The Three-Center, Two-Electron Chemical Bond Rogw L. DeKock and Wayne 6. Bosma Calvin College. Grand Rapids. MI 49506 Chemists are most familiar with the two-center electron pair bond, which finds its best expression in the landmark textbooks of Lewis (I) and Pauling (2). The concept of an electron pair delocalized over more than two nuclei was recognized by Erich Hiickel in the early 1930's (3).For example, the ally1 cation (C3Hs+) contains a three-center, twoelectron (3c-2e) r bond. The simplest 3c-2e bond is found in H3+, which was first observed in 1912 by J. J. Thomson (4) and predicted to he triangular in 1935 (5). [By 1970 its equilateral triangular shape was well established theoreticnllv (6). .-~--" ,~ ,,a fact which was confirmed exnerimentallv in 1978 (7)]. Although H3+ represents the delocalization of a u electron nair. this concent was not used in chemistrv until 1945 w h e n ~ i ~ (8) e r introduced the 3c-2e bond to rationalize the structure of B2Hs in terms of a two-proton attack on the double bond of "BzHa2-" (isoelectronic with C2Ha). ~~
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honds, we wish to place them in the context of other threecenter honds that commonly occur in chemistry. For that reason we first briefly review 3 c 4 e bonds and then the various types of 3c-2e bonds. Three-Center, Four-Electron Bonds Three-center, four-electron bonds were introduced in 1951 independently by Rundle (10) and Pimentel (11) to rationalize the bonding in linear species such as F-H-F-, 13-, and symmetric hydrogen bonds involving 0-H-0 as in [H20-H-OH2)+. The Lewis electron dot structure of F-HF- has four electrons surrounding t h e H atom. This is understood in terms of the molecular orbital diagram shown in 1. Notice that the penultimate occupied orbital is a u bond, whereas the highest occupied molecular orbital is H-F nonbonding and contains a node passing through the hydrogen atom. Hence the net bond order between the hydrogen atom and each fluorine atom is one-half.
In 1949 Rundle pointed out the close connection between the 3c bonds in B2Hs and in Hzf (9). In B2Hs the 3c-2e bond has been represented by a curved line, whereas in H3+ it is often represented by a circle. Such a representation has a distinct advantage over the alternate picture of these resonance structures.
In the case of B2Hs 20 resonance structures are required (2) if one uses only 2c-2e bonds, whereas only a single structure is needed if 3c-2e bonds are employed (eq 1). Although the intent of this article is to focus on 3c-2e
Angle
kA-H
I
180'
Figure 1. Facsimile of Walsh diagram for AHI molecules (ref 17).
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Journal of Chemical Education
A 3 c 4 e bond really has only two bonding electrons just as the 3c-2e bond. There is considerable difference between a 3c-4e bond and two 2c-2e bonds. We can illustrate this point with t h e Hg-C bonds of Hg(CH& If the Hg atom ([Xe]5d106s26p0)is treated as sp hybridized, then the bonding is better described in terms of two 2c-2e (classical) bonds. However, if the Hg 6p orbitals are not involved in the bonding, the system should be treated as a 3c-4e hond wherein two of the electrons are Hg-C bonding and two are nonbonding. Recent theoretical calculations on Hg(CH3)2 indicate that the participation of the Hg 6p orbital is small (
