A new implementation of local second-order Mo/ller-Plesset perturbation theory (LMP2) is presented for which asymptotically all computational resources (CPU, memory, and disk) scale only linearly with the molecular size. This is achieved by (i) using orbital domains for each electron pair that are independent of molecular size; (ii) classifying the pairs according to a distance criterion and neglecting very distant pairs; (iii) treating distant pairs by a multipole approximation, and (iv) using efficient prescreening algorithms in the integral transformation. The errors caused by the various approximations are negligible. LMP2 calculations on molecules including up to 500 correlated electrons and over 1500 basis functions in C1 symmetry are reported, all carried out on a single low-cost personal computer.

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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.

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