Chemistry Reference
In-Depth Information
high energy
electron
LUMO
h
ν
E
low energy
hole
HOMO
1
GS
1
ES
Figure 8.3
The change in electronic confi guration following excitation by light of a singlet
ground state chromophore (
1
GS) to a singlet electronic excited state (
1
ES) (HOMO = highest
occupied molecular orbital, LUMO = lowest unoccupied molecular orbital)
ES
GS
f
∝
∫
ψµψ
d
v
e1
e1
(8.1)
where
f
, the oscillator strength, is proportional to the integral of the product of the
GS and ES wavefunctions (y )and m, the electric dipole moment operator. The spin
selection rule states that for an electronic transition to be allowed, the spin multi-
plicity of the ground state and excited state must be the same. Electronic transitions
which are allowed by donor-acceptor orbital electronic coupling, symmetry and
electron spin are the most intense, with extinction coeffi cients, e, of
10
3
M
− 1
c m
− 1
.
Transitions which are allowed by spin, but formally forbidden by symmetry have e
between 10
0
and 10
2
M
− 1
c m
− 1
. Truly spin-forbidden transitions are not observed.
Relaxation of the selection rules can give rise to observation of transitions that are
formally forbidden. In the presence of a heavy atom, spin-orbit coupling relaxes the
spin-selection rule, giving rise to absorptions that are formally spin forbidden dis-
playing e as high as 10
3
M
− 1
c m
− 1
.
Electronic transitions often are accompanied by vibronic excitation. The con-
version between electronic energy surfaces, moving from the
1
GS to the
1
ES, is dic-
tated by the Franck-Condon principle (Figure 8.4). Electronic transitions following
absorption of a photon,
h
n, are rapid, populating the
1
ES in a nuclear confi guration
consistent with the
1
GS. The
1
ES is populated in a hot vibronic state (n
n
, where
n
is
an integer
≥
0). Vibronic relaxation to the lowest vibronic states is rapid with a rate
constant
k
vib
>
10
12
s
− 1
. Depopulation of the
1
ES to the
1
GS occurs at varying rates,
with rate constants of the decay processes greatly depending on the nature of the
1
E S .
>
8.2.2 Unimolecular Electronic Excited State Decay
The quantum effi ciency of ES processes is an important description of the relative
kinetics of ES decay. Decay from the ES by a specifi c pathway,
x
, is quantifi ed by
the quantum yield, F
x
. The quantum yield is the probability of a molecule in its
excited state decaying by a specifi c pathway. Quantum yield is defi ned as the ratio
of the observed fi rst-order rate constant of the process of interest,
k
x
, divided by the
sum of the rate constants of all pathways depopulating that state,
Σ
k
, Equation 8.2:
