[GeLe5000]

Good evening.

The well-known diagrams showing the energy levels of molecular orbitals and atomic orbitals from which they are contrived clearly indicate that an electron participating in the formation of a chemical bond falls down to a lower state of energy in the Molecular Orbital.
For example, when HF is formed from an H atom and a F atom, the H electron is now present in a sigma MO, which stays below the energy of the atomic orbital 1s of the H atom (313 kcal/mole) (the same for the electron coming from a 2p atomic orbital of atom F).

However, it's always only qualitative. There are no numerical values on the diagrams.

Is it possible to calculate the energy of a MO in Joules ?

Thank you for your answer.

[Corribus]

The best way is experimentally. E.g., with photoelectron spectroscopy or some equivalent that essentially measures ionization potentials. Technically these give you state energies and not (one electron) orbital energies, but the former is what you ultimately want, anyway.

http://en.wikipedia.org/wiki/Photoelectron_spectroscopy
http://en.wikipedia.org/wiki/Ultraviolet_photoelectron_spectroscopy

You can easily find papers that measure the molecular state energies of HF via a Google search.

For example, http://www.jstor.org/stable/2415997

[GeLe5000]

Thank you very much for your help.

It's comforting to read that there's an (experimental) interest for the numerical values of molecular state energies.

My conclusion is that when you leave the field of the atomic orbital where a simple equation like "W = - K (Z*² / n²)" gives the energy of an electron, mathematics can't help.

Perhaps quantum physics, but anyway it's out of my reach.

Thank you again for your work.

[Corribus]

To be clear, there are many ways to calculate absolute or relative molecular orbital/state energies, some of them completely theoretical, some of them semi-empirical. Anything other than a 1 electron system is by nature an approximation rather than calculation of an exact value, and the vast majority of reasonably good calculations require computers because they are mathematically intensive. Some types of systems are far easier than others, but by and large we can do a reasonably good job of calculating molecular state energies, and also molecular structures, even with reasonably simple approximations.

All that said, no calculation will ever replace experimental data. Calculations are most useful in cases were experiments are just not easy to pull off (e.g., states that are spectroscopically forbidden, nonequilibrium structures, transition states or other quasi-stable states, and so forth).