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Infrared absorption spectra of polyatomic molecules Mitchner, Morton 1948

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Co/o- ^ . I O E A R I D A B S O R P T I O N S P E C T R A O F P O L Y A T O M I C M O L E C U L E S by MORTON MITCHNER A Thesis Submitted i n Partial Fulfilment of The Requirements for the Degree of M A S T E R O F A R T S in the Department OF P H Y S I C S THE UNIVERSITY OF BRITISH COLUMBIA Ap r i l , 1948. ABSTRACT A successful method of dehumidification was designed and used to maintain the relative humidity in a specially constructed room at less than 40$ and at a temperature of 20*C. A wavelength drive and control system were designed and built to improve and simplify the operation of a Perkin-Elmer infrared spectrometer and of the recording accessories. The spectrometer was then calibrated and used to examine the infrared absorption spectrum of gaseous carbon disulphide. The wave numbers of six absorption bands of gaseous CS a were determined. The wave number value of - i . 1535 cm. which was determined for the normal frequency ^3, was found to agree with a new recently published result and a l l previously reported bands were observed. No evidence was found which might possibly lead to any inter-pretation other than that the structure of the carbon disulphide molecule is linear and symmetrical. ACKNOWLEDGMENT. The author wishes to express his appreciation to Dr. A. M. Crooker under whose able supervision this research was carried on. In addition, the author wishes to acknowledge the contributions of his colleagues:-Mr. T. H. Edwards. Mr. E. de L. Rogers. and the technical assistance supplied by the following members of the Physics Department Shop:-Mr. A. J. Fraser. Mr. E. M. Price. Mr. A. W. Pye. TABLE OF CONTENTS. Page I. INTRODUCTION 1. The application of infrared spectroscopy to the study of the molecular structure of poly-atomic moleoules. 1 2. The present state of information regarding the molecule CSj. 3 3. The object of the research undertaken i n this thesis. — 4 II. THEORY 1. Importance of the concept of the normal vibrations i n relation to polyatomic molecules. (a) Classical theory of the normal vibrations— 5 (b) Quantum mechanical calculation of the vibrational energy levels, 7 2. Determination of the normal vibrations and of the force constants for linear symmetrical (a) Solution of the secular equation. 9 (b) Assumption of speoial potential functions^—12 (o) Isotope effect. 15 3. Limitations of the concept of normal vibrations. (a) Anharmoniclty. 17 (b) Fermi resonance. — 19 Page 4. Infrared absorption speotra of polyatomic molecules. (a) Point groups and symmetry species, 20 (b) Formulation of the general selection ruler 21 (c) Selection rules for linear symmetrical XYj. . 22 III. APPARATUS. 1. The infrared spectrometer and recording accessories. 24 (a) The spectrometer. 25 (b) The amplifier. 26 (c) The recorder. 28 (d) The wavelength drive. 29 (e) The control system. •- 30 2. The humidity and temperature control-room.— 32 (a) Design of the room. 32 (b) Method of dehumidification. 33 (o) Humidity and temperature controls. 36 (d) Effectiveness of the method. 38 IV. EXPERIMENTAL 1. Calibration of the Spectrometer. ;• 39 2. Control of the temperature and pressure of the CS ? sample. 41 V. RESULTS Page 1. Experimental results. (a) Observed absorption bands of gaseous CS ^ . 45 (b) Calculation of the force constants for gaseous CSj, . 48 (o) Calculation of the isotope effect on the normal frequency,Us, of gaseous 03t. 49 2. Discussion of results. 50 VT. CONCLUSIONS — . 51 VII. BIBLIOGRAPHY 52 TABLES Page 1. Force constants of linear symmetrical XT-,. 15 2. Calibration points for the NaCl prism. 42 3. Observed and calculated infrared absorption bands of CS^. 46 ILLUSTRATIONS p a g ( 1. Displacement coordinates of linear; symmetrical XZZ. 11 2. Normal vibrations of linear symmetrical XY^. 12 3. Block diagram of the spectrometer and the recording system. 25 4. The Perkin-Slmer infrared spectrometer Model 120. — 26 5. The General Motors amplifier. 27 6. The Brown recorder. 28 7. The wavelength drive i n position relative to the spectrometer. 29 8. The humidity and temperature control-room 33 9. Top view of the dehumidifier. . 34 10 Photograph of the dehumidif ier. 35 IL The General Electric condenser unit. 36 12. The thermostat and humidistat. 37 13. The absorption c e l l . 41 14. The absorption c e l l i n position relative to the spectrometer. 43 PLATES To face page I. View of the general experimental arrangement of the apparatus. — 24 II. View of the general experimental arrangement of the apparatus. 24 III. The Perkin-Elmer infrared spectro-meter Model 12 A. 25 IV. The control system. 30 V. The humidity and temperature controls. 36 VI. NH3 calibration chart. 40 VII. CO,, and Kz0 vapour calibration chart. 40 VIII Calibration curve. — 40 IX. Calibration curve. 40 X. Calibration curve. — - 40 XI. Absorption c e l l with temperature and pressure controls. 41 XII. Structure of the i-^band. — — 4 5 XIII The difference band i ^ - ^ i . 45 XIV The combination band -v, 45 XV. The combination band2^ + 2 J^ . 45 XVI. The combination bands U3+l ux and v^l^i*"^ 45 INFRARED ABSORPTION SPECTRA OF POLYATOMIC MOLECULES I. INTRODUCTION. 1. The Application of Infrared Spectroscopy  to the,Study of the Structure of  Polyatomic Molecules. A molecule may he considered as an aggregate of atomic nuclei imbedded i n a distribution of electrons. Just as in an atom, the electron cloud associated with the molecule may be regarded as existing i n any one of various electronic  states. Transitions between these states, when accompanied by a change in the electric moment of the system, give rise to either absorption or emission lines whose frequencies l i e in the visible or the ultra-violet regions of the spectrum. In a given electronic state, the molecule may be regarded as an assembly of atoms existing i n a potential f i e l d , each atom vibrating about i t s position of stable equilibrium. Thus, corresponding to each electronic state, there w i l l exist various vibrational states. Transitions between different vibrational states for a fixed electronic state will produce absorption or emission lines whose frequencies w i l l l i e in the near infrared region (><30^ c). In additinn to the electronic and vibrational states, a molecule can exist in any one' of various rotational states, and the frequency associated with a change in rotational state only, l i e s i n (2) the f a r i n f r a r e d r e g i o n tX>30yu). Simultaneous changes i n the v i b r a t i o n a l and r o t a t i o n a l s t a t e s produces a " f i n e - s t r u c t u r e " i n t he pure v i b r a t i o n a l spectrum and s i m i l a r l y f o r s i m u l -taneous changes i n the e l e c t r o n i c , v i b r a t i o n a l and r o t a t i o n a l s t a t e s . I n what f o l l o w s , we s h a l l be concerned almost e n t i r e l y with changes i n the v i b r a t i o n a l s t a t e s o f a p o l y -atomio molecule o n l y , and the i n f o r m a t i o n o b t a i n a b l e from the a n a l y s i s o f the a s s o c i a t e d near i n f r a r e d a b s o r p t i o n s p e c t r a . Two g a n e r a l types of i n f o r m a t i o n about a molecule can be obtained from an i n v e s t i g a t i o n of the pure v i b r a t i o n spectrum b e l o n g i n g t o the moleoule. F i r s t , from the measured f r e q u e n c i e s of the observed fundamental a b s o r p t i o n bands, i t Is p o s s i b l e to c a l c u l a t e the numerical values of the co n s t a n t s appearing i n t h e v a r i o u s proposed p o t e n t i a l f u n c t i o n s . Knowing the numerical v a l u e s o f the p o t e n t i a l c o n s t a n t s , t h e r e t h e n e x i s t means of ohecking the v a l i d i t y of the f o r m of the proposed p o t e n t i a l f u n c t i o n so t h a t we can a r r i v e a t f a i r l y d e f i n i t e c o n c l u s i o n s r e g a r d i n g the type o f p o t e n t i a l f u n c t i o n e x i s t i n g i n m o l e c u l e s . Secondly, by means of c o r r e l a t i n g the a c t i v i t y o r n o n - a c t i v i t y o f fundamental, overtone, and combination f r e q u e n c i e s a p p e a r i n g i n both i n f r a -red and Raman s p e c t r a w i t h t h e o r e t i c a l l y proposed s e l e c t i o n r u l e s , i t i s p o s s i b l e t o come to d e f i n i t e c o n c l u s i o n s r e -g a r d i n g the symmetry s t r u o t u r e o f the molecule. However, i n order t o proceed beyond t h i s p o i n t and t o a c t u a l l y c a l c u l a t e i n t e r a t o m i o d i s t a n o e s , i t i s necessary to broaden our (3) i n v e s t i g a t i o n t o i n c l u d e e i t h e r the r o t a t i o n - v i b r a t i o n f i n e s t r u c t u r e or the pure r o t a t i o n spectrum of the m o l e c u l e . 