Question

For each free ion term symbols (derived from Russel-Saunders term symbols), what molecular term symbols arise when the atom is placed in an octahedral field?

Answer 1

L-S coupling or Russel-Saunders Coupling : In an atom the electron spin angular momentum may couple with the total angular momentum. L-S coupling in atoms of low atomic numbers because in these atoms spin-orbit coupling is weak.First sum the orbital angular momentum to give a total L and then spin angular momenta to give a total S separately and finally add these two momenta to give the total angular momentum J

L=l_{i ,} S= S_i

J=L + S

and J= j(j+1).h/2 where J= total angular momentum quantum number (non negative integer or half integer).

the permitted values of J can be obtain by using Clebsch-Gordan series.The coupling of L and S known as Russel-Saunders Coupling gives rise to quantum number J which is as

J= L+S,L+S-1,..............|L-S|

The terms L,S and J collectively constitute an important symbol known as atomic term symbol which is designated as ^2s+1L_J. The superscript represents the multiplicity of the term and subscript is the value of J is given by above equation.just as l=0,1,2,3 etc corrosponds to the atomic orbitals s,p,d,f respectively, Similarly L=0,1,2,3 corrosponds to atomic masses S,P,D and F respectively.

The Effect of a crystal field on the different orbitals (s, p, d, f) will result in splitting into subsets of different energies, depending on whether they are in an octahedral or tetrahedral field.So the ground term energies for free ions are also affected by the influence of a crystal field.so For each free ion term as below