Low-Rank Approximations for Accurate and Efficient Plane-Wave Second-Order Møller–Plesset Perturbation Theory

The second-order Møller-Plesset perturbation (MP2) theory is a post-Hartree-Fock method widely used to describe weak correlation energies in solids and molecules, but its high computational cost scales as <i>O</i>(<i>N</i>⁵). Herein, we present an accurate and efficient implementation of MP2 within the plane-wave (PW) basis set for both periodic and molecular systems, which incorporates the interpolative separable density fitting (ISDF) decomposition and the Laplace transformation (LT) of the energy denominator. These innovations avoid the direct construction of electron repulsion integrals (ERIs) and reduce the computational complexity of MP2 from <i>O</i>(<i>N</i>⁵) to <i>O</i>(<i>N</i>⁴). The key idea for reducing the scaling is to exploit the numerical redundancy of occupied-virtual molecular orbital pairs on the real-space grid in the plane-wave basis set, which enables ERIs to be factorized into lower-rank quantities. This leads to further cost reductions in both the direct and exchange terms of the MP2 correlation energy. For a bulk silicon system consisting of 128 atoms, the LT-ISDF-MP2 method demonstrates a 13.5-fold speedup in total computation time compared to the standard approach. Using this plane-wave LT-ISDF-MP2 method, we simulate the π-π stacking interaction in the 1,3-butadiene dimer, successfully capturing the dispersion interaction and reproducing the self-assembled configuration.