Chemistry Reference
In-Depth Information
Quantitative analysis of the absorption intensity affords values of the forma-
tion constants (
K
DA
) and extinction coefficients (
ε
CT
)listedinTable1for
comparison with the corresponding characteristics of the bromide complexes
with tetrabromomethane.
2.4
Unified Mulliken Correlations of Donor/Acceptor Complexes
with Halogen Derivatives
According to Mulliken [29-31], the donor/acceptor associates such as those in
Eqs 1 and 2, are described via the ground-state (
Ψ
GS
)andexcited-state(
E
ES
)
wave functions expressed as the combination of the principal non-bonded
van der Waals (
ψ
D,A
)anddative(
ψ
D
+
A
-
)states:
Ψ
GS
=a
ψ
D,A
+b
ψ
D
+
A
-
(3a)
Ψ
ES
=b
ψ
D,A
-a
ψ
D
+
A
-
,
(3b)
and the energies of ground and excited states
E
GS
and
E
ES
are:
E
D
+
A
-
-
E
D,A
2
+4
H
DA
1
/
2
E
GS, ES
=
E
D,A
+
E
D
+
A
-
/
2
±
/
2,
(4)
where
E
D,A
=
ψ
D
+
A
-
represent the en-
ergies of the van der Waals and dative states, respectively, and
H
DA
=
∫
ψ
∫
ψ
D,A
H
ψ
D,A
and
E
D
+
A
-
=
∫
ψ
D
+
A
-
H
D
+
A
-
represents the electronic coupling matrix element. The optical
(charge-transfer) transition is related to electron promotion from the ground
to the excited state:
D,A
H
ψ
ν
CT
=
E
ES
-
E
GS
=
E
D
+
A
-
-
E
D,A
2
+4
H
DA
1
/
2
h
.
(5)
In a series of structurally related donors with the same acceptor, or the same
donor with various acceptors, the electronic coupling element (
H
DA
)asde-
termined mostly by orbital overlap, are usually rather invariant. As such, the
changes of the absorption energy in such a series are determined mainly by
differences in the energy gap (
E
D
+
A
-
-
E
D,A
) related to the donor/acceptor
properties (i.e., HOMO/LUMO energies). In solution, these properties are
quantitatively evaluated as the oxidation and reduction potentials,
E
ox
and
E
red
, respectively, to represent the conversion energy of the donor to its
cation-radical, and the acceptor to its anion-radical. The gas-phase mea-
sures of the ionization potential (IP) and electron affinities (EA) represent
alternative and closely related measures of donor and acceptor strengths, re-
spectively [63, 64]. Equation 5 thus predicts an essentially linear relationship
between the absorption energy for the series of associates involving the same
acceptor on the oxidation (or ionization) potential of the donors. Likewise, in
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