Pauling hybridization scheme

For most of the molecules and reactions we want to consider, the Pauling hybridization scheme provides an effective structural framework, and we use VB theory to describe most of the reactions and properties of organic compounds. However, we have to keep in mind that it is neither a unique nor a complete description of electron density, and we will find cases where we need to invoke additional ideas. In particular, we discuss molecular orbital theory and density functional theory, which are other ways of describing molecular structure and electron distribution. 

Pauling developed the concept of hybrid orbitals to describe the bonding in molecules containing second-period atoms with steric numbers 2, 3, and 4. Let s discuss these hybridization schemes in sequence, starting with BeH2. We will use the lowercase Greek letter chi, x, to represent hybrid orbitals. 

On the other hand, the VB model developed by Pauling was based on a more quantum-mechanical-based model of valence electrons. Instead of simply putting electrons into spatially separated regions (domains), atomic orbitals are involved in the discussion, and all bonding interactions are considered as overlaps between orbitals of different atoms. This approach has been very useful in bridging the Lewis model to the more modem molecular orbital treatment, and similar to VSEPR, the hybridization scheme developed by Pauling has provided an important theoretical underpinning for chemistry over the years. 

Interestingly, from Pauling s hybridization scheme, there are still orbitals that are not utilized and remain unhybridized, and these orbitals also do not contribute to the M-L bondings [28]. We will therefore view these orbitals as nonbonding orbitals, and the question now becomes how to localize these nonbonding orbitals. 

Scheme 3. Representations of. T-Delocalization in Benzene (a) Hiickel s t-MO s. (b) Wheland— Pauling s Resonance Hybrid, (c) Symbolic Representation of T-Delocalization by a Dotted Circle3...

Scheme of an IT TOF hybrid mass spectrometer including a Paul IT analyser and TOF analyser equipped with a reflectron. 

Initially, hypervalent molecules like PCI5 and SFe were described in terms of sp d" hybrid orbitals, in an extension of the sp" orbital description used to characterize molecules that obey the octet rule. However, ab initio calculations have shown that d orbitals play only a minor role in the bonding of hypervalent molecules. An alternative approach proposed by Pauling invoked combinations of resonance stmctures involving four covalent bonds and one or more additional ionic bonds, as shown in Scheme 1 for PF5. 

The universally accepted argument that explains the structure of methane in terms of the well known scheme of sp orbital hybridization derives from several statements and postulates originally formulated by Linus Pauling [1], Some of these... 

The chemist has not succeeded in doing this. Pauling himself proposed the scheme of orbital hybridization as a quantum theory of covalent interaction. Despite its uncritical acceptance for many years, this approach is shown by elementary reasoning to be in direct conflict with the fundamentals of quantum theory. 

In fact almost all went the way that Mulliken proposed, using the molecular orbital model. In this approach it was possible to formulate the equations in a manner suitable for calculation and to develop consistent approximation schemes that at least allowed semi-empirical calculations to be made. A number of semi-empirical schemes were developed, particularly for aromatic and conjugated systems, which can be regarded as inspired by the initial efforts of Hiickel in 1931 to use molecular orbitals in this area. For such systems the idea of a delocalised electron distribution came immediately out of the calculations, so that there was no need to invoke the bond or the idea of resonance. However the parameterisation schemes within these semi-empirical approaches, were cast in terms of integrals between hybrid orbitals, so that aspect of Pauling s ideas remained alive both in chemistry and in quantum chemistry. 

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