Atomic electronic states: the L-S and j-j coupling schemes and their   correlation
  In the first part of this paper, we review the assumption of the L-S coupling scheme, with which we derive the electronic states arising from a given atomic configuration. Then, with the aid of the spectral data of Group 15 elements, it becomes clear that the assumption of the L-S coupling scheme is no longer valid as we go farther and farther down the Periodic Table. In the second part, we introduce the j-j coupling scheme, which is seldom covered in standard inorganic chemistry texts, and contrast the assumptions of the two schemes. Next, we use two worked examples to demonstrate the derivation of electronic states with the j-j coupling scheme. Finally, the correlation between the states derived by L-S and j-j schemes is pictorially shown. It is believed a student, by also studying j-j coupling schemes (by no means a difficult task) along with the L-S scheme, will gain a better understanding of the concept of atomic electronic states. 
Wai-Kee Li and S. M. Blinder
physics.chem-ph