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

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By D. B. Cook

ISBN-10: 0408705515

ISBN-13: 9780408705516

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Example text

I since the functions μ, and ζ. do not change when new variables are K substituted. 1 The coefficients Bf are therefore redundant in the sense that sets of n! of them are related by antisymmetry in the subscripts. Associating a spin factor ζ. with each spatial orbital y, and collecting the n! χ η ) '- k where VW···*^ = d e t { x i ( χ Ρ λ ΐ (χ2) '"Xi ( χ η ) } 1 2 n The suffix k counts the number of distinct determinants obtainable from the occupation of an infinite complete set of spin-orbitals; λ.

Rn) χ ζ ( s 1 ) C i ( s 2 ) · . 6) where the prime has been added to the symbols F and B to denote the expansion of the space to include spin. 36 The Orbital Approximation Any acceptable molecular wave function must satisfy the Pauli principle. i since the functions μ, and ζ. do not change when new variables are K substituted. 1 The coefficients Bf are therefore redundant in the sense that sets of n! of them are related by antisymmetry in the subscripts. Associating a spin factor ζ. with each spatial orbital y, and collecting the n!

4. 8) f άτ Ψ Ψ Now Ψ contains n! ) 2 terms! Fortunately, many of these terms have the same value - and many are zero since the functions Ψ are orthogonal. 8) and collecting like terms is a special case of the Slater/Lö'wdin rules which we discuss in Chapter 5 in connection with Valence-Bond theory. 10) the symmetric nature of g(1,2) ensures that Since both the functions φ. and φ. depend on the coordinates of one electron and the functions φ, and φ depend on the other 1 electron s variables we must have: The order of φ.

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


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