Fully self-consistent optimization of the Jastrow-Slater-type wave function using a similarity-transformed Hamiltonian

TL;DR

This paper introduces a self-consistent optimization method for Jastrow-Slater wave functions using a similarity-transformed Hamiltonian, improving electronic structure calculations by combining TC and VMC techniques.

Contribution

It develops a fully self-consistent approach to optimize both orbitals and Jastrow factors using the TC+VMC method, demonstrating systematic energy improvements.

Findings

Systematic energy improvements with better Jastrow functions.

Partial benefits from orbital optimization in one-shot TC+VMC.

Potential of one-shot TC+VMC as an alternative for complex systems.

Abstract

It has been well established that the Jastrow correlation factor can effectively capture the electron correlation effects, and thus, the efficient optimization of the many-body wave function including the Jastrow correlation factor is of great importance. For this purpose, the transcorrelated $+$ variational Monte Carlo (TC$+$VMC) method is one of the promising methods, where the one-electron orbitals in the Slater determinant and the Jastrow factor are self-consistently optimized in the TC and VMC methods, respectively. In particular, the TC method is based on similarity-transformation of the Hamitonian by the Jastrow factor, which enables the efficient optimization of the one-electron orbitals under the effective interaction. Through test calculations of some closed-shell atoms, He, Be, and Ne, we find that the total energy is in many cases systematically improved by using better Jastrow functions. We find that even a one-shot TC$+$VMC calculation, where the Jastrow parameters are optimized at the Hartree-Fock$+$VMC level, can yield partial benefits from orbital optimization. It is also suggested that one-shot TC$+$VMC can be a good alternative way for complex systems. Our study provides important insights for optimizing many-body wave function including the Jastrow correlation factor, which would be of great help for development of highly accurate electronic structure calculations.