Auxiliary-field quantum Monte Carlo method with seniority-zero trial wave function

TL;DR

This paper introduces a new phaseless auxiliary-field quantum Monte Carlo approach using seniority-zero wave functions, improving efficiency in capturing static and dynamic correlations for molecular systems.

Contribution

It develops a DOCI-based trial wave function for ph-AFQMC, with an orbital-optimized version, enabling more accurate and cost-effective multi-reference calculations.

Findings

OO-DOCI-AFQMC matches CAS-based methods in accuracy.

The approach outperforms coupled-cluster methods in some cases.

Limitations arise for strongly correlated systems.

Abstract

We present an approach that uses the doubly occupied configuration interaction (DOCI) wave function as the trial wave function in phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC). DOCI is a seniority-zero method focused on electron pairs. Although DOCI considers much fewer electron configurations than the complete active space (CAS) configuration interaction method, it efficiently captures the static correlation, while the consequent ph-AFQMC recovers the dynamical correlation across all orbitals. We also explore an orbital-optimized version (OO-DOCI) to further improve accuracy. We test this approach on several chemical systems, including single O-H bond breaking in water and polymer additives. In these cases, OO-DOCI-AFQMC closely matches CAS-based ph-AFQMC and even outperforms coupled-cluster singles, doubles, and perturbative triples. However, for strongly correlated systems, such as the carbon dimer and multi-bond dissociation in hydrogen systems and water, the method's accuracy drops. This suggests that seniority-zero space models may be insufficient as trial wave functions in ph-AFQMC for strongly correlated systems, suggesting the need for trial wave functions in an extended space. Despite such a limitation, our study demonstrates that DOCI- and OO-DOCI-based ph-AFQMC can reduce the steep cost of CAS approaches, offering a path to accurate multi-reference calculations for larger, more complex systems.