Ring Opening in the Dehydrocholesterol-Previtamin D Dystem Studied by Ultrafast Spectroscopy

Article abstract of DOI:10.1021/jp952536q

The rate of the electrocyclic ring opening of 7-dehydrocholesterol to previtamin D is investigated by transient absorption spectroscopy with a time resolution better than 300 fs.The dehydrocholesterol, which is a derivative of 1,3-cyclohexadiene, is excited around 267 nm.The primary product, the s-cis,Z,s-cis conformer of the triene previtamin D, appears with a time constant of 5.2 ps.This result is consistent with literature data.We found that it is temperature independent.So there is no activation energy for this electrocyclic ring opening.A barrierless process, on the other hand, is expected to proceed much faster (in about 1E-13 s), unless there is an entropy of activation.The results suggest that the molecule reaches within a few femtoseconds the lowest excited state (2A₁) of the product, from where it goes on through an entropic bottleneck.The primary product isomerizes thermally to the stable s-cis,Z,s-trans conformer of previtamin D within 125 ps in ethanol at room temperature.This time is much longer than the reported corresponding time in the cyclohexadiene/hexatriene system.We found that it depends on the solvent viscosity and on the temperature.The activation energy was determined to be 15.5 +/- 1.0 kJ/mol.

Full text of DOI:10.1021/jp952536q

J. Phys. Chem. 1996, 100, 921-927
921
Ring Opening in the Dehydrocholesterol-Previtamin D System Studied by Ultrafast
Spectroscopy
,
†
†
‡
†
†
Werner Fuss,* Thomas H o1 fer, Peter Hering, Karl L. Kompa, Stefan Lochbrunner,
†
†
Thomas Schikarski, and Wolfram E. Schmid
Max-Planck-Institut f u¨ r Quantenoptik, D-85740 Garching, Germany, and Institut f u¨ r Lasermedizin der
UniVersit a¨ t, D-40001 D u¨ sseldorf, Germany
X
ReceiVed: August 28, 1995
The rate of the electrocyclic ring opening of 7-dehydrocholesterol to previtamin D is investigated by transient
absorption spectroscopy with a time resolution better than 300 fs. The dehydrocholesterol, which is a derivative
of 1,3-cyclohexadiene, is excited around 267 nm. The primary product, the s-cis,Z,s-cis conformer of the
triene previtamin D, appears with a time constant of 5.2 ps. This result is consistent with literature data. We
found that it is temperature independent. So there is no activation energy for this electrocyclic ring opening.
A barrierless process, on the other hand, is expected to proceed much faster (in about 10- s), unless there
is an entropy of activation. The results suggest that the molecule reaches within a few femtoseconds the
13
1
lowest excited state (2A ) of the product, from where it goes on through an entropic bottleneck. The primary
product isomerizes thermally to the stable s-cis,Z,s-trans conformer of previtamin D within 125 ps in ethanol
at room temperature. This time is much longer than the reported corresponding time in the cyclohexadiene/
hexatriene system. We found that it depends on the solvent viscosity and on the temperature. The activation
energy was determined to be 15.5 ( 1.0 kJ/mol.
1
. Introduction
The main feature of the conversion of 7-dehydrocholesterol
cholesta-5,7-dien-3â-ol) to previtamin D (Figure 1) is a ring
(
opening from a cyclohexadiene structure to an open-chain
hexatriene. It is a prototype of the photochemical “electrocy-
clic” reactions. Electrocyclic reactions are cyclizations or
reverse cyclizations of polyenes with a concerted shift of double
and single bonds. The net result is the conversion of a π bond
to a σ bond or vice versa. Like the other pericyclic reactions,
this rearrangement is controlled by the principle of conservation
of orbital symmetry (Woodward-Hoffmann rules).1 In the
particular case of a photochemical reaction, these rules result
in a correlation of the excited state of the educt with the excited
state of the product, whereas each ground state tends to correlate
with a higher excited state. The latter correlation is interrupted
by an avoided crossing (see Figure 1).
Since these rules are only correlation rules, they do not predict
details of the potential surfaces and the actual dynamics: Is it
a direct reaction on a purely repulsive surface (expected rate
1
3 -1
constant about 10 s ), or is there a potential barrier? Where
on the potential energy surfaces does the molecule cross over
to the ground state? Do other states play a role? Questions of
this kind led several groups to investigate such systems.
The time constant of the product formation of dehydrocho-
lesterol was for the first time determined as 4.3 ps by end
Figure 1. Schematic potential energy diagram for the photochemical
ring opening of dehydrocholesterol. The horizontal axis has a large
projection onto the single bond to be opened; it is the reaction
coordinate, until the molecule arrives at the minimum. Then the
molecule leaves the plane of the drawing in the direction of the conical
2
product analysis as a function of the excitation pulse duration:
When dehydrocholesterol was illuminated with short pulses (4
ps), the consecutive photoreaction of the primary product was
partially suppressed and the yield of the corresponding second-
ary product, tachysterol, was significantly reduced compared
to the case with long pulses (5 ns). Reid et al.3 investigated
the analogous system 1,3-cyclohexadiene and its electrocyclic
ring opening by resonance Raman scattering. They presented
evidence that these molecules undergo a rapid (approximately
15
intersection, which is indicated by the broken lines (projection into
1
the plane of paper). Also the maximum of 1A is actually in a different
1
5
plane. The subscripts 1 and 2 for the symmetry types should be
dropped outside the Franck-Condon region, since the conrotatory
reaction does not conserve the (approximate) symmetry planes of the
reactant. The large circle in the formulas encloses the reaction center.
-6
R ) 1,5-dimethylhexyl (C
8
H17).
1
0 fs) radiationless decay from the initially excited state 1B2 to
†
Max-Planck-Institut f u¨ r Quantenoptik.
Institut f u¨ r Lasermedizin der Universit a¨ t.
Abstract published in AdVance ACS Abstracts, December 15, 1995.
‡
the “dark” 2A1 potential energy surface. (The 2A1 state is
connected with the ground state by a smaller transition moment
X
0022-3654/96/20100-0921$12.00/0 © 1996 American Chemical Society

