Use and misuse of the hybrid orbital concept

It is stressed again that, assuming a given basis set of Is orbitals for the H atoms and 2s and 2p orbitals for C, exactly the same wavefunction is obtained irrespective of using the canonical m.o.s V i (as linear combinations of a.o.s) or the molecular orbitals Xi (linear combinations of through a unitary transformation). Hence, for example the calculated molecular energy is exactly the same, provided that the residual interactions given by 

If all orbital interactions of the type described by Eq. (8.27) are included in the calculations, any result obtained is independent of the combination of a.o.s used, if any, i.e. four pure atomic orbitals, four sp hybrid orbitals, three sp and one p orbital, two sp and two p orbitals, etc. In particular, at a given level of approximation, the linear combinations of hybrid (and other) 

It is only when the interactions expressed by Eq. (8.27) are neglected that orbital hybridization seems to have an effect and, thus, seems to explain some molecular properties. This is so, both in m.o. theory and in v.b. theory. Ironically, it is more difficult to take these interactions into account in v.b. theory where the concept of hybrid orbital was first introduced. For example, it is more difficult to do a complete v.b. treatment of CH4, with inclusion of the less traditional formulae in the resonance scheme (and which accounts for the non-independence of bonds), than to do a fully delocalized treatment by m.o. theory, at the same degree of approximation. But if the complete treatment is carried out, the v.b. result is the same irrespective of the hybridization considered, just as any m.o. result is the same whether pure, hybrid orbitals or a mixture of both are taken as the basis for the linear combinations. 

At this stage, it is appropriate to draw attention to additional misuses of the concept of orbital hybridization, besides the relation with molecular geometry already discussed. We will briefly refer here to frequent interpretations of differences in bond energies, bond lengths, force constants, bond polarity, acidic character, etc. (see ref. 117). 

It is also common to attribute the fact that the CH bond is shorter in C2H2 than in C2H6 to sp hybridization in the former case, as more s-character in the hybrid orbital implies a larger overlap integral. However, it should be noted that the smaller CH bond length and the consideration of sp carbon hybrids in acetylene in order to define quasi-localized molecular orbitals are two manifestations (one physical, the other mathematical) of the same real feature the number of atoms bonded to each C atom and their geometric arrangement. 

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