Example 15.6
List all of the possible term symbols (do not neglect any due to Pauli princi-
ple considerations) for a d^2 ground-state valence electron configuration.Solution
Each delectron has an of 2, so the possible values ofLare 4, 3, 2, 1, and 0.
This implies the possible existence of G, F, D, P, and S states. Like the above
example, the two electrons each have an sof^12 , so the possible values ofSare
1 and 0. The resulting values of the multiplicity are 3 and 1. Combining the
multiplicities with the Lvalues, the possible term symbols are^3 G,^1 G,^3 F,^1 F,(^3) D, (^1) D, (^3) P, (^1) P, and (^3) S, (^1) S. (The Pauli principle and redundancy will ultimately
eliminate the^3 S,^3 D,^3 G,^1 P, and^1 F term symbols for these atoms, leaving^1 G,
(^3) F, (^1) D, (^3) P, and (^1) S.)
The rules for determining term symbols above (and more importantly, for
excluding certain term symbols) assume that the electrons in the unfilled sub-
shell are in the same atomic subshell. This is why we can apply the Pauli prin-
ciple to exclude certain term symbols. If the electrons are in differentsubshells
(as in an excited state), then we could not use the Pauli principle in this way,
and more term symbols would be necessary to describe the possible inter-
actions of the angular momenta.
All atoms having an electron configuration with a p^2 valence subshell have
the same possible term symbols. A similar statement is possible for any elec-
tron configuration of a valence subshell: atoms having the same configuration
have the same term symbols. Furthermore, it can be shown that atoms having
an electron configuration p^4 have the same term symbols as those having a p^2
configuration. Atoms having a d^2 configuration have the same term symbols
as a d^8 atom, and so on. In general, if a subshell can hold a maximum ofm
electrons, then the configuration ofm nelectrons has the same term sym-
bols as the configuration ofnelectrons. (For example,d^2 and d^8 configura-
tions have the same term symbols,d^3 and d^7 do also, and so on.) What this all
implies is that there are only a limited number of possible term symbols for
electron configurations. Table 15.1 lists those term symbols for electron con-
figurations of various valence subshells. Remember that closed shells do not
contribute any net angular momentum (orbital or spin), so the only subshell
that must be considered is any unfilled subshell.
15.5 Multiple Electrons: Term Symbols and Russell-Saunders Coupling 529
Table 15.1 Term symbols for partially filled subshells
Subshell Term symbols
s^12 S
p^1 ,p^52 P
p^2 ,p^41 S,^1 D,^3 P
p^32 P,^2 D,^4 S
d^1 ,d^92 D
d^2 ,d^81 S,^1 D,^1 G,^3 P,^3 F
d^3 ,d^72 P,^2 D,^2 D,^2 F,^2 G,^2 H,^4 P,^4 F
d^4 ,d^61 S,^1 S,^1 D,^1 D,^1 F,^1 G,^1 G,^1 I,^3 P,^3 P,^3 D,^3 F,^3 F,^3 G,^3 H,^5 D
d^52 S,^2 P,^2 D,^2 D,^2 D,^2 F,^2 F,^2 G,^2 G,^2 H,^2 I,^4 P,^4 D,^4 F,^4 G,^6 S
Note: Atoms having completely filled subshells all have a single^1 S term.