Optimal partition of the Coulomb operator

Abstract

We set up and solve the problem of optimally partitioning the Coulomb operator 1/r into a sum of two functions ${\mathrm{f}}_{1}$(r) and ${\mathrm{f}}_{2}$(r) such that both ${\mathrm{f}}_{1}$ and the Fourier transform of ${\mathrm{f}}_{2}$ decay as quickly as possible. The rigorous solution involves a Hermite function, but we find that the conventional Ewald-KWIK partition appears to be only slightly inferior.