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Cholesky Decomposition

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

first serious realization (also implemented in CFOUR within the MINT integral package)
H. Koch, A. S. de Merás, T.B. Pedersen, Reduced scaling in electronic structure calculations using Cholesky decompositions, J. Chem. Phys. 118, 9481- (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 and equation-of-motion coupled-cluster theory
E. Epifanovsky, D. Zuev, X. Feng, K. Khistayev, Y. Shao, A.I. Krylov, General implementation of the resolution-of-the-identity and Cholesky representations of electron repulsion integrals within coupled-cluster and qquation-of-motion methods: Theory and benchmarks, J. Chem. Phys. 139, 134105 (2013)

implementation in CFOUR with CASSCF
T. Nottoli, J. Gauss, F. Lipparini, to be published

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)

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CFOUR is partially supported by the U.S. National Science Foundation.