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The Lewis electron-pair bonding model: modern energy decomposition analysis

Nature Reviews Chemistry volume 3, pages 48–63 (2019)Cite this article

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Abstract

Breaking down the calculated interaction energy between two or more fragments into well-defined terms enables a physically meaningful understanding of chemical bonding. Energy decomposition analysis (EDA) is a powerful method that connects the results of accurate quantum chemical calculations with the Lewis electron-pair bonding model. The combination of EDA with natural orbitals for chemical valence (NOCV) links the heuristic Lewis picture with quantitative molecular orbital theory complemented by Pauli repulsion and Coulombic interactions. The EDA-NOCV method affords results that provide a physically sound picture of chemical bonding between any atoms. We present and discuss results for the prototypical main-group diatomics H2, N2, CO and BF, before comparing bonding in N2 and C2H2 with that in heavier homologues. The discussion on multiply bonded species is continued with a description of B2 and its N-heterocyclic carbene adducts.

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Fig. 1: Coulombic-electrostatic and Pauli-exclusion repulsion as a function of distance.
Fig. 2: Orbital overlaps and energy contributions in N≡N bond formation.
Fig. 3: Lewis structures of N2, CO and BF suggested by the EDA-NOCV calculations along with the electron configurations of the constituent atoms.
Fig. 4: Deformation densities and charge flow for bonds in N2, CO and BF.
Fig. 5: The electron density Laplacian ∇2ρ for CO and BF.
Fig. 6: Structures of E2 and Td-symmetric E4 (E = N, P).
Fig. 7: Calculated bond dissociation energies De for linear HE≡EH→2EH (a4Σ−) and excitation energies ΔEexc(X2Π→a4Σ−) for EH.
Fig. 8: Qualitative bonding models for E2H2.
Fig. 9: The bonding in B2 and its N-heterocyclic carbene adducts.
Fig. 10: Molecular valence orbitals in B2(NHCMe)2 and its fragments at the BP86/TZ2P level of theory.

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References

  1. Zhao, L., Schwarz, W. H. E. & Frenking, G. The Lewis electron-pair bonding model: the physical background, a century later. Nat. Rev. Chem. https://doi.org/10.1038/s41570-018-0052-4 (2018).

    Article  Google Scholar 

  2. Lewis, G. N. The atom and the molecule. J. Am. Chem. Soc. 38, 762–785 (1916).

    Article  CAS  Google Scholar 

  3. Lewis, G. N. Valence and the Structure of Atoms and Molecules (The Chemical Catalog Company, New York, 1923).

  4. Lewis, G. N. The chemical bond. J. Chem. Phys. 1, 17–28 (1933).

    Article  CAS  Google Scholar 

  5. Ziegler, T. & Rauk, A. On the calculation of bonding energies by the Hartree Fock Slater method. Theor. Chim. Acta 46, 1–10 (1977).

    Article  CAS  Google Scholar 

  6. Mitoraj, M. & Michalak, A. Natural orbitals for chemical valence as descriptors of chemical bonding in transition metal complexes. J. Mol. Model. 13, 347–355 (2007).

    Article  CAS  PubMed  Google Scholar 

  7. Mitoraj, M. & Michalak, A. Donor–acceptor properties of ligands from the natural orbitals for chemical valence. Organometallics 26, 6576–6580 (2007).

    Article  CAS  Google Scholar 

  8. Mitoraj, M. P. & Michalak, A. & Ziegler, T. A combined charge and energy decomposition scheme for bond analysis. J. Chem. Theory Comput. 5, 962–975 (2009).

    Article  CAS  PubMed  Google Scholar 

  9. Michalak, A., Mitoraj, M. & Ziegler, T. Bond orbitals from chemical valence theory. J. Phys. Chem. A 112, 1933–1939 (2008).

    Article  CAS  PubMed  Google Scholar 

  10. Zhao, L., von Hopffgarten, M., Andrada, D. M. & Frenking, G. Energy decomposition analysis. Wiley Interdiscip. Rev. Comput. Mol. Sci. 8, e1345 (2018).

