# Computational determination of the diagram of molecular orbitals of a polyatomic chemical species

A diagram of molecular orbitals for $$\ce{H2O}$$ would be as follows:

The above diagram has been constructed qualitatively following the steps that I have been instructed in various classes on this bonding theory.

Nevertheless, I have seen that the Guassian software allows to visualize the molecular orbitals of a species. For example, for the case of water one obtains:

The computational results agree with the qualitative diagram data, since all electrons are paired and there are also five atomic orbitals.

What I do not know is how to obtain the energy of the orbitals of the oxygen atom and the two hydrogen atoms. On the other hand, I would not know how to construct the diagram either, that is, I would not know that molecular orbital 5, the LUMO, comes only from the 2p orbital of the oxygen.

You can visualize isosurfaces of the molecular orbitals in gview. This allows you to identify the orbitals visually. That is a way to determine that the HOMO is a lone p-orbital of the oxygen atom. I think that you have to load the *.chk file with gview and not the *.log file, if you want to plot isosurfaces since the required information is saved there. Here is a figure that shows to get to the isosurface in gview,

An alternative to this qualitative/visual approach is looking at the atomic orbital coefficients of the molecular orbital. I don't know where Gaussian prints them but if you really needed a quantitative measure you would look those up. In the case of this molecular orbital, they should show that there is only 1 atomic orbital that contributes to the 5'th molecular orbital. I.e. the coefficient of the atomic oxygen p_z orbital should be 1 (or almost one if there are some numerical deviations).

For the oxygen-atom orbitals you would need to calculate a lone oxygen atom. For the $$\ce{H2}$$-orbitals you would need to calculate a lone $$\ce{H2}$$ molecule. You can also calculate with symmetry and Gaussian will assign the molecular orbitals to the irreducible representations. This helps to identify molecular orbitals. This information is given somewhere in the log file if the symmetry was properly determined by Gaussian during the calculation.

I also think you are mistaking LUMO(lowest unoccupied molecular orbital) with HOMO(highest occupied molecular orbital). Orbital 5 in the Gaussian output is the HOMO; orbital 6 is the LUMO.

• +1 But please use MathJax! Chemical formulae can be rendered with $\ce{...}$. Jul 18 at 8:23
• @SRMaiti Thank you for pointing the \ce environment out. I am familiar with mathjax but wasn't aware of this package for typesetting chemical equations. Jul 18 at 9:22