Two-center bonds

Boranes are typical species with electron-deficient bonds, where a chemical bond has more centers than electrons. The smallest molecule showing this property is diborane. Each of the two B-H-B bonds (shown in Figure 2-60a) contains only two electrons, while the molecular orbital extends over three atoms. A correct representation has to represent the delocalization of the two electrons over three atom centers as shown in Figure 2-60b. Figure 2-60c shows another type of electron-deficient bond. In boron cage compounds, boron-boron bonds share their electron pair with the unoccupied atom orbital of a third boron atom [86]. These types of bonds cannot be accommodated in a single VB model of two-electron/ two-centered bonds. 

Trivalent ( classical carbenium ions contain an sp -hybridized electron-deficient carbon atom, which tends to be planar in the absence of constraining skeletal rigidity or steric interference. The carbenium carbon contains six valence electrons thus it is highly electron deficient. The structure of trivalent carbocations can always be adequately described by using only two-electron two-center bonds (Lewis valence bond structures). CH3 is the parent for trivalent ions. 

The valence theory (4) includes both types of three-center bonds shown as well as normal two-center, B—B and B—H, bonds. For example, one resonance stmcture of pentaborane(9) is given in projection in Figure 6. An octet of electrons about each boron atom is attained only if three-center bonds are used in addition to two-center bonds. In many cases involving boron hydrides the valence stmcture can be deduced. First, the total number of orbitals and valence electrons available for bonding are determined. Next, the B—H and B—H—B bonds are accounted for. Finally, the remaining orbitals and valence electrons are used in framework bonding. Alternative placements of hydrogen atoms require different valence stmctures. 

Aldiough the van der Waals interaction is not a two-center bond interaction in diis experimental setup, the cal-... 

The NBO picture of 3c/2e T-bonding may be developed along lines parallel to those for 3c/4e tu-bonding in Eqs. (3.194) et seq. Let us first consider the special case of a homopolar two-center bond aAc = 2-1/2(hA + hB) interacting with a vacant one-center orbital nB = hB to form a three-center bond tABc of the form... 

Although the generalization to localized three-center bonds inevitably involves certain complications, important simplifications of the localized Lewis-structure picture remain. In the case of 3c/4e co-bonding, the corrections can often be adequately described in terms of two-term resonance between alternative two-center bonding patterns. In the case of 3c/2e T-bonding, the resonance-theoretic description (although possible in principle) becomes unwieldy. However, in terms of the single best three-center localized Lewis-structure description (or the resonance mixture of symmetry-equivalent structures), one can still identify specific localized donor-acceptor interactions (e.g., of type) that dominate the delocaliza-... 

Table 4.36. The NBO descriptors o/ M2H2 species (see Fig. 4.57) namely the accuracy of the natural Lewis structure (%/+). metal charge (Qu), metal hybrid (hM), percentage polarization toward metal (%m), and occupancies (Occ.) of two-center bonds and antibonds...

Figure 4.107(b) depicts formation of two-center bonding and antibonding (optn and opm ) NBOs from the constituent hybrids hpt and hp ... 

According to the E.A.N. rule, all clusters of four atoms possessing the tetrahedral geometry require a total of 60 valence electrons. A tetrahedron with six two-electron/two-center bonds corresponding to the... 

Bitter, T., Ruedenberg, K., and Schwarzl, W. H. E. 2007. Toward a physical understanding of electron-sharing two-center bonds. I. General aspects. J. Comput. Chem. 28 411-422. 

Such strong inward pyramidalization of the nitrogen atoms is stabilized by the overlapping of the nitrogen electrons forming a three-electron two-center bond in the cation-radical discussed in... 

The symbol for a symmetry designation of a molecular orbital. Such an orbital is without a nodal plane including the internuclear axis (as is the case with a tt orbital). 2. The localized two-center bond associated with an s orbital. 3. The symbol for standard deviation. 4. The symbol for wavenumber. 5. The symbol for surface tension. 

We have already shown that the energy of the system of six n electrons in benzene is equal to 8p. We must now calculate, in units of / , the energy of a Kekule structure, that is, the energy of the hypothetical molecule cyclo-hexatriene. In cyclohexatriene there are three localized n bonds. When two atomic n orbitals, say < , and (j)2, interact to form a two-center bond, two MOs, j/1 and yr2, are formed. In order that these be real, normalized, and... 

---