o f s i n g l e - q u a n t u m  spectra  [32]. The Figure  e s s e n c e o f t h i s method h a s been d e m o n s t r a t e d  2.4 where t h e c o m p o n e n t s o f a m i x t u r e o f a m i n o  were d e t e r m i n e d by r e f e r e n c e zero-quantum of L - a l a n i n e ,  spectra  above i n acids  t o the previously c o l l e c t e d  of i t s i n d i v i d u a l components t o c o n s i s t  L-threonine,  L - v a l i n e , and L - a s p a r a g i n e .  To d e t e r m i n e t h e p r e s e n c e o f a compound i n a m i x t u r e by it  zero-quantum  zero-quantum  coherence  spectrum does not r e q u i r e t h a t a l l of i t s  c o h e r e n c e s be c o m p l e t e l y other  "signature" unlike assigning a  resolved  from those produced  by t h e  c o m p o n e n t s , b u t m e r e l y t h a t enough a r e d i s c e r n i b l e s o a s  t o make t h e d e t e r m i n a t i o n  of i t s presence or absence  76 unambiguous. When u s i n g values  o f r and  the r e f o c u s s e d T ' , the l e n g t h s  zero-quantum  experiment  of t h e p r e p a r a t i o n  and  r e f o c u s s i n g p e r i o d s , c a n be v a r i e d b o t h t o e d i t o u t and a l s o t o d e t e r m i n e t h e r e l a t i v e are  left.  In the c o n t e x t  the  coherences  i n t e n s i t i e s of t h o s e which  o f s i g n a t u r e r e c o g n i t i o n t h i s has  u s e s ; t o r e d u c e t h e number o f c o h e r e n c e s spectrum hence f a c i l i t a t i n g  i n an  t h e r e c o g n i t i o n of  two  overcrowded signatures  among t h e r e m a i n i n g c o h e r e n c e s . A l s o two o r more p o s s i b l e components of a m i x t u r e produce a t t h e same f r e q u e n c y i t may b e t w e e n them by t h e way vary  with  r and  T ' . The  e x p e r i m e n t c a n be u s e d spectrum which  i n d i s t i n g u i s h a b l e coherences  be p o s s i b l e t o d i s t i n g u i s h  i n which the i n t e n s i t i e s of the broad-band  decoupled  zero-quantum  i n a s i m i l a r manner. I t p r o d u c e s  i s l e s s prone  to overlapping  peaks  as each  a  coherence  i s o n l y p r e s e n t a s a s i n g l e t . T h i s makes t h e d e t e r m i n a t i o n w h i c h peaks a r e p r e s e n t l e s s ambiguous, but i t a l s o  of  reduces  t h e amount o f i n f o r m a t i o n a v a i l a b l e i n t h a t m u l t i p l e t s t r u c t u r e , a u s e f u l p a r t o f a s i g n a t u r e , i s r e m o v e d . By way compensation the  there are a d d i t i o n a l o p p o r t u n i t i e s f o r e d i t i n g  s p e c t r u m v i a t h e l e n g t h of the e v o l u t i o n t i m e t ^ . T h i s  be u s e d  i n a s i m i l a r manner t o T and  which remain. A d d i t i o n a l i n t e n s i t y  i n t e n s i t i e s of t h o s e  i n f o r m a t i o n c a n be  i n t h e s p e c t r u m by v a r y i n g t h e a n g l e o f t h e p u l s e gives rise  to p r e f e r e n t i a l  can  r ' , t o s u p r e s s unwanted  c o h e r e n c e s and t o d e t e r m i n e t h e r e l a t i v e  This  of  a from  t r a n s f e r of c o h e r e n c e  h e n c e a s p e c t r u m whose i n t e n s i t i e s a r e no  longer  encoded  and  90°.  77  A  I—i—i—i—|—i—i—i—|—i—i—i—|—i—i—i—|—i—i—i—|—i—i—i—|—i—i—i—|—i—i—i—|—i—i—i—|—i—i—i—| 1000  800  600  400  200  0  -200  -400  -600  -800  Hz  B  C  I i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—| 300  200  100  0.0  -100  -200  Hz  F i g u r e 2.18. S p e c t r a of a s o l u t i o n of L - v a l i n e , L - l e u c i n e , L-asparagine, L - a s p a r t i c a c i d and L - i s o l e u c i n e i n D 0, a l l c o n c e n t r a t i o n s 0.1 m o l a r . A. S i n g l e - q u a n t u m s p e c t r u m . Zero-quantum s p e c t r a o b t a i n e d w i t h t h e r e f o c u s s e d zero-quantum e x p e r i m e n t ; B. T , T ' = 6 0 msec, C. T , T ' = 1 4 0 msec. F o r p a r t s B a n d C At,=1.67 m s e c , 256 b l o c k s c o l l e c t e d , 8 a c q u i s i t i o n s p e r block. 2  78 symmetrical  i s p o t e n t i a l l y a f u r t h e r way  of  d i s t i n g u i s h i n g between compounds whose r e s o l v e d c o h e r e n c e s  are  otherwise To  a b o u t 0.0  the  described  made up  A p p e n d i x I I . Due  useful  of  recognition a  s e v e r a l amino a c i d s .  t h e s e amino a c i d s a r e  to magnetic  conventional  obtained  the a p p l i c a t i o n of  above t o s i g n a t u r e  i n f o r m a t i o n . The  the mixture not  e f f e c t i v e n e s s of  c o n s i s t i n g of  zero-quantum s p e c t r a  2.18.A, t h e  This  same.  determine the  techniques was  Hz.  field  catalogued  inhomogeneity,  exception  conventional  Figure  of  the  This  those  amino a c i d s w i t h i n t h e  s m a l l peak a t ±230 Hz  r u l e s out  the  noise  level  of  2.18.B, d o e s  i n Appendix II i t i s p o s s i b l e to r u l e the  no  zero-quantum spectrum  r , r ' = 6 0 msec, F i g u r e  coherences v i s i b l e above the ±300 Hz.  in  single-quantum spectrum contained  with  t h e p r e s e n c e o f many o f With the  mixture  The  s u f f e r f r o m t h i s d r a w b a c k . By c o m p a r i s o n w i t h  spectra catalogued  the  out  mixture.  there are  i n the  no  r a n g e ±120  p r e s e n c e of L - a l a n i n e ,  to  L-arginine,  L - p r o l i n e , L-glutamine, L-methionine, L-glutamic  acid  L-threonine.  L-aspartic  Remaining p o s s i b l e c o n s t i t u e n t s are  a c i d , L-/3-phenyl a l a n i n e , L - l e u c i n e , L - v a l i n e , L - a s p a r a g i n e , L - i s o l e u c i n e and  L - s e r i n e . Of  L-cysteine,  these there  e v i d e n c e t o s u p p o r t L - l e u c i n e , as t h e peak a t ±230 c o r r e s p o n d s t o one  i n the catalogued  ( f i g u r e A 2 . 6 . A ) , and ±80  t o ±120  ( F i g u r e A2.9)  Hz  L - v a l i n e due  spectrum of  there  c o m p o n e n t s of t h e m i x t u r e .  The  Hz  to the peaks i n the  i s clearly overlap remaining  is  L-leucine  w h i c h r e s e m b l e t h o s e of t h e L - v a l i n e although  and  range  spectrum  w i t h the  coherences are  other of  79 little  use  due  t h e r e i n . The msec g i v e s greatly  t o the e x t e n s i v e  corresponding  experiment with  r i s e to a spectrum with  reduced o v e r l a p , Figure  i n the a p p r o p r i a t e  regions  p r e s e n c e of L - c y s t e i n e  ±230 Hz  disappeared  Hz  has  a l l but  may  be due  to the  A2.4.C) and  Hz.  This  r e g i o n ±80  remaining doublets  L - i s o l e u c i n e . Of  fully  possible partially and  due  region (Figure of  t h e p r e s e n c e o f a peak  L-aspartic acid, L-leucine r e s o l v e d peaks are  L - l e u c i n e , and,  were  presence  L - v a l i n e , L-asparagine,  f o r L - a s p a r a g i n e and  ±120  of L - a s p a r a g i n e  as p o s s i b l e c o m p o n e n t s of t h e  these,  to  peaks i n t h i s  L - a s p a r t i c a c i d ( F i g u r e A 2 . 1 6 ) . The  leaves  the  peak a t  might expect i f they  L - a s p a r a g i n e i s f u r t h e r s u g g e s t e d by ±67  peaks  as w o u l d be e x p e c t e d i f i t i s  as one  overlapping  and  a b s e n c e of  ( F i g u r e A 2 . 1 3 . B ) . The  ( F i g u r e A 2 . 9 ) . The  to L-valine  140  L-0-phenylalanine  t o L - l e u c i n e . Many of t h e p e a k s i n t h e have a l s o d i s a p p e a r e d  found  T ' set to  s p e c t r u m r u l e out  (Figure A2.11),  L-serine  T and  fewer c o h e r e n c e s  2.18.C. The  of t h i s  ( F i g u r e A2.5.C) and  due  d e g r e e of o v e r l a p p i n g  of t h e  at  mixture and observable  remainder,  r e s o l v e d peaks are observed f o r L - v a l i n e  L-aspartic a c i d although  t h i s by  itself  is insufficient  to  determine t h e i r presence with c e r t a i n t y . F i g u r e 2.19. B r o a d band d e c o u p l e d z e r o - q u a n t u m s p e c t r a of 0.1 m o l a r s o l u t i o n s i n D 0 o f : A. L - v a l i n e , L - l e u c i n e , L - a s p a r a g i n e , L - a s p a r t i c a c i d and L - i s o l e u c i n e . B. L - v a l i n e . C. L - l e u c i n e . D. L - a s p a r a g i n e . E. L - a s p a r t i c a c i d . F. L - i s o l e u c i n e . I n e a c h c a s e t(3=364 msec, T=60 msec, A t ^ l . 6 7 msec, 256 b l o c k s c o l l e c t e d , 8 a c q u i s i t i o n s p e r b l o c k . 2  80 34  T1 1111 1111 1 ~i—i—i—|—i—i—i—i—|—i—r  150  100  -50  1  50  1  -100  -150 Hz  0.0  L-valine (1)  L-asparagine (3)  L-aspartic acid (4)  L-isoleucine (5)  |  150  i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—r  100  50  0.0  -50  ~i—i—|—i—i—i—i—|  -100  -150 Hz  1  81 As  the main problem  coherences obtained  here encountered  the broad-band  decoupled  i s one  zero-quantum s p e c t r a  f o r both the m i x t u r e as a whole,  s e t t o 45°  unsymmetrical  to take advantage  intensity distribution  i n s p e c t i o n of the s p e c t r a i t can  was  F i g u r e 2.19.A, and  a l s o o f i t s p o s s i b l e c o m p o n e n t s , F i g u r e 2.19 c a s e s a was  o f o v e r l a p of  B-F.  of the  about  0.0  In both resulting  Hz.  From  i m m e d i a t e l y be seen  that  L - v a l i n e , L - l e u c i n e and L - i s o l e u c i n e a r e p r e s e n t . L - i s o l e u c i n e went u n d e t e c t e d  i n the c o n v e n t i o n a l zero-quantum  W h e t h e r L - a s p a r t i c a c i d as w e l l as L - a s p a r a g i n e less  i m m e d i a t e l y o b v i o u s . The  L-asparagine spectrum one  spectrum  However, t h e r e i s e v i d e n c e which  of the l a t t e r  suggest  less  i n t e n s e peaks.  would  expect  than a n t i c i p a t e d  present at t h i s  i s b o r d e r e d on  relative  from the spectrum  acid  both  intensities  o f t h e amino  are acid.  relative  s u g g e s t i n g t h a t a n o t h e r peak i s  frequency. T h i s would  i n d e e d be t h e c a s e i f  L - a s p a r t i c a c i d were p r e s e n t a s c a n be seen  from the  o f L - a s p a r t i c a c i d , F i g u r e 2.19.E. S e c o n d l y , t h e intensity  ambiguous.  that L-aspartic  c e n t r a l o f t h e t h r e e p e a k s has a g r e a t e r  intensity  acid  A l t h o u g h these peaks can a l l  be d i s c e r n e d i n F i g u r e 2.19.A, t h e i r n o t what one  i n the  most i n t e n s e peak a s s i g n a b l e t o L - a s p a r a g i n e  on t h e l e f t h a n d s i d e of t h e s p e c t r u m s i d e s by two  the  ( F i g u r e 2 . 1 9 . A ) , but t h e f r e q u e n c y o f  T h i s makes t h e p r e s e n c e  i s p r e s e n t . The  of  identified  of t h e s e c o i n c i d e s w i t h t h a t of the L - a s p a r t i c  coherence.  The  i s present i s  four outer coherences  ( F i g u r e 2.19.D) c a n be  of t h e m i x t u r e  spectrum.  