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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]
  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. https://doi.org/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. https://doi.org/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. https://doi.org/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}
}

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Figures / Tables:

Table 1 Table 1: Example Focal Point Table of CCSDT(Q)/CBS Energies

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

  • Martin, Jan M. L.; Lee, Timothy J.; Taylor, Peter R.
  • The Journal of Chemical Physics, Vol. 103, Issue 7
  • DOI: 10.1063/1.469681

Calculated stretching overtone levels and Darling–Dennison resonances in water: a triumph of simple theoretical approaches
journal, October 2007

  • Matthews, Devin A.; Vázquez, Juana; Stanton, John F.
  • Molecular Physics, Vol. 105, Issue 19-22
  • 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.
  • Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy, Vol. 53, Issue 8
  • DOI: 10.1016/S1386-1425(96)01869-0

New analysis of the ν2 band of formaldehyde : Line positions for the ν2, ν3, ν4 and ν6 interacting bands
journal, October 2007

  • Tchana, F. Kwabia; Perrin, A.; Lacome, N.
  • Journal of Molecular Spectroscopy, Vol. 245, Issue 2
  • DOI: 10.1016/j.jms.2007.07.008

High resolution spectroscopy of H 2 12 C 16 O in the 1.9 to 2.56 µm spectral range
journal, June 2006


Efficient calculation of potential energy surfaces for the generation of vibrational wave functions
journal, November 2004

  • Rauhut, Guntram
  • The Journal of Chemical Physics, Vol. 121, Issue 19
  • DOI: 10.1063/1.1804174

On the use of quartic force fields in variational calculations
journal, June 2013


Accurate calculation of vibrational frequencies using explicitly correlated coupled-cluster theory
journal, February 2009

  • Rauhut, Guntram; Knizia, Gerald; Werner, Hans-Joachim
  • The Journal of Chemical Physics, Vol. 130, Issue 5
  • DOI: 10.1063/1.3070236

High resolution infrared study of D2CO in the region of 1780–2400cm−1: assignment and preliminary analysis
journal, January 2006


The ν2 Band of Formaldehyde-d2
journal, February 2001


New High-Resolution Analysis of the ν3, ν4, and ν6Bands of D2CO Measured by Fourier Transform Spectroscopy
journal, January 1998

  • Perrin, A.; Flaud, J. -M.; Predoi-Cross, A.
  • Journal of Molecular Spectroscopy, Vol. 187, Issue 1
  • DOI: 10.1006/jmsp.1997.7469

Dispersed fluorescence spectroscopy of S0 vibrational levels in formaldehyde-d
journal, December 2008

  • Ellsworth, Kristin K.; Lajiness, Brian D.; Lajiness, James P.
  • Journal of Molecular Spectroscopy, Vol. 252, Issue 2
  • DOI: 10.1016/j.jms.2008.09.003

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


    Works referencing / citing this record:

    Laboratory spectroscopic study of isotopic thioformaldehyde, H 2 CS, and determination of its equilibrium structure
    journal, January 2019


    Vibrational analysis of the ubiquitous interstellar molecule cyclopropenylidene ( c -C 3 H 2 ): the importance of numerical stability
    journal, March 2019


    Fourth-order vibrational perturbation theory with the Watson Hamiltonian: Report of working equations and preliminary results
    journal, September 2018

    • Gong, Justin Z.; Matthews, Devin A.; Changala, P. Bryan
    • The Journal of Chemical Physics, Vol. 149, Issue 11
    • DOI: 10.1063/1.5040360

    State‐of‐the‐art computations of dipole moments using analytic gradients of high‐level density‐fitted coupled‐cluster methods with focal‐point approximations
    journal, December 2019

    • Bozkaya, Uğur; Soydaş, Emine; Filiz, Bahar
    • Journal of Computational Chemistry, Vol. 41, Issue 8
    • DOI: 10.1002/jcc.26126

    Theoretical studies of atmospheric molecular complexes interacting with NIR to UV light
    journal, January 2018

    • Biczysko, Malgorzata; Krupa, Justyna; Wierzejewska, Maria
    • Faraday Discussions, Vol. 212
    • DOI: 10.1039/c8fd00094h

    Astrophysical sulfur in diffuse and dark clouds: The fundamental vibrational frequencies and spectroscopic constants of hydrogen sulfide cation (H2S+)
    journal, August 2018

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