2. The Present S t a t e o f I n f o r m a t i o n  Regarding the Molecule CSg . C o b l e n t z (8) f i r s t i n v e s t i g a t e d the i n f r a r e d ab-s o r p t i o n spectrum of l i q u i d OS2. The I n f r a r e d a b s o r p t i o n spectrum o f gaseous CSg was p r o b a b l y f i r s t I n v e s t i g a t e d by B a i l e y and C a s s l e (3) about 1931. U s i n g a p r i s m spectrometer, B a i l e y and C a s s i e observed f o u r i n f r a r e d a b s o r p t i o n bands, th r e e of which they were ab l e t o r e s o l v e i n t o P and R branches. I n a d d i t i o n , they deduced the fundamental f r e -quencies, determined CSg to be l i n e a r , and c a l c u l a t e d the f o r c e constants as a j j ^ 7.55xl0 5 dynes/cm. 5 a 1 2 = 0.67x10 dynes/cm. a 3 3=0.24 *10 dynes/cm. U s i n g a g r a t i n g , Dennison and Wright (11) extended the work of B a i l e y and C a s s i e by d e t e r m i n i n g 4 i n gaseous CSg and a l s o confirmed the i d e n t i f i c a t i o n of the fundamental f r e q u e n c i e s . The work of Sanderson (27) on the f i n e - s t r u c t u r e of the 4.6^. band and the work of Lieberman (20) on the equal s p a c i n g o f f i n e - s t r u c t u r e r o t a t i o n l i n e s f o r e l e c t r o n i c bands have added f u r t h e r p roof o f the l i n e a r symmetrical c h a r a c t e r of CSg. The Raman spectrum of CSg has been i n v e s t i g a t e d by numerous (4) observers and the complementary I n f o r m a t i o n has proved i n -v a l u a b l e i n understanding and i n t e r p r e t i n g the s t r u c t u r e o f CS 2. The most r e c e n t work concerning the i n f r a r e d a b s o r p t i o n spectrum o f CSg has been a 1947 paper by P l y l e r and Humphreys (24) i n which 1. nine new a b s o r p t i o n bands have been observed, 2. a new v a l u e f o r z ^ h a s been advanced, and 3. the v a r i a t i o n of the a b s o r p t i o n f r e -quencies i n l i q u i d and gaseous CSg has been i n v e s t i g a t e d , A summary of the present s t a t e of i n f o r m a t i o n concerning the bands o f CSg i s c o n t a i n e d i n Table 3-3. The o b j e c t of the Researoh Undertaken i n t h i s T h e s i s * The o b j e c t of t h e r e s e a r o h c a r r i e d out i n t h i s t h e s i s may be d i v i d e d i n t o two p a r t s . The f i r s t p a r t of the r e s e a r o h was concerned w i t h p u t t i n g the i n f r a r e d spectrometer i n t o o p e r a t i n g c o n d i t i o n . I n order to accomplish t h i s t a s k , i t was f i r s t neoessary t o d e s i g n and b u i l d a humidity and t e m p e r a t u r e - c o n t r o l l e d room. A c o n t r o l system and wave d r i v e were then designed and c o n s t r u c t e d as a complement t o the purchased apparatus, i n order t o p r o v i d e f o r continuous automatic spectrum scanning. (5) The second p a r t o f the r e s e a r c h was concerned w i t h the c a l i b r a t i o n o f the spectrometer and the i n v e s t i g a t i o n of the i n f r a r e d a b s o r p t i o n spectrum o f CSg. I t was d e s i r e d f i r s t t o make an independent check on the r e s u l t s of P l y l e r and Humphreys (24) e s p e c i a l l y on the v a l u e o f Secondly, the h i g h degree of symmetry of the CSg molecule suggested t h a t the s e l e c t i o n r u l e s g o v e r n i n g the appearance and i n -t e n s i t y o f a b s o r p t i o n bands would be v e r y s e n s i t i v e to the c o n d i t i o n o f a s s o c i a t i o n i n whioh the molecule found i t s e l f . I t was t h e r e f o r e d e s i r e d t o i n v e s t i g a t e the change i n s t r u c t u r e o f the i n f r a r e d a b s o r p t i o n spectrum of CSg under v a r i o u s c o n d i t i o n s of temperature and pr e s s u r e w i t h a view to examining the e f f e c t o f a s s o c i a t i o n on the symmetry of the molecule. I I . ; THEORY. 1. Importance o f the Concept o f the Normal  V i b r a t i o n s i n R e l a t i o n to  Polyatomic M o l e c u l e s . (a) C l a s s i c a l Theory o f the Normal V i b r a t i o n s . C o n s i d e r a polyatomic molecule c o n s i s t i n g o f N atoms. L e t a.^,., cj J H be some s e t of 3N c o o r d i n a t e s g i v i n g the displacements o f the atoms from t h e i r e q u i l i b r i u m con-f i g u r a t i o n a t any time t . We now enquire as to the equations o f motion. (6) Assuming t h a t the amplitudes o f motion q;, are s m a l l oompared w i t h the e q u i l i b r i u m i n t e r a t o m i c d i s t a n c e s , we may-w r i t e T a q ; q T and V = i I j KiT q- q r (1) where the b i y and K;y are constants, f o r the k i n e t i c and p o t e n t i a l e n e r g i e s r e s p e c t i v e l y o f the system. S i n c e both T and V are p o s i t i v e q u a d r a t i c forms, there e x i s t s a unique l i n e a r t r a n s f o r m a t i o n which enables us t o w r i t e and V = i f j f c f c * (2) (3) where A;is a root of the secular equation Kj.-b^x KK~b»x = 0 (4) and where c C T i s p r o p o r t i o n a l t o the minor o f K-^-b^X when \s\y A p p l y i n g Lagrange's equations, we have t h a t 0 U.1,2,...,3N) (5) so t h a t where 2 4 - * * ^ (7) (7.) Under the c o n d i t i o n s of our assumption, then, equations (2) and (6) a l l o w us to i n t e r p r e t any g e n e r a l motion o f a p a r t i c u l a r atom as a s u p e r p o s i t i o n of 3N i n -dependent simple harmonic motions. The 3N p o s s i b l e v a l u e s f o r the f r e q u e n c i e s of v i b r a t i o n are c a l l e d the normal  f r e q u e n c i e s and as a r e s u l t of the i n v e r s e v t r a n s f o r m a t i o n o f (2) { i « Z ? d i T q T (8) we may designate ,f t , -, {,« as the normal c o o r d i n a t e s o f the system. When each atom o f the molecule i s v i b r a t i n g w i t h the same normal frequency, the molecule i s s a i d to be p e r -forming a normal v i b r a t i o n . I t i s evident on the b a s i s of c l a s s i c a l e l e c t r o -dynamics, that the normal f r e q u e n c i e s are the f r e q u e n c i e s that are emitted o r absorbed by a molecule* However, t h e a c t u a l importance of the s o l u t i o n s of the s e c u l a r equation w i l l become even more evident when we have shown that the normal f r e q u e n c i e s are indeed those f r e q u e n c i e s o f e m i s s i o n and a b s o r p t i o n p r e d i c t e d by quantum mechanics. (b) Quantum Mechanical C a l c u l a t i o n s of the V i b r a t i o n a l Energy L e v e l s . F o l l o w i n g the method o u t l i n e d by Herzberg [14], the Sohroedinger e q u a t i o n of a system o f N p a r t i c l e s o f c o -o r d i n a t e s (*;., , x; ) and masses v*; i s V 1 W*+ 2 (B-Y)lr s O (9) (8) Assuming V to be of the form (1) and i n t r o d u c i n g normal c o o r d i n a t e s by means o f .(2), i t may be shown [23] t h a t (9) becomes Sfe.+ -f.^"*^] t"0 (10) where the )\;are the r o o t s of the s e c u l a r equation ( 4 ) . Sin c e i t i s now p o s s i b l e t o separate v a r i a b l e s i n equ a t i o n (10) by means of equa t i o n (10) may be r e s o l v e d i n t o a sum of 3N equations w i t h E = 2 " (13) E q u a t i o n (12) i s the wave equation o f a s i n g l e simple harmonio o s c i l l a t o r of p o t e n t i a l energy &-*t'f»'and mass-owe whose c o o r d i n a t e i s the normal co o r d i n a t e ? i • Thus i n wave mechanics as i n c l a s s i c a l mechanics, the v i b r a t i o n a l motion of the molecule may be c o n s i d e r e d i n a f i r s t good a p p r o x i -mation as a s u p e r p o s i t i o n o f 3N simple harmonic motions i n the SN normal c o o r d i n a t e s . The eigenvalues o f equation (12) are the energy v a l u e s of the harmonio o s c i l l a t o r t , and are g i v e n by l i s h ^ ^ ) (Vi = o,l,2,... ) (14) where l/c = i i r ^ ^ - i s the c l a s s i c a l o s c i l l a t i o n frequency (9) of the normal v i b r a t i o n ^, and K i s the v i b r a t i o n a l quantum  number. T h e r e f o r e , the t o t a l v i b r a t i o n a l energy of the system can assume o n l y the v a l u e s B t e , hV;[K-+A (15) and the term v a l u e s are g i v e n by a _2L = 17 w»Yin-+^-,j (is) he <-•=', v 1 1 ' I n the case of doubly degenerate v i b r a t i o n s , i . e . , when two of t h e o j ' s i n (16) are the same, i t can be shown [23] t h a t i f quanta of the doubly degenerate v i b r a t i o n are e x c i t e d , the degree of degeneracy i s equal tovj+1. The degeneracy i s u s u a l l y denoted by the quantum number ± JLl , where i;» * £ , ^ - 2 ,^_4, •• •, 1 or 0 and i t i s shown t h a t t h e £i, may be i n t e r p r e t e d as i n d i c a t i n g an a n g u l a r momentum i n the v i b r a t i o n a l motion o f magnitude i t • I t i s important t o remember t h a t t h i s h i g h degeneracy e x i s t s o n l y as long as s t r i c t l y harmonio v i b r a t i o n s are assumed and t h a t anharmonicity which i s always p r e s e n t , produces a p a r t i a l s p l i t t i n g o f t h i s degeneracy. 