skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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

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 » 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.« less

Authors:
;  [1];  [2]
  1. Department of Chemistry, University of Zürich, Winterthurerstrasse 190, CH-8057 Zürich (Switzerland)
  2. Department of Materials, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH-8093 Zürich (Switzerland)
Publication Date:
OSTI Identifier:
22416233
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 143; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
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},
number = 10,
volume = 143,
place = {United States},
year = {Mon Sep 14 00:00:00 EDT 2015},
month = {Mon Sep 14 00:00:00 EDT 2015}
}
  • Cited by 5
  • We report an implementation of the molecular gradient using the divide-expand-consolidate resolution of the identity second-order Møller-Plesset perturbation theory (DEC-RI-MP2). The new DEC-RI-MP2 gradient method combines the precision control as well as the linear-scaling and massively parallel features of the DEC scheme with efficient evaluations of the gradient contributions using the RI approximation. We further demonstrate that the DEC-RI-MP2 gradient method is capable of calculating molecular gradients for very large molecular systems. A test set of supramolecular complexes containing up to 158 atoms and 1960 contracted basis functions has been employed to demonstrate the general applicability of the DEC-RI-MP2 methodmore » and to analyze the errors of the DEC approximation. Moreover, the test set contains molecules of complicated electronic structures and is thus deliberately chosen to stress test the DEC-RI-MP2 gradient implementation. Additionally, as a showcase example the full molecular gradient for insulin (787 atoms and 7604 contracted basis functions) has been evaluated.« less
  • A combined quantum mechanical/molecular mechanical/continuum (QM/MM/C) style second order Møller-Plesset perturbation theory (MP2) method that incorporates induced dipole polarizable force field and induced surface charge continuum solvation model is established. The Z-vector method is modified to include induced dipoles and induced surface charges to determine the MP2 response density matrix, which can be used to evaluate MP2 properties. In particular, analytic nuclear gradient is derived and implemented for this method. Using the Assisted Model Building with Energy Refinement induced dipole polarizable protein force field, the QM/MM/C style MP2 method is used to study the hydrogen bonding distances and strengths ofmore » the photoactive yellow protein chromopore in the wild type and the Glu46Gln mutant.« less
  • General analytic gradient expressions (with the frozen-core approximation) are presented for density-fitted post-HF methods. An efficient implementation of frozen-core analytic gradients for the second-order Møller–Plesset perturbation theory (MP2) with the density-fitting (DF) approximation (applying to both reference and correlation energies), which is denoted as DF-MP2, is reported. The DF-MP2 method is applied to a set of alkanes, conjugated dienes, and noncovalent interaction complexes to compare the computational cost of single point analytic gradients with MP2 with the resolution of the identity approach (RI-MP2) [F. Weigend and M. Häser, Theor. Chem. Acc. 97, 331 (1997); R. A. Distasio, R. P. Steele,more » Y. M. Rhee, Y. Shao, and M. Head-Gordon, J. Comput. Chem. 28, 839 (2007)]. In the RI-MP2 method, the DF approach is used only for the correlation energy. Our results demonstrate that the DF-MP2 method substantially accelerate the RI-MP2 method for analytic gradient computations due to the reduced input/output (I/O) time. Because in the DF-MP2 method the DF approach is used for both reference and correlation energies, the storage of 4-index electron repulsion integrals (ERIs) are avoided, 3-index ERI tensors are employed instead. Further, as in case of integrals, our gradient equation is completely avoid construction or storage of the 4-index two-particle density matrix (TPDM), instead we use 2- and 3-index TPDMs. Hence, the I/O bottleneck of a gradient computation is significantly overcome. Therefore, the cost of the generalized-Fock matrix (GFM), TPDM, solution of Z-vector equations, the back transformation of TPDM, and integral derivatives are substantially reduced when the DF approach is used for the entire energy expression. Further application results show that the DF approach introduce negligible errors for closed-shell reaction energies and equilibrium bond lengths.« less