    Article  CAS  Google Scholar 

  11. Frenking, G. & Bickelhaupt, F. M. in The Chemical Bond: Fundamental Aspects of Chemical Bonding (eds Frenking, G. & Shaik, S.) 121–158 (Wiley-VCH, Weinheim, 2014).

  12. Kitaura, K. & Morokuma, K. A new energy decomposition scheme for molecular interactions within the Hartree–Fock approximation. Int. J. Quantum Chem. 10, 325–340 (1976).

    Article  CAS  Google Scholar 

  13. Heitler, W. & London, F. Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik [German]. Z. Phys. 44, 455–472 (1927).

    Article  CAS  Google Scholar 

  14. Bickelhaupt, F. M., Nibbering, N. M. M., Van Wezenbeek, E. M. & Baerends, E. J. Central bond in the three CN· dimers NC–CN, CN–CN and CN–NC: electron pair bonding and Pauli repulsion effects. J. Phys. Chem. 96, (4864–4873 (1992).

    Google Scholar 

  15. Wagner, J. P. & Schreiner, P. R. London dispersion in molecular chemistry — reconsidering steric effects. Angew. Chem. Int. Ed. 54, 12274–12296 (2015).

    Article  CAS  Google Scholar 

  16. Fukui, K. Theory of Orientation and Stereoselection (Springer Verlag, Berlin, 1975).

  17. Woodward, R. B. & Hoffmann, R. The Conservation of Orbital Symmetry (Academic Press, Cambridge, 1971).

  18. Ruedenberg, K. The physical nature of the chemical bond. Rev. Mod. Phys. 34, 326–376 (1962).

    Article  CAS  Google Scholar 

  19. Krapp, A., Bickelhaupt, F. M. & Frenking, G. Orbital overlap and chemical bonding. Chem. Eur. J. 12, 9196–9216 (2006).

    Article  CAS  PubMed  Google Scholar 

  20. Kovács, K., Esterhuysen, C. & Frenking, G. The nature of the chemical bond revisited: an energy-partitioning analysis of nonpolar bonds. Chem. Eur. J. 11, 1813–1825 (2005).

    Article  PubMed  CAS  Google Scholar 

  21. Blanco, M. A., Pendás, A. M. & Francisco, E. Interacting quantum atoms: a correlated energy decomposition scheme based on the quantum theory of atoms in molecules. J. Chem. Theory Comput. 1, 1096–1109 (2005).

    Article  CAS  PubMed  Google Scholar 

  22. Bader, R. F. W. Atoms in Molecules: A Quantum Theory (Oxford Univ. Press, 1990).

  23. Gillespie, R. J. & Hargittai, I. The VSEPR Model of Molecular Geometry (Allyn & Bacon, Boston, 1991).

  24. Gillespie, R. J. & Popelier, P. L. A. Chemical Bonding and Molecular Geometry (Oxford Univ. Press, New York, 2001).

  25. Frenking, G. Book review: chemical bonding and molecular geometry from Lewis to electron densities. Angew. Chem. Int. Ed. 42, 143–147 (2003).

    Article  Google Scholar 

  26. Gillespie, R. J. & Popelier, P. L. A. “Chemical bonding and molecular geometry”: comments on a book review. Angew. Chem. Int. Ed. 42, 3331–3334 (2003).

    Article  CAS  Google Scholar 

  27. Levine, D. S., Horn, P. R., Mao, Y. & Head-Gordon, M. Variational energy decomposition analysis of chemical bonding. 1. Spin-pure analysis of single bonds. J. Chem. Theory Comput. 12, 4812–4820 (2016).

    Article  CAS  PubMed  Google Scholar 

  28. Levine, D. S. & Head-Gordon, M. Energy decomposition analysis of single bonds within Kohn–Sham density functional theory. Proc. Natl Acad. Sci. USA 114, 12649–12656 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Becke, A. D. & Perdew, J. P. Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. A 38, 3098–3100 (1988).

    Article  CAS  Google Scholar 

  30. Perdew, J. P. Density-functional approximation for the correlation energy of the inhomogeneous electron gas. Phys. Rev. B 33, 8822–8824 (1986).

