By D. B. Cook

ISBN-10: 0408705515

ISBN-13: 9780408705516

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**Extra resources for Ab Initio Valence Calculations in Chemistry**

**Example text**

H Φ. 2) K In certain cases symmetry requirements mean that more than one determinant must be used to describe a configuration, but the general idea is clear. 33 J The Orbital Approximation and S.. = \ άτ Φ. Φ. 1) we have Y S. E = Y D. D. H. h 1 11 · 1 J 1 (j = 1 , 2 , . . 1). 2) and D is a column matrix of the coefficients D.. 4) an obvious matrix analogue of the Schrödinger equation. and similar matrix In eigenvalue problems, This, will play a prominent role in our development of orbital theories.

1 — ij is redundant when only a single nucleus is involved and this nucleus is chosen to be the origin of coordinates). The equations which the optimum orbitals φ. 1) into the variational expression. Minimisation of this variational expression with respect to the φ. defines the optimum φ.. Clearly, in order to carry through this program, we must assume a functional form for the atomic orbitals φ. which: Y (i) i is physically realistic and (ii) contains adjustable parameters which can be optimised.

That we must look for re-usable elements of molecular electronic structure; functions reflecting the recurring, almost environment independent, regions of electron density. We should perhaps note in passing that the Schrödinger equation cannot be solved by sleight of hand - our transformations of the form of the equation have shifted the bulk of the numerical work to another area which is more amenable to systematic computation. most important practical The problem to be solved is the optimisation of the orbitals μ.

### Ab Initio Valence Calculations in Chemistry by D. B. Cook

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