# Toward Accurate High Temperature Anharmonic Partition Functions

## Abstract

We use four different methods to calculate an anharmonic correction factor f(vib) to the conventional RRHO partition functions for H2O, HO2, (CH2)-C-3, H2O2, and CH4 over a temperature range up to 3000 K. The exact quantum mechanical method benchmarks the other three approximate methods that are based on classical Monte Carlo phase space integrals, on vibrational perturbation theory, and on conventional harmonic partition functions evaluated with fundamental, rather than harmonic, frequencies. The last two of these methods converge on the exact partition function below temperatures that vary from 1500 K for the least anharmonic system (H2O) to 250 K for the most anharmonic system (H2O2). For (CH2)-C-3 and H2O2, both these methods are qualitatively incorrect because they are insensitive to a low energy barrier for internal motion. The classical method qualitatively overestimates quantum mechanical results at low temperatures because of the exclusion of zero point energy. However, here anharmonic corrections are small. At high temperatures, our anharmonic corrections can be large (up to 40% for CH4 at 3000 K) and at high enough temperatures the classical and exact quantum results will converge. Comparing perturbation theory and the classical method, the classical method becomes the approximate method of choice above similarmore »

- Authors:

- Publication Date:

- Research Org.:
- Argonne National Lab. (ANL), Argonne, IL (United States)

- Sponsoring Org.:
- USDOE Office of Science - Office of Basic Energy Sciences - Chemical Sciences, Geosciences, and Biosciences Division

- OSTI Identifier:
- 1510057

- DOE Contract Number:
- AC02-06CH11357

- Resource Type:
- Conference

- Resource Relation:
- Journal Volume: 37; Journal Issue: 1; Conference: 37th International Symposium on Combustion, 07/29/18 - 08/03/18, Dublin, IE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- partition function, anharmonicity, classical phase space integrals

### Citation Formats

```
Bross, David H., Jasper, Ahren W., Ruscic, Branko, and Wagner, Albert F.
```*Toward Accurate High Temperature Anharmonic Partition Functions*. United States: N. p., 2019.
Web. doi:10.1016/j.proci.2018.05.028.

```
Bross, David H., Jasper, Ahren W., Ruscic, Branko, & Wagner, Albert F.
```*Toward Accurate High Temperature Anharmonic Partition Functions*. United States. doi:10.1016/j.proci.2018.05.028.

```
Bross, David H., Jasper, Ahren W., Ruscic, Branko, and Wagner, Albert F. Tue .
"Toward Accurate High Temperature Anharmonic Partition Functions". United States. doi:10.1016/j.proci.2018.05.028.
```

```
@article{osti_1510057,
```

title = {Toward Accurate High Temperature Anharmonic Partition Functions},

author = {Bross, David H. and Jasper, Ahren W. and Ruscic, Branko and Wagner, Albert F.},

abstractNote = {We use four different methods to calculate an anharmonic correction factor f(vib) to the conventional RRHO partition functions for H2O, HO2, (CH2)-C-3, H2O2, and CH4 over a temperature range up to 3000 K. The exact quantum mechanical method benchmarks the other three approximate methods that are based on classical Monte Carlo phase space integrals, on vibrational perturbation theory, and on conventional harmonic partition functions evaluated with fundamental, rather than harmonic, frequencies. The last two of these methods converge on the exact partition function below temperatures that vary from 1500 K for the least anharmonic system (H2O) to 250 K for the most anharmonic system (H2O2). For (CH2)-C-3 and H2O2, both these methods are qualitatively incorrect because they are insensitive to a low energy barrier for internal motion. The classical method qualitatively overestimates quantum mechanical results at low temperatures because of the exclusion of zero point energy. However, here anharmonic corrections are small. At high temperatures, our anharmonic corrections can be large (up to 40% for CH4 at 3000 K) and at high enough temperatures the classical and exact quantum results will converge. Comparing perturbation theory and the classical method, the classical method becomes the approximate method of choice above similar to 750 K for H2O2 and CH4, similar to 2100 K for (CH2)-C-3, similar to 2700 K for HO2, and > 3000 K for H2O. (C) 2018 The Combustion Institute. Published by Elsevier Inc. All rights reserved.},

doi = {10.1016/j.proci.2018.05.028},

journal = {},

issn = {1540-7489},

number = 1,

volume = 37,

place = {United States},

year = {2019},

month = {1}

}