    Article  CAS  Google Scholar 

  31. Van Lenthe, E. & Baerends, E. J. Optimized Slater-type basis sets for the elements 1–118. J. Comput. Chem. 24, 1142–1156 (2003).

    Article  PubMed  CAS  Google Scholar 

  32. Pauling, L. The Nature of the Chemical Bond (Cornell Univ. Press, Ithaca, NY, 1960).

  33. Muenter, J. S. Electric dipole moment of carbon monoxide. J. Mol. Spectrosc. 55, 490–491 (1975).

    Article  CAS  Google Scholar 

  34. Meerts, W. L., De Leeuw, F. H. & Dymanus, A. Electric and magnetic properties of carbon monoxide by molecular-beam electric-resonance spectroscopy. Chem. Phys. 22, 319–324 (1977).

    Article  CAS  Google Scholar 

  35. Scuseria, G. E., Miller, M. D., Jensen, F. & Geertsen, J. The dipole moment of carbon monoxide. J. Chem. Phys. 94, 6660–6663 (1991).

    Article  CAS  Google Scholar 

  36. Peterson, K. A. & Woods, R. C. An ab initio investigation of the spectroscopic properties of BCl, CS, CCl+, BF, CO, CF+, N2, CN−, and NO+. J. Chem. Phys. 87, 4409–4418 (1987).

    Article  CAS  Google Scholar 

  37. Huzinaga, S., Miyoshi, E. & Sekiya, M. Electric dipole polarity of diatomic molecules. J. Comput. Chem. 14, 1440–1445 (1993).

    Article  CAS  Google Scholar 

  38. Honigmann, M., Hirsch, G. & Buenker, R. J. Theoretical study of the optical and generalized oscillator strengths for transitions between low-lying electronic states of the BF molecule. Chem. Phys. 172, 59–71 (1993).

    Article  CAS  Google Scholar 

  39. Fantuzzi, F., Cardozo, T. M. & Nascimento, M. A. C. Nature of the chemical bond and origin of the inverted dipole moment in boron fluoride: a generalized valence bond approach. J. Phys. Chem. A 119, 5335–5343 (2015).

    Article  CAS  PubMed  Google Scholar 

  40. Lovas, F. J. & Johnson, D. R. Microwave spectrum of BF. J. Chem. Phys. 55, 41–44 (1971).

    Article  CAS  Google Scholar 

  41. Kaupp, M. in The Chemical Bond: Chemical Bonding Across the Periodic Table (eds Frenking, G. & Shaik, S.) 1–24 (Wiley-VCH, Weinheim, 2014).

  42. Albright, T. A., Burdett, J. K. & Whangbo, M.-H. Orbital Interactions in Chemistry 2nd edn (Wiley, New York, 2013).

  43. Kutzelnigg, W. Chemical bonding in higher main group elements. Angew. Chem. Int. Ed. Engl. 23, 272–295 (1984).

    Article  Google Scholar 

  44. Lein, M., Krapp, A. & Frenking, G. Why do the heavy-atom analogues of acetylene E2H2 (E=Si−Pb) exhibit unusual structures? J. Am. Chem. Soc. 127, 6290–6299 (2005).

    Article  CAS  PubMed  Google Scholar 

  45. Power, P. P. π-Bonding and the lone pair effect in multiple bonds between heavier main group elements. Chem. Rev. 99, 3463–3504 (1999).

    Article  CAS  PubMed  Google Scholar 

  46. Lias, S. G. et al. Gas-phase ion and neutral thermochemistry. J. Phys. Chem. Ref. Data 17, 1–8 (1988).

    Article  Google Scholar 

  47. Jerabek, P. & Frenking, G. Comparative bonding analysis of N2 and P2 versus tetrahedral N4 and P4. Theor. Chem. Acc. 133, 1447 (2014).

    Article  CAS  Google Scholar 

  48. Jerabek, P. & Frenking, G. Erratum to: comparative bonding analysis of N2 and P2 versus tetrahedral N4 and P4. Theor. Chem. Acc. 134, 136 (2015).

    Article  CAS  Google Scholar 

  49. Pyykkö, P. On the interpretation of the ‘second periodicity’ in the periodic system. J. Chem. Res. 1979, 380–381 (1979).

