UBC Theses and Dissertations
Cusp conditions and properties at the nucleus of lithium atomic wave functions Chapman, John Alvin
The dependence of the point properties at the nucleus, electron density (Qe(0) )and spin density (Qs(0) ), on the nuclear cusp is examined for lithium atomic configuration interaction (CI) wave functions. Several series of CI wave functions with 18 and fewer terms, are studied. Importance of the triplet core spin function to Qs(0) is substantiated. Necessary, but not sufficient, spin and electron integral cusp conditions are applied as linear constraints. For the functions studied, Qs(0) improves on applying the spin cusp constraint if the free variational spin cusp is greater than -Z, but becomes worse otherwise. The electron cusp constraint invariably overcorrects Qe(0). The effect of necessary off-diagonal weighting constraints is also examined. No obvious trends could be found. It is concluded that forcing CI functions with a small number of terms to satisfy necessary diagonal or off-diagonal integral cusp conditions has very limited usefulness. A good Qs(0) can be obtained without constraining by (l) including triplet core spin terms. (2) optimizing orbital exponents. Sufficient nuclear cusp constraints are developed for CI wave functions. The generalized cusp-satisfying CI function has multiconfigurational SCF form with the correct cusp for each orbital. Sample calculations with a small basis set are presented. These simple functions give extremely good Qs(0) expectation values but convergence of Qs(0) with respect to basis set size is yet to be tested. The most interesting discovery is the appearance of Dirac [symbol omitted]-like correction basis orbitals from energy minimization of the orbital exponents. A scheme is depicted classifying previous and present work on cusp constraints in terms of necessity and/or sufficiency.
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