Main page METHANE: MOLECULAR ORBITALS
 

Methane is one of the simplest organic molecules. Its simplicity and high symmetry allows us to appreciate many nuances of its structure and explore different ways of its presentation. In a way, it is our first step in the journey toward understanding of other organic molecules. On the one hand, we describe methane's electronic structure using hybrids orbitals of the VB theory.  In that model the C-H bonds are made pairwise by overlapping of the hybrid orbitals on carbon with atomic orbitals on hydrogens. The electrons in the VB methane are localized in individual σ bonds, one electron pair with antiparallel spins per bond. On the other hand, we we have an alternative molecular orbital model. In this case we do not put any limitations on electron delocalization and use atomic orbitals without any premixing (hybridization) to construct our new "spaces" for electrons.

 
 

MO-9
   

    

on/off:   
 

MO-6 

MO-7 

MO-8 

MO-3

MO-4

MO-5

MO-2
 
 

Let's build MOs of methane. We start with the inventory of the building blocks. We have four 1s orbitals on four hydrogens, and 2s and three 2p orbitals on carbon. In our minimalistic approach, in the simplest possible construction, we are going to use only the valence atomic orbitals.  We set aside the 1s orbital on carbon (which will become MO-1) as its electrons do not participate in bonding to any appreciable degree (they are so called "core" electrons). We also do not include any higher energy orbitals on hydrogen or carbon atoms. Since we have 8 orbitals to start with, we must build 8 MOs before we are done, and then fill half of them with 8 electrons contributed by the carbon and hydrogens, in a pairwise fashion .

Since our three p orbitals on carbon are perpendicular to each other and we are not allowed to hybridize them (that would be a different molecule-building recipe) , it is probably the best to use them and the carbon s orbital individually in the MOs construction. To facilitate the presentation, we place our methane molecule in an imaginary cube, to emphasize its 3D shape.

Our lowest energy bonding MO (MO-2) is built out of s orbitals only: a fraction of the s of carbon in the center of the cube, and fractions of s orbitals of hydrogens in the four corners.  The fractions must add up to a full orbital since we want it to be normalized.  The "in-'phase" overlap generates MO-2 without any nodes (Click on its image on the left see its full 3D shape).  Give it a spin and try some other display options (add axes or remove box, or "hide" the MO-mesh) to get a feeling on how it it all works. You can always "reload" the original settings, or "reset" to the "standard" orientation. 

The next three MOs are constructed from fractions of individual p orbitals and fractions contributed by all hydrogens' s orbitals. MO-3 uses a fraction of the pz orbital (turn the axes on to verify it), MO-4 is built of of a fraction of py, and MO-5 utilizes a fraction of the px orbital.  As before all resulting molecular orbitals must be normalized. These combinations produce a set of three identical and degenerate MOs differing only in their direction in space. M0-2 and MO3 – MO-5 are all filed with electrons, a pair per orbital. Indeed, any one of the degenerate three may serve as the HOMO. The electrons in these orbitals are delocalized over the entire molecule. The individual (VB) bonds are no longer recognizable, as they were in diatomics.  In MO-2, for example, the two electrons are "everywhere" in the molecule!.

The next three MOs are the "antibonding" equivalents of MO-3 - MO-5, respectively. That complementarity may not be readily apparent from the beautiful, yet complex shapes of MO-6 MO-8, but can be made clearer by drawing these orbitals in such a way that they contain only 33% of the electron density inside. These "small lobe" representations are almost equivalent to the "cartoon" orbital pictured on the left side of the page.  When exploring the small-lobe orbitals, remember to check them off when done, so you do not mix-up the large (mesh) lobes of one orbital with small (solid) lobes of the "shrank" version of another MO.  That series of three MOs is again a degenerate set, and any one of them can serve as the LUMO.

Finally, the highest energy MO-9 is the antibonding version of MO-2.  Spend some time playing with the models using your mouse. If you "reload" the model, all MOs, including their energies, can be also explored using Jmol menu ( Surfaces Molecular Orbitals).

 

Interestingly, the MO picture of methane that we have just discussed has been confirmed  experimentally by the ESCA spectroscopy (Electron Spectroscopy for Chemical Analysis).  In these types of experiments a sample  is exposed to high-energy monochromatic X-rays and the kinetic energies of ejected electrons are measured.  Conceptually that experiment is very similar to the photoelectric effect except that much more energetic photons are used. The kinetic energy of  the ejected electrons tells us about the binding energies of these electrons; i.e. how strongly were they held by the molecule. When methane is exposed to such experimental conditions three (and only three) separate binding energies are observed. One is very large, 291 eV  (1 eV = 23.06 kcal/mol), and it corresponds to the energy of the MO-1 orbital (1s orbital on carbon),  the next represents MO-2, and the last matches MO-3, MO-4, and MO-5 which are degenerate.

You may even compare our calculated MO energies (after reloading the model select from the menu: Surfaces → Molecular Orbitals) with the experimental data. The calculated energies are in the atomic units (1 hartree = 27.1 eV = 628.1 kcal/mol). Taking into account how large are the energies involved and how simplistic our model is, the results are not bad at all. You may also appreciate why 1s electrons on carbon are not involved in bonding and why we call them "core" electrons.

 

 
Molecular Gallery Last updated 08/22/10 Copyright 1997-2013
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