o f t h e peak a t -90 Hz  spectrum  relative  i s g r e a t e r t h a n t h a t a t +90  Hz  82 i n t h e s p e c t r u m of L - a s p a r a g i n e w h e r e a s i n t h e m i x t u r e situation  this  h a s been r e v e r s e d , a g a i n s u g g e s t i n g t h e p r e s e n c e o f  a n o t h e r peak a t +90  Hz a s w e l l as t h a t due  to L-asparagine.  A g a i n t h i s i n d i c a t e s the p r e s e n c e of L - a s p a r t i c a c i d as can be s e e n If was  from i t s broad-band  a had been s e t t o 90°  decoupled zero-quantum  i t would  p r e s e n t from the zero-quantum  either  s i d e o f t h o s e a t ±90  be  spectrum.  impossible to t e l l  s p e c t r u m . The  peaks  which  on  Hz w o u l d be b u r i e d b e n e a t h  those  o f L - v a l i n e and L - i s o l e u c i n e and h e n c e u n a v a i l a b l e f o r intensity 0.0  c o m p a r i s o n s , and t h e i n t e n s i t y o f c o h e r e n c e s  Hz w o u l d be s y m m e t r i c a l m a k i n g  relative  intensities  any c o m p a r i s o n  their  pointless.  T h u s , w i t h t h e use o f c o n v e n t i o n a l and zero-quantum  s p e c t r a , making  preferential  transfer  decoupled  use o f r e l a t i v e  intensities  o f c o h e r e n c e a s w e l l as  f r e q u e n c i e s and m u l t i p l e t  structures  inhomogeneous magnetic  field  and  coherence  i t i s possible  i d e n t i f y a l l the components of a complex  m i x t u r e a s a whole  of  about  to  m i x t u r e i n an  by c o m p a r i s o n  w i t h t h o s e of i n d i v i d u a l  of s p e c t r a o f t h e possible  c o m p o n e n t s o b t a i n e d w i t h t h e same e x p e r i m e n t a l p a r a m e t e r s . .2 . 9 E x p e r i m e n t a l All and 2.5,  s p e c t r a , w i t h t h e e x c e p t i o n of t h o s e i n F i g u r e s were r e c o r d e d a t room t e m p e r a t u r e u s i n g a  s p e c t r o m e t e r e q u i p p e d w i t h an O x f o r d R e s e a r c h S y s t e m s 1.89 30 cm  2.4  h o r i z o n t a l b o r e magnet and a N i c o l e t NT-300 c o n s o l e  c o n t r o l l e d by a N i c o l e t  1280  computer  and a 293C  T,  83 p u l s e - p r o g r a m m e r o p e r a t i n g a t 80.3 u s e d were p r e p a r e d  analytically,  t h e m o l a r i t y i s g i v e n , and  MHz  by  g e n e r a t e d by  magnetic  digital-to-analogue converters  except  weighing  shim c o i l s u s i n g d r i v i n g  s e q u e n c e s were r e a d i l y  axial  field  resonator  The  and  software  consequently  list  had  f i x e d d e l a y . One  used f o r each block  of t h e  list  successively  was  value  finished  value  t h e e x p e r i m e n t was  i n the  the  used i n  T h i s was  the v a l u e s from those  i n s t e a d of  allow  them. To  afterit  appropriate  values,  block  delay  were d i s c a r d e d .  delays capable  conjunction  when t h e  list  was  list  was the  time  the  done so t h a t when  of t h e  decremental  p r e v i o u s l y used  the experiment t o  reach  r e s t a r t e d a f t e r changing first  was  decremented  i n t e g e r m u l t i p l e s of  t i m e i n t e r v a l w o u l d f o l l o w on  e q u i l i b r i u m again  delay  from the d e l a y  f i x e d d e l a y was  list.  run a g a i n  repeating  zero-quantum  stopped a u t o m a t i c a l l y . Each  through consecutive  largest delay  was  The  u s e d . T h i s was  e x p e r i m e n t , and  u s e d up t h e e x p e r i m e n t was the d e l a y  Pulse  for decremental  t o be  of c o n t a i n i n g up t o 32 v a l u e s , and with another  unit.  the  the decremental  d i d not p r o v i d e  a delay  293C  software  single-quantum J - r e s o l v e d broad-band decoupled  d  gradients  i n v o l v i n g decremental delays.  experiment which both i n c o r p o r a t e  the  probe.  b r o a d - b a n d d e c o u p l e d z e r o - q u a n t u m e x p e r i m e n t and  (t -t,/2).  where  voltages  i n the  implementable w i t h the  f o r those  samples  by v o l u m e w i t h a p i p e t t e where  S a m p l e s were p l a c e d w i t h i n a 7 cm  provided  The  1  accurate  r a t i o of t h e c o m p o n e n t s i s g i v e n . The were p r o d u c e d by' t h e  f o r H.  6 a c q u i s i t i o n s of  In a l l e x p e r i m e n t s a s i n e  the  each  apodization  84 f u n c t i o n was 2K.  u s e d on t h e F I D s w h i c h were t h e n z e r o - f i l l e d  F o r s y m m e t r i c a l s p e c t r a ( a b o u t 0.0  r e v e r s e d and a d d e d t o t h e m s e l v e s lacking  i n the o r i g i n a l  first  2-3  build  up S/N  magnetic  spectrum.  Only  field  i f this  spectra within  t o r a p i d c o l l a p s e o f t h e FID  was  the  resulting  from  inhomogeneity. r e p o r t e d a t 270 MHz  o n l y ) were r e c o r d e d on a h o m e - b u i l t NMR  upon an O x f o r d  ( F i g u r e s 2.4  pulse-programmer.  The  c o m p u t e r and  a 293B  analytically  t h e s o l v e n t a d d e d by p i p e t t e  d i a m e t e r NMR  based  T magnet, a  s a m p l e s u s e d were p r e p a r e d  by a c c u r a t e w e i g h i n g and 5 mm  1180  and  spectrometer  I n s t r u m e n t s s u p e r c o n d u c t i n g 6.35  B r u k e r WP-60 c o n s o l e and a N i c o l e t  placed within  S/N  t i m e , were c o - a d d e d t o  2  due  t h e s p e c t r a were  t o improve  msec of t , t h e a c q u i s i t i o n  Those e x p e r i m e n t s 2.5  Hz)  to  and  tubes.  References 1.  2.  Aue,  W.P.,  B a r t h o l d i , E.,  and E r n s t , R.R.,  ( 1 9 7 6 ) , 64,  2229  Wokaun, A.,  and E r n s t , R.R.,  J . Chem.  Chem. P h y s . L e t t .  Phys.  (1977),  52,  407 3.  Bax,  A.,  Two-Dimensional  Nuclear Magnetic  L i q u i d s , Delf Univ. Press, D e l f , 4.  P i n e s , A., Am.  5.  Phys.  Soc.  B o d e n h a u s e n , G., Reson.  6.  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Chem.  4209  21. M u l l e r , L., J . Magn. R e s o n . ( 1 9 8 4 ) , 59, 326 22. Nagayama, K., W u t h r i c h , K., a n d E r n s t , R.R.,  Biochem.  B i o p h y s . R e s . Comm. ( 1 9 7 9 ) , 90, 305 23. Nagayama, K., Kumar, A., W u t h r i c h , K., a n d E r n s t , R.R., J . Magn. R e s o n .  ( 1 9 8 0 ) , 4 0 , 321  24. M u l l e r , L., Kumar, A., a n d E r n s t , R.R., J . Chem.  Phys.  ( 1 9 7 5 ) , 6 3 , 5496 25. A u e , W.P.,  Karhan,  J . , a n d E r n s t , R.R., J . Chem.  Phys.  ( 1 9 7 6 ) , 64, 4226 26. M a t h i e s o n , Chemists,  D.W.,  Nuclear Magnetic  Academic P r e s s , London,  27. K a r p l u s , M. , J . Chem. P h y s .  Resonance f o r Organic (1967)  ( 1 9 5 9 ) , 3_0, 11  28. K a r p l u s , M., J . Am Chem. S o c . ( 1 9 6 3 ) , 8 5 , 2870 29. S t a n d a r d NMR S p e c t r a C o l l e c t i o n , S a d t l e r Laboratories, researchers, editors,  Research  and p u b l i s h e r s ,  U.S.A.  ( 1 9 8 0 ) , 11978 30.  Ibid.  15096  31. W i l l i a m s , D.H., a n d F l e m i n g , I . , S p e c t r o s c o p i c M e t h o d s i n Organic  Chemistry,  2nd e d . M c G r a w - H i l l ( U . K . ) ,  Maidenhead,  ( 1 9 7 3 ) , p p . 132 32. S t a n d a r d NMR S p e c t r a C o l l e c t i o n , S a d t l e r Laboratories, researchers, editors, (1980)  Research  a n d p u b l i s h e r s , U.S.A.  87  CHAPTER I I I NUCLEAR MAGNETIC RESONANCE  IMAGING IN AN  INHOMOGENEOUS MAGNETIC F I E L D  88 3.1  Nuclear Magnetic Over t h e l a s t  Resonance  twenty  Imaging  y e a r s NMR  has a d v a n c e d  e x p l o s i v e r a t e , and  f o r over h a l f  caused  of t h e e x c i t e m e n t .  not a l i t t l e  The  f i r s t account  Lauterbur  o f NMR  o f t h i s t i m e NMR  i m a g i n g was  [1] f o l l o w e d s h o r t l y  a t an  imaging  has  p u b l i s h e d i n 1973  by a number o f o t h e r s  j u s t two y e a r s a f t e r J e e n e r had  almost  by  [2-4],  i n t r o d u c e d the concept  of  the  t w o - d i m e n s i o n a l F o u r i e r t r a n s f o r m a t i o n [ 5 ] . I t has o n l y been more r e c e n t l y , a f t e r  the f i r s t  d i e d down, t h a t NMR  i m a g i n g has  research  right.  i n i t s own  waves of t h e 2-D really  A l a r g e p a r t of the i n t e r e s t relation  to b i o l o g i c a l  that t h i s  i s n o t a new  revolution  had  taken o f f as a f i e l d  i n NMR  of  i m a g i n g has been i n  e x p e r i m e n t s , though  i t s h o u l d be  phenomenon. T r a d i t i o n has  noted  i t that  30  y e a r s ago E d w a r d P u r c e l l p u t h i s h e a d i n a magnet i n an attempt NMR  to observe  t h e e f f e c t s of i n t e n s i v e t h i n k i n g on  signal[6]. The  observed  fundamental  i d e a b e h i n d NMR  signal with spatial  making the magnetic  field  and h e n c e i t s p r e c e s s i o n a l If G  the  a l i n e a r magnetic  , i s superimposed  ,assuming  imaging  i s t o encode the  i n f o r m a t i o n . T h i s i s done by  s t r e n g t h e x p e r i e n c e d by a n u c l e u s , frequency, s p a t i a l l y field  g r a d i e n t i n the x  upon t h e s t a t i c m a g n e t i c  t h a t t h e magnitude of t h e magnetic  t h e g r a d i e n t i s much l e s s t h a n B  dependent.  0  field  direction, B , and  field  c r e a t e d by  [ 7 ] , the Larmor  frequency,  89 CJ, of t h e CJ= 7 B  On  nucleus + Q  TxG  becomes: (3.1)  x  Fourier transformation  t h i s would g i v e a frequency  w h i c h i s a o n e - d i m e n s i o n a l p r o j e c t i o n of the o b j e c t interest  taken  p r o j e c t i o n of the  along  the x d i r e c t i o n , F i g u r e  the o b j e c t  shape o f an  is insufficient  o b j e c t and  experiments Lauterbur, t h e o b j e c t a b o u t an  i t s spatial  3.1.  of  Clearly  to d e f i n e  location.  spectrum  completely  In h i s  first  [ 1 ] , o v e r c a m e t h i s p r o b l e m by r o t a t i n g  axis perpendicular  t o the  gradient  d i r e c t i o n . T h i s gave a number o f p r o j e c t i o n s f r o m w h i c h image c o u l d be techniques  7  r e c o n s t r u c t e d by  g r a d i e n t s can  (xG +yG )=cj x  y  gradient  of c o n s t a n t  d e f i n e d by  the  use  s u p e r s e d e d by use  of back p r o j e c t i o n  i n s t e a d of  r o t a t i n g the  be v a r i e d s u c h t h a t : (3.2)  i s a constant  The  use  two  frequency,  t o c r e a t e an  m a g n i t u d e i n any  arbitrary  direction  i n the  plane  gradients.  of p r o j e c t i o n r e c o n s t r u c t i o n t e c h n i q u e s F o u r i e r zeugmatography  of m u l t i d i m e n s i o n a l  Experiments u t i l i s i n g  t h i s technique  image of ah  one  s u c h as x , y ,  t o a c q u i s i t i o n and  makes  object.  