Methane equivalent transformation orbital

The final molecule of this series is methane, the tetrahedral structure of which follows if a fourth unit positive charge is removed from the nucleus in the ammonia lone-pair direction. There are now four equivalent bonding orbitals, which may be represented approximately as linear combinations of carbon s-p hybrid and hydrogen Is functions. The transformation from molecular orbitals into equivalent orbitals or vice versa is exactly the same as for the neon atom. 

The expressive term equivalent orbital was introduced by Lennard-Jones to describe the two-center MOs into which the correct MOs can often be transformed by procedures analogous to that used for methane in Section 1.10. 

In the previous section, we showed how one could transform from a basis set of STOs to a basis set of symmetry orbitals. Since these two sets are related through a unitary transformation, they are equivalent and must lead to the same MOs when we do a linear variation calculation. However, there are an inhnite number of unitary transformations available, and so the set of symmetry orbitals is only one of an infinite number of possible equivalent bases. Of course, this set has the unique advantage of being a set of bases for representations of the symmetry group, which makes it easy to work with. Another set of equivalent basis functions are the hybrid orbitals. These have the distinction of being the functions that are concentrated along the directions of bonds in the system. Consider, for example, methane, which was discussed in detail in Chapter 10. The minimal basis set of valence STOs on carbon can be transformed to form four tetrahedrally directed hybrids ... 

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