Conformational Changes in Ultrafast Internal Conversion
A R T I C L E S
than about 2.4 calls for unrealistic vibrational frequencies, as
conversion from V′ ) 0 will be most efficient at such
intersections and thereby unites perturbation theory-based
-
1
25
typically vibrational frequencies do not exceed 4000 cm . To
quantify the weak energy gap dependence, we have examined
the derivative of plots as in Figure 6B for the combinations of
displacement and vibrational energy that fitted the data in Figure
approaches and quantum theoretical calculation methods. Note
that IC from levels other than V′ ) 0 could present an additional
source for deviations from standard energy gap law behavior.25
Initially, the electronic energy should predominantly be con-
verted into vibrational energy of those vibrational coordinates
along which such (conical) intersections occur. This opens up
the possibility of identifying the modes most active in the
internal conversion process by performing picosecond time-
resolved resonance Raman scattering experiments.26 Quantum
theoretical modeling of ultrafast IC aimed at identifying a
4
B. For both D ) 2.4 and D ) 3.3, the first derivative of the
logarithmic plots appears to be about 2.1 times higher at V )
4.5 than in the energy range covering our experimental data.
Plots of the first derivative further indicate that for both D )
.4 and D ) 3.3, true energy gap law behavior, exemplified by
2
2
a constant value for the derivative, has not been reached yet at
V ) 25. In the case of the fit with D ) 5.4, the experimental
data fall in the high end of our calculated range: V ) 23-25.
Experimental information on the displacement is in principle
attainable from the intensity pattern of the vibronic progression
in the absorption spectrum. However, large displacements are
expected if the excited-state structure of the molecule differs
significantly from the electronic ground-state structure. The
excited-state PES will then not only be displaced, but also have
a different shape (and associated force constant k). As a
consequence, the vibronic structure of the progression V ) 0
f V′ will in practice not be representative for that of V r V′ )
1
5
coupling mode and tuning modes is therefore supported by
our analysis.
Finally, one may wonder if the results in Figure 4 justify
pico- and femtosecond time scales for internal conversion
processes. For this, we return to Siebrand and Williams’
9-11,27
work
on T1 f S0 and S1 f S0 internal conversion in
11,27
hydrocarbons. They introduced the parameter R(E0),
which
can be interpreted as the maximum IC rate that is reached for
27
a Franck-Condon factor of 1. Their analysis on hydrocarbons
13
14 -1
led to a value R(E0) ≈ 10 -10 s . The FC-factors at 30 000
cm for the plots in Figure 4B are 0.0066 (D ) 2.4), 0.0061
D ) 3.3), and 0.0064 (D ) 5.4). Although the value of R(E0)
2
2
0
.
Another complication is that inhomogeneous and lifetime
-
1
broadening (due to ultrafast IC) often results in very little
discernible vibronic structure in absorption spectra of these
molecules, as is the case for 6-nitro-BIPS. On the other hand,
low-temperature spectra of merocyanine isomers of spiropyrans
do have clear vibronic progressions in nonpolar media. On the
basis of such spectra, we derive for the merocyanine of BIPS
(
may not be a universal constant for all types of molecules,
combining these two pieces of information indicates that for
the spiropyran molecule IC time constants in the order of 1-10
ps are fully in line with expectations. Clearly, large conforma-
tional differences between the excited and the ground state can
explain ultrafast IC, within the theoretical framework of the
23
at 10 K in argon a displacement D ) 1.9, and for the
merocyanine of 6-nitro-BIPS in methylcyclohexane at 77 K D
“
energy gap law”. On the other hand, we predict that these
)
1.5. These numbers suggest that certainly displacements of
molecules will typically not exhibit the standard energy gap
law behavior.
about D ) 2-3, as encountered in fitting the data in Figure
4
B, are not beyond reason.
Our findings have important implications for many chemical
processes, as chemical reactions by definition involve confor-
mational and structural changes. For instance, it opens interesting
avenues in the design of efficient photochromic switches.
Depending on the exact conformational changes that accompany
different electronic transitions, a tradeoff could be achieved
between ultrafast IC and rapid “internal” conversion to photo-
products. This is illustrated by efficient subpicoseond photo-
product formation in the dihydroazulene/vinylheptafulvene
photochromic switch, which has been ascribed to a conical
intersection of the reactant excited electronic state and the
The concept of large conformational changes upon optical
excitation, forwarded here, even provides a further rationale to
the relevance of conical intersections for ultrafast internal
conversion.1
4,15
Analysis of the data in Figure 6A reveals the
following relation between the vibrational quantum number with
maximum Franck-Condon factor and the displacement:
1
2
VFCmax ) / (D - 1)
D g 1
2
and
28
VFCmax ) 0
D e 1
photoproduct electronic ground state. Enhancing photochem-
istry quantum yields over IC, or vice versa, could also be an
important function of protein structures in biochemistry. As a
The condition of energy conservation during the actual internal
conversion process then requires that the excited-state PES is
raised above the ground-state PES by hνVFCmax. Graphically,
this always corresponds to a situation as depicted in Figure 1,
where the ground-state PES exactly crosses through the bottom
of the excited-state PES. Coupling of PESs at crossings can
lead to conical intersections.24 Our result indicates that internal
1
2,13,29
prime example, we mention the GFP system.
Quantum
mechanical calculations led to the conclusion that the two halves
of the free GFP chomophore are planar in the S0 electronic state,
2
9
while they are perpendicular in the S1 state. The high
fluorescence quantum yield of the GFP chromophore in the
(
25) Reference 14 mentions the question whether IC takes place at the absolute
minimum of the PES or also at other “points” as an important issue in
research on conical intersections.
(
22) So-called “mirror symmetry” of absorption and fluorescence requires the
same force constant for excited- and ground-state PESs, as well as
symmetrical PESs around the coordinate y
V(y - y) ) V(y + y).
0
where V is minimum, that is:
(26) Kozich, V.; Werncke, W.; Vodchits, A. I.; Dreyer, J. J. Chem. Phys. 2003,
118, 1808.
0
0
(
(
23) Ernsting, N. P.; Arthen-Engeland, T. J. Phys. Chem. 1991, 95, 5502.
24) Yarkony, D. R. Acc. Chem. Res. 1998, 31, 511. This paper points out that
for molecules of three atoms or more, even states of the same symmetry
are permitted to intersect, instead of resulting in an avoided crossing
(27) Siebrand, W.; Williams, D. F. J. Chem. Phys. 1968, 49, 1860.
(28) Boggio-Pasqua, M.; Bearpark, M. J.; Hunt, P. A.; Robb, M. A. J. Am.
Chem. Soc. 2002, 124, 1456.
(29) Voityuk, A. A.; Michel-Beyerle, M.-E.; R o¨ sch, N. Chem. Phys. Lett. 1998,
296, 269.
(“noncrossing rule”).
J. AM. CHEM. SOC.
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VOL. 126, NO. 12, 2004 3793