Fast evaluation of the Coulomb potential for electron densities using multipole accelerated resolution of identity approximation

A new computational approach is presented that allows for an accurate and efficient treatment of the electronic Coulomb term in density functional methods. This multipole accelerated resolution of identity for J (MARI-J) method partitions the Coulomb interactions into the near- and far-field parts. The calculation of the far-field part is performed by a straightforward application of the multipole expansions and the near-field part is evaluated employing expansion of molecular electron densities in atom-centered auxiliary basis sets (RI-J approximation). Compared to full RI-J calculations, up to 6.5-fold CPU time savings are reported for systems with about 1000 atoms without any significant loss of accuracy. Other multipole-based methods are compared with regard to reduction of the CPU times versus the conventional treatment of the Coulomb term. The MARI-J approach compares favorably and offers speedups approaching two orders of magnitude for molecules with about 400 atoms and more than 5000 basis functions. Our new method shows scalings as favorable as N-1.5, where N is the number of basis functions, for a variety of systems including dense three-dimensional molecules. Calculations on molecules with up to 1000 atoms and 7000 to 14 000 basis functions, depending on symmetry, can now be easily performed on single processor work stations. Details of the method implementation in the quantum chemical program TURBOMOLE are discussed. (C) 2003 American Institute of Physics.