Hybrid orbitals AB,

Gao J, Truhlar DG (2004) Generalized Hybrid Orbital (GHO) Method for Combining Ab Initio Hartree-Fock Wave Functions with Molecular Mechanics. J. Phys. Chem. A 108 632-650 

Pu JZ, JL Gao, DG Truhlar (2004b) Generalized hybrid orbital (GHO) method for combining ab initio Hartree-Fock wave functions with molecular mechanics. J. Phys. Chem. A 108 (4) 632-650 

There are several other symmetries of AB molecules for which hybrid orbitals on atom A are often wanted. The results for these are summarized below. 

Show that for the square planar AB inolecule a possible set of four a-hybrid orbitals on A is composed, of the atomic orbitals s, d flrt p and Py. Find explicit eicpressions for the four hybrid orbitals. 

Fig. 3.26 A tetrahiedral AB species with vectors representing central atom hybrid orbitals

C. Angeli, G. Del Re, and M. Persico Quasi-bond Orbitals from Maximum-Localization Hybrids for ab Initio Cl Calculations. Chem. Phys. Lett. 233, 102-110 (1995). 

Initially, hypervalent molecules like PCI5 and SFg 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 structures involving four covalent bonds and one or more additional ionic bonds, as shown in Scheme 1 for PF5. 

As a second example, let us consider a molecule with the formula AB( having the symmetry of a trigonal bipyramid The vector system is shown in Fig. 11-3.2. The set of five hybrid orbitals (or vectors) on A form a basis for a reducible representation of the point group, with the following character  

BiXs has three equatorial bonds, made from the usual sp hybrid orbital, and two axial bonds which use the three-center four-electron bonding, two electrons from the p orbital of bismuth and two electrons from the X ligands [94B-N]. In the three-center four-electron bonding, the central atom should be positively charged. This has been confirmed for MH5 (M = P, As, Sb, Bi) with recent ab initio calculation [95JA11790]. 

The N/2 Lewis-type NBOs of highest occupancy ( /AB) 2) can be directly associated with the localized electron pairs of the chemist s Lewis-structure diagram.46 Each Lewis-type NBO f2AB can be decomposed into constituent natural hybrid orbitals (NHOs) hA and hB on atoms A and B, 

Long before it was. possible to perform MO calculations on even the simplest molecules, the equivalence of the bonds led to the development of a different conception of the bonding in AB molecules, in which nonequivalent AOs on the central atom are combined into hybrid orbitals. These hybrid orbitals provide a set of equivalent lobes directed at the set (or subset) of symmetry equivalent B atoms. It is therefore obvious that all A—B bonds to all equivalent B atoms will be equivalent. 

In carrying out the procedure for a tetrahedral species, it is convenient to let four vectors on the central atom represent the hybrid orbitals we wish to construct (Fig. 3.26). Derivation of the reducible representation for these vectors involves performing on them, in turn, one symmetry operation from each class in the point group. As in the analysis of vibrational modes presented earlier, only those vectors that do not move will contribute to the representation. Thus we can determine the character for each symmetry operation we apply by simply counting the number of vectors that remain stationary. The result for AB is the reducible representation, f,. 

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