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

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Abstract
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 NK where 1 < K < 2.

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