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Energy decomposition analysis of single bonds within Kohn–Sham density functional theory

  1. Martin Head-Gordona,b,1
  1. aKenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, CA 94720;
  2. bChemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720
  1. Contributed by Martin Head-Gordon, October 10, 2017 (sent for review September 7, 2017; reviewed by Gernot Frenking and Roald Hoffmann)

Significance

While theoretical chemists today can calculate the energies of molecules with high accuracy, the results are not readily interpretable by synthetic chemists who use a different language to understand and improve chemical syntheses. Energy decomposition analysis (EDA) provides a bridge between theoretical calculation and practical insight. Most existing EDA methods are not designed for studying covalent bonds. We developed an EDA to characterize single bonds, providing an interpretable chemical fingerprint in the language of synthetic chemists from the quantum mechanical language of theorists.

Abstract

An energy decomposition analysis (EDA) for single chemical bonds is presented within the framework of Kohn–Sham density functional theory based on spin projection equations that are exact within wave function theory. Chemical bond energies can then be understood in terms of stabilization caused by spin-coupling augmented by dispersion, polarization, and charge transfer in competition with destabilizing Pauli repulsions. The EDA reveals distinguishing features of chemical bonds ranging across nonpolar, polar, ionic, and charge-shift bonds. The effect of electron correlation is assessed by comparison with Hartree–Fock results. Substituent effects are illustrated by comparing the C–C bond in ethane against that in bis(diamantane), and dispersion stabilization in the latter is quantified. Finally, three metal–metal bonds in experimentally characterized compounds are examined: a <mml:math><mml:msup><mml:mtext>Mg</mml:mtext><mml:mi mathvariant="normal">I</mml:mi></mml:msup></mml:math>MgI<mml:math><mml:msup><mml:mtext>Mg</mml:mtext><mml:mi mathvariant="normal">I</mml:mi></mml:msup></mml:math>MgI dimer, the <mml:math><mml:msup><mml:mtext>Zn</mml:mtext><mml:mi mathvariant="normal">I</mml:mi></mml:msup></mml:math>ZnI<mml:math><mml:msup><mml:mtext>Zn</mml:mtext><mml:mi mathvariant="normal">I</mml:mi></mml:msup></mml:math>ZnI bond in dizincocene, and the Mn–Mn bond in dimanganese decacarbonyl.

Footnotes

  • ?1To whom correspondence should be addressed. Email: mhg{at}cchem.berkeley.edu.
  • This contribution is part of the special series of Inaugural Articles by members of the National Academy of Sciences elected in 2015.

  • Author contributions: M.H.-G. designed research; D.S.L. performed research; D.S.L. and M.H.-G. analyzed data; and D.S.L. and M.H.-G. wrote the paper.

  • Reviewers: G.F., University of Marburg; and R.H., Cornell University.

  • The authors declare no conflict of interest.

  • This article contains supporting information online at www.danielhellerman.com/lookup/suppl/doi:10.1073/pnas.1715763114/-/DCSupplemental.

Published under the PNAS license.

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