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Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations

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10.1063/1.4811292

### Abstract

Hybrid molecular dynamics (MD) simulations, in which 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 103–105 molecules, pose a challenge. A corresponding computational approach should guarantee energy conservation, exclude artificial distortions of the electron density at the interface between the DFT and PMM fragments, and should treat the long-range electrostatic interactions within the hybrid simulation system in a linearly scaling fashion. Here we describe a corresponding Hamiltonian DFT/(P)MM implementation, which accounts for inducible atomic dipoles of a PMM environment in a joint DFT/PMM self-consistency iteration. The long-range parts of the electrostatics are treated by hierarchically nested fast multipole expansions up to a maximum distance dictated by the minimum image convention of toroidal boundary conditions and, beyond that distance, by a reaction field approach such that the computation scales linearly with the number of PMM atoms. Short-range over-polarization artifacts are excluded by using Gaussian inducible dipoles throughout the system and Gaussian partial charges in the PMM region close to the DFT fragment. The Hamiltonian character, the stability, and efficiency of the implementation are investigated by hybrid DFT/PMM-MD simulations treating one molecule of the water dimer and of bulk water by DFT and the respective remainder by PMM.

© 2013 AIP Publishing LLC

Received 05 April 2013
Accepted 03 June 2013
Published online 25 June 2013

Acknowledgments: This work was supported by the Deutsche Forschungsgemeinschaft (SFB749/C4) and by the Kompetenznetzwerk für wissenschaftliches Höchstleistungsrechnen in Bayern of the Bayerische Staatsministerium für Wissenschaft, Forschung und Kunst (KONWIHR-III).

Article outline:

I. INTRODUCTION

II. THEORY

A. Computational issues

B. DFT/PMM with SAMM_{ p }

C. Efficient computation of Φ_{ext}

D. Forces on the DFT atoms μ

E. Reaction forces on the PMM atoms

F. Reaction forces on the PMM atoms

G. Reaction forces on the PMM atoms , *l* ⩾ 2

H. Remarks

III. KEY POINTS OF THE IMPLEMENTATION

A. Movements of the DFT box

B. DFT/PMM-SCF iteration

IV. METHODS

A. Water dimer

B. Liquid water

V. TEST SIMULATIONS

A. Energy conservation in DFT/PMM-MD

B. Smoothness and stability of DFT/PMM-MD

C. Performance of DFT/PMM-MD

VI. SUMMARY AND OUTLOOK

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/content/aip/journal/jcp/138/24/10.1063/1.4811292

2013-06-25

2014-04-19

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