A fragment multipole approach to long-range Coulomb interactions in Hartree–Fock calculations on large systems

An efficient ab initio method for electronic structure calculations on extended molecular systems is presented, along with some illustrative applications. A division of the system into subunits allows the interactions to be separated into short- and long-range contributions, leading to a reduction of the computational effort from the original fourth-power size-dependence to one that is approximately quadratic. The short-range contributions to the Fock matrix are obtained in an essentially conventional fashion, while the long-range interactions are evaluated using a two-center multipole expansion formalism. The number of short-range contributions grows only linearly with the number of subunits, while the long-range contributions grow as N². Systematic studies of the computational efforts for systems of up to 99 water molecules organized as one-stranded chains, three-stranded chains, and three-dimensional clusters, as well as alkane chains with up to 69 carbon atoms, have been performed. In these model systems, the overall computational effort grows as N^K where 1 < K < 2.