Fixed and partial-node approximations in Slater determinant space for molecules

TL;DR

This paper explores fixed and partial-node approximations in Slater determinant space using FCIQMC, demonstrating their effectiveness and limitations in molecular systems and active spaces, including large molecules like ferrocene and acenes.

Contribution

It introduces a practical fixed-node FCIQMC method and studies the convergence and sign problem of partial-node approximations in molecular calculations.

Findings

Fixed-node FCIQMC provides accurate results for molecular systems.

Partial-node approximation's effectiveness is limited by walker population requirements.

Scaling of fixed-node FCIQMC iterations is efficient for large active spaces.

Abstract

We present a study of fixed and partial-node approximations in Slater determinant basis sets, using full configuration interaction quantum Monte Carlo (FCIQMC) to perform sampling. Walker annihilation in the FCIQMC method allows partial-node simulations to be performed, relaxing the nodal constraint to converge to the FCI solution. This is applied to ab initio molecular systems, using symmetry-projected Jastrow mean-field wave functions for complete active space (CAS) problems. Convergence and the sign problem within the partial-node approximation are studied, which is shown to eventually be limited in its use due to the large walker populations required. However the fixed-node approximation results in an accurate and practical method. We apply these approaches to various molecular systems and active spaces, including ferrocene and acenes. This also provides a test of symmetry-projected Jastrow mean-field wave functions in variational Monte Carlo (VMC) for a new set of problems. For trans-polyacetylene molecules and acenes we find that the time to perform a constant number of fixed-node FCIQMC iterations scales as O(N^{1.44}) and O(N^{1.75}) respectively, resulting in an efficient method for CAS-based problems that can be applied accurately to large active spaces.