Description of Multiple Bonding

EXERCISE 10.6 Describe the bonding in PCI5 using hybrid orbitals. 

In the previous section, we described bonding as the overlap of one orbital from each of the bonding atoms. Now we consider the possibility that more than one orbital from each bonding atom might overlap, resulting in a multiple bond. 

One hybrid orbital is needed for each bond (whether a single or a multiple bond) and for each lone pair. Because each carbon atom is bonded to three other atoms and there are no lone pairs, three hybrid orbitals are needed. This suggests the use of sp hybrid orbitals on each carbon atom (there are three sp hybrid orbitals see Table 10.2). Thus, during bonding, the 2s orbital and two of the 2p orbitals of each carbon atom form three hybrid orbitals having trigonal planar orientation. A third 2p orbital on each carbon atom remains unhybridized and is perpendicular to the plane of the three sp hybrid orbitals. 

CHAPTER 10 Molecular Geometry and Chemical Bonding Theory 

WThe formation of a cr bond by the overlap of two s orbitals. A cr bond can also be formed by the overlap of two p orbitals along their axes, fc) When twop orbitals overlap sideways, a tt bond is formed. 

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The method of moments of coupled-cluster equations (MMCC) is extended to potential energy surfaces involving multiple bond breaking by developing the quasi-variational (QV) and quadratic (Q) variants of the MMCC theory. The QVMMCC and QMMCC methods are related to the extended CC (ECC) theory, in which products involving cluster operators and their deexcitation counterparts mimic the effects of higher-order clusters. The test calculations for N2 show that the QMMCC and ECC methods can provide spectacular improvements in the description of multiple bond breaking by the standard CC approaches. 

Thus, we can expect further improvements in the description of multiple bond breaking by the QMMCC method. This statement parallels similar findings by Head-Gordon et al. (27, 28, 128, 129), who considered the quadratic variant of the ECC theory of Arponen and Bishop (114 -123), in which the energy is calculated by imposing the stationary conditions for the asymmetric, doubly connected, energy functional... 

Again, just as in the phosphine oxides2, there is disagreement about the exact electron distribution in the P=C bond with one view corresponding to the a/n description of multiple bonds and the other a bent (banana) bond description. 

As might be expected, NMR calculations that ignore electron correlation often give poor results, especially for molecules which typically require a correlated treatment in order to predict other properties accurately. For example, a good description of multiple bonds and lone pairs generally requires a correlated method. Thus, RHF NMR predictions for molecules such as CO and acetonitrile are poor (20). Furthermore, it has recently been shown that isotropic chemical shift calculations at the RHF level are unreliable for benzenium (21) and related carbenium ions which we often encounter in catalysis. 

The traditional a—ir description of multiple bonding and the expectation that conformational effects could somehow be derived from a molecular Hamiltonian function can both safely be discounted. Looking for a fresh approach in terms of quantum potential, returns the argument to the general form of polar wave functions... 

There has been some recent concern (8,9) however, that this bent bond description of multiple bonds derived from the GVB-PP model may be an artifact of the model. The concern takes two forms first, that the SOPP restrictions on the GVB wave function are the source of the bent bonds and the full GVB model will produce the usual <7,7r-bond description and second, if an MCSCF or Cl wave function which is more general than GVB is used, this will give back the c,7r description. 

The work by F.A. Cotton and his group has provided a broad range of data in this area and a remarkable description of multiple bonds including the quadruple bond. ... 

Valence-bond descriptions of multiple bonds are also similar to the simple LCAOMO description. A double bond consists of a sigma bond and api bond, and a triple bond consists of a sigma bond and two pi bonds. Each bonding factor replaces one LCAOMO, but nonbonding orbitals are the same in both methods. There are no analogues to antibonding orbitals in the simple valence-bond method, so molecules with unpaired electrons such as O2 also cannot be well described in the simple valence-bond method. The extended valence-bond methods mentioned in Chapter 20 are more versatile. 

Adequate description of multiple bonds, especially triple bonds, requires considerably more extended basis sets than that of typical single bonds. Another difficulty is the description of atoms with high electronegativity (like O and F), in which case the use of diffuse functions should be considered. 

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