# 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-onlymore »

- Authors:

- Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich (Switzerland)
- Department of Materials, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich (Switzerland)

- Publication Date:

- OSTI Identifier:
- 22416233

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 143; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ALGORITHMS; AMMONIA; ATOMS; BENZENE; CARBON DIOXIDE; COMPUTERIZED SIMULATION; GAIN; MOLECULAR CRYSTALS; MOLECULAR DYNAMICS METHOD; RELAXATION; RESOLUTION; STRESSES; TENSORS; WAVE PROPAGATION

### Citation Formats

```
Del Ben, Mauro, E-mail: mauro.delben@chem.uzh.ch, Hutter, Jürg, E-mail: hutter@chem.uzh.ch, and VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch.
```*Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach*. United States: N. p., 2015.
Web. doi:10.1063/1.4919238.

```
Del Ben, Mauro, E-mail: mauro.delben@chem.uzh.ch, Hutter, Jürg, E-mail: hutter@chem.uzh.ch, & VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch.
```*Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach*. United States. doi:10.1063/1.4919238.

```
Del Ben, Mauro, E-mail: mauro.delben@chem.uzh.ch, Hutter, Jürg, E-mail: hutter@chem.uzh.ch, and VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch. Mon .
"Forces and stress in second order Møller-Plesset perturbation theory for condensed phase systems within the resolution-of-identity Gaussian and plane waves approach". United States. doi:10.1063/1.4919238.
```

```
@article{osti_22416233,
```

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

author = {Del Ben, Mauro, E-mail: mauro.delben@chem.uzh.ch and Hutter, Jürg, E-mail: hutter@chem.uzh.ch and VandeVondele, Joost, E-mail: Joost.VandeVondele@mat.ethz.ch},

abstractNote = {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 NH{sub 3}, CO{sub 2}, formic acid, and benzene.},

doi = {10.1063/1.4919238},

journal = {Journal of Chemical Physics},

issn = {0021-9606},

number = 10,

volume = 143,

place = {United States},

year = {2015},

month = {9}

}