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A Bond-Energy/Bond-Order and Populations Relationship
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    Quantum Electronic Structure

    A Bond-Energy/Bond-Order and Populations Relationship
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    • Barbaro Zulueta
      Barbaro Zulueta
      Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States
    • Sonia V. Tulyani
      Sonia V. Tulyani
      Formerly Chemical Engineering Department, University of Massachusetts Amherst,618 North Pleasant Street, Amherst, Massachusetts 01003, United States
    • Phillip R. Westmoreland
      Phillip R. Westmoreland
      Department of Chemical and Biomolecular Engineering, North Carolina State University, Raleigh, North Carolina 27695, United States
    • Michael J. Frisch
      Michael J. Frisch
      Gaussian, Inc., Wallingford, Connecticut 06492, United States
    • E. James Petersson
      E. James Petersson
      Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
    • George A. Petersson
      George A. Petersson
      Institute for Computational Molecular Science, Temple University, Philadelphia, Pennsylvania 19122, United States
      Formerly Hall-Atwater Laboratories of Chemistry, Wesleyan University, Middletown, Connecticut 06459, United States
    • John A. Keith*
      John A. Keith
      Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States
      *Email: [email protected]
    Other Access OptionsSupporting Information (2)

    Journal of Chemical Theory and Computation

    Cite this: J. Chem. Theory Comput. 2022, 18, 8, 4774–4794
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    https://doi.org/10.1021/acs.jctc.2c00334
    Published July 18, 2022
    Copyright © 2022 American Chemical Society

    Abstract

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    We report an analytical bond energy from bond orders and populations (BEBOP) model that provides intramolecular bond energy decompositions for chemical insight into the thermochemistry of molecules. The implementation reported here employs a minimum basis set Mulliken population analysis on well-conditioned Hartree–Fock orbitals to decompose total electronic energies into physically interpretable contributions. The model’s parametrization scheme is based on atom-specific parameters for hybridization and atom pair-specific parameters for short-range repulsion and extended Hückel-type bond energy term fitted to reproduce CBS-QB3 thermochemistry data. The current implementation is suitable for molecules involving H, Li, Be, B, C, N, O, and F atoms, and it can be used to analyze intramolecular bond energies of molecular structures at optimized stationary points found from other computational methods. This first-generation model brings the computational cost of a Hartree–Fock calculation using a large triple-ζ basis set, and its atomization energies are comparable to those from widely used hybrid Kohn–Sham density functional theory (DFT, as benchmarked to 109 species from the G2/97 test set and an additional 83 reference species). This model should be useful for the community by interpreting overall ab initio molecular energies in terms of physically insightful bond energy contributions, e.g., bond dissociation energies, resonance energies, molecular strain energies, and qualitative energetic contributions to the activation barrier in chemical reaction mechanisms. This work reports a critical benchmarking of this method as well as discussions of its strengths and weaknesses compared to hybrid DFT (i.e., B3LYP, M062X, PBE0, and APF methods), and other cost-effective approximate Hamiltonian semiempirical quantum methods (i.e., AM1, PM6, PM7, and DFTB3).

    Copyright © 2022 American Chemical Society

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    Supporting Information

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    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.2c00334.

    • Derivation of the extended-Hückel theory and data for trigonal planar and trigonal pyramidal NH3 (PDF)

    • Excel file of all computed data (XLSX)

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    Cited By

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    Citation Statements
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    This article is cited by 12 publications.

    1. Dan Hong, Wei Zeng, Zheng-Tang Liu, Fu-Sheng Liu, Qi-Jun Liu. Initial Decomposition of DATB Induced by an External Electric Field. The Journal of Physical Chemistry A 2023, 127 (24) , 5140-5151. https://doi.org/10.1021/acs.jpca.3c01298
    2. Michael J. Sahre, Guido Falk von Rudorff, O. Anatole von Lilienfeld. Quantum Alchemy Based Bonding Trends and Their Link to Hammett’s Equation and Pauling’s Electronegativity Model. Journal of the American Chemical Society 2023, 145 (10) , 5899-5908. https://doi.org/10.1021/jacs.2c13393
    3. Barbaro Zulueta, John A. Keith. Vibrational Partition Functions from Bond Order and Populations Relationships. ChemPhysChem 2025, 162 https://doi.org/10.1002/cphc.202500085
    4. Roberts I. Eglitis, Juris Purans, Ran Jia, Sergei P. Kruchinin, Steffen Wirth. Comparative B3PW and B3LYP Calculations of ABO3 (A = Ba, Sr, Pb, Ca; B = Sn, Ti, Zr) Neutral (001) and Polar (111) Surfaces. Inorganics 2025, 13 (4) , 100. https://doi.org/10.3390/inorganics13040100
    5. Barbaro Zulueta, John A. Keith. A focus on delocalization error poisoning the density-functional many-body expansion. Chemical Science 2025, 16 (11) , 4566-4567. https://doi.org/10.1039/D5SC90053K
    6. Barbaro Zulueta, Colin D. Rude, Jesse A. Mangiardi, George A. Petersson, John A. Keith. Zero-point energies from bond orders and populations relationships. The Journal of Chemical Physics 2025, 162 (8) https://doi.org/10.1063/5.0238831
    7. Dominick Filonowich, Sachin Velankar, John A. Keith. The fascinating world of polymer crystal hydrates: An overview. AIChE Journal 2024, 70 (10) https://doi.org/10.1002/aic.18556
    8. R. I. Eglitis, A. I. Popov, Ran Jia, S. P. Kruchinin, I. Derkaoui, M. A. Basyooni-M. Kabatas. B3LYP and B3PW computations of BaSnO3 and BaZrO3 perovskite (001) surfaces. Low Temperature Physics 2024, 50 (10) , 905-910. https://doi.org/10.1063/10.0028638
    9. Somayeh Faraji, Mingjie Liu. Transferable machine learning interatomic potential for carbon hydrogen systems. Physical Chemistry Chemical Physics 2024, 26 (34) , 22346-22358. https://doi.org/10.1039/D4CP02300E
    10. Laura Van Dorn, Andrei Sanov. A density-matrix adaptation of the Hückel method to weak covalent networks. Physical Chemistry Chemical Physics 2024, 26 (7) , 5879-5894. https://doi.org/10.1039/D3CP05697J
    11. Shree Sowndarya S. V., Yeonjoon Kim, Seonah Kim, Peter C. St. John, Robert S. Paton. Expansion of bond dissociation prediction with machine learning to medicinally and environmentally relevant chemical space. Digital Discovery 2023, 2 (6) , 1900-1910. https://doi.org/10.1039/D3DD00169E
    12. Mohsen Doust Mohammadi, Faheem Abbas, Hitler Louis, Zonish Zeb, Martilda U. Akem, Innocent Benjamin. Computational Investigation of the Intermolecular Interactions between Decatungstate Acid and CX 2 O (X=H, F, Cl, and Br). ChemistrySelect 2023, 8 (39) https://doi.org/10.1002/slct.202300504

    Journal of Chemical Theory and Computation

    Cite this: J. Chem. Theory Comput. 2022, 18, 8, 4774–4794
    Click to copy citationCitation copied!
    https://doi.org/10.1021/acs.jctc.2c00334
    Published July 18, 2022
    Copyright © 2022 American Chemical Society

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