Stochastic Cluster Expansion for Excited State Energies

TL;DR

The paper introduces a stochastic cluster expansion method for calculating excited state energies in strongly correlated systems, avoiding large active spaces and achieving accurate results efficiently.

Contribution

It extends the stochastic cluster expansion framework to excited states, enabling systematic and efficient computation of excitation energies without large active spaces.

Findings

Accurate singlet-triplet gaps for charge-transfer complexes and polyacenes.

Convergence achieved with low-order cluster terms.

Method matches full-system results for excitation energies.

Abstract

Excited-state electronic structure in strongly correlated systems remains challenging due to the exponential scaling of the many-body Hilbert space and the difficulty of constructing systematically controlled active spaces. Building on the stochastic cluster expansion (SCE) framework previously developed for ground-state correlation energies, we extend the formalism to excitation gaps by expressing energy differences directly as a hierarchy of orbital-space cluster contributions. In this formulation, excitation energies are reconstructed from reduced-rank calculations involving a minimal frontier chemical subspace (FCS), treated exactly, together with stochastic sampling of the remaining orbital environment. This approach eliminates the need for large or chemically preselected active spaces. We demonstrate the method on charge-transfer complexes and polyacenes, where accurate singlet-triplet gaps are obtained that agree with full-system results. The method converges with low-order cluster terms and provides a systematically improvable framework for excited states in correlated systems.