Is it possible ( term symbols )

[Livethefire]

Is it possible to calculate the energy of a state from an atomic term symbol? Or are we only able to use the lande inteval rule to find spin orbit interaction splittings?

 

[cgk]

In principle: yes, that is possible (with accuracy vs time tradeoffs).

In practice: Somewhat depends on the state. What you'd do is fire up your favorite multi-reference quantum chemistry program (Molpro or Molcas, most likely) and ask it to do a state-averaged MCSCF and MRCI+Q calculation of the states you are interested in, followed by a spin-orbit CI. It might take some effort, however, to convert the term symbols into state specifications these programs would understand (they are for molecules, after all), and high lying excited states might be difficult to lock onto or to converge

Also, if you're interested in heavy elements (say, Uranium or something) you might be better off with a 4-component program like DIRAC.

 

[Livethefire]

Wow that's a detailed answer, ha, I was expecting something a bit more elementary. I mean If I have a light element, hydrogen, helium or lithium for example.

And a term symbol like doublet S (1/2), is it posible by hand to figure out the energy? As opposed to estimations by computers? I mean, in this cause we would know S= 1/2, L=0, but no information of n. So by a bohr/Schrödinger approach, I can't see any way to calculate the state energy.

 

[cgk]

Wow that's a detailed answer, ha, I was expecting something a bit more elementary. I mean If I have a light element, hydrogen, helium or lithium for example.

And a term symbol like doublet S (1/2), is it posible by hand to figure out the energy? As opposed to estimations by computers? .

For H: probably yes
For He: a good estimate might be possible. But not without months of work.
For Li and up: definitely no

The problem is that in order to obtain the state energy, the many-body Schroedinger equation must be solved in an at least approximate way. For more than four electrons[1], this can in practice only be done by some self-consistent field approximations, followed up by correlation calculations (in the latter the interaction between the electrons is directly taken into account). While it may be possible to get an estimate of the state energy without actually solving the Schroedinger equation, the accuracy of such estimates may not be sufficient to, say, obtain the correct state ordering, because for obtaining this in some elemets correlation must be taken into account.

[1] For two--four there are some cheats, but they can also not be done without a computer.