Hybridization hybrid atomic orbital

Orbital hybridization A mathematical approach that involves the combining of individual wave functions for s and p orbitals to obtain wave functions for new orbitals => hybrid atomic orbitals 

The use of hybrid atomic orbitals in qualitative valence theory has, in the past, rested on two points (i) an empirical justification of their use involving the concept of the valence state of an atom and (ii) a simple linear transformation technique for the construction of the explicit forms of the orbitals. In this section we show that both of these points can be replaced. The justification can be replaced by a derivation and this derivation can be used to suggest variational forms which render the linear transformation technique redundant. 

A set of hybridized atomic orbitals holds the same maximum number of electrons as the set of atomic orbitals from which the hybridized atomic orbitals were formed. A hybridized atomic orbital can hold a maximum of 2 electrons having opposite spin. 

See Fig. 10-7. The C s use sp hybrid atomic orbitals to form tr bonds with each other and with the H s. The remaining p orbitals at right angles to the plane of the C s overlap laterally to form a tt electron cloud. 

Fig. 6. The radially orientated sp hybrid atomic orbital (AO) and tangentially orientated p AO s that a BH unit can supply for skeletal bonding.

In the molecule Li2 the bond involves a hybrid atomic orbital as+bp formed from the 2s orbital and one of the much less stable 2p orbitals. It is shown below that the amount of p character of this bond orbital (equal to b2, with a2 + b2 = 1) is small, being about 8%. On the other hand, if each of the atoms in metallic lithium requires a bond orbital and a metallic orbital and the two are equivalent they will be 2- -p) and 2 t(s —p), with 50 % p character. The analysis of energy quantities supports this conclusion. 

See Fig. 20-1. The four C s and the heteroatom Z use ip -hybridized atomic orbitals to form the a bonds. When Z is O or S, one of the unshared pairs of e s is in an sp HO. Each C has a p orbital with one electron and the heteroatom Z has a p orbital with two electrons. These five p orbitals are parallel to each other and overlap side-by-side to give a cyclic rr system with six p electrons. These compounds are aromatic because six electrons fit Hiickel s 4n + 2 rule, which is extended to include heteroatoms. 

Sigma (O) bond A bond formed by the end to end overlap of pure or hybridized atomic orbitals. 

Similar, but different, redeployment is envisaged when a carbon atom combines with three other atoms, e.g. in ethene (ethylene) (p. 8) three sp hybrid atomic orbitals disposed at 120° to each other in the same plane plane trigonal hybridisation) are then employed. Finally, when carbon combines with two other atoms, e.g. in ethyne (acetylene) (p. 9) two sp hybrid atomic orbitals disposed at 180° to each other digonal hybridisation) are employed. In each case the s orbital is always involved as it is the one of lowest energy level. 

The use of the Lbwdin orthogonalisation technique (or any other method of or-thogonalisation) means inevitably that the final basis of orthogonalised hybrid atomic orbitals (OHAOs) does contain many-centre orbitals in the sense that each OHAO is mainly its HAO parent but necessarily contains (minimal) contributions from overlapping HAOs. 

We said in Section 1.5 that chemists use two models for describing covalent bonds valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let s look briefly at the molecular orbital approach to bonding. We ll return to the topic in Chapters 14 and 15 for a more in-depth discussion. 

CS INDO [10] (as well as the parent C INDO [9]) shares the same basic idea as the PCILO scheme [29,30] to exploit the conceptual and computational advantages of using a basis set of hybrid atomic orbitals (AOs) directed along, or nearly, the chemical bonds. 

To truly understand the geometry of bonds, we need to understand the geometry of these three different hybridization states. The hybridization state of an atom describes the type of hybridized atomic orbitals (ip, sp, or sp) that contain the valence electrons. Each hybridized orbital can be used either to form a bond with another atom or to hold a lone pair. 

We start with Salem s treatment of the Walden inversion Frontier orbital approximation is assumed the major interaction is supposed to be that between the nucleophile s HOMO and the substrate s LUMO. Now, according to ab initio calculations, the latter is essentially an out-of-phase combination of a carbon hybrid atomic orbital 0c with a leaving group hybrid atomic orbital 0x- In the first approximation, the LUMO wave function may be written as  

Of the various methods of approximating the correct molecular orbitals, we shall discuss only one- the linear combination of atomic orbitals (LCAO) method. We assume that we can approximate the correct molecular orbitals by combining the atomic orbitals of the atoms that form the molecule. The rationale is that most of the time the electrons will be nearer and hence controlled by oneor the other of the two nuclei, and when this is so, the molecular orbital should be very nearly the same as the atomic orbital for that atom. The basic process is the same as the one wc employed in constructing hybrid atomic orbitals except that now we are combining orbitals on different atoms to form new orbitals that are associated with the entire molecule. We 

---