Full configuration interaction (FCI) remains an indispensable method for strongly correlated electronic structure calculations due to its high accuracy, but its steeply scaling computational cost limits applications with large basis sets. We propose an improved optimal orbital selection algorithm for full configuration interaction with Cholesky decomposition (OptOrbFCI-CD) that significantly enhances computational efficiency without sacrificing accuracy in large basis set calculations. The computational complexities of the algorithm are systematically analyzed before and after applying Cholesky decomposition, demonstrating significant time reduction for large systems. Numerical results for H4 molecules are presented, validating the algorithm’s effectiveness across varying basis set sizes. Our findings suggest that although the energy continues to decrease with increasing basis set size, the convergence rate progressively slows without reaching full saturation. The improved algorithm exhibits strong potential for scaling to larger systems while maintaining an optimal balance between computational cost and accuracy.
Full configuration interaction (FCI) remains an indispensable method for strongly correlated electronic structure calculations due to its high accuracy, but its steeply scaling computational cost limits applications with large basis sets. We propose an improved optimal orbital selection algorithm for full configuration interaction with Cholesky decomposition (OptOrbFCI-CD) that significantly enhances computational efficiency without sacrificing accuracy in large basis set calculations. The computational complexities of the algorithm are systematically analyzed before and after applying Cholesky decomposition, demonstrating significant time reduction for large systems. Numerical results for H4 molecules are presented, validating the algorithm’s effectiveness across varying basis set sizes. Our findings suggest that although the energy continues to decrease with increasing basis set size, the convergence rate progressively slows without reaching full saturation. The improved algorithm exhibits strong potential for scaling to larger systems while maintaining an optimal balance between computational cost and accuracy.
In a recent paper, we proposed the adaptive shift method for correcting undersampling bias of the initiator-full configuration interaction (FCI) quantum Monte Carlo. The method allows faster convergence with the number of walkers to the FCI limit than the normal initiator method, particularly for large systems. However, in its application to some systems, mostly strongly correlated molecules, the method is prone to overshooting the FCI energy at intermediate walker numbers, with convergence to the FCI limit from below. In this paper, we present a solution to the overshooting problem in such systems, as well as further accelerating convergence to the FCI energy. This is achieved by offsetting the reference energy to a value typically below the Hartree–Fock energy but above the exact energy. This offsetting procedure does not change the exactness property of the algorithm, namely, convergence to the exact FCI solution in the large-walker limit, but at its optimal value, it greatly accelerates convergence. There is no overhead cost associated with this offsetting procedure and is therefore a pure and substantial computational gain. We illustrate the behavior of this offset adaptive shift method by applying it to the N2 molecule, the ozone molecule at three different geometries (an equilibrium open minimum, a hypothetical ring minimum, and a transition state) in three basis sets (cc-pVXZ, X = D, T, Q), and the chromium dimer in the cc-pVDZ basis set, correlating 28 electrons in 76 orbitals. We show that in most cases, the offset adaptive shift method converges much faster than both the normal initiator method and the original adaptive shift method.
Full configuration interaction (FCI) provides exact electronic structure within a given atomic basis, but its computational cost grows exponentially with the number of spin orbitals. Selected configuration interaction (SCI) methods alleviate this limitation by retaining only the most important Slater determinants. However, the repeated identification of important determinants remains a major computational bottleneck. We present a quantum assisted selected configuration interaction (QASCI) method that combines SCI with graph based block diagonalization (GBBD) of FCI Hamiltonian. The GBBD method partitions FCI Hamiltonian into independent blocks, within which determinant selection problem is formulated as a quadratic unconstrained binary optimization (QUBO) problem. The QUBO problems for selecting determinants to construct SCI space are iteratively solved using a fast annealing approach. We benchmark method on H8-H18 hydrogen chains and Li2S in STO3G basis. For Hn chains, chemical accuracy is achieved while retaining only a small fraction of Slater determinants, and this fraction decreases with increasing n, despite the exponential growth of the FCI Hilbert space. For Li2S, QASCI results remain within chemical accuracy while retaining substantially fewer determinants than the full FCI space. We apply QASCI to N2 using the 631G basis, considering both active orbital and full orbital treatments. The full orbital QASCI calculation, using 50000 determinants, yields a lower ground state energy than an FCI calculation within an active space comprising 12 spin orbitals and 12 electrons. These results demonstrate that the combination of QASCI and the GBBD approach can substantially reduce computational cost of determinant selection while maintaining the accuracy of FCI based electronic structure calculations, thereby enabling accurate calculations in larger orbital spaces.
