ABINITIO METHODS FOR LARGE SYSTEMS

Methods for calculations on extended systems are proposed, in which long-range Coulombic interactions are treated classically. The basic mode of description for the system is still in a quantum mechanical language, involving wave functions, Hamiltonians, etc. The electron density in a large molecular system is divided into suitable fragments, and the electrostatic potential generated by such a fragment at some distance away from it is then expressed by a generalized multipole expansion relative to a single point in space, conveniently taken as the center of charge distribution for that fragment. The computational effort required for evaluating the interactions involving those multipoles is modest and scales favorably (quadratically) with the size of the system. The remaining interactions, which need to be treated with conventional methods, i.e., with explicit one- and two-electron integrals, scale only linearly with size in extended systems. An important characteristic of the approach is that, while the approximations and shortcuts introduced have a clear physical origin, they can bc justified on strict numerical grounds, such that calculated energies and other properties are identical to those obtained with conventional methods.