Coupled Cluster (CC) theory is one of the most popular correlated wavefunction methods, yet the steep computational cost scaling of CC truncated at higher rank limits its application. Modern Selected Configuration Interaction (SCI) methods successfully exploit the sparsity of ground-state wavefunctions in the determinant space, motivating an analogous approach with the exponential CC ansatz. In this work, we introduce Selected Coupled Cluster (SCC), an arbitrary-order sparse CC method that explicitly solves the CC residual equations within a compact amplitude space guided by an SCI wavefunction. SCC optimizes the CC amplitudes in the sparse amplitude space. Using a pilot Just-in-Time (JIT) compiled implementation, we benchmark SCC against SCI, SCI+PT2, standard rank-truncated dense CC (CCSD, CCSDT), and DMRG across various chemical systems. We demonstrate that SCC exhibits fast, monotonic convergence with the SCI variational threshold, outperforming SCI and surpassing SCI+PT2 in the tight-threshold regime. SCC also provides accurate energies for high-dimensional topologies, where DMRG typically converges slowly with bond dimension. SCC thus presents an efficient drop-in enhancement for modern SCI workflows.
Coupled Cluster (CC) theory is one of the most popular correlated wavefunction methods, yet the steep computational cost scaling of CC truncated at higher rank limits its application. Modern Selected Configuration Interaction (SCI) methods successfully exploit the sparsity of ground-state wavefunctions in the determinant space, motivating an analogous approach with the exponential CC ansatz. In this work, we introduce Selected Coupled Cluster (SCC), an arbitrary-order sparse CC method that explicitly solves the CC residual equations within a compact amplitude space guided by an SCI wavefunction. SCC optimizes the CC amplitudes in the sparse amplitude space. Using a pilot Just-in-Time (JIT) compiled implementation, we benchmark SCC against SCI, SCI+PT2, standard rank-truncated dense CC (CCSD, CCSDT), and DMRG across various chemical systems. We demonstrate that SCC exhibits fast, monotonic convergence with the SCI variational threshold, outperforming SCI and surpassing SCI+PT2 in the tight-threshold regime. SCC also provides accurate energies for high-dimensional topologies, where DMRG typically converges slowly with bond dimension. SCC thus presents an efficient drop-in enhancement for modern SCI workflows.
We present the quantum-selected configuration interaction-tailored coupled-cluster (QSCI-TCC) method, a hybrid quantum-classical scheme that tailors coupled-cluster (CC) theory with a quantum-selected configuration interaction (QSCI) wave function. QSCI provides a scalable, shot-efficient approach to reconstructing the many-electron state prepared on quantum hardware on a classical computer. The resulting active-space CI coefficients, which are free from additive shot noise, are mapped to fixed cluster amplitudes within the tailored coupled-cluster framework, after which a conventional CC calculation optimizes the remaining amplitudes. This workflow embeds static (strong) correlation from the quantum device and subsequently recovers dynamical (weak) correlation, yielding a balanced description of both. The method is classically simulated and applied to the simultaneous O-H bond dissociation in H2O and the triple-bond dissociation in N2. QSCI-TCC and its perturbative-triples variant, QSCI-TCC(T), provide accurate results even where CCSD or CCSD(T) begin to break down. Shot-count tests for the N2 (6e, 6o) active space demonstrate that, with the (c) correction, chemically sufficient precision (≤1 kcal/mol) is achieved with only 1.0×105 shots in the strongly correlated regime (r=2.2 Å) -- an order of magnitude fewer than required by an earlier matchgate-shadows implementation [J. Chem. Theory Comput., 20, 5068 (2024)]. By pairing resource-efficient quantum sampling with the CC theory, QSCI-TCC provides a promising pathway to quantum-chemical calculations of classically intractable 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.
High Resolution Image Download MS PowerPoint Slide Strongly correlated molecules remain out of reach for most electronic-structure solvers because the exact wave function spans a determinant space that grows exponentially with the number of orbitals. State-of-the-art selected-CI (e.g., CIPSI and HCI) and ML-CI methods mitigate search by exploiting Hamiltonian sparsity and learned prescreening. Nonetheless, in strongly multireference regimes, the excitation-based candidate lists can grow rapidly, which may increase memory and screening costs. We present the Hamiltonian-guided autoregressive selected-configuration interaction (HAAR-SCI), a learn–sample–compress workflow that runs on a single GPU. A gated Transformer samples determinants autoregressively; Gumbel Top-K noise encourages exploration, and GPU min-heap kernels keep only configurations with the largest Hamiltonian couplings. The network is retrained after each expansion, and iterations stop when successive energies differ by ≤1 mHa. Across an 18-molecule benchmark set reaching 116 spin–orbitals, HAAR-SCI attains a mean absolute error of 0.51 mHa while using much fewer determinants than heat-bath CI. It traces the entire N 2 dissociation curve within 0.67 mHa and achieves HCI accuracy for the 40-spin-orbital [Fe 2 S 2 (SCH 3 ) 4 ] 2– cluster with a determinant reduction of 72%, demonstrating its power on systems considered intractable for conventional selected-CI solvers. A final probability-mass pruning compresses typical wave functions by a further 10–50×, retaining <0.01% of the Hilbert space yet still capturing >99.9% of the correlation energy. HAAR-SCI thus offers a compact and truly scalable route to chemical-accuracy quantum chemistry on commodity hardware.
