Treatment of the exchange interactions in Hartree-Fock LCAO calculations of periodic systems

The range of exchange interactions in realistic HF computations for solids is discussed. Results are reported for graphite, hexagonal boron nitride, all-trans-polyacetylenes, lithium, and silicon. It is shown that for insulators the convergence of the series is very rapid; for silicon, for example, the inclusion of the second (sixth) neighbors in the summation reduces the total energy error to 1 X lo-) (5 X 10”) au per cell. In the case of zero gap or metallic systems, long-range interactions are shown to give nonnegligible contributions to the total energy of the system (terms involving distances of 40 au can be as large as 1 X 10“ au per cell in graphite) but do not appreciably affect the wave function of the system.