Microstate Table for p2
Microstate table for p2 and its reduction to free-ion terms
Term splitting for carbon (1s22s22p2). The 3P, 1D and 1S terms are split as a result
of electron-electron repulsion. The 3P term is further split as a result of spin-orbit
coupling.
Terms for various electron configurations
Microstates table for a d2 ion:
MS
ML
+1
4
3
2
1
0
-1
-2
-3
-4
1x
1x
2x
2x
2x
1x
1x
0
1x
2x
3x
4x
5x
4x
3x
2x
1x
-1
1x
1x
2x
2x
2x
1x
1x
There is a total of 45 microstates.
Highest term: G (because L = 4)
For L = 4: ML = 4, 3, 2, 1, 0, -1, -2, -3, -4
There is only one column that contains microstates for all these ML values: this is
the central MS = 0 column.
Therefore, the G term is a singlet term: 1G.
There are a total of 9 microstates associtated with the 1G term. Taking these out of the
table leads to the following reduced microstates table:
MS
ML
3
2
1
0
-1
-2
-3
+1
1x
1x
2x
2x
2x
1x
1x
0
1x
2x
3x
4x
3x
2x
1x
The next highest term is: F (because L = 3).
For L = 3: ML = 3, 2, 1, 0, -1, -2, -3
All three MS columns contain microstates for these ML values!
Therefore, the F term is a triplet term: 3F.
There are 3 x 7 = 21 microstates associated with the 3F term.
-1
1x
1x
2x
2x
2x
1x
1x
Taking these out of the table leads to the following reduced microstates table:
MS
ML
+1
2
1
0
-1
-2
1x
1x
1x
0
1x
2x
3x
2x
1x
-1
1x
1x
1x
The next highest term is: D (because L = 2).
For L = 2: ML = 2, 1, 0, -1, -2
There is only one column that contains microstates for all these ML values: this is
the central MS = 0 column.
Therefore, the D term is a singlet term: 1D.
There are 5 microstates associated with the 1D term.
Taking these out of the table leads to the following reduced microstates table:
MS
+1
0
1x
1x
1
1x
2x
0
1x
1x
-1
The next highest term is: P (because L = 1).
For L = 1: ML = 1, 0, -1
All three MS columns contain microstates for these ML values!
Therefore, the P term is a triplet term: 3P.
There are 9 microstates associated with this term.
ML
-1
1x
1x
1x
Taking these out of the table leads to only one remaining microstate with ML = 0 and MS
= 0. This microstate therefore belongs to the 1S term.
Which of the just established terms is the lowest in energy?
1. Apply Hund’s first rule of maximal multiplicity:
3
F, 3P < 1D, 1S, 1G
2. Apply Hund’s second rule: term is highest L value is the ground term
3
F < 3P
3. Apply Hund’s third rule:
3
P: 3P0 < 3P1 < 3P2
3
F: 3F2 < 3F3 < 3F4
For 3d metals spin-orbit coupling is often neglected (i.e. Hund’s third rule is not applied).
In this case the ground term for a 3d2 ion (e.g. V(III)) would be the 3F term.
Electronic spectrum of [Cr(NH3)6]3+
Correlation diagram for a d1 ion in octahedral environment and electronic spectrum of [Ti(H2O)6]3+
Simplified correlation diagram for a d2 ion in octahedral environment and absorption spectrum of
[V(H2O)6]3+
Correlation diagram for d2 in octahedral ligand field
Energy of terms for a d2 configuration (A,B,C are Racah parameters)
Tanabe-Sugano diagram for the d2 configuration
Electronic spectra of octahedral hexaaqua complexes of 3d metals
Tanabe-Sugano diagrams