Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method

An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations (Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016, 144, 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017, 13, 1647–1655) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of NbasisNocc. Furthermore, we present a parallel im...