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.
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.
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as the 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 and 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 nonreacting 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.
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.
The theoretical treatment of low-lying excited states in strongly correlated (SC) systems, particularly those with multi-electron excitation character, typically requires computational methods with exponential scaling. To address this bottleneck, we develop the equation-of-motion generalized valence bond based block-correlated coupled cluster approach with up to four-block correlation (EOM-GVB-BCCC4). This method is capable of capturing low-lying excited states of SC systems with large active spaces with a polynomial O ( N 6 ) cost. We show that this approach provides a noticeable improvement over its lower-order truncated schemes, successfully identifying the doubly excited triplet–triplet pair state in singlet-fission candidates that were missed by its EOM-GVB-BCCC3 variant. Furthermore, the method achieves remarkably high accuracy for transition-metal complexes and organic diradicals, yielding excitation energies in excellent agreement with density matrix renormalization group (DMRG) benchmarks. These results highlight EOM-GVB-BCCC4 as a powerful method for investigating SC systems with large active spaces that are beyond the reach of conventional multireference approaches.
An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overheads of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS towards fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the triplet over the quintet spin state; (c) the study of an Fe4S4 cluster's spin-ladder energetics via highly truncated stochastic-GAS wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.
An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overheads of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS towards fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the triplet over the quintet spin state; (c) the study of an Fe4S4 cluster's spin-ladder energetics via highly truncated stochastic-GAS wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.
An algorithm to perform stochastic generalized active space calculations, Stochastic-GAS, is presented, that uses the Slater determinant based FCIQMC algorithm as configuration interaction eigensolver. Stochastic-GAS allows the construction and stochastic optimization of preselected truncated configuration interaction wave functions, either to reduce the computational costs of large active space wave function optimizations, or to probe the role of specific electron correlation pathways. As for the conventional GAS procedure, the preselection of the truncated wave function is based on the selection of multiple active subspaces while imposing restrictions on the interspace excitations. Both local and cumulative minimum and maximum occupation number constraints are supported by Stochastic-GAS. The occupation number constraints are efficiently encoded in precomputed probability distributions, using the precomputed heat bath algorithm, which removes nearly all runtime overheads of GAS. This strategy effectively allows the FCIQMC dynamics to a priori exclude electronic configurations that are not allowed by GAS restrictions. Stochastic-GAS reduced density matrices are stochastically sampled, allowing orbital relaxations via Stochastic-GASSCF, and direct evaluation of properties that can be extracted from density matrices, such as the spin expectation value. Three test case applications have been chosen to demonstrate the flexibility of Stochastic-GAS: (a) the Stochastic-GASSCF optimization of a stack of five benzene molecules, that shows the applicability of Stochastic-GAS towards fragment-based chemical systems; (b) an uncontracted stochastic MRCISD calculation that correlates 96 electrons and 159 molecular orbitals, and uses a large (32, 34) active space reference wave function for an Fe(II)-porphyrin model system, showing how GAS can be applied to systematically recover dynamic electron correlation, and how in the specific case of the Fe(II)-porphyrin dynamic correlation further differentially stabilizes the triplet over the quintet spin state; (c) the study of an Fe4S4 cluster's spin-ladder energetics via highly truncated stochastic-GAS wave functions, where we show how GAS can be applied to understand the competing spin-exchange and charge-transfer correlating mechanisms in stabilizing different spin-states.