Redundant parameter dependencies in truncated classic and quantum Linear Response and Equation of Motion theory

TL;DR

This paper investigates how parameter dependencies affect excitation energy calculations in truncated linear response and equation of motion theories, revealing issues with orbital dependence and proposing optimization methods for improvement.

Contribution

It identifies the dependence of excitation energies on orbital choices in truncated LR and EOM methods and proposes a constrained trace optimization approach to mitigate this issue.

Findings

Excitation energies depend on orbital choices even at FCI ground state.

Constrained trace optimization improves spectral accuracy.

Targeted state optimization further enhances results.

Abstract

Extracting molecular properties from a wave function can be done through the linear response (LR) formalism or, equivalently, the equation of motion (EOM) formalism. For a simple model system, He in a 6-31G basis, it is here shown that calculated excitation energies depend on the specifically chosen orbitals, even when the ground-state is the FCI solution, if the LR is truncated to a singles expansion. This holds for naive, projected, self-consistent, and state-transfer parametrizations of the LR operators. With a focus on the state-transfer parameterization, this problem is shown to also hold for more complicated systems, and is also present when the LR is truncated to singles and doubles. This problem can be alleviated by performing a ground-state constrained trace optimization of the Hessian matrix before performing the LR calculation. It is finally shown that spectra can be further improved for small LR expansions by targeting only a few states in the constrained trace optimization using constrained state-averaged UCC.