Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules

TL;DR

This paper develops an advanced linear optimization method for Jastrow-Slater wave functions in variational Monte Carlo, enabling highly accurate calculations of atomic and molecular systems, including potential energy curves and molecular well depths.

Contribution

It introduces a robust linear optimization approach that simultaneously optimizes all wave function parameters, including basis exponents, improving accuracy in quantum Monte Carlo calculations.

Findings

Accurate potential energy curve for C₂ molecule up to dissociation

Systematic near chemical accuracy in molecular well depths

Effective optimization of wave functions for first-row atoms and diatomics

Abstract

We pursue the development and application of the recently-introduced linear optimization method for determining the optimal linear and nonlinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely the Jastrow, configuration state function and orbital parameters. We show that the linear optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a linear combination of the energy and the energy variance. We apply the linear optimization method to obtain the complete ground-state potential energy curve of the C_2 molecule up to the dissociation limit, and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations. We perform calculations of the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.