Chemical Physics Letters, Vol.672, 47-53, 2017
Low-rank factorization of electron integral tensors and its application in electronic structure theory
In this letter, we apply reverse Cuthill-McKee (RCM) algorithm to transform two-electron integral tensors to their block diagonal forms. By further applying Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates low-rank factorizations of high-dimensional tensor contractions in post-Hartree-Fock calculations. Here, we discuss the second order Moller-Plesset (MP2) method and the linear coupled-cluster model with doubles (L-CCD) as examples to demonstrate the efficiency of this technique in representing the two-electron integrals in a compact form.(C) 2017 Elsevier B.V. All rights reserved.
Keywords:Electronic structure theory;Two-electron integral tensor;Tensor contraction;Low-rank factorization;Reverse Cuthill-McICee;Cholesky decomposition