Application of second-order Møller–Plesset perturbation theory with resolution-of-identity approximation to periodic systems

Abstract

Efficient periodic boundary condition (PBC) calculations by the second-order Møller-Plesset perturbation (MP2) method based on crystal orbital formalism are developed by introducing the resolution-of-identity (RI) approximation of four-center two-electron repulsion integrals (ERIs). The formulation and implementation of the PBC RI-MP2 method are presented. In this method, the mixed auxiliary basis functions of the combination of Poisson and Gaussian type functions are used to circumvent the slow convergence of the lattice sum of the long-range ERIs. Test calculations of one-dimensional periodic trans-polyacetylene show that the PBC RI-MP2 method greatly reduces the computational times as well as memory and disk sizes, without the loss of accuracy, compared to the conventional PBC MP2 method.

Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach

“…Reducing the formal O(n 5 ) scaling is achieved with methods such as local MP2 [6][7][8][9][10][11][12][13][14][15] (LMP2) and Laplace-Transformed MP2 [16][17][18][19][20][21][22] . The prefactor of the various terms that dominate for smaller systems can be reduced with the resolution of identity approximation [23][24][25][26][27][28] (RI-MP2), while explicitly correlated methods speedup the convergence of the MP2 energy with respect to basis set size 29 (F12-MP2). Despite this progress, calculations with good basis sets on systems containing fifty or more heavy atoms remain computationally demanding with MP2 or double hybrid DFT.…”

“…The development of efficient parallel algorithms is of prime interest in the case of MP2 energy calculation with periodic boundary condition 12,22,27,28,[41][42][43] . In fact, in this case, due to the considerably high cost, the practical applications are limited to periodic systems with small unit cell.…”

Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach

“…8 Several approaches have been proposed in order to reduce the formal O(N 5 ) scaling and they can be classified as Laplacetransformed MP2, [9][10][11][12][13][14][15][16] local MP2 (LMP2), [17][18][19][20][21][22][23][24][25][26] and stochastic [27][28][29][30] methods, while explicitly correlated schemes can be used for accelerating the convergence of the MP2 energy with respect to basis set size (F12-MP2). [31][32][33] Furthermore, the Resolution of Identity (RI) [34][35][36][37][38][39][40][41][42] approximation, sometimes referred as Density Fitting (DF), has shown to greatly speed up the evaluation of the MP2 energy giving almost a order of magnitude reduction of the computational cost without significant loss of accuracy. [43][44][45] In addition, parallel computing has become of prime importance in quantum chemistry as a tool for reducing the time to solution for these calculations.…”

Two‐level hierarchical parallelization of second‐order Møller–plesset perturbation calculations in divide‐and‐conquer method

“…To make MP2 applicable to nanosystems and biological systems, development of efficient computational techniques is desired. Recently, several efficient computational methods such as the resolution of the identity MP2 (or density fitting MP2),9–17 Cholesky decomposition MP2,18–20 pseudospectral MP2,21 local MP2,22–39 and Laplace‐transformed MP225, 27, 34, 40–49 have been developed to reduce the computational costs. Parallel algorithms of these MP2 methods have also been developed 10, 16, 45, 50–72.…”