of t h e d i m e n s i o n s of the  been  i n s t e a d of  generally involve  p h a s e e n c o d i n g of a l l but z, p r i o r  has  [4]. This technique  Fourier transformations,  back p r o j e c t i o n , t o r e c o n s t r u c t t h e  and  the  k  where a>  k  the  [ 8 - 1 2 ] . More p r a c t i c a l l y ,  o b j e c t , two  one  the  interest, frequency  90  90*  1 lllw  Gradient X 1 Acq. B  o o o  Y  A  o o X  CO F i g u r e 3.1. A. O n e - p u l s e e x p e r i m e n t w i t h a m a g n e t i c f i e l d g r a d i e n t i n t h e x - d i r e c t i o n on d u r i n g a c q u i s i t i o n t o f r e q u e n c y e n c o d e t h e x - c o o r d i n a t e s o f s p i n s c o n t r i b u t i n g t o t h e F I D . B. R e p r e s e n t a t i o n o f a phantom c o n s i s t i n g o f v i a l s o f H 0 . C. R e p r e s e n t a t i o n o f t h e s p e c t r u m o b t a i n e d when t h e p u l s e s e q u e n c e i n p a r t A i s u s e d on t h e phantom i n p a r t B. 2  91 encoding  of t h e r e m a i n i n g  encoding  may  of  dimension  be a c h i e v e d by  If  incrementing  o f a g r a d i e n t a p p l i e d f o r a f i x e d t i m e . The  method i s u s e d h e r e i n and a magnetic  field  will  precessed  through  0  y  i s a p p l i e d t o a sample  y  have  by: (3.3)  1  h e n c e t h e p h a s e change i n c u r r e d by a s p i n d u r i n g t ,  f  ACJ, w i l l  be d e p e n d e n t upon i t s y - c o o r d i n a t e . I f t h e e x p e r i m e n t repeated  n times  incrementing G  rise  t o a d a t a m a t r i x S(G  be d e p e n d e n t upon  Fourier  spectra corresponding  give rise  y  g i v e r i s e t o the frequency  o b s e r v a b l e s which  caused  f u n c t i o n of G .  As c a n  chemical  the f i r s t  y  equation,  shift,  modulation  be  i s independent  due  term of G  y  will,  y  The  and  Consequently  when F o u r i e r t r a n s f o r m e d ,  y  the  any  of t h e m a g n e t i z a t i o n as a intrinsic  i n the r i g h t h a l f consequently  of will  the not  be  phase change o c c u r r i n g d u r i n g  t o a s p i n y - c o o r d i n a t e on  d e p e n d e n t upon G .  s p e c t r a of  to  G.  t h e c o l u m n s of  s e e n f r o m e q u a t i o n 3.3  encoded i n t h i s dimension. t,  t o e a c h v a l u e of  transformation with respect to G ,  matrix, w i l l  y  2  2  frequency  G  , t ) . Fourier transformation  w i t h r e s p e c t t o t , t h e rows of t h e m a t r i x , w i l l the  is  by a c o n s t a n t amount, A t , ,  y  each time, then the a c q u i r e d s i g n a l w i l l giving  the  latter  of t h a t t i m e e a c h s p i n w i l l  an a n g l e g i v e n  A"=7B t, +7G yt  time  be d e s c r i b e d b e l o w .  gradient G  a t i m e t , , a t t h e end  Phase  i n c r e m e n t i n g the a p p l i c a t i o n  a g r a d i e n t of c o n s t a n t m a g n i t u d e , o r by  amplitude  for  during acquisition.  t h e o t h e r hand i s c l e a r l y t h i s dimension correspond  of the data  t o the  spatial  set  92 c o o r d i n a t e y and  hence t h e s p e c t r a o b t a i n e d  r e p r e s e n t a t i v e of s p i n d e n s i t y of t h e  will  be  sample i n t h e y -  direction. If  i n a d d i t i o n t o a phase encoding  gradient, a  gradient  i s applied during acquisition,  encoding  of t h e  spatial  two-dimensional  (equation  The  be a l o n g F1  frequency  3.2.  and  pulse  I t can  w e l l as t h e  be  the  the r e s u l t a n t  encoded s p a t i a l dimension  seen from e q u a t i o n  field  3.1  static shift  w i t h the g r a d i e n t  i f the  g r a d i e n t must be  frequency  induced  be e n c o d e d to  will along  shift  variation  image i s n o t  be  in Figure  that chemical  gradient w i l l  a c q u i s i t i o n . Consequently,  make c h e m i c a l  the  phase encoded s p a t i a l c o o r d i n a t e  s p a t i a l l y dependent frequency  the  to  sequence f o r t h i s experiment i s g i v e n  the s t a t i c magnetic  distorted,  3.1),  frequency  spectrum a f t e r F o u r i e r t r a n s f o r m a t i o n w i l l  a s p i n d e n s i t y map.  F 2 . The  leading to  dimension corresponding  d i r e c t i o n of t h a t g r a d i e n t  static  induced  Chemical S h i f t Resolved Chemical s h i f t  be  sufficiently  differences negligible  large to compared  spatially-dependent  imaging  experiments which besides  d i m e n s i o n s a l s o have an [13-17].  Imaging  r e s o l v e d imaging  intrinsic  experiments are  containing chemical  those  spatial  shift  by  during  frequency-variation. 3.2  as  dimension  29x  i i  Gradient Y i  Gradient X  i  1 1  '  Acq.  F i g u r e 3.2. T w o - d i m e n s i o n a l s p i n - d e n s i t y i m a g i n g e x p e r i m e n t . The y - d i m e n s i o n i s phase e n c o d e d p r i o r t o a c q u i s i t i o n a n d t h e x-dimension i s frequency encoded d u r i n g a c q u i s i t i o n .  90x  180°  Gradient X  Gradient Y  Phase encoding  Acquisition  F i g u r e 3.3. C h e m i c a l s h i f t r e s o l v e d i m a g i n g e x p e r i m e n t . Two s p a t i a l d i m e n s i o n s , x a n d y, a r e p h a s e e n c o d e d p r i o r t o a c q u i s i t i o n , and t h e c h e m i c a l s h i f t spectrum i s a c q u i r e d directly.  94 Although  l o c a l i s e d high  obtained  w i t h such t e c h n i q u e s  [18-22],  field  [24]  these  shift  profiling  methods a r e  r e s o l u t i o n s p e c t r a can as t h o s e  [ 2 3 ] , and  The  or other  first  u t i l i s i n g surface  coils  s e n s i t i v e p o i n t method  impractical for obtaining  r e s o l v e d images e i t h e r due  sensitivity,  the  be  to the  time  chemical  required,  low  technical limitations.  chemical  p r o p o s e d by L a u t e r b u r  shift  r e s o l v e d imaging  [ 1 3 ] was  experiment  b a s e d upon p r o j e c t i o n  r e c o n s t r u c t i o n , t h o u g h t h e c u r r e n t l y most w i d e l y u s e d methods a r e v a r i a t i o n s on experiment, Fourier  the F o u r i e r zeugmatography experiment.  i n t r o d u c e d by E r n s t  [ 4 ] , uses  t r a n s f o r m a t i o n s t o r e c o n s t r u c t an  multidimensional image. I n one  more common o f  i t s f o r m s , t h i s e x p e r i m e n t u s e s two  phase e n c o d i n g  g r a d i e n t s t o encode the  the data off  and  180° field  set. During the chemical  pulse  The  t o the  image i s o b t a i n e d  Slice  the  only those remaining data  x,y,  selection  through  The  and  chemical  techniques  remaining  switched  chemical  s h i f t dimension processing of  will time  three  s h i f t , are u s u a l l y acquired.  [25-26] are used t o s e l e c t a  dimension.  They do  slice  t h i s by e n s u r i n g  narrow range a l o n g  dimension are e x c i t e d . A s l i c e taken orthogonal  A  Fourier  experiments a t o t a l  spins within a certain  set obtained  three  to magnetic  by  s u b s t a n t i a l a c q u i s i t i o n and  in multidimensional  dimensions,  the  s p e c t r u m i s a c q u i r e d , F i g u r e 3.3.  transforming a l l dimensions. be F 2 . Due  or  of  d i m e n s i o n s of  i s i n c l u d e d t o r e f o c u s d e p h a s i n g due  inhomogeneities.  involved  spatial  a c q u i s i t i o n a l l gradients are shift  This  t o the c h e m i c a l  through  that  the the  s h i f t a x i s at  the  95 resonance of t h a t  f r e q u e n c y of a c h e m i c a l s p e c i e s  the degree  required to obtain high  of m a g n e t i c  1 part  i n 10  7  i n chemical s h i f t  p o o r a s 2 ppm,  this  adequate  resolved  only  in diameter.  The  the r e s o l u t i o n  images i s t y p i c a l l y  t o d i s t i n g u i s h f a t from water  s o l u t i o n t o t h i s problem  distribution. information  planar  spectra,  as  but  else.  A partial field  image  i t i s d e s i r e d t o image, s u c h as human b e i n g s ,  o f t e n somewhat l a r g e r . C o n s e q u e n t l y  little  the  homogeneity  is currently  i n v o l u m e s o f a p p r o x i m a t l y 10 cm  o b j e c t s which  obtained  field  resolution chemical s h i f t  i s of t h e o r d e r o f  attainable  are  yield  species.  Unfortunately  which  will  Assuming  irregularities  3.3  Zero-Quantum C o h e r e n c e  i n magnetic  field  Resolved  a x i s thus  distribution  is static,  for B ~ f i e l d 0  above,  [27].  resolved  imaging  i s t h e t e c h n i c a l l y demanding  homogeneity  over t h e volume of i n t e r e s t .  compensating  Imaging  drawback t o c h e m i c a l s h i f t  e x p e r i m e n t s , as d i s c u s s e d requirement  magnetic  can be u s e d t o g e n e r a t e a c u r v e d i n s t e a d of  for  major  the  that the d i s t r i b u t i o n  s l i c e through the chemical s h i f t  The  i s t o map  t o exceed  1 part  in  I t d o e s n o t seem r e a l i s t i c  10  7  at the  present time to expect t h i s  r e q u i r e m e n t t o become t e c h n i c a l l y  f e a s i b l e on a r o u t i n e b a s i s  i n the near  alternative still  future.  Consequently  s o l u t i o n s a r e needed, e x p e r i m e n t s which  a l l o w i n g the s e p a r a t i o n  of t h e s p i n d e n s i t y  while  images of  96 different field  a r e not f a t a l l y  The  basic  produce  r e q u i r e m e n t o f s u c h an e x p e r i m e n t  would  be t h a t  a d a t a s e t w h i c h e n c o d e s i n one d i m e n s i o n some i s a f u n c t i o n of t h e s p i n  I t must a l s o be i n d e p e n d e n t An o b v i o u s c a n d i d a t e w o u l d as i t f u l f i l l s  of magnetic  Consequently  system producing i t . field  inhomogeneity.  seem t o be z e r o - q u a n t u m  coherence  both of these requirements.  Zero-quantum c o h e r e n c e i t cannot  imaging experiments  cannot  be e n c o d e d  case with chemical s h i f t  be d i r e c t l y  observed [ 2 8 ] .  d u r i n g a c q u i s i t i o n as i s the  i n many c h e m i c a l s h i f t  resolved  [ 1 3 - 1 7 ] . T h e r e f o r e i t would  f r e q u e n c y e n c o d e one o f t h e s p a t i a l  a c q u i s i t i o n and t o modulate  seem  and z e r o - q u a n t u m  logical  dimensions during  the magnetization p r i o r to  a c q u i s i t i o n with respect t o the remaining s p a t i a l  encoded  shift  imaging e x p e r i m e n t s .  p r o p e r t y which  to  s u s c e p t i b l e t o magnetic  inhomogeneities as a r e a l l c u r r e n t l y used c h e m i c a l  resolved  it  s p i n systems  c o h e r e n c e . The s p a t i a l  dimensions  d i m e n s i o n s may be  a s a f u n c t i o n o f an i n c r e m e n t a l g r a d i e n t , a n d  zero-quantum  c o h e r e n c e may be e n c o d e d  a s a f u n c t i o n o f an  i n c r e m e n t a l t i m e t , . An i n c r e m e n t a l g r a d i e n t e n c o d e s a s p a t i a l c o o r d i n a t e by p h a s e e n c o d i n g zero-quantum efficiently modulation sense  coherence  ( e q u a t i o n 3 . 