We will do a brief review on how to take advantage of Cholesky decomposition to reduce the scaling of electronic structure calculations. Once the basic mathematical background has been introduced, different examples of applying Cholesky decomposition will be presented and illustrated by some numerical results. In particular, examples on interaction energies in gas adsorption, biological systems and nano-complexes, excitation energies, polarizabilities, nuclear magnetic shieldings and localization techniques will be exposed. Finally, possible future improvements will also be shown.
Université Paul Sabatier - Bat. 3R1b4 - 118 route de Narbonne 31062 Toulouse Cedex 09, France