Spin-coupled wavefunctions

Abstract

A new method of formulating the construction of spin-coupled wave-functions, in which each electron is ascribed to a different spatial function, is described. The direct use of the matrix representatives, ∪(P), of the permutation operators P, normally required in constructing antisymmetric wavefunctions, is avoided. Instead, antisymmetrizing operators are introduced as matrices, in such a way as to considerably reduce the amount of data required to characterize the spin-state, thereby increasing the computational efficiency of the method. The theory is applied to the three-electron systems Li, HeH and LiH⁺ using a simple one-configuration model, in which the orbitals are written in elliptical coordinates, and the non-linear parameters are optimized numerically.