Atomic hybridized

The next step towards increasing the accuracy in estimating molecular properties is to use different contributions for atoms in different hybridi2ation states. This simple extension is sufficient to reproduce mean molecular polarizabilities to within 1-3 % of the experimental value. The estimation of mean molecular polarizabilities from atomic refractions has a long history, dating back to around 1911 [7], Miller and Sav-chik were the first to propose a method that considered atom hybridization in which each atom is characterized by its state of atomic hybridization [8]. They derived a formula for calculating these contributions on the basis of a theoretical interpretation of variational perturbation results and on the basis of molecular orbital theory. 

Kang and Jhon [9] showed that mean molecular polarizabiHties, a, can be estimated om atomic hybrid polarizabihties, by a simple additivity scheme summing over all N atoms (Eq. (6)). 

It is recommended that the reader become familiar with the point-group symmetry tools developed in Appendix E before proceeding with this section. In particular, it is important to know how to label atomic orbitals as well as the various hybrids that can be formed from them according to the irreducible representations of the molecule s point group and how to construct symmetry adapted combinations of atomic, hybrid, and molecular orbitals using projection operator methods. If additional material on group theory is needed. Cotton s book on this subject is very good and provides many excellent chemical applications. 

The VB and MO theories are both procedures for constructing approximations to the wavefunctions of electrons, but they construct these approximations in different ways. The language of valence-bond theory, in which the focus is on bonds between pairs of atoms, pervades the whole of organic chemistry, where chemists speak of o- and TT-bonds between particular pairs of atoms, hybridization, and resonance. However, molecular orbital theory, in which the focus is on electrons that spread throughout the nuclear framework and bind the entire collection of atoms together, has been developed far more extensively than valence-bond... 

The Raman parameters reported for a-C(N) H films deposited by magnetic field enhanced RFPECVD in CH4-N2-He atmospheres also showed an intermediate N content range (about 7 at.%), with almost constant Raman parameters. In this case, the behavior was found to be associated with a nontypical variation of the C and N atom hybridization state, as discussed in Section 2.4.3. 

Number of Electron Pairs at Central Atom Hybridization State of Central Shape of Molecule or Iona Examples... 

However, we should emphasize that the NBO/NRT concepts of hybridization, Lewis structure, and resonance differ in important respects from previous empirical usage of these terms. In earlier phases of valence theory it was seldom possible to determine, e.g., the atomic hybridization by independent theoretical or experimental procedures, and instead this term became a loosely coded synonym for the molecular topology. For example, a trigonally coordinated atom might be categorized as sp2-hybridized or an octahedrally coordinated atom as d2sp3-hybridized, with no supporting evidence for the accuracy of these labels as descriptors of actual... 

Note that, if the donor and acceptor s and p orbitals refer to the same atomic center, the coupling matrix elements and /pp- are identically zero, and hybridization cannot lower the energy. Hence, atomic hybridization is intrinsically a bonding effect. 

Nearly four decades ago, American chemist Henry Bent40 formulated a remarkable principle that relates atomic hybridization to substituent electronegativity. This principle, now called Bent s rule, was originally expressed in the following words ... 

The hybridization parameter X can be estimated at each R by expressions such as (3.1 lb), which in turn are related to visual plots of the s-pz overlap. A procedure for numerically estimating X will be given at the end of this section. For present purposes, we need only recognize from the percentage s characters that the relative energies of the starting atomic hybrids satisfy... 

These atomic hybrids are the starting point for discussing the donor-acceptor interactions and two-center NBO formation at each R. 

It is inherently surprising that geminal interactions are typically weaker than vicinal interactions, because the former involve orbitals that are in closer spatial proximity. The reasons for this counterintuitive distance dependence can be seen by decomposing the geminal Fock-matrix element into individual atomic hybrid contributions. 

Hybridization occurs during the formation of a chemical bond. It is not possible to occur in an individual atom. Hybrid orbitals play an important role in determining the geometric shape of a molecule. 

Cyclic organic compounds as a basic variant of carbon nanostructures. Apparently, not only inner-atom hybridization of valence orbitals of carbon atom takes place in cyclic structures, but also total hybridization of all cycle atoms. 

The average polarizability a, defined by equation 9, is a global property, which pertains to a molecule as a whole. It is a measure, to the first order, of the overall effect of an external electric field upon the charge distribution of the molecule. We are unaware of any experimentally determined a for the molecules that are included in this chapter. However, they can be estimated using equation 12 and the atomic hybrid polarizabilities, and corresponding group values, that were derived empirically by Miller. These were found to reproduce experimental molecular a with an average error of 2.8%. The relevant data, taken from his work, are in Table 7. 

Hirshfeld (1964) pointed out that bond bending not only occurs in ring systems, but also results from steric repulsions between two atoms two bonds apart, referred to as 1-3 interactions. The effect is illustrated in Fig. 12.3. The atoms labeled A and A are displaced from the orbital axes, indicated by the broken lines, because of 1-3 repulsion. As a result, the bonds defined by the orbital axes are bent inwards relative to the internuclear vectors. When one of the substituents is a methyl group, as in methanol [Fig. 12.3(b)], the methyl-carbon-atom hybrid reorients such as to maximize overlap in the X—C bond. This results in noncolinearity of the X—C internuclear vector and the three-fold symmetry axis of the methyl group. Structural evidence for such bond bending in acyclic molecules is abundant. Similarly, in phenols such as p-nitrophenol (Hirshfeld... 

In this chapter the symmetry properties of atomic, hybrid, and molecular orbitals are treated. It is important to keep in mind that both symmetry and characteristics of orbital energetics and bonding "topology", as embodied in the orbital energies themselves and the interactions (i.e., hjj- values) among the orbitals, are involved in determining the pattern of molecular orbitals that arise in a particular molecule. 

Figure 3.14. Group orbitals for zero-coordinated atoms hybridized for formation of a single bond.

Fig. 3.26 A tetrahedral AB4 species with vectors representing central atom hybrid orbitals...

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