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Journal of Chemical Theory and Computation

Neural-Network-Based Selective Configuration Interaction Approach to Molecular Electronic Structure

Yorick L. A. Schmerwitz, Louis Thirion, Gianluca Levi, Elvar Ö. Jónsson, Pavlo V. Bilous, Hannes Jónsson, P. Hansmann

Published Feb 27, 2025• 6 citations
Publisher

Abstract

By combining Hartree–Fock with a neural-network-supported quantum-cluster solver proposed recently in the context of solid-state lattice models, we formulate a scheme for selective neural-network configuration interaction (NNCI) calculations and implement it with various options for the type of basis set and boundary conditions. The method’s performance is evaluated in studies of several small molecules as a step toward calculations of larger systems. In particular, the correlation energy in the N 2 molecule is compared with published full CI calculations that included nearly 10 10 Slater determinants, and the results are reproduced with only 4 × 10 5 determinants using NNCI. A clear advantage is seen from increasing the set of orbitals included rather than approaching full CI for a smaller set. The method’s high efficiency and implementation in a condensed matter simulation software expands the applicability of CI calculations to a wider range of problems, even extended systems through an embedding approach.

DOI
10.1021/acs.jctc.4c01479

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By combining Hartree–Fock with a neural-network-supported quantum-cluster solver proposed recently in the context of solid-state lattice models, we formulate a scheme for selective neural-network configuration interaction (NNCI) calculations and implement it with various options for the type of basis set and boundary conditions. The method’s performance is evaluated in studies of several small molecules as a step toward calculations of larger systems. In particular, the correlation energy in the N 2 molecule is compared with published full CI calculations that included nearly 10 10 Slater determinants, and the results are reproduced with only 4 × 10 5 determinants using NNCI. A clear advantage is seen from increasing the set of orbitals included rather than approaching full CI for a smaller set. The method’s high efficiency and implementation in a condensed matter simulation software expands the applicability of CI calculations to a wider range of problems, even extended systems through an embedding approach.
By combining Hartree-Fock with a neural-network-supported quantum-cluster solver proposed recently in the context of solid-state lattice models, we formulate a scheme for selective neural-network configuration interaction (NNCI) calculations and implement it with various options for the type of basis set and boundary conditions. The method's performance is evaluated in studies of several small molecules as a step toward calculations of larger systems. In particular, the correlation energy in the N2_22​ molecule is compared with published full CI calculations that included nearly 101010^{10}1010 Slater determinants, and the results are reproduced with only 4⋅1054\cdot10^{5}4⋅105 determinants using NNCI. A clear advantage is seen from increasing the set of orbitals included rather than approaching full CI for a smaller set. The method's high efficiency and implementation in a condensed matter simulation software expands the applicability of CI calculations to a wider range of problems, even extended systems through an embedding approach.
A neural-network approach to optimize the selection of Slater determinants in configuration interaction calculations for condensed-matter quantum many-body systems is developed. We exemplify our algorithm on the discrete version of the single-impurity Anderson model with up to 299 bath sites. Employing a neural network classifier and active learning, our algorithm enhances computational efficiency by iteratively identifying the most relevant Slater determinants for the ground state wave function. We benchmark our results against established methods and investigate the efficiency of our approach compared to another basis truncation scheme without a neural network. Our algorithm demonstrates a substantial improvement in the efficiency of determinant selection, yielding a more compact and computationally manageable basis without compromising accuracy. Given the straightforward application of our neural-network-supported selection scheme to other model Hamiltonians of quantum many-body clusters, our algorithm can significantly advance selective configuration interaction calculations in the context of correlated condensed matter.
Selective configuration interaction methods approximate correlated molecular ground- and excited states by considering only the most relevant Slater determinants in the expansion. While a recently proposed neural-network-assisted approach efficiently identifies such determinants, the procedure typically relies on canonical Hartree-Fock orbitals, which are optimized only at the mean-field level. Here we assess approximate natural orbitals - eigenfunctions of the one-particle density matrix computed from intermediate many-body eigenstates - as an alternative. Across our benchmarks for H2_22​O, NH3_33​, CO, and C3_33​H8_88​ we see a consistent reduction in the required determinants for a given accuracy of the computed correlation energy compared to full configuration interaction calculations. Our results confirm that even approximate natural orbitals constitute a simple yet powerful strategy to enhance the efficiency of neural-network-assisted configuration interaction calculations.
