By D. B. Cook
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Of an essentially multi-configurât ion wave function is the Valence-Bond method which is used very widely by chemists in a qualitative way, but has found little quantitative application. 7 THE LINEAR VARIATION METHOD The computation of optimum linear expansion coefficients - the D. 1) where H.. ij * = f άτ Φ. 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..
Most important practical The problem to be solved is the optimisation of the orbitals μ. and/or the linear coefficients D.. Fortunately there is an all-embracing theorem which will enable both types of optimisation to be performed. 1), is not in a form which lends itself to the systematic use of approximation 26 The Orbital methods. Approximation In this section we re-cast the equation into an equivalent form which is particularly suited to computational implementation. In order to effect this transformation we must go a little more deeply into the formal properties of the solutions of the Schrödinger equation.
2) are functions of r in this system and the spherical harmonics are functions of Θ and φ. The so-called orbital depends on the nuclear charge of the atom. r exp(-cr) i where the coefficients b. are fixed electron Schrödinger equation. by the solution of the one- If, therefore, we allow the coefficients b. and the orbital exponents ζ to vary we have a plausible form for AOs of polyelectronic atoms which contains the freedom necessary for the application of the variation principle. 3) for each atomic orbital and optimise the overall wave function with respect to the linear coefficients and orbital exponents.