    Google Scholar 

  50. Trinquier, G. & Malrieu, J. P. Nonclassical distortions at multiple bonds. J. Am. Chem. Soc. 109, 5303–5315 (1987).

    Article  CAS  Google Scholar 

  51. Driess, M. & Grützmacher, H. Main group element analogues of carbenes, olefins, and small rings. Angew. Chem. Int. Ed. Engl. 35, 828–856 (1996).

    Article  CAS  Google Scholar 

  52. Carter, E. A. & Goddard, W. A. Relation between singlet–triplet gaps and bond energies. J. Phys. Chem. 90, 998–1001 (1986).

    Article  CAS  Google Scholar 

  53. Lewis, G. N. Acids and bases. J. Franklin Inst. 226, 293–313 (1938).

    Article  Google Scholar 

  54. Sidgwick, N. V. The Electronic Theory of Valency (Clarendon Press, Oxford, 1927).

  55. Haaland, A. Covalent versus dative bonds to main group metals, a useful distinction. Angew. Chem. Int. Ed. Engl. 28, 992–1007 (1989).

    Article  Google Scholar 

  56. Zhao, L., Hermann, M., Holzmann, N. & Frenking, G. Dative bonding in main group compounds. Coord. Chem. Rev. 344, 163–204 (2017).

    Article  CAS  Google Scholar 

  57. Lischka, H. & Koehler, H. J. Ab initio investigation on the lowest singlet and triplet state of disilyne (Si2H2). J. Am. Chem. Soc. 105, 6646–6649 (1983).

    Article  CAS  Google Scholar 

  58. Binkley, J. S. Theoretical study of the relative stabilities of C2H2 and Si2H2 conformers. J. Am. Chem. Soc. 106, 603–609 (1984).

    Article  CAS  Google Scholar 

  59. Kalcher, J., Sax, A. & Olbrich, G. Ab initio and pseudopotential calculations on the singlet and triplet states of the disilyne isomers. Int. J. Quantum Chem. 25, 543–552 (1984).

    Article  CAS  Google Scholar 

  60. Köhler, H.-J. & Lischka, H. Bridged structures in multiply bonded silicon compounds: disilyne, protonated disilyne and disilene. Chem. Phys. Lett. 112, 33–40 (1984).

    Article  Google Scholar 

  61. Colegrove, B. T. & Schaefer III, H. F. Disilyne (Si2H2) revisited. J. Phys. Chem. 94, 5593–5602 (1990).

    Article  CAS  Google Scholar 

  62. Grev, R. S., Deleeuw, B. J. & Schaefer III, H. F. Germanium–germanium multiple bonds: the singlet electronic ground state of Ge2H2. Chem. Phys. Lett. 165, 257–264 (1990).

    Article  CAS  Google Scholar 

  63. Grev, R. S. Structure and bonding in the parent hydrides and multiply bonded silicon and germanium compounds: from MHn to R2M=MʹR2 and RM≡MʹR. Adv. Organomet. Chem. 33, 125–170 (1991).

    Article  CAS  Google Scholar 

  64. Grev, R. S. & Schaefer III, H. F. The remarkable monobridged structure of Si2H2. J. Chem. Phys. 97, 7990–7998 (1992).

    Article  CAS  Google Scholar 

  65. Palágyi, Z., Schaefer, H. F. & Kapuy, E. Ge2H2: a molecule with a low-lying monobridged equilibrium geometry. J. Am. Chem. Soc. 115, 6901–6903 (1993).

    Article  Google Scholar 

  66. Nagase, S., Kobayashi, K. & Takagi, N. Triple bonds between heavier group 14 elements. A theoretical approach. J. Organomet. Chem. 611, 264–271 (2000).

    Article  CAS  Google Scholar 

  67. Chen, Y., Hartmann, M., Diedenhofen, M. & Frenking, G. Turning a transition state into a minimum — the nature of the bonding in diplumbylene compounds RPbPbR (R=H. Ar). Angew. Chem. Int. Ed. 40, 2051–2055 (2001).

