Equation of Motion Theory for Excited States in Variational Monte Carlo and the Jastrow Antisymmetric Geminal Power in Hilbert Space

Abstract

An equation of motion formalism for excited states in variational Monte Carlo is derived and a pilot implementation for the Jastrow-modified antisymmetric geminal power is tested. In single excitations across a range of small molecules, this combination is shown to be intermediate in accuracy between configuration interaction singles and equation of motion coupled cluster with singles and doubles. For double excitations, energy errors are found to be similar to those for coupled cluster.

Communication: Variation after response in quantum Monte Carlo

“…(5) VMC, and in general are much more expensive to evaluate than the first derivatives that are used in both ground state VMC [13][14][15] and EOM-VMC. 7 To avoid the explicit evaluation of wave function second derivatives, we will therefore adopt a finite difference approximation to our EOM ansatz,…”

“…7 In our previous work minimizing Ω for the JAGP, we found that it can be quite challenging to choose a good initial guess for the excited state. In our work on EOM-JAGP, we observed unacceptably large biases in favor of the ground state, the origin of which can be traced to its accuracy for ground states despite its compact parameterization.…”

“…This compactness limits the flexibility of the EOM ansatz and thus excited state accuracy, which in the presence of an accurate ground state leads to a bias that overestimates excitation energies. 7 Using the VAR-JAGP ansatz, we can address both the initial guess and ground state bias issues. To do so, we start with the JAGP ground state values for ⃗ x and make an initial guess for ⃗ µ either by hand or in difficult cases using EOM-JAGP.…”

“…In our results below, we have taken similar care to adjust ω to ensure energy insensitivity is satisfied. We first tested the methodology in H 2 O and C 2 by adopting the straightforward approach of using the EOM-JAGP wave functions 7 as the initial guesses for the VAR excited state optimizations. In Figures 2 and 3, we see that VAR-JAGP is competitive in accuracy with EOM-CCSD for single excitations, while surpassing it in C 2 's low-lying double excitations.…”

“…In Figures 2 and 3, we see that VAR-JAGP is competitive in accuracy with EOM-CCSD for single excitations, while surpassing it in C 2 's low-lying double excitations. To understand how this accuracy comes about, it is important to recognize that in a molecule with a single-reference ground state, the LR space of JAGP contains all single excitations and some double excitations, 7 and so we would expect it to be at least qualitatively accurate even at the EOM level of theory. By relaxing ⃗ x, VAR-JAGP lowers the excitation energies as compared with EOM-JAGP and improves their overall accuracy.…”