A FAMILY OF ATTENUATED COULOMB OPERATORS

We discuss a family of computationally useful approximations to the Co ulomb operator. These operators, which we term CAP(m), are systematic improvements to our earlier CASE operator. In particular, we have CAP( 0) = CASE and CAP(infinity) = 1/r. Because the CAP(m) approximations a re all short-ranged, the computational cost of using one to compute th e Coulomb energy of N localized charge distributions scales linearly w ith N. To investigate their accuracy, we have applied a number of CAP( m) approximations to the computation of the hydrogen atom energy and t he NaCl Madelung constant. We find that the higher approximations mode l the original Coulomb operator quite well and the half-integer approx imations, though non-vanishing at infinity, are especially accurate.