    Article  Google Scholar 

  68. Li, Q.-S., Lü, R.-H., Xie, Y. & Schaefer III, H. F. Molecules for materials: germanium hydride neutrals and anions. Molecular structures, electron affinities, and thermochemistry of GeHn/GeHn − (n=0–4) and Ge2Hn/Ge2Hn − (n=0–6). J. Comput. Chem. 23, 1642–1655 (2002).

    Article  CAS  PubMed  Google Scholar 

  69. Bogey, M., Bolvin, H., Demuynck, C. & Destombes, J. L. Nonclassical double-bridged structure in silicon-containing molecules: experimental evidence in Si2H2 from its submillimeter-wave spectrum. Phys. Rev. Lett. 66, 413–416 (1991).

    Article  CAS  PubMed  Google Scholar 

  70. Cordonnier, M., Bogey, M., Demuynck, C. & Destombes, J.-L. Nonclassical structures in silicon-containing molecules: the monobridged isomer of Si2H2. J. Chem. Phys. 97, 7984–7989 (1992).

    Article  CAS  Google Scholar 

  71. Wang, X., Andrews, L. & Kushto, G. P. Infrared spectra of the novel Ge2H2 and Ge2H4 species and the reactive GeH1,2,3 intermediates in solid neon, deuterium and argon. J. Phys. Chem. A 106, 5809–5816 (2002).

    Article  CAS  Google Scholar 

  72. Wang, X., Andrews, L., Chertihin, G. V. & Souter, P. F. Infrared spectra of the novel Sn2H2 species and the reactive SnH1,2,3 and PbH1,2,3 intermediates in solid neon, deuterium, and argon. J. Phys. Chem. A 106, 6302–6308 (2002).

    Article  CAS  Google Scholar 

  73. Andrews, L. & Wang, X. Infrared spectra of the novel Si2H2 and Si2H4 species and the SiH1,2,3 intermediates in solid neon, argon, and deuterium. J. Phys. Chem. A 106, 7696–7702 (2002).

    Article  CAS  Google Scholar 

  74. Wang, X. & Andrews, L. Infrared spectra of group 14 hydrides in solid hydrogen: experimental observation of PbH4, Pb2H2, and Pb2H4. J. Am. Chem. Soc. 125, 6581–6587 (2003).

    Article  CAS  PubMed  Google Scholar 

  75. Sekiguchi, A., Kinjo, R. & Ichinohe, M. A stable compound containing a silicon–silicon triple bond. Science 305, 1755–1757 (2004).

    Article  CAS  PubMed  Google Scholar 

  76. Stender, M., Phillips, A. D., Wright, R. J. & Power, P. P. Synthesis and characterization of a digermanium analogue of an alkyne. Angew. Chem. Int. Ed. 41, 1785–1787 (2002).

    Article  CAS  Google Scholar 

  77. Phillips, A. D., Wright, R. J., Olmstead, M. M. & Power, P. P. Synthesis and characterization of 2,6-Dipp2-H3C6SnSnC6H3-2,6-Dipp2 (Dipp=C6H3-2,6-iPr2): a tin analogue of an alkyne. J. Am. Chem. Soc. 124, 5930–5931 (2002).

    Article  CAS  PubMed  Google Scholar 

  78. Pu, L., Twamley, B. & Power, P. P. Synthesis and characterization of 2,6-Trip2H3C6PbPbC6H3-2,6-Trip2 (Trip=C6H2-2,4,6-i-Pr3): a stable heavier group 14 element analogue of an alkyne. J. Am. Chem. Soc. 122, 3524–3525 (2000).

    Article  CAS  Google Scholar 

  79. Andrada, D. M., Casalz-Sainz, J. L., Pendás, A. M. & Frenking, G. Dative and electron-sharing bonding in C2F4. Chem. Eur. J. 24, 9083–9089 (2018).

    Article  CAS  PubMed  Google Scholar 

  80. Tonner, R. & Frenking, G. Divalent carbon(0) chemistry, part 1: parent compounds. Chem. Eur. J. 14, 3260–3272 (2008).

    Article  CAS  PubMed  Google Scholar 

  81. Krapp, A., Pandey, K. K. & Frenking, G. Transition metal−carbon complexes. A theoretical study. J. Am. Chem. Soc. 129, 7596–7610 (2007).

