A Self Consistent Field Formulation of Excited State Mean Field Theory

TL;DR

This paper introduces a self-consistent field approach for excited state mean field theory, enabling efficient orbital optimization similar to Hartree Fock, and significantly reducing computational costs when combined with configuration interaction methods.

Contribution

It develops a self-consistent field formulation for excited state mean field theory that parallels Hartree Fock, improving optimization speed and computational efficiency.

Findings

Orbital optimization speed is within a factor of two of ground state mean field theory.

The approach reduces computational cost compared to previous quasi-Newton methods.

Combining with CI singles Davidson solver enhances efficiency in excited state calculations.

Abstract

We show that, as in Hartree Fock theory, the orbitals for excited state mean field theory can be optimized via a self-consistent one-electron equation in which electron-electron repulsion is accounted for through mean field operators. In addition to showing that this excited state ansatz is sufficiently close to a mean field product state to admit a one-electron formulation, this approach brings the orbital optimization speed to within roughly a factor of two of ground state mean field theory. The approach parallels Hartree Fock theory in multiple ways, including the presence of a commutator condition, a one-electron mean-field working equation, and acceleration via direct inversion in the iterative subspace. When combined with a configuration interaction singles Davidson solver for the excitation coefficients, the self consistent field formulation dramatically reduces the cost of the theory compared to previous approaches based on quasi-Newton descent.