3 ) , and t o c o n v e r t  i n t o single-quantum coherence  r e q u i r e s a 90° p u l s e w h i c h  implies  ( e q u a t i o n 2.15). Consequently  amplitude  i t d o e s n o t make  t o phase encode t h e m a g n e t i z a t i o n ( s p a t i a l  before amplitude encoding  (zero-quantum  most  coherence  encoding) encoding) as  97 the  l a t t e r destroys Therefore  the  sense of phase  the m a g n e t i z a t i o n  (±)  of the  m u s t . f i r s t be  former.  amplitude  m o d u l a t e d t o encode z e r o - q u a n t u m c o h e r e n c e d u r i n g incremental  time  incremental  g r a d i e n t s t o e n c o d e a l l but  dimensions,  and  t , . Then i t must be p h a s e e n c o d e d  lastly  frequency  s p a t i a l d i m e n s i o n by a s t a t i c antiphase  single-quantum  be d e t e c t e d  so  one  zero-quantum experiment,  to  c a n c e l out  It  w o u l d a l s o be d e s i r a b l e t o c o l l e c t  of  just  The  d e p h a s i n g due  pulse  logically  give r i s e to a data  gradient  amplitude modulation  the whole echo i n s t e a d  set S ( t  i s i n c r e m e n t e d ) and  1 f  G , t  set w i l l  inhomogeneities.  i s applied for a constant  y  this  c o n s i d e r a t i o n s would  i n F i g u r e 3.4  d i m e n s i o n of t h e d a t a  of the G  inhomogeneities.  t o p of t h e e c h o as  i s given  d i s t o r t i o n s by m a g n e t i c f i e l d encoding  a refocussing pulse  to magnetic f i e l d  sequence t o w h i c h t h e s e  2  t o i n c l u d e , as  resolution.  seem t o l e a d one,  Only the t  i s o c c u r r i n g and  to a c q u i r e at the and  experiment w i l l  from  i t w o u l d seem t o make s e n s e t o p h a s e encode  the  i m p r o v e S/N  The  to rephase before i t  in  will  remaining  coherence o r i g i n a t i n g  while t h i s  starting  spatial  gradient during a c q u i s i t i o n .  the m a g n e t i z a t i o n refocussed  with  of t h e  encoded i n the  z e r o - q u a n t u m c o h e r e n c e must be a l l o w e d can  an  consequently  d i m e n s i o n due  to  . This ) .  2  be The  time  subject phase  (only  there w i l l  inhomogeneities.  Z e r o - q u a n t u m c o h e r e n c e s a r e u n a f f e c t e d by  them.  the be  no  to  Gradient X  Gradient Y -  Gradient Z Preparation  Zero-quantum  Spatial encoding  evolution  F i g u r e 3.4. Zero-quantum c o h e r e n c e experiment.  Relaxation delay  resolved  imaging  99 If  three s p a t i a l dimensions are required, the z-gradient  may a l s o be u s e d f o r p h a s e e n c o d i n g y-gradient  i s . If this  independently,  i s done t h e y must be  and z e r o - o r d e r  s e l e c t e d by p h a s e c y c l i n g at can  techniques  coherence  [28]. A two-dimensional  slice  unencoded s p a t i a l  by t h e u s e o f e x i s t i n g  [25,26].  slice  T h e s e work by e n s u r i n g  dimension  that only the spins coordinate  t h e u n e n c o d e d d i m e n s i o n a r e e x c i t e d by a g i v e n  radiofrequency to  image  selection  i n a s l i c e a few m i l l i m e t e r s t h i c k a t t h e d e s i r e d in  that the  incremented  multiple-quantum  a p a r t i c u l a r value of the t h i r d be o b t a i n e d  a t t h e same t i m e  p u l s e , and would r e q u i r e o n l y minor  the experiment.  The f i r s t  normal  ( i . e . h a r d ) 90° p u l s e i s  r e p l a c e d by a s o f t p u l s e w h i c h w i l l frequency  range than  soft pulse a s l i c e  e x c i t e a much n a r r o w e r  t h e normal hard  pulse would. During the  selection gradient corresponding  unencoded d i m e n s i o n  i s switched  to the  on t o make t h e r e s o n a n c e  f r e q u e n c i e s of t h e s p i n s s p a t i a l l y  dependent. Consequently the  n a r r o w r a n g e o f f r e q u e n c i e s e x c i t e d by t h e s o f t corresponds  alterations  pulse  t o a range i n t h e unencoded d i m e n s i o n ,  the s p a t i a l  c o o r d i n a t e o f w h i c h i s d e p e n d e n t upon t h e t r a n s m i t t e r frequency.  The t h i c k n e s s o f t h e s l i c e  i s d e p e n d e n t upon t h e  magnitude of t h e g r a d i e n t and t h e c h a r a c t e r i s t i c s of t h e s o f t p u l s e . The s l i c e  selection  that the frequency  t o those  large  d i f f e r e n c e s o f t h e s p i n s due t o c h e m i c a l  s h i f t s and magnetic relative  g r a d i e n t must be s u f f i c i e n t l y  field  induced  inhomogeneities  are negligible  by t h e g r a d i e n t  (equation 3.1).  100 It to  i s p o s i b l e t o reduce the t h r e e d i m e n s i o n a l experiment  two d i m e n s i o n s by i n c r e m e n t i n g t h e phase  simultaneously with t rise  1  f  i n s t e a d of i n d e p e n d e n t l y . T h i s g i v e s  d i m e n s i o n and t h e z e r o - q u a n t u m  become p a r a l l e l a l o n g one a x i s , spatial  dimension  coherence  zero-quantum computer  encoded  i s along the other. E f f e c t i v e l y  c o h e r e n c e . Due t o t h e l i m i t e d  encoded  dimension  and t h e f r e q u e n c y  t h e image o f a s p e c i e s b e i n g s u p e r i m p o s e d  the  gradient  t o a t w o - d i m e n s i o n a l d a t a s e t i n which t h e phase  spatial  in  encoding  this  results  on t o p o f i t s  ability  of the  used t o h a n d l e m u l t i d i m e n s i o n a l d a t a t h i s v e r s i o n of  e x p e r i m e n t was p e r f o r m e d . The  e x p e r i m e n t was d e m o n s t r a t e d w i t h a phantom c o m p r i s i n g  seven v i a l s c o n t a i n i n g p r o p i o n i c a c i d , Figure  3.5.A. The z e r o - q u a n t u m  2 - p r o p a n o l , and water,  coherence  resolved  image o f t h e  p h a n t o m i s g i v e n i n F i g u r e 3.5'B. The images o f 2 - p r o p a n o l a n d propionic acid top  of t h e i r  longitudinal respect  a r e c o m p l e t e l y r e s o l v e d and a r e s u p e r i m p o s e d  zero-quantum during t  1  f  coherences. M a g n e t i z a t i o n which  a n d h e n c e was n o t m o d u l a t e d  t o i t , produced a c o n v e n t i o n a l  was  with  image c e n t r e d a t 0.0 Hz  in F1. This magnetization originated  from s i n g l e  w a t e r , 2 - p r o p a n o l and p r o p i o n i c a c i d  w h i c h was n o t c o n v e r t e d  into  zero-quantum  zero-quantum  c o h e r e n c e , and s p i n - l a t t i c e  coherence. A s i m i l a r  on  s p i n s such as  relaxation  complete r e s o l u t i o n  of  of these  c h e m i c a l s p e c i e s w o u l d h a v e been i m p o s s i b l e w i t h t h e t r a d i t i o n a l chemical s h i f t the  magnetic  field  resolved  imaging experiment given  inhomogeneity e v i d e n t i n the corresponding  s i n g l e - q u a n t u m s p e c t r u m o f t h e phantom, F i g u r e  3.5.D.  101  2-Propanol  Propionic acid  Magnetisation longitudinal during t i  |—i—i—i—i—|—i—i—i—i—|—i—i—i—i—p—i—i—i—i—|—i—i—i—i—|—i—r—i—i—|  300  240  180  120  60  0  Hz  102  F i g u r e 3.5. A. The s t r u c t u r e a n d c o m p o s i t i o n o f t h e phantom u s e d . B. t h e t w o - d i m e n s i o n a l z e r o - q u a n t u m c o h e r e n c e r e s o l v e d image o b t a i n e d w i t h t h e p h a n t o m i n p a r t A, t , a n d G were i n c r e m e n t e d s i m u l t a n i o u s l y . T=60 msec, At,=1.67 m s e c , AGy=1.84x10~ Gem ( a p p l i c a t i o n t i m e = l 0 m s e c ) , G =0.41 G e m , 255 b l o c k s c o l l e c t e d , 16 a c q u i s i t i o n s p e r b l o c k . T o t a l a c q u i s i t i o n t i m e 75 m i n u t e s . C. Z e r o - q u a n t u m s p e c t r u m o f t h e phantom o b t a i n e d w i t h t h e r e f o c u s s e d z e r o - q u a n t u m e x p e r i m e n t . T=60 msec, At,=1.67 msec, 256 b l o c k s c o l l e c t e d , 8 a c q u i s i t i o n s p e r b l o c k . T o t a l a c q u i s i t i o n t i m e 35 m i n u t e s . D. S i n g l e - q u a n t u m s p e c t r u m o f t h e phantom. v  3  -1  -1  x  103 It the  s h o u l d be n o t e d t h a t  experiment  demonstrated  image i n F1 r e s u l t i n g  i n t h e t w o - d i m e n s i o n a l v e r s i o n of here t h e r e i s d i s t o r t i o n  from t h e m u l t i p l e t  zero-quantum  coherences. This s t r u c t u r e  discernible,  particularly  of t h e  s t r u c t u r e o f f the i s readily  i n the case of p r o p i o n i c a c i d i n  F i g u r e 3 . 5 . B . I n t h e t h r e e and f o u r d i m e n s i o n a l v e r s i o n s o f t h e experiment m u l t i p l e t coherence  structure  dimension. A s l i c e  a certain  density In  a slice  a specific  yield  resolved  imaging  taken through the chemical s h i f t  dimension  r e s o n a n c e may be n o n - p l a n a r due t o s p a t i a l  coherence  independent  coherence useful  B  Q  F i g u r e 3.6.A. A l t h o u g h t h i s may be c o m p e n s a t e d  resolved  of magnetic  field  As d e s c r i b e d p r e v i o u s l y  with  i m a g i n g , F i g u r e 3.6.B, a s i t inhomogeneity.  ( s e c t i o n 2.2) t h e  d i m e n s i o n c a n be e d i t e d , w h i c h  zero-quantum  i s particularly  i n p r e v e n t i n g o v e r l a p p i n g o f images i n t h e  t w o - d i m e n s i o n a l e x p e r i m e n t . T h i s i s because excitation  of zero-quantum  coherence  l e n g t h of t h e p r e p a r a t i o n p e r i o d constants and  the spin  by d a t a m a n i p u l a t i o n [ 2 7 ] t h e p r o b l e m does n o t a r i s e  zero-quantum is  a x i s a t the frequency  coherence, w i l l  the conventional chemical s h i f t  inhomogeneity, for  coherence  image o f t h e c h e m i c a l s p e c i e s p r o d u c i n g i t .  experiment at  zero-quantum  zero-quantum  taken through the data s e t  o r t h o g o n a l t o t h e zero-quantum of  i s confined to the  the e f f i c i e n c y of  i s d e p e n d e n t upon t h e  T and t h e s c a l a r  i n v o l v e d . E d i t i n g may a l s o be u s e f u l  four dimensional  coupling  i n the three  104  B  F i g u r e 3.6. A. D a t a s e t f o r a c h e m i c a l s h i f t r e s o l v e d i m a g i n g e x p e r i m e n t . S l i c e s t a k e n t h r o u g h t h e t h e F2 ( c h e m i c a l s h i f t ) d i m e n s i o n may h a v e t o be n o n - p l a n a r t o c o m p e n s a t e f o r a s p a t i a l l y i n h o m o g e n e o u s m a g n e t i c f i e l d . B. D a t a s e t f o r a zero-quantum coherence r e s o l v e d imaging experiment. S l i c e s t a k e n t h r o u g h t h e F1 ( z e r o - q u a n t u m c o h e r e n c e ) d i m e n s i o n a r e p l a n a r , i n d e p e n d e n t t o m a g n e t i c f i e l d i n h o m o g e n e i t y , and r e q u i r e no s p e c i a l m a n i p u l a t i o n .  