Three-center molecular orbitals

As the substrate approaches the 7(FeO)2+ core, the Opx orbital, which is singly occupied, interacts with the C-H a-bonding orbital to form two three-centered molecular orbitals (MOs), Ocho and > as shown in Fig. 3 (right). Therefore, Opx acts as the electron acceptor orbital. Since it is a -bonding orbital this pathway is referred to as the pathway. ... 

Fig. 16.40 Qualitative description of atomic orbitals (loft). resulting three-center molecular orbitals (right), and the approximate energy level diagram (center) for one B—H—B bridge in diborane...

The bonds are considered to arise from the combination of two boron orbitals that are hybrids of s and p orbitals with a b orbital on the hydrogen atom. Graphically, the formation of the three-center molecular orbital can be represented as shown here ... 

Bonding. —In the valence-bond description of XeF2, Coulson has emphasized the dominance of the canonical forms (F-Xe)+F and F (Xe-F) in the resonance hybrid. This representation accounts well for the polarity FXe F , indicated by nmr, Moss-bauer, ESCA, and thermodynamic data. It is particularly impressive that the enthalpy of sublimina-tion derived for the XeFy case, by Rice and his co-workers in 1963, on the basis of the charge distribution "FXe+F , is 13.3 kcal mol , whereas the experimental value reported in 1968 is 13.2 kcal mol . It should be recognized that the Coulson valence-bond model is not, in the final analysis, significantly different from the Rundle and Pimentel three-center molecular orbital description or the Bilham and Linnett one-electron-bond description, but it does provide for a more straightforward estimation of thermodynamic stabilities of compounds than the other approaches do. 

It treats a molecule like ABC as a combination of two resonance structures, A B-C > A-B C . This is a description of three-center molecular orbitals as resonance structures of two-center orbitals. As such, it can be considered as a variant of the 3c-4e model that avoids the question of d orbital occupancy. Some theoreticians prefer to view hypervalent bonding in this manner this model and the 3c-4e model will be considered equivalent in this chapter. 

Piepho has treated intervalence transitions using a relatively simple three-center molecular orbital model in which vibronic coupling is introduced as a pseudo-Jahn-Teller perturbation. This could be a valuable approach, and it can probably be generalized to a great variety of problems. In this report, Piepho uses the approach to calculate intervalence transition band shapes for a range of vibronic couplings, and she discusses the vibronic criteria for valence trapped and delocalized systems. 

Fig. 10.7. The combination of s and dxz atomic orbitals on the metal atom with ligand symmetry orbitals to form three-center molecular orbitals.

It must be emphasized that this type of topological theory is not limited to three-center bonds. Its extension to other types of semilocal-ized multi-centered molecular orbitals might well prove useful in an extensive study of valence in certain intermetallic compounds in which... 

Localized and Alternative bonding descriptions are often possible in polyatomic molecules, involving delocalized either localized (two center) or delocalized (three or more center) molecular orbitals. The orbitals overall electron distributions predicted may be the same in both models. 

Fig. 12.7. Above the molecular structures of 84014 and B4(CMe3)4 (methyl groups excluded). Below bonding in 84014. Left the three sp hybrids on each B that are directed towards points above the centers of the three neighboring B3 faces. Right formation of a three-center bonding orbital over a triangular B3 face.

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. 

The boranes are electron-deficient compounds (Section 3.8) we cannot write valid Lewis structures for them, because too few electrons are available. For instance, there are 8 atoms in diborane, so we need at least 7 bonds however, there are only 12 valence electrons, and so we can form at most 6 electron-pair bonds. In molecular orbital theory, these electron pairs are regarded as delocalized over the entire molecule, and their bonding power is shared by several atoms. In diborane, for instance, a single electron pair is delocalized over a B—H—B unit. It binds all three atoms together with bond order of 4 for each of the B—H bridging bonds. The molecule has two such bridging three-center bonds (9). 

The electrostatic energy is calculated using the distributed multipolar expansion introduced by Stone [39,40], with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion points (three at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. The induction or polarization term is represented by the interaction of the induced dipole on one fragment with the static multipolar field on another fragment, expressed in terms of the distributed localized molecular orbital (LMO) dipole polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in the molecule. One can opt to include inner shells as well, but this is usually not useful. The induced dipoles are iterated to self-consistency, so some many body effects are included. 

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