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The Journal of Chemical Physics

Comment on “Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure” [J. Chem. Phys. 143, 064103 (2015)]

Robert M. Parrish, Edward G. Hohenstein, Todd J. Martı́nez

Published Jul 11, 2016• 1 citation
Publisher
DOI
10.1063/1.4955316

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Treatment of two-electron excitations is a fundamental but computationally expensive part of ab initio calculations of many-electron correlation. In this paper we develop a low-rank spectral expansion of two-electron excitations for accelerated electronic-structure calculations. The spectral expansion differs from previous approaches by relying upon both (i) a sum of three expansions to increase the rank reduction of the tensor and (ii) a factorization of the tensor into geminal (rank-two) tensors rather than orbital (rank-one) tensors. We combine three spectral expansions from the three distinct forms of the two-electron reduced density matrix (2-RDM), (i) the two-particle (2)D, (ii) the two-hole (2)Q, and the (iii) particle-hole (2)G matrices, to produce a single spectral expansion with significantly accelerated convergence. While the resulting expansion is applicable to any quantum-chemistry calculation with two-particle excitation amplitudes, it is employed here in the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. The low-rank parametric 2-RDM method scales quartically with the basis-set size, but like its full-rank version it can capture multi-reference correlation effects that are difficult to treat efficiently by traditional single-reference wavefunction methods. Applications are made to computing potential energy curves of HF and triplet OH(+), equilibrium bond distances and frequencies, the HCN-HNC isomerization, and the energies of hydrocarbon chains. Computed 2-RDMs nearly satisfy necessary N-representability conditions. The low-rank spectral expansion has the potential to expand the applicability of the parametric 2-RDM method as well as other ab initio methods to large-scale molecular systems that are often only treatable by mean-field or density functional theories.
Accurate evaluation of electron correlations is essential for the reliable quantitative description of electronic structures in strongly correlated systems, including bond-dissociating molecules, polyradicals, large conjugated molecules, and transition metal complexes. To provide a user-friendly tool for studying such challenging systems, our team developed Kylin 1.0 [J. Comput. Chem. 44, 1316 (2023)], an ab initio quantum chemistry program designed for efficient density matrix renormalization group (DMRG) and post-DMRG methods, enabling high-accuracy calculations with large active spaces. We have now further advanced the software with the release of Kylin 1.3, featuring optimized DMRG algorithms and an improved tensor contraction scheme in the diagonalization step. Benchmark calculations on the Mn4CaO5 cluster demonstrate a remarkable speed-up of up to 16 fater than Kylin 1.0. Moreover, a more user-friendly and efficient algorithm [J. Chem. Theory Comput. 17, 3414 (2021)] for sampling configurations from DMRG wavefunction is implemented as well. Additionally, we have also implemented a spin-adapted version of the externally contracted multi-reference configuration interaction (EC-MRCI) method [J. Phys. Chem. A 128, 958 (2024)], further enhancing the program’s efficiency and accuracy for electron correlation calculations.
We describe an algorithm to reduce the cost of auxiliary-field quantum Monte Carlo (AFQMC) calculations for the electronic structure problem. The technique uses a nested low-rank factorization of the electron repulsion integral (ERI). While the cost of conventional AFQMC calculations in Gaussian bases scales as, where N is the size of the basis, we show that ground-state energies can be computed through tensor decomposition with reduced memory requirements and subquartic scaling. The algorithm is applied to hydrogen chains and square grids, water clusters, and hexagonal BN. In all cases, we observe significant memory savings and, for larger systems, reduced, subquartic simulation time.