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

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 »- Publication Date:

- Grant/Contract Number:
- SC0014437

- Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 144; Journal Issue: 5; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Research Org:
- Univ. of California, Merced, CA (United States)

- Sponsoring Org:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

- OSTI Identifier:
- 1469204

- Alternate Identifier(s):
- OSTI ID: 1236991

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

```
Marsalek, Ondrej, & Markland, Thomas E.
```*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. 2016.
"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. https://www.osti.gov/servlets/purl/1469204.
```

```
@article{osti_1469204,
```

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.},

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. In conclusion, 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 = {2016},

month = {2}

}

Works referenced in this record:

Generalized Gradient Approximation Made Simple

journal, October 1996

journal, October 1996

- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868

Density‐functional thermochemistry. III. The role of exact exchange

journal, April 1993

journal, April 1993

- Becke, Axel D.
- The Journal of Chemical Physics, Vol. 98, Issue 7, p. 5648-5652