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Title: 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 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.

Authors:
ORCiD logo [1];  [2];  [3]; ORCiD logo [1];  [2];  [3];  [1]; ORCiD logo [4]; ORCiD logo [1]
+ Show Author Affiliations
  1. Univ. of Georgia, Athens, GA (United States)
  2. Univ. of Texas at Austin, Austin, TX (United States)
  3. Univ. of Tromso - The Arctic Univ. of Norway, Tromso (Norway)
  4. 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)
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.
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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. https://doi.org/10.1021/acs.jctc.7b01138
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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. https://doi.org/10.1021/acs.jctc.7b01138. https://www.osti.gov/servlets/purl/1468297.
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@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}
}
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https://doi.org/10.1021/acs.jctc.7b01138
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Figures / Tables:

Table 1 Table 1: Example Focal Point Table of CCSDT(Q)/CBS Energies
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The Vibration-Rotation Energies of Polyatomic Molecules Part II. Accidental Degeneracies
journal, October 1945

The anharmonic force field of ethylene, C 2 H 4 , by means of accurate ab initio calculations
journal, August 1995

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Calculated stretching overtone levels and Darling–Dennison resonances in water: a triumph of simple theoretical approaches
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  • Matthews, Devin A.; Vázquez, Juana; Stanton, John F.
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  • DOI: 10.1080/00268970701618424

Quantitative analysis of Fermi resonances by harmonic derivatives of perturbation theory corrections
journal, October 2009

Accurate ab initio quartic force field for trans-HNNH and treatment of resonance polyads
journal, July 1997

  • Martin, Jan M. L.; Taylor, Peter R.
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New analysis of the ν2 band of formaldehyde : Line positions for the ν2, ν3, ν4 and ν6 interacting bands
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High resolution spectroscopy of H 2 12 C 16 O in the 1.9 to 2.56 µm spectral range
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Efficient calculation of potential energy surfaces for the generation of vibrational wave functions
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  • Rauhut, Guntram
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On the use of quartic force fields in variational calculations
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Accurate calculation of vibrational frequencies using explicitly correlated coupled-cluster theory
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  • DOI: 10.1063/1.3070236

High resolution infrared study of D2CO in the region of 1780–2400cm−1: assignment and preliminary analysis
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The ν2 Band of Formaldehyde-d2
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New High-Resolution Analysis of the ν3, ν4, and ν6Bands of D2CO Measured by Fourier Transform Spectroscopy
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  • Perrin, A.; Flaud, J. -M.; Predoi-Cross, A.
  • Journal of Molecular Spectroscopy, Vol. 187, Issue 1
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Dispersed fluorescence spectroscopy of S0 vibrational levels in formaldehyde-d
journal, December 2008

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Submillimeter spectroscopy of H2C17O and a revisit of the rotational spectra of H2C18O and H2C16O
journal, January 2017

The rotational levels of the ground vibrational state of formaldehyde
journal, April 1997

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    • Morgan, W. James; Huang, Xinchuan; Schaefer, Henry F.
    • Monthly Notices of the Royal Astronomical Society, Vol. 480, Issue 3
    • DOI: 10.1093/mnras/sty2134
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