Accurate description of electron correlation is a central challenge in computational chemistry, with selected configuration interaction (SCI) emerging as a powerful tool to approach the full CI limit. While recent machine learning (ML) integrations have accelerated determinant selection, existing regression and classification approaches suffer from a fundamental objective-loss mismatch: they evaluate the importance of determinants in isolation without explicitly accounting for their relative importance ranking. Here, we introduce ranking configuration interaction (RCI), a novel ML-supported SCI framework that reframes determinant selection as a pairwise ranking problem. Building upon a Transformer-based architecture to capture complex, nonlocal orbital dependencies, RCI progressively optimizes the partial ordering of determinants. By doing so, RCI aligns the training objective more closely with the intrinsic ranking nature of SCI. Extensive benchmarks across both plane-wave and Gaussian basis sets, including the molecules N2, CO, H2O, NH3, and C2, demonstrate the efficiency of RCI. Compared to previously reported classification baselines, RCI consistently accelerates convergence─reducing overall computational time by 23% to over 50% depending on the system and requiring only 55% of the determinant count in representative cases such as N2 and CO. Furthermore, RCI exhibits robust performance and reaches chemical accuracy on the highly challenging iron-sulfur cluster using only 12% of the full CI space. Notably, RCI outperforms recent regression-based SCI methods by delivering a more than 15% improvement in accuracy at comparable determinant counts. RCI also demonstrates higher efficiency than heat-bath CI on the strongly correlated chromium dimer, yielding a compact and accurate wave function. This pairwise learning-to-rank model provides a lightweight and modular plugin that can be seamlessly incorporated into other supervised learning frameworks.
The Coupled-Cluster (CC) method is one of the most popular and efficient correlation methods in quantum chemistry. \nEspecially the CCSD(T) approximation, which includes single and double excitations by means of the application of the cluster operator \nto a reference determinant and triple excitations via a perturbative treatment, has become a standard tool \nin quantum chemical applications. However, the method is restricted to relatively small system sizes due to its unfavourable scaling (N^7, where N is the number of basis functions applied). \nFor the full treatment of triple excitations the scaling advances to N^8 and every further excitation level increases the exponent by two. \n \nThe goal of this work is to reduce the calculation time for closed shell systems at least by a factor growing with the excitation level for arbitrary truncation levels. \nThis is done by restricting the spatial parts of the spin orbitals and thus treat pairs of spin orbitals on the same footing. The restrictions can be easily constructed \nfor the CCSD model by spin integration. \nThe derivation of the restrictions arising in higher excited case will be done employing \nthe spatial orbital excitation operators E. \n \nIn the first part of this work an algorithm is derived that is capable of the derivation of the energy and amplitude equations for arbitrary excitation levels. In the second part \nan implementation of this algorithm is presented.
In single-reference coupled-cluster (CC) methods, one has to solve a set of non-linear polynomial equations in order to determine the so-called amplitudes that are then used to compute the energy and other properties. Although it is of common practice to converge to the (lowest-energy) ground-state solution, it is also possible, thanks to tailored algorithms, to access higher-energy roots of these equations that may or may not correspond to genuine excited states. Here, we explore the structure of the energy landscape of variational CC and we compare it with its (projected) traditional version in the case where the excitation operator is restricted to paired double excitations (pCCD). By investigating two model systems (the symmetric stretching of the linear H4 molecule and the continuous deformation of the square H4 molecule into a rectangular arrangement) in the presence of weak and strong correlations, the performance of variational pCCD (VpCCD) and traditional pCCD is gauged against their configuration interaction (CI) equivalent, known as doubly occupied CI, for reference Slater determinants made of ground- or excited-state Hartree–Fock orbitals or state-specific orbitals optimized directly at the VpCCD level. The influence of spatial symmetry breaking is also investigated.