    Article  CAS  PubMed  Google Scholar 

  82. Celik, M. A., Frenking, G., Neumüller, B. & Petz, W. Exploiting the twofold donor ability of carbodiphosphoranes: theoretical studies of [(PPh3)2C→EH2]q (Eq=Be, B+, C2+, N3+, O4+) and synthesis of the dication [(Ph3P)2C=CH2]2+. ChemPlusChem 78, 1024–1032 (2013).

    Article  CAS  PubMed  Google Scholar 

  83. Zhang, Q. et al. Formation and characterization of the boron dicarbonyl complex [B(CO)2,]−. Angew. Chem. Int. Ed. 54, 11078–11083 (2015).

    Article  CAS  Google Scholar 

  84. Andrada, D. M. & Frenking, G. Stabilization of heterodiatomic SiC through ligand donation: theoretical investigation of SiC(L)2 (L=NHCMe, CAACMe, PMe3). Angew. Chem. Int. Ed. 54, 12319–12324 (2015).

    Article  CAS  Google Scholar 

  85. Mohapatra, C. et al. The structure of the carbene stabilized Si2H2 may be equally well described with coordinate bonds as with classical double bonds. J. Am. Chem. Soc. 138, 10429–10432 (2016).

    Article  CAS  PubMed  Google Scholar 

  86. Li, Z. et al. (L)2C2P2: dicarbondiphosphide stabilized by N-heterocyclic carbenes or cyclic diamido carbenes. Angew. Chem. Int. Ed. 56, 5744–5749 (2017).

    Article  CAS  Google Scholar 

  87. Scharf, L. T., Andrada, D. M., Frenking, G. & Gessner, V. H. The bonding situation in metalated ylides. Chem. Eur. J. 23, 4422–4434 (2017).

    Article  CAS  PubMed  Google Scholar 

  88. Hermann, M. & Frenking, G. Carbones as ligands in novel main-group compounds E[C(NHC)2]2 (E=Be, B+, C2+, N3+, Mg, Al+, Si2+, P3+). Chem. Eur. J. 23, 3347–3356 (2017).

    Article  CAS  PubMed  Google Scholar 

  89. Georgiou, D. C., Zhao, L., Wilson, D. J. D., Frenking, G. & Dutton, J. L. NHC-stabilised acetylene — how far can the analogy be pushed? Chem. Eur. J. 23, 2926–2934 (2017).

    Article  CAS  PubMed  Google Scholar 

  90. Wu, Z. et al. Parent thioketene S-oxide H2CCSO: gas-phase generation, structure, and bonding analysis. Chem. Eur. J. 23, 16566–16573 (2017).

    Article  CAS  PubMed  Google Scholar 

  91. Yang, T., Andrada, D. M. & Frenking, G. Dative versus electron-sharing bonding in N-oxides and phosphane oxides R3EO and relative energies of the R2EOR isomers (E=N, P; R=H, F, Cl, Me, Ph). A theoretical study. Phys. Chem. Chem. Phys. 20, 11856–11866 (2018).

    Article  CAS  PubMed  Google Scholar 

  92. Luo, Y. R. Comprehensive Handbook of Chemical Bond Energies (CRC Press, Boca Raton, 2007).

  93. Poater, J., Solà, M. & Bickelhaupt, F. M. A. Model of the chemical bond must be rooted in quantum mechanics, provide insight, and possess predictive power. Chem. Eur. J. 12, 2902–2905 (2006).

    Article  CAS  PubMed  Google Scholar 

  94. Holzmann, N., Stasch, A., Jones, C. & Frenking, G. Structures and stabilities of group 13 adducts [(NHC)(EX3)] and [(NHC)2(E2Xn)] (E.=B. to In; X.=H, Cl; n=4, 2, 0; NHC=N-heterocyclic carbene) and the search for hydrogen storage systems: a theoretical study. Chem. Eur. J. 17, 13517–13525 (2011).

    Article  CAS  PubMed  Google Scholar 

  95. Braunschweig, H. et al. Ambient-temperature isolation of a compound with a boron–boron triple bond. Science 336, 1420–1422 (2012).

