A generalized variational principle with applications to excited state mean field theory

TL;DR

This paper introduces a generalized variational principle compatible with various electronic structure methods, enabling efficient targeting of excited states and improving optimization in excited state mean field theory, leading to more accurate results.

Contribution

It presents a new generalized variational principle that can target excited states and enhance optimization efficiency across multiple electronic structure methods.

Findings

Improved optimization efficiency by an order of magnitude.

Achieved accuracy comparable to coupled cluster methods.

Applicable to a broad range of molecules.

Abstract

We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of electronic structure methods, including mean-field theory, density functional theory, multi-reference theory, and quantum Monte Carlo. Like the standard variational principle, this generalized variational principle amounts to the optimization of a nonlinear function that, in the limit of an arbitrarily flexible wave function, has the desired Hamiltonian eigenstate as its global minimum. Unlike the standard variational principle, it can target excited states and select individual states in cases of degeneracy or near-degeneracy. As an initial demonstration of how this approach can be useful in practice, we employ it to improve the optimization efficiency of excited state mean field theory by an order of magnitude. With this improved optimization, we are able to demonstrate that the accuracy of the corresponding second-order perturbation theory rivals that of singles-and-doubles equation-of-motion coupled cluster in a substantially broader set of molecules than could be explored by our previous optimization methodology.