# Accelerated path integral methods for atomistic simulations at ultra-low temperatures

## Abstract

Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH{sub 5}{sup +}. We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH{sub 4} to illustrate the limits of using such colored noise thermostats close to the many body quantummore »

- Authors:

- Lehrstuhl für Theoretische Chemie, Ruhr–Universität Bochum, 44780 Bochum (Germany)
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne (Switzerland)

- Publication Date:

- OSTI Identifier:
- 22679015

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Chemical Physics; Journal Volume: 145; Journal Issue: 5; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; EXPERIMENTAL DATA; GROUND STATES; KINETIC ENERGY; LANGEVIN EQUATION; MANY-BODY PROBLEM; PATH INTEGRALS; QUANTUM MECHANICS; SIMULATION

### Citation Formats

```
Uhl, Felix, E-mail: felix.uhl@rub.de, Marx, Dominik, and Ceriotti, Michele.
```*Accelerated path integral methods for atomistic simulations at ultra-low temperatures*. United States: N. p., 2016.
Web. doi:10.1063/1.4959602.

```
Uhl, Felix, E-mail: felix.uhl@rub.de, Marx, Dominik, & Ceriotti, Michele.
```*Accelerated path integral methods for atomistic simulations at ultra-low temperatures*. United States. doi:10.1063/1.4959602.

```
Uhl, Felix, E-mail: felix.uhl@rub.de, Marx, Dominik, and Ceriotti, Michele. Sun .
"Accelerated path integral methods for atomistic simulations at ultra-low temperatures". United States.
doi:10.1063/1.4959602.
```

```
@article{osti_22679015,
```

title = {Accelerated path integral methods for atomistic simulations at ultra-low temperatures},

author = {Uhl, Felix, E-mail: felix.uhl@rub.de and Marx, Dominik and Ceriotti, Michele},

abstractNote = {Path integral methods provide a rigorous and systematically convergent framework to include the quantum mechanical nature of atomic nuclei in the evaluation of the equilibrium properties of molecules, liquids, or solids at finite temperature. Such nuclear quantum effects are often significant for light nuclei already at room temperature, but become crucial at cryogenic temperatures such as those provided by superfluid helium as a solvent. Unfortunately, the cost of converged path integral simulations increases significantly upon lowering the temperature so that the computational burden of simulating matter at the typical superfluid helium temperatures becomes prohibitive. Here we investigate how accelerated path integral techniques based on colored noise generalized Langevin equations, in particular the so-called path integral generalized Langevin equation thermostat (PIGLET) variant, perform in this extreme quantum regime using as an example the quasi-rigid methane molecule and its highly fluxional protonated cousin, CH{sub 5}{sup +}. We show that the PIGLET technique gives a speedup of two orders of magnitude in the evaluation of structural observables and quantum kinetic energy at ultralow temperatures. Moreover, we computed the spatial spread of the quantum nuclei in CH{sub 4} to illustrate the limits of using such colored noise thermostats close to the many body quantum ground state.},

doi = {10.1063/1.4959602},

journal = {Journal of Chemical Physics},

number = 5,

volume = 145,

place = {United States},

year = {Sun Aug 07 00:00:00 EDT 2016},

month = {Sun Aug 07 00:00:00 EDT 2016}

}