Cholesky decomposition techniques in electronic structure theory

We review recently developed methods to efficiently utilize the Cholesky decomposition technique in electronic structure calculations. The review starts with a brief introduction to the basics of the Cholesky decomposition technique. Subsequently, examples of applications of the technique to ab inito procedures are presented. The technique is demonstrated to be a special type of a resolution-of-identity or density-fitting scheme. This is followed by explicit examples of the Cholesky techniques used in orbital localization, computation of the exchange contribution to the Fock matrix, in MP2, gradient calculations, and so-called method specific Francesco Aquilante Department of Physical Chemistry, Sciences II, University of Geneva, Quai E. Ansermet 30, 1211 Geneva 4, Switzerland e-mail: [email protected] Linus Boman Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway e-mail: [email protected] Jonas Boström Department of Theoretical Chemistry, Chemical Center, University of Lund, P.O. Box 124 S221 00 Lund, Sweden e-mail: [email protected] Henrik Koch Department of Chemistry, Norwegian University of Science and Technology, N-7491 Trondheim, Norway e-mail: [email protected] Roland Lindh Department of Quantum Chemistry, Uppsala University, P.O. Box 518, SE-751 20, Uppsala, Sweden. e-mail: [email protected] Alfredo Sánchez de Merás Instituto de Ciencia Molecular, Universitat de València, P.O. Box 22085, ES-46071 Valencia, Spain e-mail: [email protected] Thomas Bondo Pedersen Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033, Blindern, N-0315 Oslo, Norway e-mail: [email protected].