Linear-scaling atomic orbital-based second-order Møller–Plesset perturbation theory by rigorous integral screening criteria

A Laplace-transformed second-order Moller-Plesset perturbation theory (MP2) method is presented, which allows to achieve linear scaling of the computational effort with molecular size for electronically local structures. Also for systems with a delocalized electronic structure, a cubic or even quadratic scaling behavior is achieved. Numerically significant contributions to the atomic orbital (AO)-MP2 energy are preselected using the so-called multipole-based integral estimates (MBIE) introduced earlier by us J. Chem. Phys. 123, 184102 (2005). Since MBIE provides rigorous upper bounds, numerical accuracy is fully controlled and the exact MP2 result is attained. While the choice of thresholds for a specific accuracy is only weakly dependent upon the molecular system, our AO-MP2 scheme offers the possibility for incremental thresholding: for only little additional computational expense, the numerical accuracy can be systematically converged. We illustrate this dependence upon numerical thresholds for the calculation of intermolecular interaction energies for the S22 test set. The efficiency and accuracy of our AO-MP2 method is demonstrated for linear alkanes, stacked DNA base pairs, and carbon nanotubes: e.g., for DNA systems the crossover toward conventional MP2 schemes occurs between one and two base pairs. In this way, it is for the first time possible to compute wave function-based correlation energies for systems containing more than 1000 atoms with 10 000 basis functions as illustrated for a 16 base pair DNA system on a single-core computer, where no empirical restrictions are introduced and numerical accuracy is fully preserved.