144
6 Interactions
Table 6.5 Transfer-term contributions to 1 A 1 → 1 E CT transitions, with ψ and χ acceptor orbitals
ψ ligand orbitals
χ ligand orbitals
1 E(a 1 → e(ψ))
0
1 E(a 1 → e(χ))
√
2κ ′
1 E(e → a 2 (ψ))
3
2 κ
1 E(e → a 1 (χ ))
1
√
2
κ ′
1 E(e → e(ψ))
3
2 κ
1 E(e → e(χ))
1
√
2
κ ′
The resulting state transition-moments are then expressed in terms of orbital
transition-moments as:
1 A 1 |µ|
1 E θ (e → a 2 )
=
√
2
e ǫ (t 2 g)|µ|a 2 (ψ)
=
3/2κ
1 A 1 |µ|
1 E θ (e → e)
= 2
e θ (t 2 g)|µ|e θ (ψ)
=
3/2κ
(6.108)
On the other hand, the a 1 (t 2g ) orbital does not delocalize over the ligands. As a
result, there can be no transfer term associated with transitions from this orbital. One
expects only a weak contact term. The lowest transition corresponds to a 1 (t 2g ) →
a 2 (ψ). The only non-zero coupling coefficient for this transition is A 1 |A 2 A 2 .This
transition will thus be dipole allowed under μ z ′ . Polarized absorption spectra are
in line with this analysis: the spectral onset of the CT region is characterized by
a weak absorption band in parallel polarization, followed by two strong absorption
bands in perpendicular polarization. This assignment is based on the assumption that
the vertical Franck–Condon excitations reach delocalized charge-transfer states. At
least in the case of Ru(bipy)
2+
3 , this is supported by detailed spectral measurements
[18]. An entirely similar analysis can be performed in the case when the ligand
orbital is of χ -type. The transition-moments are collected in Table 6.5. In this case,
the ligand and metal part both transform as a 1 + e (see Table 6.4). As a result, three
transitions are found to carry transfer-term intensity, as indicated in Fig. 6.6.
Circular Dichroism
The tris-chelate compounds are chiral compounds, with an apparent helical structure, which can easily be related to their circular-dichroic properties by use of
symmetry selection rules. The CT transitions that we have just discussed cannot
be responsible for the primary CD strength, since they are in-plane polarized, and
thus do not carry intrinsic helicity. Instead, the prominent peaks in the CD spectrum are observed at higher energies, and are associated with the intra-ligand ππ ∗ -
transitions. These transitions take place between occupied and virtual ligand-centred
orbitals which are of opposite signature, and hence are of type ψ → χ or vice-versa.
Such transitions are long-axis polarized, i.e. the transition dipole moment is oriented
along the ligand bridge as shown in Fig. 6.7.
6 Interactions
Table 6.5 Transfer-term contributions to 1 A 1 → 1 E CT transitions, with ψ and χ acceptor orbitals
ψ ligand orbitals
χ ligand orbitals
1 E(a 1 → e(ψ))
0
1 E(a 1 → e(χ))
√
2κ ′
1 E(e → a 2 (ψ))
3
2 κ
1 E(e → a 1 (χ ))
1
√
2
κ ′
1 E(e → e(ψ))
3
2 κ
1 E(e → e(χ))
1
√
2
κ ′
The resulting state transition-moments are then expressed in terms of orbital
transition-moments as:
1 A 1 |µ|
1 E θ (e → a 2 )
=
√
2
e ǫ (t 2 g)|µ|a 2 (ψ)
=
3/2κ
1 A 1 |µ|
1 E θ (e → e)
= 2
e θ (t 2 g)|µ|e θ (ψ)
=
3/2κ
(6.108)
On the other hand, the a 1 (t 2g ) orbital does not delocalize over the ligands. As a
result, there can be no transfer term associated with transitions from this orbital. One
expects only a weak contact term. The lowest transition corresponds to a 1 (t 2g ) →
a 2 (ψ). The only non-zero coupling coefficient for this transition is A 1 |A 2 A 2 .This
transition will thus be dipole allowed under μ z ′ . Polarized absorption spectra are
in line with this analysis: the spectral onset of the CT region is characterized by
a weak absorption band in parallel polarization, followed by two strong absorption
bands in perpendicular polarization. This assignment is based on the assumption that
the vertical Franck–Condon excitations reach delocalized charge-transfer states. At
least in the case of Ru(bipy)
2+
3 , this is supported by detailed spectral measurements
[18]. An entirely similar analysis can be performed in the case when the ligand
orbital is of χ -type. The transition-moments are collected in Table 6.5. In this case,
the ligand and metal part both transform as a 1 + e (see Table 6.4). As a result, three
transitions are found to carry transfer-term intensity, as indicated in Fig. 6.6.
Circular Dichroism
The tris-chelate compounds are chiral compounds, with an apparent helical structure, which can easily be related to their circular-dichroic properties by use of
symmetry selection rules. The CT transitions that we have just discussed cannot
be responsible for the primary CD strength, since they are in-plane polarized, and
thus do not carry intrinsic helicity. Instead, the prominent peaks in the CD spectrum are observed at higher energies, and are associated with the intra-ligand ππ ∗ -
transitions. These transitions take place between occupied and virtual ligand-centred
orbitals which are of opposite signature, and hence are of type ψ → χ or vice-versa.
Such transitions are long-axis polarized, i.e. the transition dipole moment is oriented
along the ligand bridge as shown in Fig. 6.7.