    Article  CAS  PubMed  Google Scholar 

  96. Frenking, G. & Holzmann, N. A boron–boron triple bond. Science 336, 1394–1395 (2012).

    Article  CAS  PubMed  Google Scholar 

  97. Böhnke, J. et al. Diborabutatriene: an electron-deficient cumulene. Angew. Chem. Int. Ed. 53, 9082–9085 (2014).

    Article  CAS  Google Scholar 

  98. Böhnke, J. et al. The synthesis of B2(SIDip)2 and its reactivity between the diboracumulenic and diborynic extremes. Angew. Chem. Int. Ed. 54, 13801–13805 (2015).

    Article  CAS  Google Scholar 

  99. Köppe, R. & Schnöckel, H. The boron–boron triple bond? A thermodynamic and force field based interpretation of the N-heterocyclic carbene (NHC) stabilization procedure. Chem. Sci. 6, 1199–1205 (2015).

    Article  PubMed  Google Scholar 

  100. Holzmann, N., Hermann, M. & Frenking, G. The boron–boron triple bond in NHC→B≡B←NHC. Chem. Sci. 6, 4089–4094 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  101. Böhnke, J. et al. Experimental assessment of the strengths of B–B triple bonds. J. Am. Chem. Soc. 137, 1766–1769 (2015).

    Article  PubMed  CAS  Google Scholar 

  102. Perras, F. A. et al. Spying on the boron–boron triple bond using spin–spin coupling measured from 11B solid-state NMR spectroscopy. Chem. Sci. 6, 3378–3382 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  103. Dijkstra, E. W. On the nature of computing science. UT Austin Computer Science https://www.cs.utexas.edu/users/EWD/transcriptions/EWD08xx/EWD896.html (1984).

  104. Bollermann, T. et al. Molecular alloys: experimental and theoretical investigations on the substitution of zinc by cadmium and mercury in the homologous series [Mo(MʹR)12] and [M(MʹR)8] (M=Pd, Pt; Mʹ=Zn, Cd, Hg). Chem. Eur. J. 16, 13372–13384 (2010).

    Article  CAS  PubMed  Google Scholar 

  105. von Hopffgarten, M. & Frenking, G. Building a bridge between coordination compounds and clusters: bonding analysis of the icosahedral molecules [M(ER)12] (M=Cr, Mo, W; E=Zn, Cd, Hg). J. Phys. Chem. A 115, 12758–12768 (2011).

    Article  CAS  Google Scholar 

  106. Nguyen, T. A. N. & Frenking, G. Transition-metal complexes of tetrylones [(CO)5W-E(PPh3)2] and tetrylenes [(CO)5W-NHE] (E=C-Pb): a theoretical study. Chem. Eur. J. 18, 12733–12748 (2012).

    Article  CAS  PubMed  Google Scholar 

  107. Celik, M. A. et al. End-on and side-on π-acid Ligand adducts of gold(I): carbonyl, cyanide, isocyanide, and cyclooctyne gold(I) complexes supported by N-heterocyclic carbenes and phosphines. Inorg. Chem. 52, 729–742 (2013).

    Article  CAS  PubMed  Google Scholar 

  108. Mousavi, M. & Frenking, G. Bonding analysis of the trimethylenemethane (TMM) complexes [(η6-C6H6)M-TMM] (M=Fe, Ru, Os), [(η5-C5H5)M-TMM] (M=Co, Rh, Ir), and [(η4-C4H4)M-TMM] (M=Ni, Pd, Pt). Organometallics 32, 1743–1751 (2013).

    Article  CAS  Google Scholar 

  109. Das, A. et al. Tris(alkyne) and Bis(alkyne) complexes of coinage metals: synthesis and characterization of (cyclooctyne)3M+ (M=Cu, Ag) and (cyclooctyne)2Au+ and coinage metal (M=Cu, Ag, Au) family group trends. Organometallics 32, 3135–3144 (2013).

    Article  CAS  Google Scholar 

  110. Weinberger, D. S. et al. Isolation of neutral mono- and dinuclear gold complexes of cyclic(Alkyl)(amino)carbenes. Angew. Chem. Int. Ed. 52, 8964–8967 (2013).

