Quantum Monte Carlo with Variable Spins

TL;DR

This paper extends quantum Monte Carlo methods to include variable spins and spin-orbit interactions, providing a detailed methodology, theoretical proofs, and applications to atomic and molecular systems with results aligning closely with experimental data.

Contribution

It introduces a variable spin quantum Monte Carlo approach with a proof of an upper-bound property for complex operators, enhancing the method's accuracy and applicability.

Findings

Accurate calculation of binding energies and geometries for PbH and Sn2 molecules.

Electron affinities of 6p elements closely match experimental values.

Method ensures variational property through T-moves and handles spin-orbit interactions.

Abstract

We investigate the inclusion of variable spins in electronic structure quantum Monte Carlo, with a focus on diffusion Monte Carlo with Hamiltonians that include spin-orbit interactions. Following our previous introduction of fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC), we thoroughly discuss the details of the method and elaborate upon its technicalities. We present a proof for an upper-bound property for complex nonlocal operators, which allows for the implementation of T-moves to ensure the variational property. We discuss the time step biases associated with our particular choice of spin representation. Applications of the method are also presented for atomic and molecular systems. We calculate the binding energies and geometry of the PbH and Sn$_2$ molecules, as well as the electron affinities of the 6$p$ row elements in close agreement with experiments.