Selected configuration interaction methods achieve near-exact electronic structure calculations by iteratively constructing compact variational spaces, but their efficiency depends critically on the heuristics used to identify important determinants. Here, we introduce a data-driven selection framework that recasts determinant importance as a binary classification task and integrates a neural-network classifier into the iterative CI workflow through an active-learning loop. At each iteration, a random subset of candidate determinants is labelled via temporary diagonalisation, and the trained classifier guides selection of the remaining configurations. We demonstrate the utility of this framework for both classical and quantum CI methods by calculating the ground-state energy of a diatomic molecule. Our method achieves result parity with traditional configuration interaction methods at substantially lower computational cost: roughly a ×5\times 5×5 reduction in memory and per-iteration cost for the classical cHCI variant, and convergence in markedly fewer iterations for the quantum-classical cSQD variant. These results establish classifier-assisted determinant selection as a lightweight, method-agnostic tool for compressing variational spaces and accelerating both classical and hybrid quantum-classical configuration interaction algorithms.
Quantum many-body calculations are fundamentally limited by the exponential growth of the configuration space, making accurate treatment of strongly correlated systems computationally prohibitive. Here we present the Generative Transformer Neural Network Selected Configuration Interaction (GTNN-SCI), a Transformer-based machine learning approach that generatively samples important configurations to accelerate many-body quantum chemistry calculations. By leveraging the Transformer architecture’s self-attention mechanism to capture long-range electron correlations, GTNN-SCI achieves up to 10× speedup compared to state-of-the-art neural network methods while maintaining high accuracy. We demonstrate the efficacy of GTNN-SCI by calculating correlation and binding energies for representative molecules including N 2, H 2 O, and C 2 using both Gaussian (cc-pVDZ) and plane-wave basis sets, achieving faster convergence and lower energies than previously reported neural network-based selected CI techniques. Most significantly, our generative approach identifies higher-order excitations missed by conventional coupling schemes, yielding lower variational energies than established methods including heat-bath CI. This capability enables GTNN-SCI to accurately treat the strongly correlated [Fe 2 S 2 (SCH 3 ) 4 ] 2– ([2Fe–2S]) cluster system, achieving ground-state energies within chemical accuracy of DMRG benchmarks, whereas conventional selected CI methods have failed on this system. The GTNN-SCI method thus combines modern deep learning with high-performance electronic structure computation, providing an efficient and precise avenue for solving the electronic Schrödinger equation in challenging molecular systems.
Selected configuration interaction (SCI) methods are currently enjoying a resurgence due to several recent developments which improve either the overall computational efficiency or the compactness of the resulting SCI vector. These recent advances have made it possible to get full CI (FCI) quality results for much larger orbital active spaces compared to conventional approaches. However, due to the starting assumption that the FCI vector has only a small number of significant Slater determinants, SCI becomes intractable for systems with strong correlation. This paper introduces a method for developing SCI algorithms in a way which exploits local molecular structure to significantly reduce the number of SCI variables. The proposed method is defined by first grouping the orbitals into clusters over which we can define many-particle cluster states. We then directly perform the SCI algorithm in a basis of tensor products of cluster states instead of Slater determinants. While the approach is general for arbitrarily defined cluster states, we find significantly improved performance by defining cluster states through a Tucker decomposition of the global (and sparse) SCI vector. To demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), we present numerical results for a diverse set of examples: (1) modified Hubbard model with different inter- and intracluster hopping terms, (2) less obviously clusterable cases of bond breaking in N 2 and F 2, and (3) ground state energies of large planar π-conjugated systems with active spaces of up to 42 electrons in 42 orbitals. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems.