Linear-Scaling Techniques in Computational Chemistry and Physics

Abstract

We review recently developed methods to efficiently utilize the Choleskydecomposition technique in electronic structure calculations. Thereview starts with a brief introduction to the basics of the Choleskydecomposition technique. Subsequently, examples of applications ofthe technique to ab inito procedures are presented. The techniqueis demonstrated to be a special type of a resolution-of-identityor density-fitting scheme. This is followed by explicit examplesof the Cholesky techniques used in orbital localization, computationof the exchange contribution to the Fock matrix, in MP2, gradientcalculations, and so-called method specific Cholesky decomposition.Subsequently, examples of calibration of the method with respectto computed total energies, excitation energies, and auxiliary basisset pruning are presented. In particular, it is demonstrated thatthe Cholesky method is an unbiased method to derive auxiliary basissets. Furthermore, details of the implementational considerationsare put forward and examples from a parallel Cholesky decompositionscheme is presented. Finally, an outlook and perspectives are presented,followed by a summary and conclusions section. We are of the opinionthat the Cholesky decomposition method is a technique that has beenoverlooked for too long. We have just recently started to understandhow to efficiently incorporate the method in existing ab initio programs.The full potential of the Cholesky technique has not yet been fullyexplored.