105 e x p e r i m e n t s i n c a s e s where c o h e r e n c e s o v e r l a p w h i c h may a considerable  problem at lower B  c  fields. Alternatively  use o f " a c c o r d i o n "  [ 2 9 ] p r e p a r a t i o n and r e f o c u s s i n g  ( s e c t i o n 2.3)  ensure a f a i r l y  zero-quantum intensity 3.4  will  become  even e x c i t a t i o n  sequences of a l l  coherences a l t h o u g h a t the c o s t of reduced  and hence  Broad-Band  S/N  the  signal  ( s e c t i o n 2.3).  Decoupled  Zero-Quantum C o h e r e n c e  Resolved  Imaging The  zero-quantum  coherence  resolved  zero-quantum their  c o h e r e n c e d i m e n s i o n of a  image h a s  i n common w i t h  conventional  s p e c t r a a number o f d i s a d v a n t a g e s r e l a t i v e  single-quantum counterparts.  at the d i f f e r e n c e i n frequencies generally  zero-quantum  Occurring  a s t h e y do  to only  o f two c o u p l e d s p i n s t h e y  o c c u p y a n a r r o w e r f r e q u e n c y r a n g e . Hence t h e y a r e  more i n c l i n e d t o be c r o w d e d p r o b l e m s when t r y i n g  and t o o v e r l a p . T h i s may  to assign  separate the s p i n d e n s i t y  s p e c t r a , when t r y i n g  images  c o h e r e n c e s , and o v e r l a p p i n g  may  o f two  lead to to  overlapping  l e a d t o mutual c a n c e l l a t i o n of  coherences. A p o s s i b l e s o l u t i o n t o a l l o f t h e s e p r o b l e m s w o u l d be t o broad-band  decouple the zero-quantum  t h e e x p e r i m e n t . As d i s c u s s e d reducing  the zero-quantum  would decrease o v e r l a p , and may time.  c o h e r e n c e d i m e n s i o n of  p r e v i o u s l y ( s e c t i o n 2.4),  coherence m u l t i p l e t s to  singlets  reduce mutual c a n c e l l a t i o n of  r e q u i r e l o w e r r e s o l u t i o n and hence  I f a l l the i n t e n s i t y  peaks  less acquisition  o f a f o r m e r m u l t i p l e t now  goes  into  1 06 one p e a k , f e w e r a c q u i s i t i o n s p e r b l o c k may b u i l d up an a c c e p t a b l e l e v e l o f A broad-band  the undecoupled experiment  coherence  resolved  can be c o n s t r u c t e d i n a s i m i l a r manner t o  zero-quantum  coherence  resolved  imaging  d i s c u s s e d p r e v i o u s l y . T h i s i s done by t h e  to the e x i s t i n g  spectroscopic experiment  t h e r e f o c u s s i n g and a c q u i s i t i o n s p a t i a l dimensions. Also, zero-quantum  coherence  of g r a d i e n t s d u r i n g  t i m e s t o encode t h e  i n analogy to the  resolved  addition  desired  undecoupled  imaging e x p e r i m e n t , the whole  s p i n echo i s a c q u i r e d i n s t e a d of j u s t  the second h a l f  at the t o p of the echo. T h i s improves  t h e S/N  of t h e image. The F i g u r e 3.7. to produce  resulting  imaging experiment  As w i t h t h e u n d e c o u p l e d  experiment  and  zero-quantum  coherence  one  resolution  i s given in i t c a n be  encodes broad-band  and a l s o t h e t h r e e s p a t i a l  x, y, and z, u s i n g two p h a s e and one  frequency  g r a d i e n t s . In the t h r e e - d i m e n s i o n a l experiment s p a t i a l dimensions are encoded,  used  one  through the t h i r d h a r d 90°  two  by a f r e q u e n c y and one be  two-dimensional experiment  (section  the  selection  3.3). In the  the a c q u i r e d s i g n a l  is  s p a t i a l d i m e n s i o n s and b r o a d - b a n d  coherence  by  selected  u n e n c o d e d s p a t i a l d i m e n s i o n by r e p l a c i n g  g r a d i e n t as d e s c r i b e d p r e v i o u s l y  zero-quantum  dimensions,  only  p u l s e w i t h a s o f t p u l s e and a s l i c e  w i t h two  decoupled  encoding  a p h a s e e n c o d i n g g r a d i e n t . I f d e s i r e d , a s l i c e may  encoded  starting  a f o u r , t h r e e , or two-dimensional data s e t . In the  four d i m e n s i o n a l experiment  first  to  S/N.  decoupled zero-quantum  imaging experiment  be r e q u i r e d  still decoupled  but the i n c r e m e n t a l d e l a y t , ,  90S  I80  T/2  901  Y  I  8  0  t,/2  T/2  Wx  Y  '80°  T/2 f f l  t -1,/2 d  •  L  Gradient X •  Gradient Y  Gradient Z  i i  Zero-quantum evolution  Preparation  Spatial  i i i i  I  F i g u r e 3.7. B r o a d band d e c o u p l e d r e s o l v e d imaging experiment.  [  •  zero-quantum  coherence  encoding  108 which l e a d s t o zero-quantum  c o h e r e n c e e n c o d i n g , and t h e  encoding gradient are incremented simultaneously  phase  i n s t e a d of  independently. This gives r i s e to a two-dimensional data set w i t h one d i m e n s i o n m o d u l a t e d t h e o t h e r m o d u l a t e d due zero-quantum  t o t h e f r e q u e n c y e n c o d i n g and  t o both broad-band  c o h e r e n c e and t h e phase  d i m e n s i o n . When F o u r i e r data set gives r i s e  coherences. I t i s i n the two-dimensional v e r s i o n  coherence  t o broad-band  i s most s i g n i f i c a n t .  presence of the zero-quantum T h i s d i s t o r t i o n can c l e a r l y c o n s i s t s of the zero-quantum phantom o f s i x v i a l s o f i n a hexagon.  zero-quantum when t h e i r  1:1  structure.  be s e e n i n F i g u r e 3.8.A coherence r e s o l v e d  2 - P r o p a n o l and e t h a n o l  which  image of a  2 - p r o p a n o l and e t h a n o l  in  coherence m u l t i p l e t  impossible to d i s t i n g u i s h  D 0 2  produce  frequencies. Consequently  i m a g e s a r e s u p e r i m p o s e d on t o p o f  coherences i t r e s u l t s  of  i n t o t h e image by t h e  in their  o v e r l a p p i n g . The a d d i t i o n a l d i s t o r t i o n s zero-quantum  decouple  In the absence  coherence m u l t i p l e t  coherences at s i m i l a r  respective  zero-quantum  spatial  be s u p e r i m p o s e d on t o p o f i t s  decoupling d i s t o r t i o n s are introduced  arranged  encoded  image i n w h i c h t h e image of a  of t h e e x p e r i m e n t t h a t t h e a b i l i t y zero-quantum  decoupled  transformed i n both dimensions, t h i s  t o an  chemical species w i l l zero-quantum  due  their  images  i n t r o d u c e d by t h e  s t r u c t u r e makes i t a l m o s t  t h e shape o f t h e phantom and i t s  c o n s i s t e n t v i a l s and l e a d s t o c o n s i d e r a b l e m e r g i n g of p e a k s . The  broad-band  d e c o u p l e d e x p e r i m e n t was  used t o o b t a i n  the  c o r r e s p o n d i n g d e c o u p l e d image o f t h e phantom, F i g u r e 3.8.B. I n  109  1 10  T — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i  200  100  -100  0  -200  r~  Hz  F i g u r e 3.8. Images a n d s p e c t r a o f a phantom c o n s i s t i n g o f 6 v i a l s , d i a m e t e r 6 mm, c o n t a i n i n g 2 - p r o p a n o l a n d e t h a n o l , 1:1 i n D 0 , a r r a n g e d i n a h e x a g o n w i t h s i d e s o f l e n g t h 9mm. A. Z e r o - q u a n t u m c o h e r e n c e r e s o l v e d image o f t h e p h a n t o m ; r=60 msec, At,=1.67 msec, A G = 1 . 5 X 1 0 ~ G e m ( a p p l i e d f o r 10 m s e c ) , G = 0.34 G e m , 256 b l o c k s c o l l e c t e d , 16 a c q u i s i t i o n s p e r b l o c k . B-D, b r o a d b a n d d e c o u p l e d z e r o - q u a n t u m c o h e r e n c e r e s o l v e d i m a g e s o f t h e p h a n t o m : B. t j=443 msec ( b o t h e t h a n o l and 2 - p r o p a n o l p r e s e n t ) , C. t j = 4 l 3 msec ( 2 - p r o p a n o l e d i t e d o u t ) , D. t j=493 msec ( e t h a n o l e d i t e d o u t ) . F o r B-D r=60 msec, A t , = 1.67 msec, A G y = 5 . 5 5 x 1 0 Gem ( a p p l i e d f o r 27 m s e c ) , G =0.34 G e m , 25b b l o c k s c o l l e c t e d , 4 a c q u i s i t i o n s p e r b l o c k . E. S i n g l e - q u a n t u m s p e c t r u m o f p h a n t o m . A s s i g n m e n t s : -100 H z , 100 Hz - o v e r l a p p i n g p e a k s o f b o t h e t h a n o l a n d 2 - p r o p a n o l , 200 Hz -HDO. 2  3  -1  v  - 1  x  (  (  (  - 4  - 1  x  -1  111 shape o f t h e phantom i s much more r e a d i l y d e t e r m i n e d a s a r e the shapes  of i t s c o n s t i t u e n t v i a l s and t h e merging  has been g r e a t l y resolution  reduced. Despite t h i s  of peaks  improvement i n  t h e images o f t h e two s p i n s y s t e m s  still  overlap.  T h i s i s one o f t h e b i g g e s t d i s a d v a n t a g e s o f t h e two-dimensional  experiment.  As was d i s c u s s e d p r e v i o u s l y decoupled experiment editing this  (section  2.4 ) t h e  broad-band  i s more f l e x i b l e w i t h r e g a r d s t o s p e c t r a l  than t h e c o n v e n t i o n a l zero-quantum  e x p e r i m e n t , and  i s e q u a l l y an a t t r i b u t e o f t h e i m a g i n g e x p e r i m e n t . By  altering  t h e v a l u e of t ^ i t i s p o s s i b l e t o e d i t  out unwanted  c o h e r e n c e s , and hence t h e images a s s o c i a t e d w i t h them. T h i s i s demonstrated  i n F i g u r e 3.8 C a n d D where 2 - p r o p a n o l a n d  e t h a n o l r e s p e c t i v e l y h a v e been e d i t e d o u t l e a v i n g t h e undistorted  image o f t h e r e m a i n i n g c o h e r e n c e . The  c o r r e s p o n d i n g zero-quantum  s p e c t r a a r e g i v e n i n F i g u r e 3.9.  In a d d i t i o n t o d i s t o r t i n g presence of m u l t i p l e t intensity  t h e shape o f t h e image t h e  s t r u c t u r e was a l s o f o u n d t o d i s t o r t i t s  i n t h e t w o - d i m e n s i o n a l e x p e r i m e n t . I t c a n be s e e n  f r o m t h e c r o s s s e c t i o n s t a k e n t h r o u g h t h e image i n F i g u r e 3.7.A w h i c h a r e g i v e n i n F i g u r e 3.8 B a n d C t h a t distortion  makes t h e e x p e r i m e n t p r a c t i c a l l y  determining the r e l a t i v e  this  useless for  i n t e n s i t i e s , and hence  spin  densities,  of a p a r t i c u l a r  experiment  however d o e s n o t e x p e r i e n c e t h i s p r o b l e m  seen  s p e c i e s . The b r o a d - b a n d  decoupled a s c a n be  f r o m t a k e n f r o m t h e images i n F i g u r e 3.8 B-D g i v e n i n  1 12  F i g u r e 3.9. S p e c t r a c o r r e s p o n d i n g t o t h e images i n F i g u r e 3.8 A-D o f e t h a n o l a n d 2 - p r o p a n o l , 1:1 i n D 0 . A. Z e r o - q u a n t u m spectrum o b t a i n e d w i t h t h e r e f o c u s s e d zero-quantum e x p e r i e m e n t ; T=60 msec, A=1.67 msec, 256 b l o c k s c o l l e c t e d , 4 a c q u i s i t i o n s p e r b l o c k . B-D. B r o a d band d e c o u p l e d z e r o - q u a n t u m s p e c t r a : B. t j=443 msec ( b o t h e t h a n o l and 2 - p r o p a n o l p r e s e n t ) , C. tj3=4l3 msec ( 2 - p r o p a n o l e d i t e d o u t ) , D. t^=493 msec ( e t h a n o l e d i t e d o u t ) . F o r B-D T=60 msec, At,=1.67 msec, 256 b l o c k s c o l l e c t e d , 4 a c q u i s i t i o n s p e r b l o c k . Peak assignments: e t h a n o l ±197 H z , 2 - p r o p a n o l ±225 Hz. 2  (  113  n  D  H  u 800  260  200  ' I ' 160  100  Fl  T  60  " 0.0 1  T-,-1 Hi  T | I I I . |  SOO  250  .  