Orbital, 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. 

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. 

For example, in formaldehyde, H2CO, one forms sp hybrids on the C atom on the O atom, either sp hybrids (with one p orbital "reserved" for use in forming the n and 7i orbitals and another p orbital to be used as a non-bonding orbital lying in the plane of the molecule) or sp hybrids (with the remaining p orbital reserved for the n and 7i orbitals) can be used. The H atoms use their 1 s orbitals since hybridization is not feasible for them. The C atom clearly uses its sp2 hybrids to form two CH and one CO a bondingantibonding orbital pairs. 

So far, we have not considered whether terminal atoms, such as the Cl atoms in PC15, are hybridized. Because they are bonded to only one other atom, we cannot use bond angles to predict a hybridization scheme. However, spectroscopic data and calculation suggest that both s- and p-orbitals of terminal atoms take part in bond formation, and so it is reasonable to suppose that their orbitals are hybridized. The simplest model is to suppose that the three lone pairs and the bonding pair are arranged tetrahedrally and therefore that the chlorine atoms bond to the phosphorus atom by using sp hybrid orbitals. 

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... 

Figure 1.5 The shapes of some s and p orbitals. Pure, unhybridized p orbitals are almost-touching spheres. The p orbitals in hybridized atoms are lobe-shaped (Section 1.14).

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. 

We can also verify that the usual ECAO-MO description (3.2) and (3.4) leads to predicted hybridizations that are generally consistent with the donor-acceptor estimates (3.8). Suppose that each H atom is associated with a valence spin-orbital of hybridized form (3.6). According to Eq. (3.2), the optimal electronic energy of bond formation is obtained by choosing the hybridization parameter k to maximize the magnitude of the interaction element... 

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. 

Figure 3.7. Common representations of the s, p, d and atomic orbitals, sp3 hybridized orbitals, and some representations of how they overlap to form bonds between atoms.

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. 

Each external (i.e., terminal) B-H bond is regarded as a typical two-center two-electron single bond requiring the hydrogen Is orbital, one hybridized boron orbital, and one electron each from the H and the B atoms. Because of the small electronegativity difference between hydrogen and boron, these bonds are assumed to be non-polar. In the polynuclear boron hydrides every boron atom may form zero or one but never more than two such external B-H bonds. 

The VSEPR theory is only one way in which the molecular geometry of molecules may be determined. Another way involves the valence bond theory. The valence bond theory describes covalent bonding as the mixing of atomic orbitals to form a new kind of orbital, a hybrid orbital. Hybrid orbitals are atomic orbitals formed as a result of mixing the atomic orbitals of the atoms involved in the covalent bond. The number of hybrid orbitals formed is the same as the number of atomic orbitals mixed, and the type of hybrid orbital formed depends on the types of atomic orbital mixed. Figure 11.7 shows the hybrid orbitals resulting from the mixing of s, p, and d orbitals. 

The valence bond theory describes covalent bonding as the overlap of atomic orbitals to form a new kind of orbital, a hybrid orbital. 

Hybridisation is the process of mixing atomic orbitals within an atom to generate a set of new atomic orbitals called hybrid orbitals. In the case of a carbon atom, the one 2s orbital can mix with the three 2p orbitals to form four hybrid orbitals known as sp hybrid orbitals. 

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... 

---