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The Covalent Bond Classification Method and Its Application to Compounds That Feature 3-Center 2-Electron Bonds

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The Chemical Bond III

Part of the book series: Structure and Bonding ((STRUCTURE,volume 171))

Abstract

This article provides a means to classify and represent compounds that feature 3-center 2-electron (3c–2e) interactions according to whether (1) the two electrons are provided by one or by two atoms; (2) the central bridging atom provides two, one, or zero electrons; and (3) the interaction is open or closed. Class I 3c–2e bonds are defined as those in which two atoms each contribute one electron to the 3-center orbital, while Class II 3c–2e bonds are defined as systems in which the pair of electrons are provided by a single atom. The use of appropriate structure-bonding representations enables the [ML l X x Z z ] covalent bond classification of the element of interest to be evaluated. This approach is of considerable benefit in predicting metal–metal bond orders that are in accord with theory for dimetallic compounds that feature bridging hydride and carbonyl ligands.

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Notes

  1. 1.

    It is interesting to note that the bridged structure of B2H6 was first proposed in 1943, 27 years after Lewis’ introduction of the 2c–2e bond and only 3 years prior to his death; see [5–7].

  2. 2.

    Kossel also recognized the tendency for atoms to form ions with the adjacent noble gas configuration but did not extend this concept to the formation of molecules; see [10].

  3. 3.

    For examples of textbooks that employ the classification of ligands as L, X, or Z type, see [18–24].

  4. 4.

    The formal charge is the charge remaining on an atom when all ligands are removed homolytically. See [17].

  5. 5.

    The notion of using an arrow to represent donation of electron density from a bond to another atom was first introduced by Walsh to describe the bonding in B2H6; see [31].

  6. 6.

    For other examples in which 3c–2e bonding is represented as donation of a M–M bonding pair of electrons to Au+, see [39].

  7. 7.

    Another closely related species is the hydride derivative, [([IPr]Au)2H]+, in which a gold center is formally replaced by hydrogen and which possesses an Au–Au distance of 2.701 Å. See [41, 42].

  8. 8.

    For a highlight of this article, see [70].

  9. 9.

    For a discussion of the bonding in B5H9, see [90–92].

  10. 10.

    It is pertinent to note that, in contrast to B5H9, the iron and cobalt compounds have additional valence electrons such that they could support additional 2c–2e bonds. For such a situation, the iron and cobalt compounds would be, respectively, categorized as ML3X4 and ML2X5, which are much less common than ML4X2 and ML3X3 for these elements.

  11. 11.

    It should be emphasized that not all M–H–Y interactions must be described as 3c–2e bonds because some are better represented as 3c–4e “hydrogen bond” interactions. See, e.g., [97].

  12. 12.

    Compounds that feature coordination of Ge–H and Sn–H bonds have also been investigated; see, e.g., [112].

  13. 13.

    Note that the hypervalent representation of the silicon of {[PhBCH2CH2PPh2]Ru}2(μ-SiH6) is drawn for convenience.

  14. 14.

    Although the hapto “ηx” notation [178] is often used to describe the coordination mode of borohydride ligands [175–177], such notation is strictly inappropriate because ηx refers to the number of contiguous atoms that are attached to a specific element [179]. If the atoms are not contiguous, as in borohydride, the kappa “κx” notation [180] should be used instead.

  15. 15.

    Note that alternative structure-bonding representations involving donation of electron density from a B–H bond of anionic [BH4]− to cationic M+ can also be drawn. Such representations, however, are equivalent to those shown in Fig. 44, which do not portray formal charges.

  16. 16.

    This view of the bonding in agostic compounds is necessarily simplistic. For more detailed discussions, see [188–191].

  17. 17.

    Compounds with triply bridging PF3 ligands are also known; see, e.g., [203–205]; for an early speculation of a complex with a bridging PR3 ligand, see [206]; for compounds with asymmetrically bridging PR3 ligands, see [207–210]; for calculations on hypothetical bridging PF3 complexes, see [211].

  18. 18.

    In addition to bridging in a symmetric manner, carbonyl ligands are also known to adopt bent semibridging and linear semibridging coordination modes; the bonding in these complexes is highly varied and is not part of the scope of the present article; for key references, see [228–237].

  19. 19.

    A subsequent higher-quality structure revealed an Fe–Fe distance of 2.523(1) Å; see [242].

  20. 20.

    Although some theoretical articles have suggested the possibility of a weak direct Fe–Fe attractive interaction in Fe2(CO)9, the interpretation has been questioned [271].

  21. 21.

    We are aware of only two textbooks that discuss the absence of a direct Fe–Fe bond in Fe2(CO)9. Of these, one does not include a drawing of the molecule [272], while the other draws the molecule both without an Fe–Fe bond and also with a dotted FeċċċFe bond [273]; however, there is no discussion as to how the latter description should be employed with respect to electron counting purposes. Also of note, [CpM(CO)(μ-CO)]2 has been represented on the cover of a textbook, without including a M–M bond, but the bonding was not discussed [274].

  22. 22.

    Co2(CO)8 exists as an equilibrium between bridged, (CO)3Co(μ-CO)2Co(CO)3, and non-bridged isomers, (CO)4Co–Co(CO)4, of which the former is the major isomer.

  23. 23.

    Experimental charge-density studies are also in accord with the absence of a direct Co–Co bond in the bridged form of Co2(CO)8; see [276].

  24. 24.

    For other articles that describe the absence of M–M bonds in other carbonyl bridged compounds, for a similar reason, see [287].

  25. 25.

    The 2π* orbitals of CO which are perpendicular to the Fe–Fe axis are neglected from the analysis on the basis that there is little overlap with the metal d-orbitals.

  26. 26.

    For discussion pertaining to bonding in [CpFe(CO)(μ-CO)]2, see [293].

  27. 27.

    For example, the B…B distance of 2.11 Å is ca. 0.4 Å longer than the value in catBBcat derivatives; see [298].

  28. 28.

    The structure-bonding representation for the zirconium compound is one in which only one of the oxygen lone pairs of each aryloxide ligand participates in π-donation; additional π-donation would result in an 18-electron ML6X2 classification.

  29. 29.

    For other calculations on this system which propose a Mn–Mn bond, see [335].

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Acknowledgments

G. P. thanks the US Department of Energy Office of Basic Energy Sciences (DE-FG02-93ER14339) for support. This report was prepared as an account of work sponsored by an agency of the US government. Neither the US government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the US government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US government or any agency thereof.

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  1. Inorganic Chemistry Laboratory, South Parks Road, Oxford, OX1 3QR, UK

    Malcolm L. H. Green

  2. Department of Chemistry, Columbia University, New York, NY, 10027, USA

    Gerard Parkin

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Correspondence to Malcolm L. H. Green or Gerard Parkin .

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  1. Inorganic Chemistry Laboratory, University of Oxford Inorganic Chemistry Laboratory, Oxford, United Kingdom

    D. Michael P. Mingos

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Green, M.L.H., Parkin, G. (2016). The Covalent Bond Classification Method and Its Application to Compounds That Feature 3-Center 2-Electron Bonds. In: Mingos, D. (eds) The Chemical Bond III. Structure and Bonding, vol 171. Springer, Cham. https://doi.org/10.1007/430_2015_206

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