9
22 J. Phys. Chem., Vol. 100, No. 2, 1996
Fuss et al.
7
and is probably very close to 1B2 in cyclohexadiene; for other
polyenes see refs 8-12. Both states correspond to ππ*
excitation.) The ring opening propagates on this surface, until
barrier. An early barrier is required to explain that fluorescence
of 7-dehydrocholesterol has been observed in a low-temperature
2
1
matrix, although at room temperature it is not observed;
cyclohexadiene fluoresces at room temperature with a quantum
6
ps after the initial photoexcitation the ground state hexatriene
appears, which due to its high vibrational temperature then
-6 20
yield of only 2 × 10 . So the existing evidence in part
suggests an early barrier (the fluorescence, the qualitative
consideration, and the early quantum mechanical calculation),
in part no early barrier (the resonance Raman experiments) and
in part a late barrier (the recent quantum mechanical calculation).
Therefore, it seemed important to us to measure the activation
energy by studying the temperature dependence of the reaction
rate.
rapidly isomerizes to its stable conformer.5
,6
These time constants of the ring openings are in reasonable
agreement with each other, but too long for a direct reaction.
The reason for the delay can be an activation energy or barrier,
an activation entropy or statistical factor, or another bottleneck.
The traditional view of a groundstate forbidden, photochemically
allowed reaction is that there is an avoided crossing, which
creates a minimum in the excited potential surface along the
reaction coordinatesthe so-called pericyclic minimumsand a
In this work, we use the technique of femtosecond transient
absorption spectroscopy to study the ring-opening reaction of
dehydrocholesterol. This time-resolved measurement of tran-
sient excited and intermediate state absorption provides a direct
observation of the time required for the electrocyclic reaction.
We found that it is temperature independent, whereas the
subsequent conformational rearrangement depends on the tem-
perature and on the solvent viscosity in the expected way.
1
3
corresponding maximum of the ground state potential. This
is shown in Figure 1, which is based (with some modifications)
on an early quantum mechanical calculation.14 The energy gap
between minimum and maximum might present a bottleneck
for the reaction. However, in a more recent quantum mechanical
investigation, Celani et al.15 found that with an additional
distortion of the molecular frame, the surfaces can come much
closer and in fact touch each other in a conical intersection
2. Experimental Section
6-18
(
Figure 1). More work of this kind1
has shown that such
The photochemical reaction of 7-dehydrocholesterol to pre-
vitamin D was studied by transient absorption measurements
with femtosecond pulses. Dehydrocholesterol was excited by
intense, frequency-tripled pulses (pump pulses) of a Ti-sapphire
laser system, and the resulting transmission change of the sample
was monitored by weak pulses (probe pulses) at the same
wavelength as a function of the delay time. Only in a few
measurements did we employ for the probe longer wavelengths
intersections are very frequent in photochemistry. A conical
intersection is not a bottleneck. The molecule passes through
it very rapidly.
1
8,19
In the conical region the energy is a function of two critical
coordinates. One of them corresponds to the distance of the
two C atoms between which the ring opening occurs (C1 and
C6, see Figure 6). The second coordinate characterizes a shift
of C1 in the direction of C5.15 The conical intersection is located
a bit away from the 2A1 minimum along the second coordinate
(302-316 nm) than for the pump (267 nm), which were not
absorbed by the dehydrocholesterol. They were synthesized by
frequency-quadrupling the signal from a commercial (Topas)
optical parametric generator (OPG; details to be published later).
In one more experiment, we used the 267 nm for probing after
pumping at 292 nm. This wavelength was synthesized by
addition of the idler from the OPG to the Ti-sapphire frequency
and subsequent frequency doubling.
(
Figure 1). Celani et al.15 calculated a reaction path as
follows: After the rapid relaxation from the 1B2 state to the
A1 state, the excited cyclohexadiene propagates over a
2
negligible barrier along this potential surface to the 2A1
minimum. From there to the conical intersection the molecule
requires an activation energy of about 4 kJ/mol, which together
with a small activation entropy can explain the observed time
constant of several picoseconds.
All experiments were performed with 7-dehydrocholesterol
(
Sigma-Chemie) dissolved in UV grade ethanol (for some
3
The two quantum mechanical calculations differ strikingly
in the prediction for the barrier. The older one14 suggested a
substantial barrier near the initial geometry, although its exact
height depends on the way of interpolation between the few
experiments, methanol) at a concentration of 160 mg/dm (0.42
mmol/dm ). The samples were kept under a nitrogen atmo-
3
sphere to avoid oxidation. The solution was exposed to the
laser radiation in a reaction cell of 500 µm length with UV
15
calculated points of the surfaces. The more recent calculation
grade CaF windows. The transverse flow of the solution was
2
predicted a small, but noticeable, barrier only about half-way
along the reaction coordinate. Since such calculations are not
quantitatively reliable for excited states of molecules with this
size, a qualitative consideration also appears appropriate: The
electronic excitation almost only affects the π system. (The
sufficient to replace the irradiated volume between subsequent
laser pulses. The reaction cell was thermally isolated by a
surrounding vacuum chamber with CaF windows. The tem-
2
perature of the solution was varied from 217 to 323 K with an
accuracy of (2 K during a measuring period. For determination
of the temperature a Ni-CrNi thermocouple was placed in the
main stream directly after the cell.
2
A1 state is also a ππ* state.) It will change primarily the
lengths and torsional angles between the π-bonded atoms. The
σ bond between C1 and C6 can initially not interact, because it
is too low in energy and is nearly in the plane of the π-bonded
atoms. If this bond is, however, stretched (and thus raised in
energy) and twisted out of the plane by a thermal activation,
the σ bond begins to interact with the π bonds and the potential
energy begins to decrease. So this consideration suggests an
early barrier.
Part of the experimental system is depicted schematically in
Figure 2. Intense femtosecond pulses of tunable wavelength
between 780 and 830 nm were generated in a laser system
consisting of an argon ion laser pumped Ti-sapphire oscillator
(Spectra Physics) and a Q-switched Nd:YLF laser pumped Ti-
sapphire amplifier (Quantronix) with grating stretcher and
compressor unit. The amplified pulses generated at a repetition
rate of 1 kHz had in this spectral region an energy of up to 800
µJ and a pulse duration of 100 fs (from autocorrelation
measurements). The transverse mode profileschecked by a
CCD cameraswas close to Gaussian.
From their resonance Raman scattering measurements, Trul-
20
son et al. found evidence that the single bond is instantaneously
stretched and twisted, i.e. accelerated in the direction of the
reaction coordinate. This might suggest the absence of a barrier.
The observation is, however, also compatible with an excited
state minimum, shifted in this direction and followed by a
For the initiation of the photochemical reaction and the study
of the transient absorption of dehydrocholesterol and its

