The Three Center-Two Electron Bond

The stability of this well-established bonding pattern can be understood from simple MO arguments. The B-H-B arrangement in diborane is another three-orbital mixing problem, like allyl. In fact, the mixing diagram we developed for allyl translates directly to the 

Note that it is generally better to make two, conventional, two center—two electron bonds rather than a single three center-two electron bond. However, boranes are electron deficient there just are not enough valence electrons to make the requisite number of conventional bonds. The system does the best it can by forming a pair of three center-two electron bonds. 

---

A secondary feature of the cis-M(CO)(RC=CR) molecular orbital description is the three-center-two-electron bond built from carbonyl tt, alkyne 77, and metal dyz (Fig. 15) (45). EHMO calculations locate the completely in-phase bonding combination, dominated by dyz, approx-... 

Let us compare the MO descriptions of six and four sep R4E4 tetrahedral clusters. In Figure 2.5 the cluster MO energies for E = C and E = Ga are shown alongside the localized descriptions discussed above. The number of filled and unfilled MOs is equal for E = C a consequence of the two-center-two-electron bond model. Conversely, the number of filled MOs is less than the number of empty MOs for E = Ga a consequence of the three-center-two-electron bond model. Note also that an e symmetry pair of orbitals lies in between lower-energy filled orbitals and... 

An ORTEP representation (b) schematic showing the three-center, two-electron bonding... 

As expected, there is generally a large dependence of the modes for bound H2 on both the metal center and coligands. Vibrational analysis of a M-T 2-H2 system is further complicated by the three-center, two-electron bonding. The bonding is of the Dewar-Chatt-Duncanson type present in metal-olefin complexes, where there is a strong M —> H2 G component, FBD, to the bonding in addition to electron donation, Ed, to the empty metal d-orbital from the H2 electron pair (Scheme 5.18). 

Fig. 40.7. Fragment molecular orbitals that produce the three-center/two-electron bonds (one of three by symmetry), which constitute the principal metal-to-metal bonding interactions of Ru3(CO)i2[Pd(PR3)].

However, the discovery of a--coordination by H2 is an important recent advance in this area. The three-center, two-electron bond is also recognized in intramolecular agostic C—H metal interactions. Recently evidence has been mounting in support of a C—H (7-interaction for free hydrocarbons (vide infra). 

We might anticipate, however, that the three center-two electron bonding of carbonium ions might lead to atypical values of Av. In particular, we might expect the chemical shifts of hypervalent carbons to be unusual, and indeed they are shifted far upheld from what is seen for carbenium centers. This leads to greatly reduced values of A. ... 

Displacement by carbon-carbon Jt or a bonds can lead to delocahzed ions about which there has been much controversy. It now appears that such intermediates are involved in some ionizations, and that the three-center, two-electron bonding required is an energetically favorable situation, at least for highly electron-deficient systems such as carbocations (Fig. 21.57). 

Similarly to CNDO/2, the MINDO/3 method overestimates stability of the three-center two-electron bonds and reduces a good deal their length (see Table 5.1 in Chap. 5 ... 

The hydroxy isomers lack the reactivity of the three-center, two-electron bond characteristic of the [B2oH,8] isomers. As a result, the anion would be expected to be unreactive to intracellular protein moieties and clear from the tissues in biodistribution experiments. The biodistribution of liposomally encapsulated [c -B2oH,70H], with a boron dose of 200 Xg B ( 11 mg/kg body weight), exhibited rapid clearance of the boron concentration from all tissues, consistent with the working hypothesis (Shelly et al 1992). At 48 h, the tumor boron concentration was only 7.3 ig B/g tumor. 

---