Toward linear scaling auxiliary field quantum Monte Carlo with local natural orbitals

TL;DR

This paper introduces a local natural orbital-based auxiliary field quantum Monte Carlo method that achieves linear scaling, significantly reducing computational costs for large molecular systems while maintaining accuracy.

Contribution

The authors develop a novel LNO-AFQMC method that enables linear scaling by performing localized calculations, improving efficiency over traditional AFQMC for large systems.

Findings

LNO-AFQMC converges energies with reduced computational cost.

The method is more efficient for larger systems and basis sets.

Energy differences converge faster than total energies.

Abstract

We develop a local correlation variant of auxiliary field quantum Monte Carlo (AFQMC) that is based on local natural orbitals (LNO-AFQMC). In LNO-AFQMC, independent AFQMC calculations are performed for each localized occupied orbital using a truncated set of tailored orbitals. Because the size of this space does not grow with system size for a target accuracy, the method has linear scaling. Applying LNO AFQMC to molecular problems containing a few hundred to a thousand orbitals, we demonstrate convergence of total energies with significantly reduced costs. The savings are more significant for larger systems and larger basis sets. However, even for our smallest system studied, we find that LNO-AFQMC is cheaper than canonical AFQMC, in contrast with many other reduced-scaling methods. Perhaps most significantly, we show that energy differences converge much more quickly than total energies, making the method ideal for applications in chemistry and material science. Our work paves the way for linear scaling AFQMC calculations of strongly correlated systems, which would have a transformative effect on ab initio quantum chemistry.