By performing a stochastic dynamic in a space of Slater determinants, the full configuration interaction quantum Monte Carlo (FCIQMC) method has been able to obtain energies which are essentially free from systematic error to the basis set correlation energy, within small and systematically improvable error bars. However, the weakly exponential scaling with basis size makes converging the energy with respect to basis set costly and in larger systems, impossible. To ameliorate these basis set issues, here we use perturbation theory to couple the FCIQMC wavefunction to an explicitly correlated strongly orthogonal basis of geminals, following the [2](R12) approach of Valeev et al. The required one- and two-particle density matrices are computed on-the-fly during the FCIQMC dynamic, using a sampling procedure which incurs relatively little additional computation expense. The F12 energy corrections are shown to converge rapidly as a function of sampling, both in imaginary time and number of walkers. Our pilot calculations on the binding curve for the carbon dimer, which exhibits strong correlation effects as well as substantial basis set dependence, demonstrate that the accuracy of the FCIQMC-F12 method surpasses that of all previous FCIQMC calculations, and that the F12 correction improves results equivalent to increasing the quality of the one-electron basis by two cardinal numbers.
We propose an efficient deterministic method to calculate the full configuration interaction (FCI) ground state energy. This method leverages the sparseness of the Lanczos basis vectors that span the Krylov subspace associated with the Hamiltonian to rapidly calculate the lowest eigenvalue of the effective Hamiltonian formed in this basis. By iteratively performing the spanning and diagonalization steps, this method is capable of rapidly reaching chemical accuracy for a variety of strongly correlated molecules, including stretched N2 and C2, in merely several tens of iterations. To accelerate our algorithm, we implement parallelized sparse matrix-sparse vector multiplication, which features a novel hashing method that establishes a one-to-one correspondence between the set of full configuration Slater determinants and a set of consecutive integers. A near-linear acceleration was observed.
Recently, a new distributed implementation of the full configuration interaction (FCI) method has been reported [Gao et al. J. Chem Theory Comput. 2024, 20, 1185]. Thanks to a hybrid parallelization scheme, the authors were able to compute the exact energy of propane (\ce{C3H8}) in the minimal basis STO-3G. This formidable task involves handling an active space of 26 electrons in 23 orbitals or a Hilbert space of \SI{1.3d12} determinants. This is, by far, the largest FCI calculation reported to date. Here, we illustrate how, from a general point of view, selected configuration interaction (SCI) can achieve microhartree accuracy at a fraction of the computational and memory cost, via a sparse exploration of the FCI space. The present SCI calculations are performed with the \textit{Configuration Interaction using a Perturbative Selection made Iteratively} (CIPSI) algorithm, as implemented in a determinant-driven way in the \textsc{quantum package} software. The present study reinforces the common wisdom that among the exponentially large number of determinants in the FCI space, only a tiny fraction of them significantly contribute to the energy. More importantly, it demonstrates the feasibility of achieving comparable accuracy using more reasonable and sustainable computational resources, hence reducing the ever-growing carbon footprint of computational chemistry.
Cholesky decomposition (CD) is widely used to reduce the cost of storing two-particle integrals and has been extended to multicomponent nuclear–electronic orbital (NEO) methods. Although NEO-CD lowers memory demands, single-node implementations can still face memory bottlenecks due to the size of the mixed asymmetric nuclear–electronic tensors. In this study, we present a two-stage hybrid-layout distributed NEO-CD framework suitable for large NEO calculations at scale. Cholesky vectors are first generated and orthonormalized using an atomic orbital (AO)-index distribution. During Fock matrix construction, mixed nuclear–electronic vectors retain the AO-index layout, while pure electronic and pure nuclear vectors are redistributed over the auxiliary index. This design avoids costly inter-rank communication and provides efficient construction of both Coulomb and exchange matrices. Benchmark calculations on water clusters with all protons treated quantum mechanically show excellent scaling and load balance. Using only 104 MPI ranks, a full NEO-Fock build for (H2O)250 with 500 quantum protons, the largest NEO calculation to date, completes in 96.2 s per Fock matrix construction. The distributed NEO-CD framework enables NEO-DFT calculations for liquid-like water clusters up to (H2O)100. Extrapolation of the binding energies yields a bulk-limit value of ΔEn→∞ = −10.35 ± 0.19 kcal/mol, in excellent agreement with the experimental vaporization enthalpy of water. These results demonstrate that fully quantum mechanical simulations of large molecular systems are now practical on modern computing architectures.