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

Abstract

The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scalability and efficiency up to thousands of nodes. Additionally, the computationally more demanding quintic scaling steps can be accelerated by employing graphics processing units (GPU's) showing, for large systems, a gain of almost a factor two compared to the standard central processing unit-only case. In this way, the evaluation of the derivatives of the RI-MP2 energy can be performed within a few minutes for systems containing hundreds of atoms and thousands of basis functions. With good time to solution, the implementation thus opens the possibility to perform molecular dynamics (MD) simulations in various ensembles (microcanonical ensemble and isobaric-isothermal ensemble) at the MP2 level of theory. Geometry optimization, full cell relaxation, and energy conserving MD simulations have been performed for a variety of molecular crystals including NH3, CO2, formic acid, and benzene. The forces acting on the atoms as well as the stress tensor are crucial ingredients for calculating the structural and dynamical properties of systems in the condensed phase. Here, these derivatives of the total energy are evaluated for the second-order Møller-Plesset perturbation energy (MP2) in the framework of the resolution of identity Gaussian and plane waves method, in a way that is fully consistent with how the total energy is computed. This consistency is non-trivial, given the different ways employed to compute Coulomb, exchange, and canonical four center integrals, and allows, for example, for energy conserving dynamics in various ensembles. Based on this formalism, a massively parallel algorithm has been developed for finite and extended system. The designed parallel algorithm displays, with respect to the system size, cubic, quartic, and quintic requirements, respectively, for the memory, communication, and computation. All these requirements are reduced with an increasing number of processes, and the measured performance shows excellent parallel scala...

Probing the structural and dynamical properties of liquid water with models including non-local electron correlation

“…This class of simulations, including the RPA, double-hybrids, and MP2, has been enabled by the RI-GPW method and its high performance implementation. 99,111,115 These simulations demonstrate that MP2 and RPA, which treat hydrogen bonding and van der Waals interactions at equal footing, provide a density of water that is in good agreement with experiment. Indeed, a variety of methods including dispersion in a less seamless way lead to densities that are too high, while plain GGA methods lead to too low densities, consistent with these approaches favoring different phases (LDL and HDL) of water.…”

“…If the forces on the ions can be computed, and nuclear quantum effects ignored, BornOppenheimer molecular dynamics simulations in the microcanonical (NVE) ensemble can be employed to generate trajectories and compute dynamical properties. Recently, we have developed the theory and implemented the forces for the RI-GPW-MP2 method, 99 which for the first time allows for a quantitative assessment of the dynamical properties of liquid water at this level of theory. Here, the analysis is based on two trajectories of each roughly 10 ps, obtained in the NVE ensemble, started from equilibrated configurations of earlier MC runs.…”

Calculating free energies of organic molecules on insulating substrates

“…These calculations were performed using the CP2K code [47], the PBE GGA density functional [48], the MOLOPT basis set [49], and semi-empirical long-range dispersion corrections [50]. Since vdW interactions are poorly described in DFT, we assessed the accuracy of the semi-empirical corrections against higher-accuracy second-order Møller–Plesset perturbation theory (MP2) [51–52] calculations of smaller molecular fragments [43]. A genetic algorithm was employed to fit parameters against that dataset, where the fitness criterion was defined as the force between the molecule and the surface.…”

MPI/OpenMP hybrid parallel algorithm for resolution of identity second‐order Møller–Plesset perturbation calculation of analytical energy gradient for massively parallel multicore supercomputers

“…Parallel algorithms of RI‐MP2 energy and energy gradient calculations have been developed for calculations related to large molecules. A remarkable massively parallel implementation enables to perform RI‐MP2 energy gradient calculations of condensed matter containing more than 100 atoms with periodic boundary condition was developed recently . This code was applied successfully to the first‐principle molecular dynamics simulation of bulk liquid water at MP2 level .…”