# Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde

## Abstract

Here, geometric energy derivatives which rely on core-corrected focal-point energies extrapolated to the complete basis set (CBS) limit of coupled cluster theory with iterative and noniterative quadruple excitations, CCSDTQ and CCSDT(Q), are used as elements of molecular gradients and, in the case of CCSDT(Q), expansion coefficients of an anharmonic force field. These gradients are used to determine the CCSDTQ/CBS and CCSDT(Q)/CBS equilibrium structure of the S _{0} ground state of H _{2}CO where excellent agreement is observed with previous work and experimentally derived results. A fourth-order expansion about this CCSDT(Q)/CBS reference geometry using the same level of theory produces an exceptional level of agreement to spectroscopically observed vibrational band origins with a MAE of 0.57 cm ^{–1}. Second-order vibrational perturbation theory (VPT2) and variational discrete variable representation (DVR) results are contrasted and discussed. Vibration–rotation, anharmonicity, and centrifugal distortion constants from the VPT2 analysis are reported and compared to previous work. Additionally, an initial application of a sum-over-states fourth-order vibrational perturbation theory (VPT4) formalism is employed herein, utilizing quintic and sextic derivatives obtained with a recursive algorithmic approach for response theory.

- Authors:

- Univ. of Georgia, Athens, GA (United States)
- Univ. of Texas at Austin, Austin, TX (United States)
- Univ. of Tromso - The Arctic Univ. of Norway, Tromso (Norway)
- Univ. of Florida, Gainesville, FL (United States)

- Publication Date:

- Research Org.:
- Univ. of Georgia, Athens, GA (United States)

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

- OSTI Identifier:
- 1468297

- Grant/Contract Number:
- SC0018412

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Chemical Theory and Computation

- Additional Journal Information:
- Journal Volume: 14; Journal Issue: 3; Journal ID: ISSN 1549-9618

- Publisher:
- American Chemical Society

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

### Citation Formats

```
Morgan, W. James, Matthews, Devin A., Ringholm, Magnus, Agarwal, Jay, Gong, Justin Z., Ruud, Kenneth, Allen, Wesley D., Stanton, John F., and Schaefer, III, Henry F. Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde. United States: N. p., 2018.
Web. doi:10.1021/acs.jctc.7b01138.
```

```
Morgan, W. James, Matthews, Devin A., Ringholm, Magnus, Agarwal, Jay, Gong, Justin Z., Ruud, Kenneth, Allen, Wesley D., Stanton, John F., & Schaefer, III, Henry F. Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde. United States. doi:10.1021/acs.jctc.7b01138.
```

```
Morgan, W. James, Matthews, Devin A., Ringholm, Magnus, Agarwal, Jay, Gong, Justin Z., Ruud, Kenneth, Allen, Wesley D., Stanton, John F., and Schaefer, III, Henry F. Fri .
"Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde". United States. doi:10.1021/acs.jctc.7b01138. https://www.osti.gov/servlets/purl/1468297.
```

```
@article{osti_1468297,
```

title = {Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde},

author = {Morgan, W. James and Matthews, Devin A. and Ringholm, Magnus and Agarwal, Jay and Gong, Justin Z. and Ruud, Kenneth and Allen, Wesley D. and Stanton, John F. and Schaefer, III, Henry F.},

abstractNote = {Here, geometric energy derivatives which rely on core-corrected focal-point energies extrapolated to the complete basis set (CBS) limit of coupled cluster theory with iterative and noniterative quadruple excitations, CCSDTQ and CCSDT(Q), are used as elements of molecular gradients and, in the case of CCSDT(Q), expansion coefficients of an anharmonic force field. These gradients are used to determine the CCSDTQ/CBS and CCSDT(Q)/CBS equilibrium structure of the S0 ground state of H2CO where excellent agreement is observed with previous work and experimentally derived results. A fourth-order expansion about this CCSDT(Q)/CBS reference geometry using the same level of theory produces an exceptional level of agreement to spectroscopically observed vibrational band origins with a MAE of 0.57 cm–1. Second-order vibrational perturbation theory (VPT2) and variational discrete variable representation (DVR) results are contrasted and discussed. Vibration–rotation, anharmonicity, and centrifugal distortion constants from the VPT2 analysis are reported and compared to previous work. Additionally, an initial application of a sum-over-states fourth-order vibrational perturbation theory (VPT4) formalism is employed herein, utilizing quintic and sextic derivatives obtained with a recursive algorithmic approach for response theory.},

doi = {10.1021/acs.jctc.7b01138},

journal = {Journal of Chemical Theory and Computation},

number = 3,

volume = 14,

place = {United States},

year = {2018},

month = {2}

}

*Citation information provided by*

Web of Science

Web of Science

#### Figures / Tables:

Works referencing / citing this record:

##
Laboratory spectroscopic study of isotopic thioformaldehyde, H _{2} CS, and determination of its equilibrium structure

journal, January 2019

- Müller, Holger S. P.; Maeda, Atsuko; Thorwirth, Sven
- Astronomy & Astrophysics, Vol. 621

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*