2. D e t e r m i n a t i o n of the Normal V i b r a t i o n s  and of the Force Constants f o r  L i n e a r Symmetrical XYg. (a) S o l u t i o n of the S e c u l a r E q u a t i o n . The s o l u t i o n of the s e c u l a r e q u a t i o n (4) i s i n (10) general a v e r y t e d i o u s and slow p r o c e s s , owing t o the h i g h degree I n A, There a r e , however, s e v e r a l methods of s o l u t i o n , some e a s i e r than o t h e r s . The s o l u t i o n i n C a r t e s i a n , c o o r d i n a t e s i s s t r a i g h t -forward and u n i n s p i r e d , hut the c a l c u l a t i o n may be shortened u s i n g the methods of James and C o o l i d g e [ l 8 ] • The r e l a t i v e p o s i t i o n s of the atoms i n a moleoule are determined by 3N-6 ( o r 3ff«5 i n the case of a l i n e a r moleoule) s o - c a l l e d " i n t e r n a l " c o o r d i n a t e s . S e v e r a l c h o i c e s of i n t e r n a l c o o r d i n a t e s are p o s s i b l e [28] • The main d i f f i -c u l t y o f s o l u t i o n o f the s e c u l a r e q u a t i o n w i t h these co-o r d i n a t e s l i e s i n the d e t e r m i n a t i o n of the K i n e t i c energy. The best method of determining the normal v i b r a t i o n s i n the case o f symmetrical molecules i s the method o f symmetry c o o r d i n a t e s f i r s t i n t r o d u c e d by Howard and W i l s o n [ l o ] (see a l s o [26] and [25] ). The a p p l i c a t i o n of symmetry c o o r d i n a t e s a l l o w s an immediate f a c t o r i s a t i o n o f the s e c u l a r equation, thus p r o v i d i n g s e v e r a l p o l y n o m i a l s i n A , each o f g r e a t l y reduced degree. (11) I n the oase of the l i n e a r symmetrical XTg molecule, i t i s customary to express 3 0) C2) Y 7 10. 1. Displacement c o o r d i n a t e s i n l i n e a r symmetrical XY g r the p o t e n t i a l energy i n terms of the changes Q, and QjZ o f the two e q u i l i b r i u m i n t e r n u c l e a r d i s t a n c e s Jtt{ zi) and^ t(sj^) r e s p e c t i v e l y , and the angle o f d e v i a t i o n from a s t r a i g h t l i n e e i t h e r in1ti«xjor xx p l a n e , which we denote by and <9* r e s p e c t i v e l y . "With t h i s n o t a t i o n , the most g e n e r a l ex-p r e s s i o n f o r the p o t e n t i a l energy i n accordance w i t h our assumptions becomes t 2 and the s o l u t i o n of the s e c u l a r e quation g i v e s the f r e -quencies of the normal v i b r a t i o n s as 4 1 V - * (18) (12) Here cn i s the f o r c e constant of the X-Y bond,Q 4t i s the f o r c e constant t h a t g i v e s the i n t e r a c t i o n o f the two bonds, and i s the f o r c e constant f o r the bending of the mo l e c u l e . Having found the normal f r e q u e n c i e s , i t I s now p o s s i b l e t o determine the normal v i b r a t i o n s and these appear as i n d i c a t e d i n F i g u r e 2. Y X Y I I o © — t o 'lo. <—e ©—> <—e 1^3 FIG. 2. Normal V i b r a t i o n s o f l i n e a r symmetrical XY g. I t i s seen t h a t the frequency o f the degenerate v i b r a t i o n i>i o f the molecule depends on Qs,as was to be expected, w h i l e the f r e q u e n c i e s o f the non-degenerate v i b r a t i o n s V, and a>5 depend o n l y on q„ and <*,,.. (b) Assumption of S p e c i a l P o t e n t i a l F u n o t i o n s . E q u a t i o n s (18) as s t a t e d , express the normal f r e -quencies o f v i b r a t i o n o f the molecule i n terms of the f o r c e c o n s t a n t s . A c t u a l l y , the f o r c e c o n s t a n t s are not known i n (13) g e n e r a l , but the normal f r e q u e n c i e s are known as a r e s u l t o f experiment, so that we may use equations (18) to determine the f o r c e oonstants from the o b s e r v a t i o n o f s p e c t r a . I n -deed, t h i s d e r i v a t i o n o f the f o r c e c o n s t a n t s i s the f i r s t major a p p l i c a t i o n of the i n f r a r e d a b s o r p t i o n s p e c t r o s c o p y to the study o f the s t r u c t u r e o f polyatomic molecules* Having determined the f o r c e oonstants, the p o t e n t i a l f u n c t i o n i s , of course, a l s o determined. Knowing the valu e s of v„xtKjJZjJlt m , , and m Y , i t i s p o s s i b l e u s i n g the t h r e e equations (18) to c a l c u l a t e the three unknown f o r c e constants a„, &ltt and a, 5. I n g e n e r a l , however, f o r a g i v e n molecule, the number of f o r c e constants i s f a r i n excess of the number of normal f r e -quencies o f v i b r a t i o n , and henoe t h e r e do not e x i s t s u f f i c i e n t equations t o determine completely a l l the f o r c e constants whioh appear i n the most g e n e r a l q u a d r a t i c p o t e n t i a l f u n c t i o n . Indeed, even f o r the case of l i n e a r symmetrical XY^, having once determined the f o r c e c o n s t a n t s , there e x i s t s no means of c h e c k i n g the v a l i d i t y o f the assumption of the form of the p o t e n t i a l f u n c t i o n . One way o f overcoming t h i s d i f f i c u l t y i s t o make c e r t a i n more s p e c i f i c assumptions about the f o r c e s i n the molecule such t h a t the number of f o r c e constants t o be de-termined i s reduced. Perhaps the most obvious assumption i s the assumption o f c e n t r a l f o r c e s . T h i s assumption c o n s i s t s of the statement t h a t the f o r c e a c t i n g on a g i v e n (14) atom i n a molecule i s the r e s u l t a n t of the a t t r a c t i o n s and r e p l u s i o n s hy a l l the other atoms, and that these a t t r a c t i o n s and r e p u l s i o n s depend o n l y on the d i s t a n c e s from these other atoms and l i e i n the l i n e s c o n necting them w i t h the one c o n s i d e r e d . The mathematical e q u i v a l e n t of t h i s s t a t e -ment i s t h a t the p o t e n t i a l energy i s a p u r e l y q u a d r a t i c f u n c t i o n of the changes Q i of the d i s t a n o e s between the n u c l e i without any c r o s s - p r o d u c t s so t h a t V s r i g a u Q ; (19) A p p l i e d to the case o f l i n e a r symmetrical XY a, the assumption of c e n t r a l f o r c e s l e a d s to the f a l s e p r e d i c t i o n t h a t Ut s 0 so that the assumption of c e n t r a l f o r c e s cannot be made f o r l i n e a r molecules and one would expect i t t o be a very poor approximation f o r v e r y wide-angled t r i a t o m i o molecules. The assumption o f valence f o r c e s f i r s t made by Bjerrum [5] s t a t e s t h a t t h e r e i s a s t r o n g r e s t o r i n g f o r o e i n the l i n e o f every valence bond i f the d i s t a n c e of the two atoms bound by t h i s bond i s changed, and i n a d d i t i o n , t h a t t h e r e i s a r e s t o r i n g f o r o e ppposing a change of the angle between two va l e n c e bonds c o n n e c t i n g one atom w i t h two o t h e r s . The a p p l i c a t i o n o f the assumption o f v a l e n c e f o r c e s t o l i n e a r symmetrical XT t l e a d s t o 4 i r V • k. (20) 4T2^- i . ( U I Ks (21) (15) Wri - (i*e=x) J£L ( 2 2 ) i n whioh k , a a M , k$- a„, and a , z » 0 by comparison w i t h (18), A comparison o f the v a l u e s of as ob t a i n e d from equations (20) and (22) thus p r o v i d e s a check on the v a l i d i t y o f the assumption of valence f o r o e s . T a b l e 1 | l 4 l g i v e s the r e s u l t s of t h i s check f o r the l i n e a r molecules C0 g and C S a , as w e l l as the v a l u e s of a u , a, a , and a 5 3 as determined from ( 1 8 ) . TABLE 1. Force constants o f l i n e a r symmetrical XY 2 Molecule Obs. Normal Freqs (cm.