Title  A fullpivoting algorithm for the Cholesky decomposition of twoelectron repulsion and spinorbit coupling integrals 
Publication Type  Journal Article 
Year of Publication  2017 
Authors  Piccardo, M, Soncini, A 
Journal  Journal of Computational Chemistry 
Volume  38 
Pagination  2775–2783 
Date Published  dec 
ISSN  1096987X 
Keywords  Cholesky, decomposition, electron repulsion integrals, fullpivoting, spinorbit coupling 
Abstract  A significant reduction in the computational effort for the evaluation of the electronic repulsion integrals (ERI) in ab initio quantum chemistry calculations is obtained by using Cholesky decomposition (CD), a numerical procedure that can remove the zero or small eigenvalues of the ERI positive (semi)definite matrix, while avoiding the calculation of the entire matrix. Conversely, due to its antisymmetric character, CD cannot be directly applied to the matrix representation of the spatial part of the two‐electron spin‐orbit coupling (2e‐SOC) integrals. Here, we present a computational strategy to achieve a Cholesky representation of the spatial part of the 2e‐SOC integrals, and propose a new efficient CD algorithm for both ERI and 2e‐SOC integrals. The proposed algorithm differs from previous CD implementations by the extensive use of a full‐pivoting design, which allows a univocal definition of the Cholesky basis, once the CD δ threshold is made explicit. We show that urn:xwiley:01928651:media:jcc25062:jcc25062math0001 is the upper limit for the errors affecting the reconstructed 2e‐SOC integrals. The proposed strategy was implemented in the ab initio program Computational Emulator of Rare Earth Systems (CERES), and tested for computational performance on both the ERI and 2e‐SOC integrals evaluation.

URL  http://doi.wiley.com/10.1002/jcc.25062 
DOI  10.1002/jcc.25062 
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