# Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface

## Abstract

A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a densitymore »

- Authors:

- National Key Laboratory of Shock Wave and Detonation Physics, Institute of Fluid Physics, CAEP, P.O. Box 919-102, Mianyang, Sichuan, 621900 (China)
- (United States)

- Publication Date:

- OSTI Identifier:
- 22382190

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 283; Other Information: Copyright (c) 2014 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; CRYSTALS; EV RANGE; EXTRAPOLATION; FCC LATTICES; FREE ENERGY; HYDROGEN; MOLECULAR DYNAMICS METHOD; PATH INTEGRALS; POTENTIAL ENERGY; POTENTIALS; PRESSURE RANGE GIGA PA; PROTONS; STATISTICS; SURFACES

### Citation Formats

```
Geng, Hua Y., E-mail: huay.geng@gmail.com, and Department of Chemistry and Chemical Biology, Cornell University, Baker Laboratory, Ithaca, NY 14853.
```*Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface*. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2014.12.007.

```
Geng, Hua Y., E-mail: huay.geng@gmail.com, & Department of Chemistry and Chemical Biology, Cornell University, Baker Laboratory, Ithaca, NY 14853.
```*Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface*. United States. doi:10.1016/J.JCP.2014.12.007.

```
Geng, Hua Y., E-mail: huay.geng@gmail.com, and Department of Chemistry and Chemical Biology, Cornell University, Baker Laboratory, Ithaca, NY 14853. Sun .
"Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface". United States.
doi:10.1016/J.JCP.2014.12.007.
```

```
@article{osti_22382190,
```

title = {Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface},

author = {Geng, Hua Y., E-mail: huay.geng@gmail.com and Department of Chemistry and Chemical Biology, Cornell University, Baker Laboratory, Ithaca, NY 14853},

abstractNote = {A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of r{sub s}=0.912.},

doi = {10.1016/J.JCP.2014.12.007},

journal = {Journal of Computational Physics},

number = ,

volume = 283,

place = {United States},

year = {Sun Feb 15 00:00:00 EST 2015},

month = {Sun Feb 15 00:00:00 EST 2015}

}