Orthogonality-constrained variational calculation of excited state wavefunctions and energies: a penalised-functional-based strategy

Abstract

A viable strategy is developed for the general variational calculation of excited state wavefunctions which are constrained to remain orthogonal to all the lower lying states of the same symmetry. A key element of the strategy is to employ the penalised-functional procedure for enforcing the relevant orthogonality constraints and a gradient-based direct method to locate the constrained minima, bypassing the problem of Hessian singularity. The workability of the algorithm is tested on some model problems.