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Title: 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 (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.

Authors:
 [1]; ORCiD logo [2]; ORCiD logo [3]; ORCiD logo [4]
+ Show Author Affiliations
  1. The Univ. of Texas at Austin, Austin, TX (United States)
  2. The Univ. of Texas, Austin, TX (United States)
  3. Univ. of Colorado, Boulder, CO (United States)
  4. 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:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; 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.
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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. https://doi.org/10.1063/1.5040360
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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. https://doi.org/10.1063/1.5040360. https://www.osti.gov/servlets/purl/1540231.
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@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 = {Tue Sep 18 00:00:00 EDT 2018},
month = {Tue Sep 18 00:00:00 EDT 2018}
}
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https://doi.org/10.1063/1.5040360
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Cited by: 24 works
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Figures / Tables:

TABLE I TABLE I: Fundamental and two-quantum vibrational levels of water, obtained with the CCSD(T)/ANO1 potential surface described in the text. Energies in boldface differ from the “exact” variational results by more than 1 cm -1 for fundamentals and 2 cm -1 for two-quantum states. Note the near coincidence of variational andmore » AVCI(3) + VMP2 results, especially for all levels not affected by the Darling-Dennison resonance that mixes 2$ν$1 and 2$ν$3.« less
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