A way to calculate orbital energy of an electron

Maybe this is just not included in my course, but I still wonder how to calculate the binding energy of an electron .at a certain electron orbital.


Intuitively,The ionization energy of an element should vary depending on which orbital the valence electron is in. 


PS: I only know how to calculate ionization energy using principle level.




You are correct that the ionization energy of an electron depends on the orbital. **There is no easy formula,** because the electrons in atoms are governed by quantum mechanics and for multi-electron atoms, the equations are un-solvable algebraically.


That said, there are some reasonable tabulations, which have been verified by calculations and by spectroscopy, e.g., <http://www.colby.edu/chemistry/PChem/notes/AOIE.pdf> (from a quick Google search).


Both ultraviolet photoelectron spectroscopy and x-ray photoelectron spectroscopy can be used to eject electrons from various materials, and you can thus identify elemental composition (and other properties) from the known orbital energy levels


 3

I just stumbled across this question ... a little late....


A common approximation in XPS to solve this question is Koopmans theorem (frozen-orbital approximation). If the remaining (those were not photo-electron was removed) orbitals of the exited atom after photo-ionisation do not change between the initial and final state (no relaxation) the experimental binding energies are than taken to be equal to the respective negative Hartree-Fock/KS orbital energy.
A good way to start reading is this Book:
[Book](https://www.springer.com/de/book/9783540418023)
See also:
[Link](https://onlinelibrary.wiley.com/doi/abs/10.1002/sia.6319)
[Link2](https://pubs.rsc.org/en/Content/ArticleLanding/2015/CP/C4CP05434B#!divAbstract)


 1