-) from (20) from (22) 'rom 21) 'rom 18) Tom from 18) ;i8) C0» 1337 657 667 397 2349 1523 16.8 8.1 14.2 0.57 6.9 0.234 5.5 7.5 0.57 0.234 1.3 .6 x 1 0 r dy'ries/cm. I n g e n e r a l , the assumption o f valence f o r c e s has-proved t o be q u i t e s a t i s f a c t o r y i n r e p r e s e n t i n g the observed funda-mental f r e q u e n c i e s . (o) I s o t o p e E f f e c t , The i n v e s t i g a t i o n o f the v i b r a t i o n a l i s o t o p e e f f e c t f o r the case of polyatomic moleoules has a t l e a s t t h r e e important a p p l i c a t i o n s . F i r s t , s i n c e i s o t o p i o (16) molecules have the same e l e c t r o n i c s t r u c t u r e , the p o t e n t i a l f u n c t i o n f o r i s o t o p i c molecules i s the same t o a ve r y h i g h degree o f approximation. T h i s i n v a r i a n o e of the p o t e n t i a l f u n c t i o n f o r i s o t o p i c molecules may be a p p l i e d to the de t e r m i n a t i o n o f a d d i t i o n a l f o r c e c o n s t a n t s , s i n c e the d i f f e r e n c e i n masses changes the normal f r e q u e n c i e s and hence p r o v i d e s a d d i t i o n a l equations f o r the f o r c e c o n s t a n t s . Secondly, the i n v e s t i g a t i o n o f the i s o t o p e e f f e c t i s i n -v a l u a b l e i n c o r r e l a t i n g the observed v i b r a t i o n a l f r e q u e n c i e s w i t h the t h e o r e t i c a l normal modes of a c e r t a i n molecule. T h i s c o r r e l a t i o n i s p o s s i b l e as a r e s u l t of the f a c t t h a t the change i n v i b r a t i o n a l frequency when an atom i n the molecule i s r e p l a c e d by i t s i s o t o p e i s p r o p o r t i o n a l t o the amplitude o f v i b r a t i o n o f the atom i n the p a r t i c u l a r normal mode. T h i r d l y , i n c e r t a i n oases, i n f o r m a t i o n about the g e o m e t r i c a l s t r u c t u r e of the molecule may be obt a i n e d s i n c e the r e l a t i v e amplitude o f v i b r a t i o n o f a c e r t a i n nucleus (t o be r e p l a c e d by an i s o t o p e ) depends on the g e o m e t r i c a l arrangements of the n u c l e i . I n the case of l i n e a r symmetrical XY^., i f the s u p e r s c r i p t ( t ) - d e s i g n a t e s q u a n t i t i e s r e f e r r i n g to the i s o t o p i c molecule, then from (18) we have (17) From (23), the s h i f t s Ai> between the f r e q u e n c i e s of XIZ and I T ^ a r e g i v e n f o r s m a l l A«r by (24) ^i. Jjs • Z m y ) ( * v t Y + / ^ ™ Y ) a n d the s h i f t s between l i n e a r symmetrical XT,, and X H * ° are g i v e n approximately by h a l f the v a l u e s i n (24). 3. L i m i t a t i o n s of the Concept o f  Normal V i b r a t i o n s . (a) Anharmonicity. The e n t i r e conoept of the normal v i b r a t i o n s as developed up u n t i l t h i s p o i n t has r e s t e d upon the assumption t h a t the amplitudes o f v i b r a t i o n of the atomio n u c l e i are s u f f i c i e n t l y s m a l l so as o n l y the q u a d r a t i c terms i n the p o t e n t i a l f u n c t i o n need be c o n s i d e r e d . T h i s motion i s c a l l e d harmonic* A c t u a l l y , however, f o r a more accurate r e p r e s e n t a t i o n of the m o l e c u l a r v i b r a t i o n s , we must i n c l u d e c u b i c , q u a r t i o , and h i g h e r terms i n the p o t e n t i a l f u n c t i o n . I n o t h e r words, the o s c i l l a t i o n s of the atoms i n the molecule are a c t u a l l y enharmonic. Assuming anharmonicity, N i e l s e n [ 2 l ] has d e r i v e d the f o l l o w i n g e x p r e s s i o n f o r the v i b r a t i o n a l energy l e v e l s o f a polyatomic molecule w i t h doubly degenerate v i b r a t i o n s : (18) fit yjf SJf ^jjf yji v t. ) M&'i V e A rv r S /Aitw J (25) where d^s 1 or 2 and where 1 ; « 0 , or *\ ; -2,--depending on "'' whether t refers to a non-degenerate or doubly degenerate vibration respectively. In the case of linear symmetrical XYg , (25) reduces to G(V| tV e , V 3 , l j , ) = w, {vl*-%)+vtz{Vi+l)-mfJ{v3 + :k) + x11(v, + i) iVx 2 i,(v e + l ) % g e £l£ , j, (26) + XjjJVj + t J + X.j, (v, + £) (t**l) + (v y+i)+X 2 5(v £^l)(v 5+i) Adel and Dennison [l] have calculated the con-stants W; ,xiK and^ i Kin terms of the quadratic, cubic and quartic potential constants, and as was to be expected, the w- depend on the force constants associated with the quadratic terms only and are given by equations (18) when thev.are replaced by the w; • Actually, the observed  fundamentals z/: as obtained from (26) are v*/c = w£+Sxjg + ix.j.+i xs,+ 9e t (27) It i s thus evident that i n computing the potential constants a n » a i £ » and a J 3 by equations ( 18 ) , we should actually use the zero-order frequencies w,:, instead of the observed fundamentals Vi. Fortunately, x t K^w; and the approximation •^/c = wc i s f a i r , although, (19) s m a l l i n c o n s i s t e n c i e s should be expected, (b) Fermi Resonanoe. I t was f i r s t r e c o g n i z e d by Fermi [12] t h a t the i n t e r a c t i o n s between d i f f e r e n t v i b r a t i o n s of a polyatomic molecule are s u f f i c i e n t t o produce a p e r t u r b a t i o n when two energy l e v e l s happen to l i e very c l o s e t o g e t h e r ( a c c i d e n t a l degeneracy). T h i s resonanoe between the two v i b r a t i o n a l l e v e l s t h at have n e a r l y the same energy i n zero approximation causes the two l e v e l s t o 1>e " r e p e l l e d " (the magnitude of the r e p u l s i o n depending i n v e r s e l y upon the zero approximation d i f f e r e n c e i n energy) and the a c t u a l l e v e l s are not a c c u r a t e l y g i v e n by a formula such as (25). I f the resonance i s f a i r l y c l o s e between the unperturbed l e v e l s E * and E * , the magnitude of the s h i f t can be shown t o be A E s B - E M t - + i v ^ l W V i l N £*• (28) where E M i r E; * E» 2 s = E ; - E I (29) W - the p e r t u r b a t i o n f u n c t i o n g i v e n by the c u b i c and q u a r t i c terms i n the p o t e n t i a l f u n c t i o n , / (20) Since (28) shows that there i s no perturbation when W„; s 0, we have the important rule that Fermi resonance can occur only between levels of the same species. 4 . Infrared Absorption Spectra of  Polyatomic Molecules.-(a) Point Groups and Symmetry Species. Given any molecule consisting of a configuration of atoms i n their equilibrium positions, we define a symmetry operation as either a rotation about a specific axis by a certain angle or a reflection i n a specific plane which causes the configuration to remain invariant. A possible combination of symmetry operations that leaves at least one point unchanged i s called a point group* I t may be shown that a point group obeys the postulates of a group i n the mathematical sense and furthermore, that only a limited number of such point groups exist. Thus, given any moleoule, It i s possible to classify i t according to the point group to which i t belongs (see 0.4] and \26] )« Let us now consider the forms of the normal vibrations for any given molecule. Brewster [6] has shown that only certain combinations of symmetry properties of the normal vibrations and vibrational eigenfunctions are possible for any given point group. In group theory, such combinations are called the irreducible representations (21) of the point group considered, but we shall c a l l them symmetry species. It i s thus possible to classify each moleoule according to i t s point group and each normal vibration or vibrational eigenfunotion to i t s symmetry species (see p.4] or [Z&\ ) • (b) Formulation of the General Selection Rule. According to quantum mechanics, an infrared absorption band w i l l occur as a result of a transition of the molecule from a lower (v') to a higher (v M) vibrational energy level, whenever the matrix element [M3„.„„ = Y^yYv" M dr ( 3 0 ) i s not equal to zero for some component of the electric moment M . It may now be shown |l4j that the general selection rule may be formulated thus: A vibrational  transition v'<-»v" i s allowed only when there ls at least  one component of the dipole moment M that has the same  species as the product Yv' ^Cv" • Since this selection rule is dependent only upon the essential symmetry of the molecule, i t i s independent of whether or not the vibrations are harmonio. Thus, in order to ascertain whether a certain transition i s allowed i n the infrared, i t i s only necessary to see whether the species of ^ .Y^is the same as that of M -x , M«j , or M Z from tabulated symmetry species tables £l4] • Spectral frequencies which are allowed i n the infrared are called infrared active. The application of the (22) general selection rule now shows that i n general not only are the fundamental frequencies (v,> 1 and v^s G for a l l i*? i n (15) or (25) ) infrared active, but overtones (vt-s-2, 3, 4,... and y^r 0 for a l l and combination bands (v;, v,, v K M.. positive or negative integers) are also i n -frared active. However, depending on the point group to which the molecule belongs, certain fundamental, overtone, and combination bands w i l l be infrared inactive. The converse statement of this fact gives rise to the second  major application of Infrared spectroscopy to the study  of molecular structure. Thus from the activity or i n -activity of certain fundamental overtone, and combination frequencies i n the infrared spectrum of a given molecule, i t i s possible to ascertain (among other things) the point group to which the molecule belongs and hence the symmetry structure of the molecule. (c) Selection Rules for Linear Symmetrical XYt. The more important selection rules for linear symmetrical XY t may be summarized as follows: 1. Since linear symmetrical XYt has a center of symmetry, i t obeys the "rule of mutual exclusion 1 1 which may be stated as follows: For moleoules with a center of symmetry, transitions that are allowed i n the inf r a -red are forbidden i n the Raman spectrum and conversely. (23) 2. -v, i s infrared inactive while ^ and are infrared active, 3. Transitions corresponding to vibrations of the electric moment perpendicular to the symmetry axis are Infrared active i f and only i f A VJJ i s odd and A V 5 is even, A V, may be odd or even a n d ^ l - i l . 