Hybrid orbital nonorthogonality functions

More recently, the Landis group" has used valence bond concepts to derive new angular potential energy functions and to develop rules for parameterization. The VALBOND force field angular energy function is based on Pauling s hybrid orbital nonorthogonality functions and can be derived for any arbitrary combination of s, p, d, and f orbitals. 

In the spin-coupled description of a molecule such as SF6, the sulfur atom contributes six equivalent, nonorthogonal sp -like hybrids which delocalize onto the fluorine atoms. Each of these two-centre orbitals overlaps with a distorted F(2p) function and the perfect-pairing spin function dominates. Of course, using only 3s, 3px, 3p and 3pz atomic orbitals, we can at most form four linearly independent hybrid orbitals localized on sulfur, with a maximum occupancy of 8 electrons, as in the octet rule. However, the six sulfur+fluorine hybrids which emerge in the spin-coupled description are not linearly dependent, precisely because each of them contains a significant amount of F(2p) character. It is thus clear that the polar nature of the bonding is crucial. 

Orbitals within the same parentheses are nonorthogonal. Orbitals in different parentheses are orthogonal.) The valence orbitals y i and (pi and the core orbital 4 are related to

reflection operation. One of the orbitals in a given pair is 5p-hybrid-//fce, the other is Isn-like. In order to develop a hierarchy of models, we find it convenient to write the valence pair functions in the form... 

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