200 1  160  100  60  o.o  Hi  Fl  F i g u r e 3.10. A. R e p r e s e n t a t i o n of the phantom used t o o b t a i n the images i n F i g u r e 3.8 i n d i c a t i n g s l i c e s taken through them which are given i n p a r t s B-I. B and C: s l i c e s taken through F i g u r e 3.8.A. D and E: s l i c e s taken through F i g u r e 3.8.B. F and G: s l i c e s taken through F i g u r e 3.8.C. H and I : s l i c e s taken through F i g u r e 3.8.D.  114 F i g u r e 3.10 The are  D-I.  relative  s p i n d e n s i t i e s of d i f f e r e n t  even more d i f f i c u l t  d e c o u p l e d zero-quantum  chemical species  t o determine w i t h the  broad-band  experiment than f o r i t s undecoupled  c o u n t e r p a r t . In the l a t t e r case the i n t e n s i t y  of a  coherence  i s a f u n c t i o n o f t h e r e l e v a n t c o u p l i n g c o n s t a n t s and  the  p r e p a r a t i o n and r e f o c u s s i n g t i m e s . I n t h e f o r m e r c a s e  i t is  a d d i t i o n a l l y d e p e n d e n t upon t ^ . The  b i g g e s t d i s a d v a n t a g e of the broad-band  zero-quantum  coherence  resolved  applies to a s i g n i f i c a n t experiment msec may  decoupled  imaging experiment  but l e s s e r e x t e n t t o t h e  which undecoupled  i s t h e t i m e i n v o l v e d . I n b o t h e x p e r i m e n t s up  be t a k e n up by t h e p r e p a r a t i o n and  p e r i o d s a l o n e . With the the broad-band every experiment  200  refocussing  decoupled  i s l o n g e r by a t l e a s t n A t ,  to  experiment  ( as t ^ n A t , )  where n i s t h e number o f t , i n c r e m e n t s u s e d . T h e s e c o n s i d e r a t i o n s w o u l d seem t o make in  vivo  applications  these experiments i m p r a c t i c a l , given the short relaxation 3.5  times encountered  J-Resolved The  [ 3 0 , 3 1 ] s h a r e s one  field  spin-spin  therein.  Imaging  homonuclear  zero-quantum  of  two-dimensional J-resolved important a t t r i b u t e with  homonuclear  coherence experiments, independence  inhomogeneity  i n t h e F1  dimension.  experiment  of  magnetic  115 Why  i s this  s o ? L i k e any o t h e r  property,  i f i t i s t o be  encoded i n t h e t , dimension of a two-dimensional the extent field  t o which magnetization  e v o l v e s due t o m a g n e t i c  i n h o m o g e n e i t y must c h a n g e i n e a c h s u c c e s s i v e  a s a f u n c t i o n o f an i n c r e m e n t a l being  experiment  delay  s y s t e m a t i c a l l y incremented.  two-dimensional  data matrix  dimension corresponding delay or other  experiment  o r some o t h e r  property  This produces a  i n which the magnetization  t o the s y s t e m a t i c a l l y  i n the  incremented  v a r i a b l e i s m o d u l a t e d by t h e p r o p e r t y  one  d e s i r e s t o encode. In  the b a s i c homonuclear two-dimension J - r e s o l v e d  experiment, the  F i g u r e 3.11.A, a t t h e e n d o f t h e e v o l u t i o n t i m e t ,  system has o n l y e v o l v e d  Chemical s h i f t out  and magnetic f i e l d  by t h e 180° p u l s e  dimension of the data f u n c t i o n of the extent This  due t o i t s s c a l a r c o u p l i n g s . inhomogeneity a r e canceled  i n the middle set w i l l  of t , . Consequently t h e t ,  o n l y be p h a s e m o d u l a t e d a s a  o f e v o l u t i o n due t o s c a l a r c o u p l i n g s .  i s demonstrated f o r the  3 1  P  s p e c t r a of adenosine  t r i p h o s p h a t e and a d e n o s i n e d i p h o s p h a t e which a r e c l e a r l y  u n a f f e c t e d by m a g n e t i c  whereas t h e c o r r e s p o n d i n g  S(t,,t ), 2  field  single-quantum  F i g u r e 3.12 C a n d D, a r e , t h e i r unresolved.  i n Figure  coherence  Only the t , dimension of t h e data  shift  or s c a l a r coupling  spectra,  being  set acquired,  g i v i n g S ( F 1 , t ) . In  t h e c a s e o f e x t r e m e i n h o m o g e n e i t y F2 w i l l chemical  inhomogeneity  scalar couplings  h a s been F o u r i e r t r a n s f o r m e d ,  3.12 A a n d B  2  c o n t a i n no u s e f u l  information.  1 16  A  2  2  Phase encoding  Acquisition  B 90x  Gradient X  Gradient Y  Gradient Z  Phase encoding  Acquisition  F i g u r e 3.11. A. H o m o n u c l e a r t w o - d i m e n s i o n a l J - r e s o l v e d e x p e r i m e n t . B. H o m o n u c l e a r J - r e s o l v e d i m a g i n g e x p e r i m e n t two p h a s e e n c o d e d a n d o n e f r e q u e n c y e n c o d e d s p a t i a l dimensions.  with  11 7  T—i—i—|-1—i—i—r—i—i—i | i—i—i—|—i—i—i—[•  200  0  -200  Hz  —  i  i—i—|—i—i—i—|—i—i—i—|—i—i—i—|—i—i—i—r  200  0  -200  Hz  F i g u r e 3.12. P s p e c t r a o b t a i n e d a t 32.5 MHz. A. J - s p e c t r u m o f ATP, 0.5 m o l a r i n H 0 o b t a i n e d w i t h t h e h o m o n u c l e a r t w o - d i m e n s i o n a l J - r e s o l v e d e x p e r i m e n t . B. J - s p e c t r u m o f ADP, 0.5 m o l a r i n H 0 , o b t a i n e d w i t h t h e h o m o n u c l e a r t w o - d i m e n s i o n a l J - r e s o l v e d e x p e r i m e n t . F o r p a r t s A and B A t , = 11.1 msec, 64 b l o c k s c o l l e c t e d , 8 a c q i s i t i o n s p e r b l o c k . C. S i n g l e - q u a n t u m s p e c t r u m o f ATP. D. S i n g l e - q u a n t u m s p e c t r u m o f ADP. 3 1  2  2  118 Incorporated chemical  shift  i n t o an imaging  experiment  r e s o l v e d dimension J-encoding  a l l o w one t o o b t a i n t h e image o f a c h e m i c a l magnetic  field  resolved  image t o be u s e f u l .  It and  would  therefore  s p e c i e s where t h e  i s t o o inhomogeneous f o r a c h e m i c a l  was f o u n d t o be i n s u f f i c i e n t  phase encoding  desired  i n s t e a d of a  magnetic  field  m e r e l y t o add  frequency  g r a d i e n t s t o encode t h e  s p a t i a l dimensions t o the e x i s t i n g  J-resolved experiment.  shift  two-dimensional  T h i s was b e c a u s e t h e r a p i d d e c a y o f t h e  FID  under t h e i n f l u e n c e s of t h e f r e q u e n c y  and  magnetic f i e l d  encoding  gradient  inhomogeneity r e s u l t e d i n inadequate  r e s o l u t i o n a n d S/N. T h i s p r o b l e m was o v e r c o m e by d e s i g n i n g a pulse just  s e q u e n c e i n w h i c h t h e whole e c h o i s a c q u i r e d , the second h a l f ,  magnetic f i e l d experiment  and which y e t r e t a i n s independence of  inhomogeneity with respect  i s given  field  the  data  t , would r e s u l t i n shift  being  encoded  with scalar coupling evolution.  an a d d i t i o n t i m e  p e r i o d r / 2 was i n t r o d u c e d  180° p u l s e a n d T- s e t e q u a l  results  time  i n h o m o g e n e i t y and c h e m i c a l  with respect to t , along Therefore  t o t , . The r e s u l t i n g  i n F i g u r e 3.11.B. B e g i n i n g  a c q u i s i t i o n w i t h i n the incremental magnetic  i n s t e a d of  i n the a c q u i s i t i o n  to the acquisition  before  time.  This  of t h e whole s p i n echo which  r e a c h e s i t s maximum a t t h e c e n t r e o f t h e F I D g i v i n g r i s e t o maximum r e s o l u t i o n a n d S/N w i t h o u t inhomogeneity  i n t r o d u c i n g magnetic  i n t o t h e F1 d i m e n s i o n o f t h e image.  field  119 This  s e q u e n c e was i n i t i a l l y  evaluated  w i t h a phantom  c o n t a i n i n g e t h a n o l , p r o p i o n i c a c i d and 2-propanol  i n water.  O n l y one s p a t i a l d i m e n s i o n was e n c o d e d , w i t h a  frequency  encoding gradient during a c q u i s i t i o n .  d i m e n s i o n was  The o t h e r  J - e n c o d e d . The e x p e r i m e n t was f o u n d t o be i n a d e q u a t e . T 's  together  2  with the r e l a t i v e l y  proton-proton obtainable  coupling constants  Short  s m a l l s i z e s o f most limited  the r e s o l u t i o n  i n F 1 . The n e c e s s i t y of u s i n g t h e a b s o l u t e  mode o f d i s p l a y due t o p h a s e d i s t o r t i o n s w h i c h made phase c o r r e c t i o n i m p o s s i b l e , a l s o h e l p e d to separate  out the d i f f e r e n t  value automatic  t o make i t u n f e a s i b l e  c o n s t i t u e n t s (by t a k i n g  slices  t h r o u g h t h e F1 d i m e n s i o n o f t h e i m a g e ) . T h i s p r o b l e m may be exacerbated  by t h e l a r g e number o f m u l t i p l e t s a s s o c i a t e d  many compounds w h i c h may l e a d t o s i g n i f i c a n t  with  overlapping of  p e a k s i n t h e F1 d i m e n s i o n . A p h a n t o m c o n s i s t i n g o f a row o f s i x v i a l s adenosine triphosphate constructed, x-gradient.  a n d a d e n o s i n e d i p h o s p h a t e was  and a l i g n e d p a r a l l e l Observing  encoding gradient  3 1  t o the d i r e c t i o n of the  P , and again  using only a  t h e e x p e r i m e n t was  be  than t h e i r proton  frequency  repeated.  Phosphorus-phosphorus c o u p l i n g constants larger  containing  counterparts.  are considerably  Consequently they  could  e x p e c t e d t o be b e t t e r r e s o l v e d . As o n l y ATP a n d ADP o f  those  p h o s p h o r u s compounds f o u n d in  singlets,  vivo  are other  than  t h e J - r e s o l v e d d i m e n s i o n o f t h e e x p e r i m e n t may be  e x p e c t e d t o be l e s s s u s c e p t i b l e t o peak o v e r l a p . The r e s u l t i n g image i s g i v e n  i n Figure  3.13. U n f o r t u n a t e l y  t h e T ' s o f ADP 2  120  F2  Cx+6)  F i g u r e 3.13. P h o m o n u c l e a r J - r e s o l v e d image o f a phantom c o n s i s t i n g o f a row o f 6 e q u a l l y s p a c e d v i a l s p a r a l l e l t o t h e d i r e c t i o n o f t h e x - g r a d i e n t c o n t a i n i n g a l t e r n a t l y ATP a n d ADP, 0.5 m o l a r i n H 0 . D i a m e t e r o f v i a l s 6 mm, d i s t a n c e b e t w e e n c e n t r e s o f a d j a c a n t v i a l s 7mm. O n l y a f r e q u e n c y e n c o d i n g g r a d i e n t , G , was u s e d . I n f o r m a t i o n e n c o d e d i n image d i m e n s i o n s : F 1 = J , F2=x+5. G =0.27 Gem" , At!=20 msec, 64 blocks collected, 200 a c q u i s i t i o n s p e r b l o c k , t o t a l acquisition time=7.4 h o u r s . 3 1  2  x  1  x  121 were f o u n d t o be s h o r t , and t h i s , apodisation resulted  f u n c t i o n used  i n i t s absence  spin-spin  B. The  poor  f r o m t h e i m a g e . The  S/N  relative  of ADP  t o ATP  s e p a r a t i o n o f t h e d o u b l e t and  dimension  i s due  to the d i f f e r e n c e  two o f t h e p h o s p h o r u s  sine  i n t h e F1 d i m e n s i o n o f t h e d a t a s e t  r e l a x a t i o n t i m e of ADP  in the r e l a t i v e l y  combined w i t h the  peaks  o f ATP  s h o r t n e s s of t h e  t o ATP  i s reflected  i n F i g u r e 3.12  triplet  i n the  A  and  F2  in chemical s h i f t s  between  (20ppm) w h i c h t h e  magnitude  of t h e f r e q u e n c y e n c o d i n g g r a d i e n t u s e d was  insufficient  to  overcome. C l e a r l y , although the experiment severe l i m i t a t i o n s that a c t u a l l y significant species.  