4. Transitions corresponding to vibrations of the electric moment along the symmetry axis are infrared active i f and only i f A V k i s even and A V } is odd. A v, may be either odd or even and A 1 « 0. 5. It follows from 3 and 4 that the sum of the frequencies of any two observed bands w i l l not be the frequency of another active or observable band f9] • 6. Fermi resonance may occur only between those levels which have the same.value of 1. 7. A difference band i s allowed or for-bidden depending on whether the corresponding summation band ^i*^f% is allowed or forbidden. It may be noted that the wave no. uc-u* i s exactly the difference of the wave nos. of the bands -ui and even i f anharmonicity i s taken into account. (24) I I I . APPARATUS. 1. The I n f r a r e d Spectrometer and  R e c o r d i n g A c c e s s o r i e s . F i g u r e 3 shows the r e l a t i o n s h i p of the major p i e c e s of apparatus c o n s t i t u t i n g the spectrometer and the r e c o r d i n g a c c e s s o r i e s . The r a d i a t i o n source f o r the s p e c t r o -meter i s a g l o b a r whose power output (150 to 250 watts) i s r e g u l a t e d by a v a r i a c and i s measured by a wattmeter (not shown i n F i g u r e 3 ) . A c r o s s the primary of the v a r i a o i s a p p l i e d a r e g u l a t e d 110 v o l t s s u p p l i e d by a 250 watt S o l a Transformer. The output r a d i a t i o n of the spectrometer r e a c h i n g the thermocouple i s a m p l i f i e d and t h e D.C. output v o l t a g e o f the a m p l i f i e r i s a p p l i e d to a continuous s s l f -b a l a n o i n g potentiometer-type r e c o r d e r . The wavelength d r i v e permits continuous s p e c t r a scanning and the c o n t r o l p a n e l c o n v e n i e n t l y groups most o f the e l e c t r i c a l c o n t r o l s f o r the spectrometer and the r e c o r d i n g a c c e s s o r i e s . View of the General Experimental Arrangement of the Apparatus. (25) ar IdC e I j Sola jTra ns -!f o r mer tt 110 v. C otntrol P c m e l W a v e D r i v e -^S pecf ro tmeter R e c o r d e r A m p l i f i e r P o w e r S u p p l y A impl i f ier FIG. 3. B l o c k diagram of the spectrometer and the r e c o r d i n g system. (a) The Spectrometer.. A complete d e s c r i p t i o n of the spectrometer i s p r o v i d e d i n the Perkin-Elmer I n s t r u c t i o n Manual [16] • For the sake of completeness, however, the f o l l o w i n g d e s c r i p t i o n i s quoted: "The o p t i c a l path o f the spectrometer, as viewed from above, i s shown i n P l a t e I I I . Continuous r a d i a t i o n from the g l o b a r source, G>, i s focussed through the sample c e l l , C, on t h e entrance s l i t , S i , by the s p h e r i c a l m i r r o r , M c i . The p o r . t i o n of the beam which passes through the entrance s l i t i s o o l l i m a t e d by the PLATE I I I . The Perkin-Slmer infrared spectrometer Model 12A. (26) off-axis paraboloid, M.uL, dispersed by the prism, P; returned to the Littrow mirror, Miv ; dispersed again by the prism; and brought to a focus by Hi,' i n a spectrum that f a l l s across the exit s l i t , Sci • The exit s l i t allows rays of a narrow frequency band to pass through, after which they are collected and focused on the upper junction of a compensated vacuum thermocouple, T c, by the spherical mirror Mvii FIG. 4,The Perkin-Elmer infrared spectrometer Model 12C. (b) The Amplifier The General Motors amplifier i s described i n detail in the General Motors Research Laboratories In-struction Manual . The following outline of the (27) amplifier's operation i s quoted from the Perkin-Elmer Instruction Manual [17] : "Current from the thermocouple i s fed into a pair of breaker points operated at 80 cycles per FIG. 5. The General Motors Amplifier, second by a synchronous motor mounted i n the amplifier. This converts the low voltage direct current to a low voltage alternating current, which i s then stepped up by a transformer to a voltage where i t can be amplified by the customary methods of audio frequency amplifiers. Three stages of R-C coupled amplifications are used to give a signal large enough to be rectified by a second pair of breaker points. The two pairs of breaker points are operated (28) directly from the same control shaft." (c) The Recorder. The recorder i s described i n detail i n the Brown Instrument Company Instruction Manual [i\ • The operating principle of the Brown recorder consists of the application of the amplified unbalance voltage existing between any imput voltage and a standardized potentiometer voltage, to a motor controlling the magnitude of the potentiometer voltage. Depending on the phase of this voltage, the motor w i l l always move in such a direction as to decrease this unbalance voltage. The pen is attached to the variable FIG. 6. The Brown Recorder. (29) contact on the potentiometer which i s actuated hy the motor The reading of the pen i s thus direotly proportional to the imput voltage provided the fluctuations i n imput voltage are not rapid. (d) The Wavelength Drive. The wavelength drive i s a four-speed selective gear mechanism of our own design driven hy a 12 watt Tele-chron synchronous motor. The mechanism permits scanning FIG. 7. The Wavelength Drive i n Position Relative to the Spectrometer, the infrared spectrum at rates approximately one, two, four or eight minutes per revolution of the wavelength drum. The drive causes the f l a t Littrow mirror M;v , behind the (30) prism, to rotate i n such a direction, that the infrared spectrum passes across the thermaoouple from longer to shorter wavelengths. (e) The Control System. In order to provide for more efficient operation of the spectrometer and the recording accessories, a control system was designed and constructed. The cirouit i s shown in Plate IV. The power switoh,#l, i s the only connection between any part of the spectrometer or the recording accessories and the 110 volt line voltage. A, B, C, F, and G- represent contact points on the terminal block of the recorder 0.71. When the power switch i s on, the pilot light, #2, i s on, and 110 volts i s now available. (a) i n the wavelength drive motor ci r c u i t , (b) to the recorder (at F and G), and (c) for the sola transformer. The normally-closed microswitch, #3, is a safety switch attached to the wavelength drive lever arm i n such a way as to open when approximately twenty-two revolutions have been made. The wave drive switch, #4, i s an on-off control for the wavelength drive motor. The spectrometer wiring diagram (Figure 4 in[l7l) indicates that the pen motor i n the recorder i s on, when terminal A is connected to terminal B, and that the chart PLATE IV. The Control System, (31) motor in the reoorder i s on, when terminal 0 is connected to terminal B. Thus, switches #5 and #6 represent the pen and chart switches respectively. The normally-closed microswitch, #7, is opened once i n every revolution of the wavelength drum hy a cam arrangement on the drive shaft. The auto-step switJon, #8, in i t s off position, shorts out the effects of #7. #9 represents the secondary of a normally-open, single-throw, double-pole mercury relay which i s energized and closed when the single-throw, double-pole switch, #10 i s closed (provided either #7 or #8 is closed). Switch #10 i s actually the master switch for the pen, chart, and wave-length drive, since i f #7 i s closed, and #4, #5, #6 are off, then the right side of #10 when closed, immediately causes #9 to close and hence (a) completes the wavelength drive c i r c u i t , and (b) connects A to B and 0 to B, thus starting the pen and chart. If the automatic stop switch, #8, is on, i t i s evident that onoe i n every