A condition to remove the indeterminacy in interelectronic correlation functions

Abstract

It can easily be seen that there is an infinity of different ways of expressing a correlated wavefunction which consists of a Slater determinant multiplied by two-electron correlation functions. It is shown that it is possible to introduce an extra condition which does not affect the wavefunction but which causes the correlation factors to have the least effect on the Slater determinant. Here such a contraction condition is proposed in a form which only involves six-dimensional integrals and which has been found to give a very systematic procedure in a thorough calculation of a correlated wavefunction for neon. Certain correlation expansion functions can be defined so that any combination of these gives a function which satisfies this contraction condition. This contracted form provides canonical expressions for the correlation function and the orbitals so that if two different calculations are made in this form it is possible to compare the two correlation functions and the two sets of orbitals because in the completely accurate wavefunction they should be the same. Such a property has not occurred in previous calculations or theories.