works i t s u f f e r s  i n t e r m s of t h e r e s o l u t i o n  o b t a i n a b l e , and, p a r t i c u l a r l y  from  required  and  with protons,  o v e r l a p of m u l t i p l e t s of d i f f e r e n t  chemical  I n c a s e s where i t d o e s w o r k , s u c h as p h o s p h o r u s ,  the  c h e m i c a l s h i f t s e n c o u n t e r e d a r e l a r g e enough t o make c h e m i c a l shift  resolved  imaging experiments adequate  of extreme  magnetic  experiment  would  3.6  inhomogeneity.  seem t o be  Consequently  cases this  redundant.  Experimental The  s p e c t r o m e t e r u s e d was  described previously The for  field  i n a l l but  in section  t h a t b a s e d upon a 1.98  T magnet  2.9.  s o f t w a r e used t o generate the i n c r e m e n t a l g r a d i e n t s  the zero-quantum  f o u n d t o be  coherence  resolved  imaging experiment  i n a d e q u a t e f o r t h e b r o a d band  decoupled  was  1 22 zero-quantum coherence r e s o l v e d imaging n o t a l l o w one t o c h o o s e t h e i n i t i a l gradient. This be  acquired  value, had  Consequently,  the incremental  repeating  left  itself,  value of the  incremented  f o r t h i s experiment as i t has t o  i n s e t s o f 32 b l o c k s  spectrometer. restarted  i s essential  experiment as i t d i d  ( s e e s e c t i o n 2.9) on t h i s  every  time  gradient  the experiment i s  s t a r t e d a t t h e same  i n s t e a d o f c a r r y i n g on f r o m where i t  o f f a t t h e end o f t h e p r e v i o u s  s e t o f 32 b l o c k s .  p r o b l e m was o v e r c o m e by c o n s t r u c t i n g an i n c r e m e n t a l w i t h a time two  d e l a y of c o n s t a n t  l e n g t h which i t s e l f  d e l a y s . One was d e c r e m e n t a l ,  were c h a n g e d f r o m b l o c k keeping  the o v e r a l l  This  gradient  c o n s i s t e d of  a n d one was i n c r e m e n t a l .  Both  t o b l o c k by t h e same amount, h e n c e  time  o f t h e two c o n s t a n t .  During the  i n c r e m e n t a l d e l a y a p o s i t i v e g r a d i e n t was s w i t c h e d during the decremental delay  on, and  t h e same g r a d i e n t was i n v e r t e d ,  t h o u g h i t s m a g n i t u d e was k e p t  constant.  e f f e c t a s u s i n g an i n c r e m e n t a l "increment  initial  T h i s h a s t h e same  gradient, producing  an  e q u i v a l e n t " d e p e n d e n t upon t h e m a g n i t u d e o f t h e  g r a d i e n t a n d t h e s i z e o f t h e i n c r e m e n t / d e c r e m e n t o f t h e two d e l a y s u s e d . The d e l a y s effect  the incremental  evolution  time  consequently  u s e d were t h e same a s t h o s e  and d e c r e m e n t a l d e l a y s w i t h i n t h e  t ^ of t h e experiment  ( s e c t i o n 2.9) a n d  r e q u i r e d no a d d i t i o n a l m a n i p u l a t i o n  b e t w e e n s e t s o f 32 b l o c k s t o e n s u r e  continuity.  References 1.  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S h a k a , A . J . , and Freeman,  R., J . Magn. R e s o n .  ( 1 9 8 4 ) , 59,  169 2 1 . T y c k o , R., and P i n e s , A., J . Magn. R e s o n . 22. S h a k a , A . J . , and Freeman,  ( 1 9 8 4 ) , 60, 156  R. , J . Magn. R e s o n .  ( 1 9 8 5 ) , 6_2,  340 23. G o r d a n , R., H a n l e y , P., Shaw, D., G a d d i a n , D., G.K.,  Radda,  S t y l e s , P., B o r e , P., a n d Chan, L., N a t u r e , ( 1 9 8 0 ) ,  287, 736 24. H i n s h a w ,  W.S.,  25. G a r r o w a y ,  J . A p p l . Phys.  ( 1 9 7 6 ) , 47, 3709  A.N., G r a n n e l l , P.K., and M a n s f i e l d , P., J .  P h y s . C: ( 1 9 7 4 ) , 7, L457 26. S u t h e r l a n d , R . J . , a n d H u t c h i s o n , J.M.S., J . P h y s . E. ( 1978) , JM, 79 27. M a u d s l e y , A.A., H i l a l , Reson.  S.K., a n d P e r m a r , W.H.,  J . Magn.  ( 1 9 8 3 ) , 5J_, 147  28. Wokaun, A., and E r n s t , R.R., Chem. P h y s . L e t t .  ( 1 9 7 7 ) , 5_2,  407 29. B r a u n s c h w e i l e r , L., B o d e n h a u s e n ,  G., a n d E r n s t ,  R.R.,  M o l e c . P h y s . ( 1 9 8 3 ) , 4 8 , 535 30. M u l l e r , L., Kumar, A., a n d E r n s t , R.R., J . Chem. P h y s . ( 1 9 7 5 ) , 6 3 , 5496 3 1 . Aue, W.P.,  K a r h a n , J . , a n d E r n s t , R.R., J . Chem. P h y s .  ( 1 9 7 6 ) , 64, 4226  126  CHAPTER I V CONCLUSION  1 27 Conclusion At  the  already and  s t a r t of t h e s e  studies  (September  available  that  t o o l s . For  example, the  initial  use  of a  180°  motivation  f i e l d s of  rather  1 part  radiofrequency  The  of t h e s e  and  first  which i s u s u a l l y  group of e x p e r i m e n t s  was  d e m o n s t r a t e d u n d e r c o n d i t i o n s of  information. their  necessary,  techniques  a d a p t e d f o r use  I n a d d i t i o n , a new  e x p e r i m e n t was  10  5  used  To  to the  it's components. magnetic  This  field usefull  t o o v e r l a p more t h a n solve t h i s  were e v a l u a t e d i n an  in  identifying  low  Zero-quantum s p e c t r a tend  editing  information  used).  s p e c t r a c o n t a i n no  single-quantum counterparts.  existing  by  z e r o - q u a n t u m c o h e r e n c e s of  h o m o g e n e i t y where c o n v e n t i o n a l  methods  ( s e c t i o n s 2.1-2.3) soon  t h e c o m p o n e n t s of a m i x t u r e  characteristic  magnetic  other  (1 p a r t  d e m o n s t r a t e d t h a t z e r o - q u a n t u m s p e c t r a c o u l d be identify  by  couplings.  l i m i t e d homogeneity 9  pulse  s t u d i e s summarized i n t h i s  the p o t e n t i a l  i n 10  was  conceptual  t h e measurement of c h e m i c a l l y u s e f u l  in magnetic than  of t h e  field  of s p i n p h y s i c s  the phase d i s p e r s i o n i n t r o d u c e d  to explore  facilitate  measured  powerful  i n h o m o g e n e i t y , o r t o remove s c a l a r  t h e s i s was to  legacy  included several extremely  to refocus  The  was  l i n e w i d t h s were i n d e p e n d e n t of m a g n e t i c  inhomogeneity. Furthermore, a r i c h  field  it  known t h a t z e r o - q u a n t u m c o h e r e n c e s c o u l d be  that t h e i r  either  1984)  and,  problem where  inhomogeneous m a g n e t i c  field.  developed to broad-band  decouple zero-quantum s p e c t r a ( s e c t i o n 2.4).  This  experiment  128 was  found t o g r e a t l y  r e d u c e t h e p r o b l e m o f peak o v e r l a p ,  t o have a d d i t i o n a l e d i t i n g  and  possibilities.  A u s e f u l e x t e n s i o n o f t h i s t e c h n i q u e w o u l d be t o use broad-band  decoupling i n multiple-quantum coherence  connectivity fields  e x p e r i m e n t s p e r f o r m e d i n homogeneous m a g n e t i c  t o improve the r e s o l u t i o n of peaks.  A l t h o u g h zero-quantum "signature"  recognition  s p e c t r a c a n r e a d i l y be u s e d f o r  they are of l i t t l e  unknown compounds. T h i s i s l a r g e l y b e c a u s e they present chemical s h i f t T h e r e f o r e a new  of t h e way  and s c a l a r c o u p l i n g  e x p e r i m e n t was  which the c o n v e n t i o n a l  use f o r i d e n t i f y i n g  information.  designed (section  2.5-6) f r o m  s i n g l e - q u a n t u m s p e c t r u m c a n be  r e c o n s t r u c t e d . S i n g l e - q u a n t u m s p e c t r a a r e much more interpretable  i n which  i n t h i s c o n t e x t than t h e i r  largely  readily  zero-quantum  counterparts. A c o m b i n a t i o n of c o n v e n t i o n a l zero-quantum broad-band  decoupled zero-quantum  purpose  and  s p e c t r a have been shown t o  be p o w e r f u l t o o l s f o r a n a l y s i n g c o m p l e x For zero-quantum  spectra  mixtures(sect ion  2.8).  s p e c t r a t o become w i d e l y u s e d f o r t h i s  i t w o u l d be n e c e s s a r y t o a s s e m b l e a c a t a l o g u e o f  s p e c t r a o b t a i n e d under a s e t o f s t a n d a r d c o n d i t i o n s f o r t h o s e compounds w h i c h a r e o f Chemical s h i f t  interest.  resolved  s u s c e p t i b l e t o magnetic  field  imaging experiments are inhomogeneity. Three  e x p e r i m e n t s were d e v e l o p e d t o t r y and overcome  this  fatally  new  1 29 p r o b l e m ( s e c t i o n s 3.3-3.5).  A zero-quantum  imaging experiment, a broad-band coherence  resolved  coherence  decoupled  zero-quantum  imaging e x p e r i m e n t , and a J - r e s o l v e d  imaging experiment. Although the l a t t e r use t h e e x p e r i m e n t s u t i l i z i n g  p r o v e d t o be o f  zero-quantum  coherence  demonstrated  t o be e f f e c t i v e . The l e n g t h o f t h e s e  makes f u t u r e  in  short s p i n - s p i n It future  vivo  relaxation  i s too early  little  were  experiments  a p p l i c a t i o n s o f them u n l i k e l y , g i v e n t h e times encountered  therein.  t o p r o v i d e a mature overview of t h e  i m p l i c a t i o n s of t h e s e s t u d i e s , b o t h s p e c t r o s c o p i c and  i m a g i n g . However, s e v e r a l p o i n t s a r e c l e a r . form t h e d a t a a c q u i s i t i o n m e a s u r e m e n t s t o be a p p l i e d  important c r i t e r i o n . emphasis  t o s t u d i e s of c l i n i c a l  I t i s towards  present  i s a less  these areas t h a t t h e next i t i sconceivable  find application  o r g a n i c products produced  problems.  f o r which time  s h o u l d be d i r e c t e d . F o r e x a m p l e ,  that these procedures w i l l  In t h e i r  times are too long f o r these  H o w e v e r , t h e r e a r e many o t h e r s y s t e m s  the  resolved  i n t h e mapping of  by b i o - r e a c t o r s .  130  APPENDIX I PRODUCT OPERATOR EVOLUTION  131 A1.1 I n t r o d u c t i o n This  t o the E v o l u t i o n  of Product  a p p e n d i x c o n s i s t s of a d i s c u s s i o n of t h e t i m e  evolution  of product o p e r a t o r s  w h i c h i s a summary o f t h e  d e f i n i t i v e p u b l i c a t i o n on t h e s u b j e c t thesis  i s strongly  here w i l l strong  Operators  recommended t o r e a d  be c o n f i n e d  coupling  additional  which t h e reader of t h i s [ 1 ] . The  discussion  t o weakly coupled spin systems,  complicates  the s i t u a t i o n without  since  providing  i n s i g h t i n t o an e x p e r i m e n t . The e v o l u t i o n o f t h e  density matrix  c a u s e d by t h e H a m i l t o n i a n  c a n be  abbreviated  thus: o(t) 1 1 H  r  ^ a(t+r,) 2 2 H  If a f t e r the time i n t e r v a l frequency pulse  indicates that  operator  such as t , there operator and o ( t  1 +  radio  o(t^_) describes )  the  the system a f t e r the  the expression  i n d i c a t i n g that  p a r t i a l density matrix  of t h e d e n s i t y  the expression  operator  unperturbed weakly coupled Hamiltonian  Pk kz (I  ) +  W kl J  such  c o n s i s t s of the  o f a s p i n d e n o t e d A.  