Low-order scaling local correlation methods II: Splitting the Coulomb operator in linear scaling local second-order Møller–Plesset perturbation theory

A novel multipole approximation for the linear scaling local second-order Møller–Plesset perturbation theory (MP2) method is presented, which is based on a splitting of the Coulomb operator into two terms. The first one contains the singularity and is rapidly decaying with increasing distance. It is treated by a conventional two-electron transformation, where the rapid decay leads to significant savings. The second term is long range, but nonsingular and can therefore be approximated by a multipole expansion. Reliability, accuracy, and efficiency of this method are demonstrated by an extensive benchmark study. It is shown that the goal to further improve the efficiency of the existing linear scaling local MP2 algorithm has been achieved. Moreover, the new method is a promising starting point for future developments, such as coupling of MP2 with density functional theory.