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A Generalized Variational Principle with Applications to Excited State Mean Field Theory
journal contribution
posted on 2020-02-22, 13:03 authored by Jacqueline
A. R. Shea, Elise Gwin, Eric NeuscammanWe
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, multireference 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.