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

By D. B. Cook

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4). 5) does not follow from It is still possible, however, to choose the functions Ψ -, Ψ 0,... 6) holds. The whole set of functions which are solutions of a particular Schrödinger equation form a complete symmetric functions in 3n variables. set of anti- Any anti-symmetric, continuous, normalisable function can be expanded as a linear 28 The Orbital Approximation combination of the solutions of a Schrödinger equation of the same dimension. 8) <1τΨΨ The proof of this inequality is quite simple and illustrates some of the formal methods of quantum mechanics in manipulating functions whose forms are known.

Within our orbital approximation scheme the independent-particle model is realised by using a wave function consisting of a single determinant of spin-orbitals; Ψ = a single orbital configuration: det{X1(x])X2(x2) ... 1) Here, each spin-orbital λ. is occupied by just one electron; the n! terms in the determinant only differ by which electron is in λ.. For the moment, we make the restriction that the electronic system shall be of "closed-shell" or "spinpaired" structure with each spatial orbital doubly occupied by two electrons of opposite spin.

5) This form of the expression shows that it is the mean repulsion energy of the charge distribution X^Xo with the charge density in curly brackets - the sum of all the possible products χ χ multiplied by the weights with which they occur in the total It electron density. XX and the rest is the mean repulsion of the electronic system. 5) and also includes the effect of the Pauli principle on the orbital model. The sum of the two terms is the mean potential which an electron having distribution χ, χ experiences due to all the other electrons.

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