• PNAS Chemistry Ad
  • Science Sessions: The PNAS Podcast Program

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)


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.


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.


  • ?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.

Online Impact

  • 864971864 2018-01-22
  • 258841863 2018-01-22
  • 957295862 2018-01-22
  • 553518861 2018-01-22
  • 983792860 2018-01-22
  • 539694859 2018-01-22
  • 956115858 2018-01-22
  • 730379857 2018-01-22
  • 346624856 2018-01-22
  • 201609855 2018-01-22
  • 72549854 2018-01-21
  • 795928853 2018-01-21
  • 752345852 2018-01-21
  • 566508851 2018-01-21
  • 615722850 2018-01-21
  • 689612849 2018-01-21
  • 846903848 2018-01-21
  • 674896847 2018-01-21
  • 11197846 2018-01-21
  • 986896845 2018-01-21