A method of determination of quantum yields of
S
3
S
2
,
S
3
S
1
,
and
S
3
S
0
intramolecular radiationless transitions
Andrzej Maciejewski
a)
Apparatus Laboratory, Adam Mickiewicz University, Grunwaldzka 6, 60-780 Poznan
´
, Poland and Faculty
of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60-780 Poznan
´
, Poland
Marek Milewski
Faculty of Chemistry, Adam Mickiewicz University, Grunwaldzka 6, 60-780 Poznan
´
, Poland
Marian Szyman
´
ski
Institute of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznan
´
, Poland
͑Received 6 January 1999; accepted 13 August 1999͒
An effective method for determination of the quantum yields of the S
3
S
2
, S
3
S
1
and S
3
S
0
intramolecular radiationless transitions, based on steady-state measurements of absorption, S
2
fluorescence and T
1
phosphorescence or S
1
fluorescence under selective excitation to the S
2
and S
3
states has been described and used for three aromatic thioketones. The results show that in the
compounds studied the deactivation of the S
3
state is not strictly sequential and the S
3
S
1
as well
as, unexpectedly, S
3
S
0
transitions occur with relatively high yields. Measurement of the quantum
yields of S
3
S
2
, S
3
S
1
, and S
3
S
0
intramolecular radiationless transitions is essential for the
determination of the intramolecular properties of molecules in the S
3
state as well as pathways of
their decay. © 1999 American Institute of Physics. ͓S0021-9606͑99͒00542-5͔
INTRODUCTION
The rate of the radiationless transitions between two
electronic states is governed by the Fermi Golden Rule. Ap-
plying the Born–Oppenhimer approximation, it can be writ-
ten in the form
1–6
k
nr
ϭ
2
h
B
2
F, ͑1͒
where B is the electronic coupling matrix element between
the two states,
is the effective density of the vibrational
states in the final electronic state equiergic with the initially
populated state, and F is the Franck–Condon factor at the
appropriate energy. For many groups of compounds, a linear
correlation between F and exp(Ϫ⌬E), where ⌬E is an en-
ergy difference between the lowest vibrational states of the
two electronic states, has been reported.
1–7
Usually it is as-
sumed that B and
do not differ substantially for a certain
transition within a group of similar compounds. If this is the
case, an inverse proportionality between lnk
nr
and ⌬E is
observed.
1,2,7–15
This relation between k
nr
and ⌬E is known
as the Energy Gap Law.
1–6,16
Validity of the Energy Gap
Law has been confirmed in studies of the same transition for
a number of groups of compounds, including the cases of the
T
1
S
0
transition in aromatic hydrocarbons
2,10,17
and the
S
2
S
1
transition in azulene and its derivatives.
7,8,11
As follows from the Energy Gap Law, fluorescence is
usually preceded by a quantitative stepwise internal conver-
sion to the fluorescent state S
fl
.
S
0
ϩh
→S
n
͑Scheme 1͒.
S
n
→
IC
S
nϪ1
→
IC
S
nϪ2
¯S
flϩ1
→
IC
S
fl
According to Kasha’s rule
18
the fluorescent state is the S
1
one, but for a number of compounds including azulene and
its derivatives
7,8,19
as well as thioketones
9,20
it is the second
excited singlet state. The mechanism consistent with Scheme
1 leads to Vavilov’s rule,
21
which states that fluorescence
quantum yield does not depend on the excitation wavelength
over the whole absorption spectrum. Such a mechanism does
not describe the transitions from higher excited states to the
ground state bypassing one or more of the lower excited
states. However, to the best of our knowledge, no convincing
and unambiguous experimental evidence for a fully sequen-
tial mechanism of the deactivation of higher excited states
(S
n
, nу3͒ has been given in the literature, although such a
mechanism is usually assumed to describe the deactivation
of higher excited singlet states properly. A constant quantum
yield of fluorescence from the S
1
state, independent of the
excitation wavelength has been reported for quinine
sulfate,
22
Rhodamine B,
23
and Rhodamine 101.
24
However,
even for these compounds it is not obvious whether the in-
ternal conversion to the fluorescent state is really sequential
or runs partly with bypassing one or more excited singlet
states lying above S
1
. On the basis of measurements of fluo-
rescence quantum yield and the shape of emission spectra
under two-step excitation, Ermolaev et al.
25
have found that
for some aromatic hydrocarbons and dyes the deactivation of
higher excited states seems to follow Scheme 1. However,
the uncertainty of their measurements ͑ϳ50% error of fluo-
rescence quantum yields͒ makes a fully quantitative analysis
of the data impossible.
a͒
Corresponding author. Electronic mail: maciejew@rovib.amu.edu.pl
JOURNAL OF CHEMICAL PHYSICS VOLUME 111, NUMBER 18 8 NOVEMBER 1999
84620021-9606/99/111(18)/8462/7/$15.00 © 1999 American Institute of Physics