Term Symbols in Strong Field Limit
In Class Activity
• determine the term symbols for the (eg)2 configuration, draw out the 6
possible microstates for this configuration and identify the multiplicity of
each state
o determine the state term symbols from taking the direct product of the
orbitals occupied
(e2 g )2 = Eg ⊗ Eg = A1g + A2 g + Eg
o the multiplicities associated with each state cannot be determined just
from the direct product, however looking back at Figure 4 from the notes
(e2 g )2 = Eg ⊗ Eg = 1 A1g + 3 A2 g + 1Eg
o working out the individual states and their spin/multiplicity:
eg
eg
eg
eg
S=1 multiplicity 2S+1=3
S=0 multiplicity 2S+1=1
eg
eg
Figure 1 Multiplicities
In Class Activity
• What is the ground state term symbol for [Cr(NH3)6)]Cl3? How many
transitions can be expected for the Cr ion? What are the possible transitions?
What is the electronic configuration for each state? Would you expect all of
these to be visible in a UV-vis spectrum?
o first work out the dn configuration,
Cr is in group 6, d6 in zero
oxidation state, ammonia ligands
are neutral, the Cl are -1 each so
the complex must be [Cr(NH3)6)]3+
so removing 3e for the charge
gives d3.
o using the Tanabe-Sugano diagram,
Error! Reference source not
found., the ground state term
symbol at the free ion is 4F and in
the strong field is 4A2g
we can associate these transitions
with specific electronic
configurations, assuming spin
conservation, the allowed
excitations are to the 4T2g 4T1g(P)
Figure 2 Tanabe-Sugano diagram for d31
and 4T1g levels
1
diagram from http://wwwchem.uwimona.edu.jm/courses/Tanabe-Sugano/TScalcs.html, 25Feb
2014
1
o the 4T1g(P) is much higher in energy and may be outside of the visible
range.
o none of these levels cross so the excitation states will not change with the
ligand field
o now we consider the relevant electronic configurations.
o the ground state is (t2g)3 with multiplicity of 4, there are 3 unpaired
electrons, the term symbols for d3 cannot be determined from the direct
product, we must use Table 1 from the notes,
(t 2 g )3 = 4 A2 g + 2 Eg + 2T1g + 2T2 g
o this result is consistent with the Tanabe-Sugano diagram, the ground state
must be 4A2g as this is the only symbol with a multiplicity of 4
o possible excitations conserving spin are (t2g)2(eg)1 and (t2g)1(eg)2 we do not
consider (t2g)0(eg)3 because that would require a spin change
(t 2g)3
4A
2g
(t 2g)2(e g)1
4
4T
1g T2g
(t 2g)1(e g)2
4T
1g
Figure 3 Possible distributions of electrons for d3
o we could try to determine the state term symbols from taking the direct
product of the orbitals occupied, information for the basic configurations
(ie (t2g)2 etc) taken from Table 2 in the notes
(t 2 g )2 (eg )1 = (A1g + Eg + T1g + T2 g ) ⊗ Eg = Eg + (A1g + A2 g + Eg ) + (T1g + T2 g ) + (T1g + T2 g )
(t 2 g )1 (eg )2 = T2 g ⊗ (A1g + A2 g + Eg ) = T2 g + T1g + (T1g + T2 g )
o it is clear the lowest energy states cannot be determined just from the
direct product, however looking at the Orgel diagrams from the notes
these are:
(t 2 g )2 (eg )1 ⇒ 4T1g + 4T2 g
(t 2 g )1 (eg )2 ⇒ 4T1g
o thus the transitions to the 4T2g and 4T1g states are single excitations while
the transition to the 4T2g(P) state (the P is known from the Tanabe-Sugano
diagram) is a double excitation
o using the the Tanabe-Sugano diagram we might also expect to see one or
two very weak spin-forbidden transitions to the 2T1g and 2Eg levels
o thus overall we can expect to see two lower energy excitations, the higher
energy one may be in the UV or hidden by higher energy transitions such
as charge transfer
o we may also so some lower energy spin forbidden transitions, a weak
signal from the spin forbidden transition (t2g)3(eg)0 an 2Eg state now with
two electrons paired.
o the spectrum below (Figure 4) is that for [Cr(NH3)6)]3+, weak 2Eg spinforbidden transitions appear below the d-d forbidden 4A2g(F)→ 4T1g, 4T2g
transitions, a strong charge transfer band dominates at higher energies, we
can assume that NH3 is a relatively high field ligand with a Δoct/B of
greater than ≈2
2
500nm
λ/nm
200nm
800nm
Figure 4 Sketch of the spectrum for [Cr(NH3)6)]
3+
o relevant transitions are shown on an energy diagram for ML6 for L=sigma
ligand below, Figure 5. The CT band is shown in grey, note that the
ligand based eg level is not used because this would be parity forbidden
and thus would not give rise to an intense transition, the transition must be
from the t1u levels.
t1u
a1g
a1g
4p
t1u
eg
4s
a1g
eg
3d eg t 2 g
t2 g
eg
t1u
a1g
eg
t1u
eg
t1u
z
a1g
L
L
L
y
L x
L
L
L
L
M
L
L
M
L
L
L
L
L
L
L
L
Figure 5 Energy diagram for ML6 for L=sigma ligand: [Cr(NH3)6)]
3
3+