Term dependence

The $1s,\;2s,\; 2p,\ldots$ terminology for electrons in configurations overlooks the fact that the motion of an electron depends also on the coupling, particularly the final LS term. As an example, consider the 1s²2s2p configuration in Be which may couple to from either a 3 P/ or 1 P/ term. The energy expression differs only in the exchange interaction, $\pm (1/3)G^{1}(2s,2p)$, where the + sign refers to 1 P/ and the - to 3 P/. Clearly, the energies of these two terms will differ. What is not quite as obvious is the extent to which the P(2p;r) radial functions differ for the two states.

Figure: A comparison of the 2p Hartree-Fock radial functions for the $1s2p\;^{1,3}\!P$ states of Be.

Clearly, the most affected orbital will be the one that is least tightly bound, which in this case is the 2porbital. fig:be1P3P shows the two radial functions. The 1 P/ orbital is far more diffuse (not as localized) as the one for 3 P/. Such a change in an orbital is called LS-term dependence.
 

2001-01-09