C.A. Zoto, R.E. Connors / Journal of Molecular Structure 982 (2010) 121–126
125
Table 4
8.00x109
6.00x109
4.00x109
2.00x109
0.00x100
TD-DFT computed energy gaps between the lowest (n, pꢁ) and (
p,
pꢁ) states and
23
6
experimental knr
.
22
CCl4
Toluene
CHCl3
T3(n, pꢁ)–T1(
p
,
pꢁ
pꢁ
)
)
7138 cmꢃ1
4465 cmꢃ1
57.7
7234 cmꢃ1
4592 cmꢃ1
17.0
8112 cmꢃ1
5384 cmꢃ1
3.37
18
1
21
16
17
S2(n, pꢁ)–S1(
p,
knr ꢂ 10ꢃ8/sꢃ1
19
20
15
2
pꢁ)–T (n, pꢁ) energy gap relative to kBT. In this
pꢁ and n, pꢁ states in
12
13
tude of the S1(p,
mechanism, spin–orbit coupling between p,
different spin manifolds and vibronic coupling within the same
spin manifold are operative in promoting intersystem crossing.
3
4
5
8
9
10
14
pꢁÞ SOC ! Tmðn; pꢁÞ VC ! T1ð
p
;
pꢁ
pꢁ
Þ
Þ
11
7
S1ð
p
p
;
;
S1ð
pꢁÞ VC ! Smðn; pꢁÞ SOC ! T1ð
p;
12000
14000
16000
18000
20000
νf (cm-1)
A solvent induced increase in the spacing between S1/T1 and the
appropriate intermediate n, pꢁ state(s) attenuates the degree of
state mixing which in turn reduces the rate of S ? T intersystem
crossing [22]. Both the thermally activated mechanism and the
vibronic spin–orbit coupling mechanism are favored over direct
Fig. 8. Nonradiative decay constant plotted against fluorescence maxima of I in
various solvents. Circles represent aprotic solvents; diamonds represent protic
solvents.
spin–orbit coupling between S1(p, p,
pꢁ) and T1( pꢁ) because of
positions for their fluorescence maxima, suggesting a hydrogen
bonding influence on the nonradiative decay of I. In discussing
the major routes for nonradiative decay in aprotic solvents, we
separate the data in Fig. 8 into two regions, the region from the
minimum to the low frequency side (region 1) and the region from
the minimum to the high frequency side (region 2). In region 1, knr
the well established understanding that the matrix element for
spin–orbit coupling between states of different orbital configura-
tion is greater than the matrix element for spin–orbit coupling be-
tween states of the same orbital configuration [23]. The smooth
decrease in knr shown in region 2 is consistent with a gradual, sol-
vent induced increase in the spacing between S1/T1 and higher en-
ergy (n, pꢁ) states. Table 4 provides theoretical support for this
interpretation with the results of TD-DFT calculations modeled in
CCl4, toluene, and CHCl3 solvent environments. It is seen that there
is an inverse relation between the magnitude of the computed en-
increases from 3.3 ꢂ 108 sꢃ1 (o-dichlorobenzene,
m )
f = 16,000 cmꢃ1
to 5.9 ꢂ 109 sꢃ1 (acetonitrile,
m
f = 13,868 cmꢃ1). In region 2, knr de-
creases from 5.8 ꢂ 109 sꢃ1 (CCl4,
m
f = 19,487 cmꢃ1) to 3.4 ꢂ 108 sꢃ1
(CHCl3, m
f = 16,597 cmꢃ1). Noting that knr = kic + kisc, where kic is the
rate of internal conversion from S1 to S0 and kisc is the rate of inter-
system crossing from the singlet to the triplet manifold of states,
we believe that the variation in knr shown in Fig. 8 can be attrib-
uted to opposing behavior for these two rates with respect to sol-
ergy gaps between the lowest (n, pꢁ) and ( pꢁ) states and the
p,
experimental values for knr. At this level of theory, the qualitative
trend calculated is expected to be more meaningful than the nu-
meric values calculated for the (n, pꢁ)–( pꢁ) energy gaps. It is pos-
p,
vent polarity. In shifting from nonpolar (high
(low f), kic increases while kisc decreases. In region 1, where knr in-
creases with a decrease in f, the increase in kic dominates the de-
crease in kisc; whereas in region 2, where knr decreases with a
decrease in f, the decrease in kisc dominates the increase in kic.
mf) to polar solvents
sible that a combination of thermally activated and vibronic spin–
orbit coupling mechanisms contribute to solvent dependent S ? T
intersystem crossing observed for I at room temperature.
The radiative rates (kf) vary less with solvent and, although
somewhat scattered, show a general trend toward lower values
m
m
m
The order of magnitude increase in knr found in region 1 is
attributed to the energy gap law for internal conversion which pre-
dicts an exponential dependence of kic on the S0–S1 energy gap,
with lower mf, as predicted by Einstein’s treatment of electronic
transitions [24].
(D
E).
4. Conclusion
kic
¼
a
expðꢃb
D
EÞ
ð6Þ
The spectroscopic and photophysical properties of I have been
found to vary considerably with solvent. The natures of the low ly-
ing excited states have been assigned with the assistance of exper-
imental and theoretical data. The behavior of knr with respect to
fluorescence wavelength and solvent polarity can be divided into
two regions. In region 1, the increase in the rate of internal conver-
sion dominates the decrease in the rate of intersystem crossing;
whereas in region 2, intersystem crossing is the dominant channel
of decay from S1.
According to the energy gap law, kic is expected to increase as
the S0–S1 energy gap decreases due to greater vibrational overlap
(Frank–Condon factor) between the S0 and S1 states [18].
In region 2, where intersystem crossing is the major nonradia-
tive decay channel, we believe that the solvent modulated location
of (n, pꢁ) states relative to the S1( pꢁ) and T1( pꢁ) states influ-
p, p,
ences the rate of S ? T intersystem crossing. The positions of (n,
pꢁ) states and ( pꢁ) states behave differently under the influence
of a change in solvent polarity. Whereas (n, pꢁ) states undergo a
hypsochromic shift with increased solvent polarity; (
pꢁ) states
undergo a bathochromic shift [19]. Data presented in Fig. 5 and Ta-
ble 2 confirm the bathochromic shift expected for S1(
pꢁ). A
mechanism involving thermally activated intersystem crossing
from S1(
pꢁ) to a higher lying 3(n, pꢁ) state has been offered to ex-
p,
The variation in the rates of internal conversion and intersystem
crossing are interpreted to be related to solvent induced changes in
energy gaps on the singlet and triplet spin manifolds.
p,
p,
p,
References
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intersystem crossing mechanism in its requirement for the magni-
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