revolution of the wavelength drum, #7 w i l l open, thus causing #9 to open and hence simultaneously stopping the pen, chart, and wavelength drive (provided these were i n i t i a l l y put Into operation by the master, #10). #7 may be again closed merely by brie f l y closing and then reopening #8. (32) 2. The Humidity and Temperature  Control-Room* Owing to the absorption of infrared radiation by glass and quartz, a l l the windows of the spectrometer and the sample cells are made from rock salt, which i s slightly hygroscopic. . Exposure to an atmosphere with more than 60% relative humidity causes a thick fog to appear on the windows, and exposure to relative humidities higher than 80%, causes the windows and prisms to dissolve and to flow away i n the moisture condensing on them. It i s therefore recommended i n the Perkin-Elmer Instruction ManualCl6] that the relative humidity be kept between 30% and 50%. In the summer of 1947, when work was f i r s t begun on this project, i t was observed that the relative humidity rarely f e l l below 60% i n the room i n which the spectrometer was to be set up. It was therefore decided to design and construct a room, i n which the humidity and temperature might be controlled, so that uninterrupted research could be carried out. (a) Design of the Room. It was decided that the room should be made as small as possible within the limits of convenience (see Figure 8) i n order that the volume of a i r to be dehumidified be kept at a minimum, and the figure 6 X 9 X 8 feet resulted. (33) The walls, ceiling, and floor of the room, consist of a two-inch rock-wool center covered on either side by vapour-sealed tar paper and contained i n a plywood shel l . The room was so constructed by the University Carpentry Shop that i t may be taken apart, moved, and reassembled with re-lative ease. The entrance to the.room consists of a two-door air-lock, the outside door being of the same con-struction as the walls. FIG. 8. The Humidity and Temperature-Control -Room. (b) Method of Dehumidification. The dehumi dification of the air inside the room (34) is accomplished essentially by cooling the a i r , removing the resulting condensed water vapour from the room, and then reheating the dehumidified a i r . In reference to Figures 9 and 10, the air is circulated about the room by a fan which is placed i n front of a bank of cooling c o i l s . The cooling coils are kept at about 0° C by the refrigerant whioh i s compressed and circulated by means of a standard one-half H.P. General Electric condenser located outside the room (see Figure 11). The air i s reheated as i t is blown Cool ing - coi I r I r- , Cone Hea+er L o o l i n q - t m s \ = Asbestos = C o l l a r R a d i a t i o n / O o o Dr«j air ^Outlet A— x—Air--f|ou; S c r e e n H u m . d a i r c o „ t r o | Heating Ckawber FIG. 9. Top View of the Dehumidifier. through the heating chamber, oonnected to the cooling chamber by an asbestos collar. The radiant heat from three 600 watt heaters in the heating chamber, whioh would decrease the efficiency of the cooling coils, i s dissipated to a considerable extent by means of three sheets of wire netting (35) which separate the heaters from the cooling c o i l s . Two modifications were found to be necessary in adapting the standard fan and cooling c o i l unit to our own special requirements. F i r s t , the standard drainage system FIG. 10. Photograph of the Dehumidifier. provided i n the unit was found to be much too slow so that a rapid drainage system of our own design was constructed. Secondly, i t was found that the temperature of the cooling fins was very sensitive to the rate of flow of air through the cooling chamber. It was therefore necessary to box i n the fan from the rear and control the rate of flow of air by means of a sliding door. (36) FIG. 1 1 . The General Electric Condenser Unit. (c) Humidity and Temperature Controls (Plate Y.) The back-pressure control which i s situated on the condenser unit, controls the on-off operation of the pump. It i s actuated by the pressure of the returning re-frigerant in such a manner that i f the pressure is low, corresponding to a low return-temperature, the pump wi l l stop, and i f the pressure is high, corresponding to over-heated returning refrigerant, the pump w i l l start. In our system, this control is set at approximately the pressure o corresponding to a return-temperature of 0 C. The throttle-valve i s a variable control on the output side of the condenser, which regulates the input rate of flow of refrigerant to the cooling c o i l s . The valve i s operated by a gas-pressure bellows, which i n turn, i s BacK-Pr ess/Cow fro! PLATS V. The Humidity and Temperature Controls, (37) actuated by a thermal probe attached to the r e f r i g e r a n t e x i t flow-tube from the evaporator ( c o o l i n g c o i l s ) . Thus, i f the e x i t r e f r i g e r a n t i s c o o l , the bellows i n the t h r o t t l e -v a l v e c o n t r a c t s and decreases the input f l o w o f r e f r i g e r a n t to the c o i l s . The s o l e n o i d - v a l v e i s p l a c e d on the output s i d e o f the condenser. I t i s an on-off c o n t r o l f o r the flow of r e f r i g e r a n t and i s operated by the h u m i d i s t a t , s i t u a t e d i n s i d e the room (see F i g u r e 12). The room temperature i s c o n t r o l l e d by a thermostat which i s i n the primary o f a 20 amp. r e l a y c o n t r o l l i n g the f l o w of c urrent to the th r e e cone h e a t e r s . I t was found that FIG. 12. The Thermostat when the pump had ceased o p e r a t i o n , and Humidistat the f a n continued t o blow warm a i r over the c o o l i n g c o i l s . T h i s warm a i r tended to absorb condensed moisture s t i l l on the c o o l i n g f i n s and thus decreased the e f f i c i e n c y of the de-h u m i d i f i c a t i o n p r o c e s s . A r e l a y was t h e r e f o r e put i n t o the fa n c i r c u i t so that the fan motor was on only when the pump was o p e r a t i n g and so t h a t the f a n ceased o p e r a t i o n im-mediately the pump stopped. (38) Under c e r t a i n c o n d i t i o n s , i t was found that the heaters might remain on, when the f a n and pump had ceased o p e r a t i o n . Under such c o n d i t i o n s , there was no c i r c u l a t i o n o f a i r through the h e a t i n g chamber and the r e s u l t i n g con-c e n t r a t i o n o f heat presented a p o t e n t i a l f i r e h a zard. T h i s danger was e a s i l y removed, merely by p l a c i n g a r e l a y i n s e r i e s w i t h the thermostat. The r e l a y was then energized i n e x a c t l y the same manner as the f a n r e l a y , so that the h e a t e r s c o u l d be on, o n l y when the f a n was a l s o on. (d) E f f e c t i v e n e s s o f the Method. The humidity c o n t r o l has proved to be q u i t e s a t i s f a c t o r y . With the c o n t r o l system as o u t l i n e d above, we have been a b l e to m a i n t a i n the r e l a t i v e humidity i n the room at 4 0 ± 2$ ( a t a temperature of 20*C) with no un-due s t r a i n on the pump motor. No c o n t r o l l e d o b s e r v a t i o n s have been made, but i t i s b e l i e v e d that the system c o u l d m a i n t a i n the r e l a t i v e humidity a t a minimum of about 30$ (at a temperature o f 20*0). The temperature r e g u l a t i o n has not proved t o be q u i t e as s a t i s f a c t o r y f o r our purposes. A l t h o u g h the temperature d i f f e r e n t i a l i s o n l y about 3 WF, the r a t e o f temperature f l u c t u a t i o n i n t h i s r e g i o n i s r e l a t i v e l y r a p i d . I n a d d i t i o n , although the temperature d i f f e r e n t i a l at the thermostat may o n l y be 3°F, owing t o the nature o f our d e h u m i d i f i e r , c o l d and warm a i r masses having (39) temperatures considerably outside t h i s region move about i n the room at various times, depending on the phase of the dehumidificafcion cycle. I t i s suggested that the e f f e c t s of these d i f f i c u l t i e s may be decreased by (1) operating either one or two of the cone heaters continuously and using the second or t h i r d heater i n conjunction with the thermostat, to maintain the temperature at the desired value, and by (2) s i t u a t i n g the thermostat more advantageously i n the room. IV. EXPERIMENTAL. 