# Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory

## Abstract

Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the timemore »

- Authors:

- Department of Chemistry, Stanford University, Stanford, California 94305 (United States)

- Publication Date:

- OSTI Identifier:
- 22493713

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 144; Journal Issue: 5; Other Information: (c) 2016 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; CAPTURE; CONVERGENCE; DENSITY FUNCTIONAL METHOD; DIMERS; ELECTRONIC STRUCTURE; ELECTRONS; LIGHT NUCLEI; LIQUIDS; MOLECULAR DYNAMICS METHOD; PATH INTEGRALS; POLYMERS; QUANTUM MECHANICS; SIMULATION; WATER

### Citation Formats

```
Marsalek, Ondrej, and Markland, Thomas E., E-mail: tmarkland@stanford.edu.
```*Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory*. United States: N. p., 2016.
Web. doi:10.1063/1.4941093.

```
Marsalek, Ondrej, & Markland, Thomas E., E-mail: tmarkland@stanford.edu.
```*Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory*. United States. doi:10.1063/1.4941093.

```
Marsalek, Ondrej, and Markland, Thomas E., E-mail: tmarkland@stanford.edu. Sun .
"Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory". United States. doi:10.1063/1.4941093.
```

```
@article{osti_22493713,
```

title = {Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory},

author = {Marsalek, Ondrej and Markland, Thomas E., E-mail: tmarkland@stanford.edu},

abstractNote = {Path integral molecular dynamics simulations, combined with an ab initio evaluation of interactions using electronic structure theory, incorporate the quantum mechanical nature of both the electrons and nuclei, which are essential to accurately describe systems containing light nuclei. However, path integral simulations have traditionally required a computational cost around two orders of magnitude greater than treating the nuclei classically, making them prohibitively costly for most applications. Here we show that the cost of path integral simulations can be dramatically reduced by extending our ring polymer contraction approach to ab initio molecular dynamics simulations. By using density functional tight binding as a reference system, we show that our ring polymer contraction scheme gives rapid and systematic convergence to the full path integral density functional theory result. We demonstrate the efficiency of this approach in ab initio simulations of liquid water and the reactive protonated and deprotonated water dimer systems. We find that the vast majority of the nuclear quantum effects are accurately captured using contraction to just the ring polymer centroid, which requires the same number of density functional theory calculations as a classical simulation. Combined with a multiple time step scheme using the same reference system, which allows the time step to be increased, this approach is as fast as a typical classical ab initio molecular dynamics simulation and 35× faster than a full path integral calculation, while still exactly including the quantum sampling of nuclei. This development thus offers a route to routinely include nuclear quantum effects in ab initio molecular dynamics simulations at negligible computational cost.},

doi = {10.1063/1.4941093},

journal = {Journal of Chemical Physics},

number = 5,

volume = 144,

place = {United States},

year = {Sun Feb 07 00:00:00 EST 2016},

month = {Sun Feb 07 00:00:00 EST 2016}

}