Term symbols offer an extremely compact way of describing the different energy levels of a system. It takes into account many corrections, including the central field, spin-orbit interaction, and electrostatic repulsion.

Using Hund's rules, you can easily predict the energy levels, and compare them - showing which one has higher energy and so on and so forth.

However, my question is, how do I find out the exact value of energy from an atomic term symbol. For example, if I have, say, $^3P_{1}$. Is there any way, I can get an exact value of energy in electron-volts corresponding to this particular term symbol? How do I do that?

My intuition is that I'd have to calculate the individual energies due to spin-orbit interaction and other corrections and add them separately. However, how do I calculate the energy from the central field approximation and the electrostatic repulsions? Maybe then, I can add all these to get a compact expression for energy.

The Hamiltonian is given by :

$$H = H_c + H_{repulsion} + H_{S-O}$$

Out of these, I only know how to calculate the last. What about the first two terms ?


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