    Article  CAS  Google Scholar 

  111. Mondal, K. C. et al. Stabilization of a cobalt–cobalt bond by two cyclic alkyl amino carbenes. J. Am. Chem. Soc. 136, 1770–1773 (2014).

    Article  CAS  PubMed  Google Scholar 

  112. Jerabek, P., Roesky, H. W., Bertrand, G. & Frenking, G. Coinage metals binding as main group elements: structure and bonding of the carbene complexes [TM(cAAC)2] and [TM(cAAC)2]+ (TM=Cu, Ag, Au). J. Am. Chem. Soc. 136, 17123–17135 (2014).

    Article  CAS  PubMed  Google Scholar 

  113. Caramori, G. F. et al. Cyclic trinuclear copper(I), silver(I), and gold(I) complexes: a theoretical insight. Dalton Trans. 44, 377–385 (2015).

    Article  CAS  PubMed  Google Scholar 

  114. Couzijn, E. P. A., Lai, Y.-Y., Limacher, A. & Chen, P. Intuitive quantifiers of charge flows in coordinate bonding. Organometallics 36, 3205–3214 (2017).

    Article  CAS  Google Scholar 

  115. Raupach, M. & Tonner, R. A periodic energy decomposition analysis method for the investigation of chemical bonding in extended systems. J. Chem. Phys. 142, 194105 (2015).

    Article  PubMed  CAS  Google Scholar 

  116. Pecher, J. & Tonner, R. Precursor states of organic adsorbates on semiconductor surfaces are chemisorbed and immobile. ChemPhysChem 18, 34–38 (2017).

    Article  CAS  PubMed  Google Scholar 

  117. Pecher, J., Schober, C. & Tonner, R. Chemisorption of a strained but flexible molecule: cyclooctyne on Si(001). Chem. Eur. J. 23, 5459–5466 (2017).

    Article  CAS  PubMed  Google Scholar 

  118. Pecher, L., Laref, S., Raupach, M. & Tonner, R. Ethers on Si(001): a prime example for the common ground between surface science and molecular organic chemistry. Angew. Chem. Int. Ed. 56, 15150–15154 (2017).

    Article  CAS  Google Scholar 

  119. Pecher, L. & Tonner, R. Bond insertion at distorted Si(001) subsurface atoms. Inorganics 6, 17 (2018).

    Article  CAS  Google Scholar 

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Acknowledgements

G.F. and L.Z. acknowledge financial support from Nanjing Tech University (grant nos 39837132 and 39837123) and a SICAM Fellowship from Jiangsu National Synergetic Innovation Center for Advanced Materials. L.Z. also acknowledges financial support from the Natural Science Foundation of Jiangsu Province for Youth (grant no. BK20170964) and the National Natural Science Foundation of China (grant no. 21703099). W.H.E.S. thanks Jun Li and the Theoretical & Computational Chemistry Laboratory at Tsinghua University and Holger Schönherr and the PCI group of Siegen University.

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Authors and Affiliations

  1. Institute of Advanced Synthesis, School of Chemistry and Molecular Engineering, Jiangsu National Synergetic Innovation Center for Advanced Materials, Nanjing Tech University, Najing, China

    Lili Zhao & Gernot Frenking

  2. Fachbereich Chemie, Philipps-Universität Marburg, Marburg, Germany

    Markus Hermann & Gernot Frenking

  3. Theoretical Chemistry Center, Tsinghua University, Beijing, China

    W. H. Eugen Schwarz

  4. Physical and Theoretical Chemistry Group, Universität Siegen, Siegen, Germany

    W. H. Eugen Schwarz

  5. Donostia International Physics Center, Donostia-San Sebastián, Spain

    Gernot Frenking

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  1. Lili Zhao
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  3. W. H. Eugen Schwarz
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All authors contributed equally to the preparation of this manuscript.

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Zhao, L., Hermann, M., Schwarz, W.H.E. et al. The Lewis electron-pair bonding model: modern energy decomposition analysis. Nat Rev Chem 3, 48–63 (2019). https://doi.org/10.1038/s41570-018-0060-4

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