CFOUR | Main / Colesky Decomposition

review
T.B. Pedersen, S. Lehtola, I.F. Galván, R. Lindh, The versatility of the Cholesky decomposition in electronic structure theory, WIREs Comput. Mol. Sci. 14, e1692 (2024)

idea
N.H.F. Neebe and J. Linderberg, Simplifications in the generation and transformation of two‐electron integrals in molecular calculations, Int. J. Quantum Chem. 12, 683-705 (1977)

first serious realization
H. Koch, A. Sánchez de Merás, T.B. Pedersen, Reduced scaling in electronic structure calculations using Cholesky decompositions, J.Chem. Phys. 118, 9481–9484(2003)

efficient realization
S.D. Folkestad, E.F. Kjønstad, H. Koch, An efficient algorithm for Cholesky decomposition of electron repulsion integrals, J. Chem. Phys. 150, 194112 (2019)

realization with coupled cluster
E. Epifanovsky, D. Zuev, X. Feng, K. Khistyaev, Y. Shao, A.I. Krylov, General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and equation-of-motion methods: Theory and benchmarks, J. Chem. Phys. 139, 134105 (2013)

implementation in CFOUR with CASSCF
T. Nottoli, J. Gauss, F. Lipparini, Second-order CASSCF algorithm with the Cholesky decomposition of the two-electron integrals, J. Chem. Theory Comput. 17, 6819-6831 (2021)

implementation in CFOUR with coupled cluster
T. Nottoli, J. Gauss, F. Lipparini, A novel coupled-cluster singles and doubles implementation that combines the exploitation of point-group symmetry and Cholesky decomposition of the two-electron integrals, J. Chem. Phys. 159, 231101 (2023)

geometrical gradients with Cholesky decomposition
X. Feng, E. Epifanovsky, J. Gauss, A.I. Krylov, Implementation of analytic gradients for CCSD and EOM-CCSD using Cholesky decomposition of the electron-repulsion integrals and their derivatives: Theory and benchmarks, J. Chem. Phys. 151, 014110 (2019)

A.K. Schnack-Petersen, H. Koch, S. Coriani, E.F. Kjønstad, Efficient implementation of molecular CCSD gradients with Cholesky-decomposed electron repulsion integrals, J. Chem. Phys. 156, 244111 (2022)

NMR shieldings with GIAOs and Cholesky decomposition
S. Burger, F. Lipparini, J. Gauss, S. Stopkowicz, NMR chemical shift computations at second-order Møller–Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals, J. Chem. Phys. 155, 074105 (2021)

T. Nottoli, S. Burger, S. Stopkowicz, J. Gauss, F. Lipparini, Computation of NMR shieldings at the CASSCF level using gauge-including atomic orbitals and Cholesky decomposit, J. Chem. Phys. 157, 084122 (2022)

J. Gauss, S. Blaschke, S. Burger, T. Nottoli, F. Lipparini, S. Stopkowicz, Cholesky decomposition of two-electron integrals in quantum-chemical calculations with perturbative or finite magnetic fields using gauge-including atomic orbitals, Mol. Phys. 121, e2101562 (2023)

Magnetizability tensors with GIAOs and Cholesky decomposition
S. Burger, S. Stopkowicz, J. Gauss, Cholesky decomposition and the second-derivative two-electron integrals required for the computation of magnetizabilities using gauge-including atomic orbitals, J. Phys. Chem. A 129, 623-632 (2025)

Finite-field calculations using GIAOs and Cholesky decomposition
S. Blaschke, S. Stopkowicz, Cholesky decomposition of complex two-electron integrals over GIAOs: Efficient MP2 computations for large molecules in strong magnetic fields, J. Chem. Phys. 156, 044115 (2022)

S. Blaschke, M.-P. Kitsaras, S. Stopkowicz, Finite-field Cholesky decomposed coupled-cluster techniques (ff-CD-CC): theory and application to pressure broadening of Mg by a He atmosphere and a strong magnetic field, Phys. Chem. Chem. Phys. 26, 28828-28848 (2024)

Two-component relativistic calculations using Cholesky decomposition
C. Zhang, F. Lipparini, S. Stopkowicz, J. Gauss, L. Cheng, Cholesky decomposition-based implementation of relativistic two-component coupled-cluster methods for medium-sized molecules, J. Chem. Theory Comput. 20, 787-798 (2024)

Four-component relativistic calculations using Cholesky decomposition
T. Uhlířová, D. Cianchino, T. Nottoli, F. Lipparini, J. Gauss, Cholesky decomposition in spin-free Dirac–Coulomb coupled-cluster calculations, J. Phys. Chem. A 128, 8292-8303 (2024)