## Fourth-order vibrational perturbation theory with the Watson Hamiltonian: Report of working equations and preliminary results

## Abstract

A derivation of fourth-order vibrational perturbation theory (VPT4) based on the Watson Hamiltonian in dimensionless rectilinear normal coordinates is presented. Terms that are linear and cubic in the (n _{k} + 1/2), with n _{k} being the zeroth-order harmonic oscillator quantum numbers, appear in fourth order and extend the much simpler second-order vibrational perturbation theory model. The rather involved expressions for the fourth-order terms are derived with Rayleigh-Schrödinger perturbation theory, the process of verifying their correctness is described, and a computer code to generate the VPT4 constants from the potential energy surface derivatives is provided. Here, the paper concludes with numerical examples featuring the H _{2}O, Si _{2}C, and cyclic-C _{3}H _{2} molecules.

- Authors:

- The Univ. of Texas at Austin, Austin, TX (United States)
- The Univ. of Texas, Austin, TX (United States)
- Univ. of Colorado, Boulder, CO (United States)
- Univ. of Florida, Gainesville, FL (United States)

- Publication Date:

- Research Org.:
- Univ. of Hawaii, Honolulu, HI (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1540231

- Alternate Identifier(s):
- OSTI ID: 1471270

- Grant/Contract Number:
- FG02-07ER15885

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Physics

- Additional Journal Information:
- Journal Volume: 149; Journal Issue: 11; Journal ID: ISSN 0021-9606

- Publisher:
- American Institute of Physics (AIP)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- Chemistry; Physics

### Citation Formats

```
Gong, Justin Z., Matthews, Devin A., Changala, P. Bryan, and Stanton, John F. Fourth-order vibrational perturbation theory with the Watson Hamiltonian: Report of working equations and preliminary results. United States: N. p., 2018.
Web. doi:10.1063/1.5040360.
```

```
Gong, Justin Z., Matthews, Devin A., Changala, P. Bryan, & Stanton, John F. Fourth-order vibrational perturbation theory with the Watson Hamiltonian: Report of working equations and preliminary results. United States. doi:10.1063/1.5040360.
```

```
Gong, Justin Z., Matthews, Devin A., Changala, P. Bryan, and Stanton, John F. Tue .
"Fourth-order vibrational perturbation theory with the Watson Hamiltonian: Report of working equations and preliminary results". United States. doi:10.1063/1.5040360. https://www.osti.gov/servlets/purl/1540231.
```

```
@article{osti_1540231,
```

title = {Fourth-order vibrational perturbation theory with the Watson Hamiltonian: Report of working equations and preliminary results},

author = {Gong, Justin Z. and Matthews, Devin A. and Changala, P. Bryan and Stanton, John F.},

abstractNote = {A derivation of fourth-order vibrational perturbation theory (VPT4) based on the Watson Hamiltonian in dimensionless rectilinear normal coordinates is presented. Terms that are linear and cubic in the (nk + 1/2), with nk being the zeroth-order harmonic oscillator quantum numbers, appear in fourth order and extend the much simpler second-order vibrational perturbation theory model. The rather involved expressions for the fourth-order terms are derived with Rayleigh-Schrödinger perturbation theory, the process of verifying their correctness is described, and a computer code to generate the VPT4 constants from the potential energy surface derivatives is provided. Here, the paper concludes with numerical examples featuring the H2O, Si2C, and cyclic-C3H2 molecules.},

doi = {10.1063/1.5040360},

journal = {Journal of Chemical Physics},

number = 11,

volume = 149,

place = {United States},

year = {2018},

month = {9}

}

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