Energy-level diagram for HHe

Qualitative consideration of the symmetry and geometric properties of the atomic orbitals involved in more complex molecules can also help to elucidate the molecular orbital description of the molecules. Methane can be used as an example. Molecular orbital calculations at the SCF level lead to the energies shown in Fig. 1.10  

This particular calculation used as a basis set the I5-, 2s-, and three 2p-orbitals of carbon and the l5-orbitals of the four hydrogens. The lowest molecular orbital is principally Is in character. A significant feature of this and other MO calculations on methane is that unlike a picture involving localized bonds derived from 5p -hybrid carbon orbitals, there are not four equivalent orbitals. We can obtain an understanding of this feature of the MO picture by a qualitative analysis of the origin of the methane molecular orbitals. For simplicity, we will consider the orbitals to be derived from the carbon 2s-, 2p -, 2py-, and 2p -orbitals and ignore the carbon Is-orbital. The most convenient frame of reference for the tetrahedral methane molecule is described by a cube with hydrogen atoms at alternate corners and the carbon atom, centered in the cube, as shown below  

This orientation of the molecule reveals that methane possesses three twofold symmetry axes, one each along the x, y, and z axes. Because of this molecular symmetry, the proper molecular orbitals of methane must possess symmetry with respect to these same axes. There are two possibilities the orbital may be unchanged by 180° rotation about the axis (symmetric), or it may be transformed into an orbital of identical shape but opposite sign by the symmetry operation (antisymmetric). The carbon 2s-orbital is symmetric with respect to each axis, but the three 2p-orbitals are each antisymmetric to two of the axes and symmetric with respect to one. The combinations which give rise to molecular orbitals that meet these symmetry requirements are shown in Fig. 1.11. 

The most direct and practical way to assess the validity of the conclusions based on MO considerations versus intuition based on qualitative notions of localized valence bonds is to measure the binding energies of the electrons in methane. The ionization potential is the energy required to remove an electron from a molecule and 

This equation is simply that for the photoelectric effect initially observed for emission from metallic surfaces, except that the work function term has been replaced by the energy required to remove an electron, i.e., the ionization potential. Such measurements allow the construction of molecular orbital energy diagrams directly from experimental data and provide a way of critically examining bonding theories without recourse to intuition. 

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