A Stochastic Cluster Expansion for Electronic Correlation in Large Systems

TL;DR

This paper introduces a stochastic cluster expansion method that efficiently estimates total correlation energy in large systems without pre-selecting active spaces, achieving near-DMRG accuracy and enabling high-precision studies of condensed phase chemistry.

Contribution

The novel stochastic cluster expansion framework allows accurate correlation energy calculations in large systems without prior active space selection, reducing computational cost.

Findings

Reproduces total energies with near-DMRG accuracy

Reduces computational cost significantly

Provides a diagnostic for molecule-solvent correlation

Abstract

Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size. Downfolding and embedding approaches mitigate this cost but typically require prior selection of a correlated subspace, which can be difficult to determine in heterogeneous or extended systems. Here, we introduce a stochastic cluster expansion framework for efficiently recovering the total correlation energy of large systems with near-DMRG accuracy, without the need to select an active space a priori. By combining correlation contributions from randomly sampled environment orbitals with an exactly treated subspace of interest, the method reproduces total energies for non-reacting and reactive systems while drastically reducing computational cost. The approach also provides a quantitative diagnostic for molecule-solvent correlation, guiding principled embedding decisions. This framework enables systematically improvable many-body calculations in extended systems, opening the door to high-accuracy studies of chemical processes in condensed phase environments.