The determination of energies and wavefunctions with full electronic correlation

Abstract

It has been widely thought that the use of wavefunctions with full electronic correlation would involve integrals of 3N dimensions, where N is the number of electrons. Here it is shown that by a method similar to that of variation theory a set of equations which determine the orbitals and correlation function can be derived so that they only involve integrals of up to nine dimensions. Even these nine-dimensional integrals have some special characteristics which make them equivalent to six-dimensional integrals in some methods of integration. The method is formulated for the particular canonical choice of correlation function that has been previously investigated by the authors and is based on a particular trans-correlated kind of wave equation and on some particular convergence properties recently shown for bi-variational problems. This appears to provide a solution to the problem of including all r$_{ij}$ quantities in wavefunctions: a problem which has been variously discussed for the last thirty years.