The e v o l u t i o n o f t h e d e n s i t y  written  is a  i s i n c o m p l e t e , and t h e a d d i t i o n of a s u b s c r i p t  as A t o g i v e  H=  (A1.1)  2  the density  system p r i o r t o the p u l s e , pulse,  ^ a(t+T,+T )  r  < 2 I  kz lz I  under t h e  i s given  by:  )  i n terms of p r o d u c t o p e r a t o r s .  ( A U 2 )  The c h e m i c a l  f r e q u e n c i e s , fi, c o r r e s p o n d t o r o t a t i n g frame  shift  frequencies.  132 Positive  rotations are defined  i n t h e r i g h t hand s e n s e ,  positive  r o t a t i o n about the z - a x i s  will  lead  i.e. a  f r o m x t o y t o -x  to -y. S i n c e a l l t e r m s i n e q u a t i o n A1.2 commute, t h e e v o l u t i o n c a u s e d by t h e i n d i v i d u a l t e r m s may be computed s e p a r a t e l y i n arbitrary  order,  0,7-1. a  1  symbolically: Q~TI~„  1z^  2  Zz^  .... ^ n ^ l z ^ z ,  ^ ^ i z ^ z , ,  A1.2 C h e m i c a l S h i f t The I  l  n  k  fl  T l  kz  I  ; i  k kz^  k x  I  Tl  cosn T  k y  (A1.3)  Evolution  e f f e c t s o f a f r e q u e n c y s h i f t fl  t x  .... o ( t + r )  +I  R  cosn r k  k y  a  r  described  e  k  sinQ r  by (A1.4)  k  -I^sinJ^r  (A1.5)  For  a . p r o d u c t o p e r a t o r o f more t h a n one s p i n t h e p r o d u c t o f  the  e f f e c t s of e v o l u t i o n  on e a c h s p i n c o m p u t e d s e p a r a t e l y i s  taken 2I  k  x  I  l  Vilz,.  x  I  The  l x  C  O  S  f  i  l  T  +  I  iy i s  2 l ( I n  f  e f f e c t s of s c a l a r c o u p l i n g  pulses  l  k  x  c o s  +  I  k  y  s i n  V  ) (  i )  (A1.6)  T  evolution  on m u l t i - s p i n p r o d u c t o p e r a t o r s  same way.  V  and  radio-frequency  are dealt with  i n the  133 A1.3  Spin-Spin Coupling Evolution The I  k  rules for scalar coupling evolution are ^kl^kzhz,  x  I. ky  The  kl  7 r J  r 2 I  kz lz I  corresponding  magnetization 2I  k  x  I  l  >  I  k x  cosUJ  r) 2I +  k y  I  sin(7rJ  l z  i n t o in-phase  k y  I,  ffJ  ky l z -I  k x  I  l z  cosUJ  k l  (A1.9)  T2I  I  >  sin(irJ  K L  21.  I , COS(7TJ,,T)  ky l z  kl  T)  (Al .10)  Pulse Evolution  e f f e c t o f a r a d i o - f r e q u e n c y p u l s e o f f l i p a n g l e /3  a b o u t t h e x - a x i s f o r one s i n g l e - s p i n o p e r a t o r I  ^ kx  (A1.11)  I. ^ k x I , cos/3 +1. sin/3 ky > ky ^ kz  (A1.12)  z  3  I cos|3  i s g i v e n by  -I sin/3  X  k  kz  k y  X  K  and  (A1.8)  r)  k l  A1.4 R a d i o - F r e q u e n c y The  (A1.7)  magnetization are 2I  kl kz lz.  k x  r)  r u l e s f o r the e v o l u t i o n of a n t i p h a s e  +I sin(7rJ r)  21.  k l  I. c o s d r J . .. T) -21. I . s i n ( j r J . , T ) ky kl kx l z kl  ^ " k z h z ,  2  k l  about the y - a x i s  134 I  For  k  I cos/3 - I  x  k x  sin^  k z  ( A L U )  o p e r a t o r s o f more t h a n one s p i n  calculated  s e p a r a t e l y and t h e p r o d u c t of t h e r e s u l t s t a k e n .  Effectively  a summation o f t h e t r a n s f o r m a t i o n o v e r a l l s p i n s  a f f e c t e d by t h e p u l s e  c(t_)  P I  kv  3  ^ l v  A1 .5 Z e r o - q u a n t u m The and 2 I  k y  i scarried out,  ?  coherence  evolution  2  (  2  I  k  x  I  l  x  ,  21  k y  I  l y  ,  2I  k  I  x  l  y  each c o n t a i n both z e r o - and double-quantum  x  '/^^kx^x  /  (A1.15)  +  two-spin product operator 2 I I^  i.e.  ^mv^... o ( t )  coherence. Pure zero-quantum  1  t h e e f f e c t s on e a c h may be  +2I  kyV  =  - kx ly 2I  ky lx I  I  )  and p u r e d o u b l e - q u a n t u m  1  /  2  (  2  I  kx lx  1  /  2  (  2  I  kx ly  ky lx  +2I  I  Z  =  Q  {  C  Z  x  }  Q  C  )  =  =  {  D  Q  C  }  {  D  Q  C  }  y  The p r e c e s s i o n o f z e r o - q u a n t u m may be d e s c r i b e d  }  i s g i v e n by  ( A 1  y  <  x  ( A 1  (  A  1 6 )  A  K  1  7  )  K  '  1  l 8 )  9  )  c o h e r e n c e due t o c h e m i c a l s h i f t  i n a manner a n a l o g o u s t o s i n g l e - q u a n t u m  coherence except that  -  c o h e r e n c e by  ""kyV  I  I  {  coherence  i tprecesses at the difference i n  1 35 frequencies  o f i t s two s p i n s ,  f o r example, i n analogy t o  e q u a t i o n A1.4,  {ZQC}  ( f l  k kz X  + 1 1Z Q  I  ) t  .  {ZQC} c o s ( f l , ^  j£  +{ZQC} sin(n y  k  X  coupling  not a c t i v e w i t h i n  eff  of s p i n s  exhibit scalar couplings  that  A m  P=AM = £ A m  with  c o h e r e n c e . The e f f e c t i v e  k may be g i v e n  coherence  by  =£ k km J  where t h e o r d e r ,  and  (A1.20)  1  c o n s t a n t o f a s p i n m t o a m u l t i p l e quantum  consisting  J  X  -0 )T  Multiple-quantum coherences only those spins  -fl,)r K  (  P, o f t h e c o h e r e n c e  i s given  A  1  '  2  1  )  by (A1.22)  k  scalar coupling  evolution,  like  chemical s h i f t  evolution,  i s analogous t o single-quantum coherence, f o r example, i n a n a l o g y t o e q u a t i o n A1.7,  {zqc}  ^  7 r J  +  2I  km m z  r 2 I  kz mz. I  {ZQC} COSTTJ  {ZQC} sin7rJ y  e f f  f  f  r  r  (A1.23)  References 1.  S o r e n s e n , O.W., and  Ernst,  R.R.,  E i c h , G.W.,  L e v i t t , M.H.,  Progr. Nucl.  Magn. R e s o n .  Bodenhausen, Spectrosc.  G.,  1 36 (1981),  14, 137  1 37  APPENDIX I I ZERO-QUANTUM SPECTRA OF AMINO ACIDS  1 38 Appendix I I T h i s appendix c o n s i s t s of a c a t a l o g u e  of t h e zero-quantum  c o h e r e n c e s p e c t r a o f 16 amino a c i d s o b t a i n e d three  s e t s of standard  a t 80.3 MHz  p a r a m e t e r s . Where d i f f e r e n t  with  s e t s of  p a r a m e t e r s p r o d u c e d u p l i c a t e r e s u l t s o n l y one o f t h e s p e c t r a i s g i v e n . I f no c o h e r e n c e s were v i s i b l e i n a s p e c t r u m this  t o o i s not given. S o l u t i o n s o f t h e a m i n o a c i d s i n D 0 were u s e d  with  2  c o n c e n t r a t i o n s of e i t h e r solubility,  0.1 m o l a r o r t h e i r maximum  w h i c h e v e r was l e s s . The t h r e e s e t s o f p a r a m e t e r s  used d i f f e r o n l y  i n the values  of b o t h  time  of these  msec. A l l o t h e r  given  t o T a n d T'. The v a l u e s  i n t e r v a l s were e q u a l  v a l u e s chosen f o r T and T  1  w e r e : 60 msec,  i n e a c h c a s e . The 100 msec, a n d 140  p a r a m e t e r s were t h e same: A t ^ l . 6 7  blocks collected, time  then  4 acquisitions  14-17 m i n u t e s . An e x c e p t i o n  per block, t o t a l  msec, 256 acquisition  was made f o r L - t r y p t o p h a n f o r  w h i c h , a s i t i s o n l y s p a r i n g l y s o l u b l e i n w a t e r , 32 acquisitions  p e r b l o c k were  collected.  139  300 F i g u r e A 2 . 1 . Z e r o - q u a n t u m s p e c t r a o f L - g l u t a m i n e : A. msec, B. T,T'=100 msec, C. T,T'=140 msec.  T,T'=60  T—i—i—i—i—i—i—i—i—I—r T—I—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—r 300  200  100  0.0  -100  -200  Hz  F i g u r e A2.2 Z e r o - q u a n t u m s p e c t r a o f L - m e t h i o n i n e : A. T,T'=60 msec, B. T,T'=100 msec, C. T,T'=140 msec.  1 40 A  I—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—| 300 200 100 0.0 -100 -200 Hz F i g u r e A 2 . 4 . Z e r o - q u a n t u m s p e c t r a o f L - a s p a r a g i n e : A. T , T ' = 6 0 msec, B. T , T * = 1 0 0 msec, C. r , r ' = 1 4 0 msec.  A  I i i i i—| i 300 200  i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—| 100 0.0 -100 -200 Hz  F i g u r e A2.6. Z e r o - q u a n t u m s p e c t r a o f L - l e u c i n e : A. msec, B. T , T ' = 1 0 0 msec, C. r , r ' = 1 4 0 msec.  T,T'=60  142 A  I—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i 300  200  100  0.0  i—i  |  i  i  i  -100  F i g u r e A2.7. Zero-quantum s p e c t r a of L - t h r e o n i n e : msec, B. T , T ' = 1 0 0 msec, C. T , T ' = 1 4 0 msec.  i  |  -200  i  i  i  i | Hz  A. T,T'=60  A  300  200  100  0.0  -100  -200  Hz  F i g u r e A 2 . 8 . Z e r o - q u a n t u m s p e c t r a o f L - i s o l e u c i n e : A. T,T'=60 msec, B. T , T * = 1 0 0 msec, C. T , T ' = 1 4 0 msec.  143  I — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — n — i — | — i — i — i — i — | — i — i — i — i — |  300  200  100  0.0  -100  -200  Hz  F i g u r e A2.9. Z e r o - q u a n t u m s p e c t r u m o f L - v a l i n e f o r T , T ' = 6 0 msec. (The same f o r T , T ' = 1 0 0 msec, no c o h e r e n c e s o b s e r v e d f o r T , T * = 1 4 0 msec)  B  " i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — i — I — I — i — i — i — I — i — i — i — r  200  300  100  0.0  •100  -200  Hz  F i g u r e A 2 . 1 0 . Z e r o - q u a n t u m s p e c t r a f o r L - p r o l i n e : A. T , T ' = 6 0 msec, B. T , T ' = 1 4 0 msec. (No c o h e r e n c e s o b s e r v e d f o r T , T ' = 1 0 0 msec)  " i — i — i — i — I — i — i — i — r  ~t—i—r  300  200  100  (  o!o  ~ i — i — i — i — | — i — i — i — i — | — i — i — i — i — |  -100  -200  Hz  F i g u r e A2.11. Zero-quantum spectrum o f L - c y s t e i n e f o r T , T ' = 1 0 0 msec. ( F o r T , T ' = 6 0 msec a n d 140 msec s p e c t r a t h e same.)  144  | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i — i — i — i — | — i  300  200  100  0.0  i  i  -100  i  |  i  i  '  '  -200  |  Hz  F i g u r e A 2 . 1 2 . Z e r o - q u a n t u m s p e c t r a o f L - t r y p t o p h a n : A. T , T ' = 6 0 msec, B. T , T ' = l 0 0 m s e c , C. T , T ' = 1 4 0 msec.  |—i—i—i—i—|—i—i—i—i—|—r—i—i—i—|—i—i—i—i—|  300  200  100  0.0  i  -100  i  i  i  f ! -  -200  1  1  |  1  Hz  F i g u r e A2.13. Zero-quantum s p e c t r a o f L - s e r i n e : A. T , T ' = 6 0 msec, B. T , T ' = 1 4 0 msec. ( F o r T , T ' = 1 0 0 msec s p e c t r u m t h e same a s p a r t B.)  145 A  I—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—j 300 200 100 0.0 -100 -200 Hz F i g u r e A 2 . 1 4 . Z e r o - q u a n t u m s p e c t r a o f L - a r g i n i n e : A. T , T ' = 1 0 0 msec, B. T , T ' = 1 4 0 msec. ( F o r T , T ' = 6 0 msec no c o h e r e n c e s i n spectrum.)  | i i i i |—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—| 300 200 100 0.0 -100 -200 Hz F i g u r e A2.15. Zero-quantum spectrum o f L - a l a n i n e f o r TT'=100 msec. ( F o r T , T ' = 6 0 msec s p e c t r u m t h e same, f o r T , T ' = 1 4 0 m s e c no coherences i n spectrum.)  |—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—|—i—i—i—i—| 300 200 100 0.0 -100 -200 Hz F i g u r e A2.16. Zero-quantum spectrum o f L - a s p a r t i c a c i d f o r T , T ' = 100 msec. ( F o r T , T ' = 60 msec a n d 140 msec s p e c t r a t h e same.)  

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