Molecular Symmetry and Group Theory
From a conventional viewpoint we might expect all eight bonding electrons in CH4 to be indistinguishable with identical energies. UV photoelectron spectroscopy experiments, however, indicate that while six valence electrons have an ionization energy of 14 eV, two are more strongly bound (23 eV).
Use the following procedure to develop a qualitative MO energy level diagram for CH4:
As the 2s orbital is spherically symmetric, it is unaffected by any operation. This is true of all s orbitals, which as a result always belong to the totally symmetric irreducible representation (the first one in any character table). The symmetry of the 2s orbital in Td is therefore a1.
iii) Select appropriate orbitals on the outer atoms (H 1s) and use these as a basis to obtain a reducible representation. Reducing this will give irreducible representations (i.e. symmetries) appropriate to the orbitals in the basis.
Use the 4 H 1s orbitals in the CH4 molecule as a basis to obtain a representation in the tetrahedral point group Td, and reduce this to its component irreducible representations.
Reducing to find the constituent irreducible representations tells us the symmetry of linear combinations of atomic orbitals on the outer atoms that can be combined with atomic orbitals of the same symmetry on the central atom, and thus enables an energy level diagram to be constructed. Group theory and considerations of symmetry alone, however, cannot help us in determining the energies of atomic orbitals, the degree of overlap and the strength of bonding interactions, for which we must resort to quantum mechanics or experimental data.
Constructing the molecular orbital diagram - All the required information has been determined above (spectroscopic data can be used to assist in determining the relative energies of the bonding molecular orbitals in CH4.
[Note that the experimental data given above provides strong evidence for the validity of MO theory.]
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