# Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations

## Abstract

Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10{sup 3}-10{sup 5} molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of themore »

- Authors:

- Lehrstuhl für BioMolekulare Optik, Ludwig–Maximilians Universität München, Oettingenstr. 67, 80538 München (Germany)

- Publication Date:

- OSTI Identifier:
- 22415495

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 142; 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:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; ALANINES; DENSITY FUNCTIONAL METHOD; EFFICIENCY; GAIN; HAMILTONIANS; MOLECULAR DYNAMICS METHOD; MOLECULES; PERFORMANCE; QUANTUM MECHANICS; SOLUTES; SOLVENTS; WATER

### Citation Formats

```
Schwörer, Magnus, Lorenzen, Konstantin, Mathias, Gerald, and Tavan, Paul, E-mail: paul.tavan@physik.uni-muenchen.de.
```*Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations*. United States: N. p., 2015.
Web. doi:10.1063/1.4914329.

```
Schwörer, Magnus, Lorenzen, Konstantin, Mathias, Gerald, & Tavan, Paul, E-mail: paul.tavan@physik.uni-muenchen.de.
```*Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations*. United States. doi:10.1063/1.4914329.

```
Schwörer, Magnus, Lorenzen, Konstantin, Mathias, Gerald, and Tavan, Paul, E-mail: paul.tavan@physik.uni-muenchen.de. Sat .
"Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations". United States.
doi:10.1063/1.4914329.
```

```
@article{osti_22415495,
```

title = {Utilizing fast multipole expansions for efficient and accurate quantum-classical molecular dynamics simulations},

author = {Schwörer, Magnus and Lorenzen, Konstantin and Mathias, Gerald and Tavan, Paul, E-mail: paul.tavan@physik.uni-muenchen.de},

abstractNote = {Recently, a novel approach to hybrid quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations has been suggested [Schwörer et al., J. Chem. Phys. 138, 244103 (2013)]. Here, the forces acting on the atoms are calculated by grid-based density functional theory (DFT) for a solute molecule and by a polarizable molecular mechanics (PMM) force field for a large solvent environment composed of several 10{sup 3}-10{sup 5} molecules as negative gradients of a DFT/PMM hybrid Hamiltonian. The electrostatic interactions are efficiently described by a hierarchical fast multipole method (FMM). Adopting recent progress of this FMM technique [Lorenzen et al., J. Chem. Theory Comput. 10, 3244 (2014)], which particularly entails a strictly linear scaling of the computational effort with the system size, and adapting this revised FMM approach to the computation of the interactions between the DFT and PMM fragments of a simulation system, here, we show how one can further enhance the efficiency and accuracy of such DFT/PMM-MD simulations. The resulting gain of total performance, as measured for alanine dipeptide (DFT) embedded in water (PMM) by the product of the gains in efficiency and accuracy, amounts to about one order of magnitude. We also demonstrate that the jointly parallelized implementation of the DFT and PMM-MD parts of the computation enables the efficient use of high-performance computing systems. The associated software is available online.},

doi = {10.1063/1.4914329},

journal = {Journal of Chemical Physics},

number = 10,

volume = 142,

place = {United States},

year = {Sat Mar 14 00:00:00 EDT 2015},

month = {Sat Mar 14 00:00:00 EDT 2015}

}