1. C a l i b r a t i o n of the Spectrometer. The wavelength or frequency s e t t i n g of the spectrometer i s controlled by the wavelength micrometer, M*,, whioh rotates the Littrow mirror M.v (Plate I I I ) . The drum c a l i b r a t i o n i s a r b i t r a r y , each small d i v i s i o n corres-ponding to 16.1 seconds of aro. In order to determine the wavelength or frequency value at whioh an absorption band occurs, one must therefore be able to t r a n s l a t e the drum readings into terms of either wavelength or frequency. This determination of the r e l a t i o n s h i p between drum reading (40) and, i n our p a r t i c u l a r case , wave number, c o n s t i t u t e s the c a l i b r a t i o n of the spec t rometer , i t i s ev ident t h a t the c a l i b r a t i o n w i l l be d i f f e r e n t f o r d i f f e r e n t p r i s m s . The f o l l o w i n g method of c a l i b r a t i o n f o r the NaCl p r i s m was u s e d . The wave numbers of the a b s o r p t i o n bands i n the near i n f r a r e d f o r C 0 2 , H^O vapour , and N f i s have been determined by numerous observers {22] t and are known q u i t e a c c u r a t e l y to at l e a s t f o u r s i g n i f i c a n t f i g u r e s . Together , these t h r e e substances p r o v i d e an almost s u f f i c i e n t number of c a l i b r a t i o n p o i n t s i n the NaCl p r i s m range from 3 to 15 m i c r o n s . P l a t e s VT and vTI are sample c a l i b r a t i o n c h a r t s showing N H 5 and 00t p l u s Ez0 vapour a b s o r p t i o n r e g i o n s r e s p e c t i v e l y . As may be seen , a c a l i b r a t i o n p i p was made on the a b s o r p t i o n curve every 25 wavelength drum d i v i s i o n s . T h i s p i p i s made u s i n g the t e s t m i c r o v o l t c o n t r o l of the General E l e c t r i c A m p l i f i e r * The purpose o f t h i s c o n t r o l i s a c t u a l l y to determine the a b s o l u t e g a i n o f the a m p l i f i e r , and t h i s i s accompl ished by superimposing a s m a l l known d i r e o t c u r r e n t v o l t a g e t o the v a r y i n g thermocouple imput s i g n a l . Table 2 i s a c o m p i l a t i o n of observed c o r r e l a t i o n s between wavelength drum r e a d i n g s and a b s o r p t i o n minima* The wave numbers o f the a b s o r p t i o n bands are taken from R. S . I . [22] • From Table 2 , the c a l i b r a t i o n curves shown i n P l a t e s v T U , I X , and X were drawn to cover t h e range from about 800 cm: to 4000 cm. , The accuracy of these f-o*. P £ . Inm* CALtBAATIOfV K&D *^.fc from e to CHRP. T r Al.de/ 11. a So ;*/ if JUS With MLCI fk/iirt /ntttt '^ta.owT'*'"""" t* *p on" /f.X«8 tolif* CitlnnntroN from tho lo /V/V, g~~o Per for m *<t TnAKcfr. to, M^i- T J otht t 11 * * t tor from If.Si I. &Leert* Po*/**. /•>¥*. S /so u*r' lit Wtoltt % Gtr/1 • o IS w*rt ».* Hon. T'mrnp •t'ty IZ. 7. ..••>. e Mil'* Sfeeo «-'« PATOH/HC /oo trim Hy "per r*e V. CEIL CertOt TH fo CM routes get. 9tJ CfoTfe 0rte fx <*« <. < -vests if* c<~* •* •>< • t*f/H*£ Q**V<. . PLATE VI. NH 3 C a l i b r a t i o n Chart, (41) calibration curves w i l l vary, depending upon the variation of the density of the calibration points. 2. Control of the Temperature and  Pressure of the CSp, Sample. Plate XI indicates diagrammatically, the ab-sorption cell(see Figure 13) and the method of control of the temperature and pressure of the gas sample. The ab-sorption c e l l provides a path length of 100 cm. and si t s i n the spectrometer as shown i n Figure 14. Heat for keeping the gas sample at any desired temperature i s supplied by a six-foot, 1000 watts, Lolag FIG. 13. The Absorption C e l l , heating c o i l which i s wound about the c e l l as shown i n Figure 13. The current flowing i n this heater i s regulated (42) TABLE 2. C a l i b r a t i o n p o i n t s f o r the NaCl P r i s n u Drum ( d i v i s i o i Wave No. LS) (cm:1) Drum ( d i v i s i o n s Wave No. ) (cm.") i Drum ( d i v i s i o n s l Wave No. ) (cm.-) 517 667.0 1284 1159.7 1514 1618 589 720.7 1298 1177.9 1516 1624 748 807.7 1313 1195.9 1519 1637 765 812.4 1325 1213.4 1524 1649 798 828.2 1337 1231.1 1527 1664 807 830.9 1356 1261 1529 1671 812 833.0 1362 1272 1533 1685 814 834.9 1389 1314 1537 1700 843 848.0 1392 1320 1542 1718 855 854.0 1403 1340 1546 1736 885 868.2 1415 1363 1549 1751 893 872.7 1420 1376 1554 1774 947 888.3 1428 1388 1560 1794 955 892.4 1431 1396 1562 1812 984 908.4 1435 1406 1567 1830 1049 948.8 1442 1420 1570 1846 1055 952.0 1447 1431 1575 1870 1082 972.4 1449 1437 1579 1891 1111 992.8 1454 1449 1582 1911 1131 1007.2 1458 1459 1585 1922 1136 1012.6 1461 1466 1588 1944 1155 1027.3 1464 1474 1592 1968 1161 1033.8 1470 1491 1597 1993 1177 1046.9 1473 1498 1640 2336 1184 1054.4 1477 1498 1640 2336 1198 1066.3 1480 1518 1703 3217 1207 1075.8 1482 1523 1708 3337 1218 1085.1 1486 1535 1711 3434 1228 1096.1 1489 1542 1718 3617 1236 1104.1 1495 1560 1722 3741 1248 1117.4 1498 1571 1726 3882 1253 1268 1123.0 1141.3 1501 1507 1578 1596 PLATE X. PLATS XL. Absorption Cell with Temperature and Pressure Controls. (43) by a variable phase, thyratron-control ci r c u i t . The phase of the thyratron 1s grid i s i t s e l f controlled by a resistance thermometer abound about the c e l l and i n thermal contact with the c e l l . In order to reduce heat losses through con-duction, and convection, the c e l l i s completely covered with a layer of asbestos and then sewn into a f e l t stocking. The CS^is continuously supplied by evaporation to the c e l l , from a Florence flask container which i s kept in a water bath. Heat is supplied to this water bath by a 300 watt heating c o i l and the temperature of the bath is main-tained at any desired value by means of an Aminco "Quickset" Bimetal Thermoregulator. FIG. 14. The Absorption Cell i n Position Relative to the Spectrometer. Ua).. The glass tubing between the flask and th© c e l l i s heavily-insulated and i t i s assumed that the pressure of the gas in the e e l l w i l l remain equal to the maximum vapour pressure of the gas corresponding to the bath temperature. This method of control was decided upon as being more stable than any simple available type of absolute pressure control. On the outlet side of the c e l l i s attached a vacuum pump and a mercury-type pressure gauge with a range from zero to two atmospheres. The gauge is available as a check on the degree of validit y of the preceding assumption. (45) V. RESULTS. 1. Experimental Results. (a) Observed Absorption Bands of Gaseous C S v For purposes of comparison, the wave numbers of a l l the absorption bands which were observed are tabulated i n Table 3, together with the results of some other experimenters. Plates XII, XIII, XIV, XV, and XVI are plots of percent trans-mission against wavelength drum readings for each of the six observed absorption bands. In general, transmission curves were plotted as follows: The extent of the region of absorption of a given band is first-narrowed 'down so that a maximum gain may be used in the region without the recorder pen going off the scale. The gain of the amplifier and the ^ s l i t width are then simul-taneously adjusted until a satisfactory compromise between the " noise to signal ratio and the resolution has been attained. Then, with the pressure of the gas sample adjusted so that the transmission never becomes zero anywhere i n the region of absorption (this allows the band structure to be observed), one or more traces of the absorption band are taken. The c e l l is then thoroughly evacuated, and more reoorder traces are taken with the c e l l i n position. The region of interest on the chart is then marked off into wavelength drum divisions and the ratios of radiation energy i n -cident on the thermocouple through CS, to the radiation TABLE 3. Observed and Calculated Infrared Absorption Bands of O'S, (cm."'). Term •ll Transition Plyler and Humphreys C24] Bailey and Cassie w Edwards, Mitenner, and Rogers• i Liquid Vapour Vapour Vapour Prob. Obs. Calo. Obs. Calc. Obs. Calo. Observed Error Vs 00°0-»10°0 655 655* 655* 655* 00o0-»0l' 0 397" 397* 397* oo°o-»oo°i 1510 1510* 1535 L535* 1523 1523* 1535 i2 o o ° o ^ i r o 1048 1052 2 x>t 00°0-*02°0 01' 0-»03' 0 807 794 783 10°0-»00°1 855 855 879 880 878 868 877 tl 3 27* 1180 . 1191 1197 1910 1907 00° 0*10° 1 2163 2165 2184 2190 2179 2178 2185 ±5 00°0-»02°l 2303 2304 2336 2329 2330 2317 2332 ±5 2815 2821 2857 2845 2833 2838 16 2949 2960 2959 2984 2972 2959 i 6 3105 3098 3472 3475 4504 4530 PLATE XII THE DIFFERENCE" BAND T e wiper a to re : P r e s s u r e : Ce II Lev>^trj : 20°G 3 Oc»n 100cm 370 960 950 94-0 930 920 Wavelength D r u m 910 PLATE 2III« THF COMBINATION BAND T e w » p e r a t u r e '. Z O ° C . P r e s s u r e ; 20c«n Cell L e ^ t k ; IOOCM. -1618 I6a0 1622 I G 2 4 1626 1628 1630 P L A T E X I V . s THE COMBINATION BAND v3 + z Vi Temperature . 2 0 ° C Pressure . 