Localized bond terms

For example, for the square pyramidal cation C5H5+ and derivatives thereof (Figs. 1.7 and 1.15), there are four ways of assigning the 3c-2e C—C—C bond and two 2c-2e C-C bonds that, in localized bonding terms, link the apical... 

The natural localized orbital transformations provide useful tools for analyzing various molecular properties or energy components in localized bonding terms. We briefly summarize the underlying principles of several such analyses that are implemented in the general NBO program, restricting attention primarily to HF-level treatment. 

Although, as proposed by Lewis, the octet rule is a purely empirical rule, the advent of orbital models appeared to add some theoretical support to the octet rule. For period 2 elements a maximum of only four orbitals, the 2s and the three 2p orbitals, are available for describing the bonds in terms of localized bonding and nonbonding orbitals, because other orbitals such as 3s, 3p, and 3d have energies that are too high. As a consequence, the octet rule came to be regarded more as a physical law than as a purely empirical rule. So it was... 

A satisfactory description of the bonding in hypervalent molecules can also be given in terms of molecular orbitals but this does not directly correspond to the very useful picture of five or more localized bonds (see, for example, Mingos, 1998, p. 250). 

The NBOs are an optimized set of localized bonding, antibonding, and lone pair orbitals. The bond orbitals typically have occupancies of 1.98e in molecules with one simple Lewis structure. In C2H6, Weinhold and coworkers36 have shown that the barrier height V3 = 1025 cm-1 can be understood in the NBO terms in the form of aCH — donor-acceptor interactions. When the corresponding off-diagonal... 

The bonding of H atoms in amorphous Si has received considerable attention, with review articles summarizing the experimental results and their interpretation in terms of local bonding groups by Cardona (1983) and by Lucovsky and Pollard (1984). The result that is pertinent here... 

Table 4.30. Statistical frequency distributions of electron countsa, common formulasa, and localized bonding descriptions (in terms of number of metal-centered lone pairs, 2c/2e bonds, tu bonds, and average sd hybridization) for organometallic complexes of groups 3-10...

Although the structural pattern outlined in the foregoing can be rationalized at a simple quabtative level by using a molecular orbital approach to the skeletal bonding of boranes and carboranes (see Section III, B) it is useful to consider first what problems are encountered if one attempts to describe the bonding in terms of localized bonds. 

The chemical bonding can be completely described in terms of localized bonds between neighbouring atoms. This condition excludes only metals and aromatic compounds where the bonding is provided by delocalized electrons. 

The perfectly octahedral species conform to the expectations based on the simple MO derivation given above. The nonoctahedral fluoride species do not, but this difficulty is a result of the oversimplifications in the method. There is no inherent necessity for delocalized MOs to be restricted to octahedral symmetry. Furthermore, it is possible to transform delocalized molecular orbitals into localized molecular orbitals. Although the VSEPR theory is often couched in valence bond terms, it depends basically on the repulsion of electrons of like spins, and if these are in localized orbitals the results should be comparable. 

Roth and coworkers41 42 have chosen carefully recalibrated force fields to predict reliable heats of formation with errors intended by the authors to be as small as 0.5 kcal mol"1. They started with the MM2 force field of Allinger98 and added to this parameters for the C(sp2)—C(sp2) and the C(cyclopropyl)—C(sp2) single bonds of reference compounds such as substituted 1,3-butadienes and vinylcyclopropanes41. Particular care was given to the correct description of the torsion potential of the reference compounds. The modified MM2 force field (MM2ERW) developed by Roth and coworkers describes polyenes and cyclopolyenes in terms of localized bond structures without any reference to quantum chemical methods such as the Pariser-Parr-Pople (PPP) approach (see Section II.C)41. 

Boron trifluoride has a trigonal-planar structure. Formulate the bonding in terms of molecular orbitals for the Dsjj symmetry. In addition, construct wave functions for three equivalent sp2 hybrid orbitals, using the 2px, 2p, and 2s boron valence orbitals, which may be used to form three localized bonds with the three fluorines. Compare and contrast the molecular-orbital and the hybrid-orbital descriptions. 

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