Determination of a wave function functional: the constrained search–variational method

Abstract

In a recent paper we proposed the expansion of the space of variations in energy calculations by considering the approximate wave function, ψ, to be a functional of functions χ : ψ = ψ [χ], rather than a function. The space of variations is expanded because such a functional can in principle be adjusted through the function χ to reproduce the true wave function. For the determination of an approximate wave function functional, a constrained search is first performed over the subspace of all functions χ such that ψ [χ] satisfies a physical constraint or leads to the known value of an observable. A rigorous upper bound to the energy is then obtained by application of the variational principle. To demonstrate the advantages of the expansion of variational space, we apply the constrained search–variational method to the ground state of the negative ion of atomic hydrogen, the helium atom, and its isoelectronic sequence. The method is equally applicable to excited states, and its extension to such states in conjunction with the theorem of Theophilou is described. We also briefly describe our approach to the many-electron problem.

Acknowledgements

This work was supported in part by the Research Foundation of CUNY. L. M. was supported in part by NSF through CREST, and by a “Research Centers in Minority Institutions” award, RR-03037, from the National Center for Research Resources, National Institutes of Health.