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Is usually referred to as the diagonal isat ion of Thus the variational calculation associated with the Valence-Bond method reduces to a single matrix di agonalis at i on. The application of the variation method to the optimisation of the orbitals of a single configuration is important enough to merit a separate chapter - Chapter 4. 8 Approximation ADDENDUM - THE FORMAL CONTENT OF CHAPTER 3 "Wittgenstein held mathematics to consist of equations which are dispensable in principle . . n * Many chemists can find much more pressing and personal reasons than Wittgenstein's for regarding mathematics as dispensible.

5) with different energies (the product integrates to of the zero). 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.

10) have been collected into the matrix GJ the "total electron interaction matrix1' of Roothaan: Gk = m I r,s=l {[2(k£,rs)-(kr,*s)] = m I r,s=l {2(k*,rs)-(kr,*s)} n/2 ... 13) ( C C )rs The integrals involving the basis functions χ. and the electron repulsion operator g(1,2) have been abbreviated to (ki,,rs) where (U,rs) = fdr 1 fdr 2 x k (r 1 ) Xjl (r 1 )è(l,2)x r (r 2 )x s (r 2 ) The matrix H i s u s u a l l y r e f e r r e d t o as t h e Hamiltonian matrix one-electron and t h e b a s i s f u n c t i o n i n t e g r a l s as the electron repulsion two-electron integrals.

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