50cm Cell Length ; lOcw. IG43 |64a | C 4 f 1640 1639 1638 1637 Wavelength Drum PLATE XV. w PLATE XVI. (47) energy incident on the thermocouple through vacuum are cal -culated for each drum division (or more often i f necessary) to give the transmission. The ^absorption band is very intense and just a trace of CS a was necessary i n order to obtain proper percent transmission. As may be seen from Plate XII, i t was possible to resolve this band into P and R branches (which arise as a result of vibration-rotation interaction), the center of the band occurring at 1486.7 drum divisions or at 1535 cm. ' . Owing to the necessity of high resolutions and resultant small s l i t widths, the noise to signal ratio was quite large for this band. Consequently, Plate XII was actually drawn from the averaged percentage transmissions of six separate sets of CSZ and vaouum traces. The difference band,2^-2J L T was resolved with l i t t l e d i f f i c u l t y and a wave number of 877 cmr' was determined for the center of the band, corresponding to 928 drum divisions. It was not possible to observe the combination band,^^- - ^ j , using a 10 cm. path length so that i t was necessary to use the 100 cm. path length absorption c e l l . The ZJ,-24absorp-tion minimum as measured from Plate XIV, which i s an average of four sets of readings, occurs at a wave number of 2185 cm, corresponding to a drum reading of 1623.5 divisions. Plates XV and XVI show that the combination bands 2 ^ ,-^s-* 2 •*•/», and i>, + Z2Jt*if3 occur at wavelength drum readings of 1640, 1681, -1 and 1688.5 divisions, corresponding to wave members of 2332 cm. (48) 2838 cm."', and 2959 cm."' respectively. The probable errors, as shown i n Table 3, were calculated assuming a probable error in the reading of the wavelength drum of i .5 divisions. It i s evident that the probable error w i l l vary inversely with the dispersion of the prism, depending upon the region of the spectrum under investigation. (b) Calculation of the Foroe Constants for Gaseous CS*. Solving equations (18) for the force constants a n » aia» a n d a?3 » o f a linear symmetrical XY£ molecule, we obtain a ( | = 4¥m Yf^,* + m< (31) L m x+ 2m y J a(i, = 4 T l m Y L ^ - m* JJ* \ (32) j_ m* + 2m Y J *8 - 4irm Ym» J A * (33) ~P 2lmx*2mY) Applying these equations to the case of CS £ where mx = 12.0 a.m.u. *my*s 32.0 a.m.u. (34) -24 1 a.m.u. • 1.66*10 gms. we obtain a ( | e .945[£/,Z + .158i>,e] a,i- = .945[X;,2 - .158 £^*] a^ s . 1 4 9 JJI and using the values (35) (49) JJK - 655 cm. JJX Z 3 9 7 c m«"' t 3 6 ) j j y - 1535 cm. we obtain the following values for the foroe constants of gaseous CSft . a„ - 7.58 « 10 dynes / cm. a.j.2 .529 * 10 r dynes / cm. (37) a 3 J = ,0,235 * 10^ dynes / cm. T (c) Calculation of the Isotope Effects on the Normal  Frequency,&3 , of Caseous CS&. The relative abundances of the various nuclear species of carbon and sulphur are as follows: Nuolear Species $ Abundance c' £ 98.9 C'5 1.1 S" 95.1 S" 0.74 S5* 4.2 It is evident that although twelve molecular species of CS t are theoretically possible, only four w i l l actually occur with sufficient abundance to produce an.absorption effect, these being C , J s " C'^S55, C '^'s* 4 , and C,5S?. Applying equations (23) and (24) to the case of gaseous CS£, and using the values (33) and (35), the following values for the shifts in the fundamental^, from the C,zs"molecule's ^j, may (50) be calculated for the various other molecular species. Molecular Species A^s (cm. ) c V s " -2 c W -4 C'5sr -49 2. Discussion of Results. Until 1947, the accepted value of us for gaseous CSj. had been 1523 cm."' . In July 1947, Plyler and Humphreys[24] remeasured this absorption band and con-eluded that i t occurred at 1535 cm. , stating that this new value gave much better agreement between calculated and observed combination band frequencies. The position of the ju} absorption band was therefore measured with great care i n the present research, and the results certainly confirm the measurements of Plyler and Humphreys. The values of the wave numbers of the combination bands JJ^-LI^^ •* -u$ and-Uj + 2^ agree with the results of previous observers to within the limits of experimental error. Plyler and Humphreys f24] i n their 1947 paper stated that they had observed two new gaseous CS e absorption bands occurring at 2857 cm."' and 2959 cmT* . The existence of these bands has been verified and the agreement with the position of the latter band i s good. However, the slight discrepancy i n the value of the-^j+2^, band cannot be explained.' (51) Comparing the values of the force constants calculated on the basis of the new z^frequenoy, with those calculated by Bailey and CassieD3]as tabulated i n the intro-duction, i t appears that change i n a„ i s negligible. The value of a 3 3 / i * w i l l not change, since this constant depends only onH> however, the effect on a,j.is considerable. It would therefore appear that the interaction between the two C-S bonds i s considerably less than had been previously thought. The side band appearing on the long-wavelength side of the 2J3 absorption band (Plate XII) has been attributed by Plyler and Humphreys to the isotope effect of C^s" • However, the measured shift of -8 cm. does not agree with the calculated shift of -49 cm/' which i s to be expected with c"s" • I f this side band is indeed due to an isotope effect, i t would seem more probable i n view of the greater relative abundance of C'*SrtSM and the closer agreement with calculation, that this side band is due to the molecular species C S S . VI. CONCLUSIONS. The wave numbers of six infrared absorption bands of gaseous CS e have been determined. The results of Plyler and Humphreys 1.241 have been verified within the limits of experimental error and the force constants for the CS Z molecule have been recalculated on the basis of the new (52) value of 1535 om."' for the normal frequency^. The results of this present investigation have not indicated anything which would deny the conclusion that the structure of the carbon disulphide molecule i s linear and symmetrical. VII. BIBLIOGRAPHY. 1. Adel, A., and Dennison, D. M. "Infrared Spectrum of COj.. Part I." Phys. Rev., 43 : 716-723, (1933). 2. Bailey, C. R., and Cassie, A. B. D. "Raman Displacements and the Infrared Absorption Bands of CSj,." Nature, 126 : 350, (1930). 3. Bailey, C. R., and Cassie, A . B. D. ."Investigations i n the Infrared Region of the Spectrum. Part III: Absorption Spectrum of CS £. Part IV: Monaohromator Method i n the Infrared." Proc. Roy. Soc, 132 : 236-257 (1931). 4. Barnes, R. B., McDonald, R. S., Williams, V. Z., and Kinnard, R. P. "Small Prism Infrared Spectrometry." Jour, of App. Phys., 16 : 77, (1945). 5. Bjerrum, N. Verh. d. d. phys. Geo., 16 : 737, (1914). (53) 6. Brewster, C. J. "Kristallsymmetrie und Restrahlen." Z. Physik, 24 : 324, (1924). 7. Brown Co. Ltd. Instruction Manual No. 4078. 8. Coblentz, W. W. • Pub. Carnegie Inst, of Washington, No. 35 (1935). 9. Dennison, D. M. -' . ' "Infrared Spectra of Polyatomic Molecules. Part I." Rev. Mod. Phys., 3 : 280-345, (1931). 10. Dennison, D. M.• "Infrared Spectra of Polyatomic Molecules. Part I I . " Rev. Mod. Phys., 12 : 175-214, (1940). 11. Dennison, D. M. and Wright,•N.• "A New Long Wavelength Absorption Band of CSj»". Phys. Rev., 38 : 2077 L (1931) 12. Fermi, E. "Raman Effect i n COj," Z e i t s f . Physik, 71 : 250-259, (1931) 13. General Motors Instruction Manual. 14. Herzberg, G. "Infrared and Raman Spectra." (54) 15. Howard, J. B., and Wilson, B. J. Chem'.v Phys., 2 : 620 (1934). 16. Instruction Manual for the Perkin-Elmer Infrared Spectrometer. Part I. 17. Instruction Manual for the Perkin-Elmer Infrared Spectrometer. Part I I . 18. James, H. M., and Cooledge, A. S., J. Chem. Phys., 1 : 834 (1933). 19. Langseth, A., Sorensen, J. U., and Nielsen, J. R. "Raman Spectrum of CS 2" J. Chem. Phys., 2 : 402-409, (1934). 20. Liebermann, L. N. "A Rotational Analysis of some CS^ Bands." Phys. Rev., 60 : 496-505, (1941). 21. Nielsen, H. H. Phys. Rev., 60 : 794 (1941). 22. Oetjen, R. A., Kao, C. L., and Randall, H. M. "Infrared Prism Spectrograph as a Precision Instrument". R. S. I., 13 : 515 (1942). 23. Pauling, L., and Wilson, E. B. "Introduction to Quantum Mechanics.*' (55) 24. Plyler, E. K., and Humphreys, C. J. "Infrared Absorption Spectrum of CS*." Jour, of Research of the National Bureau of  Standards, 39 : 59-65, (1947). 25. Redlich, 0., and Tompa, H. J. Chem. Phys., 5 : 529 (1937). 26. Rosenthal, J. E., and Murphy, G. M. "Group Theory and the Vibrations of Polyatomic Molecules." Rev. Mod. Phys., 8 : 317-346, (1936). 27. Sanderson, J. A. "Infrared Absorption of CS * at 4.57^. ". Phys. Rev., 50 : 209-211, (1936) 28. Wilson, E. B., and Crawford, B. L., J. Chem. Phys., 6 : 223, (1938). 

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