Multipole approximation of distant pair energies in local MP2 calculations

An approximation for treating the weak correlation of distant pairs in local MP2 calculations by multipole expansions is proposed. This leads to computational savings in the transformation of the two-electron integrals, which is the bottleneck in MP2 calculations. The method works well for orbital pairs that are at least 7 bohr apart. The accuracy is mainly limited by the neglect of ionic excitations in the first-order wavefunction, while the error of the multipole expansion is almost negligible.