Ring Opening in the Dehydrocholesterol-Previtamin D System
J. Phys. Chem., Vol. 100, No. 2, 1996 923
Figure 2. Schematic of the experimental system. RR: variable delay
line with retroreflector.
products, ultrashort UV pulses were employed. These pulses
were generated from the laser pulses described above by
frequency doubling and tripling, using a commercial unit (CSK).
This systemsconsisting of a 1.5 mm lithium borate (LBO)
crystal for frequency doubling and a 1 mm barium â-borate
(BBO) crystal for the generation of the third harmonicsprovided
UV pulses from 260 to 277 nm by tuning the oscillator and the
compressor-stretcher unit. The pulse duration was 300 fs, and
more than 10% of the energy of the fundamental wavelength
was converted to the UV.
A beam splitter was inserted after the tripler unit. The
reflected beam (99%) served for pumping, the transmitted beam
Figure 3. Ultraviolet absorption spectra22,23 of 7-dehydrocholesterol
(
D, solid curve) and previtamin D (P, dashed curve) in ethanol at room
temperature. Preliminary values for absorption cross sections of excited
D (D*) and for the primary conformer of P (P ) are also indicated.
0
(1%), for probing. After passing separate delay units, the pulses
were focused by two lenses: Lpump (focal length 100 cm) and
Lprobe (50 cm). The beams overlapped in the sample with an
intersection angle of 50 mrad. The foci had an almost perfect
Gaussian transversal shape with 100 µm diameter for the pump
and 50 µm for the probe pulse. The average energy of the pump
pulses was about 3 µJ in front of the cell.
The delay unit of the pump beam was controlled by a stepper
motor with a personal computer, and a retroreflector (RR) was
used for high pointing stability. The delay zero and the pulse
duration were determined by recording the correlation function
between pump and probe pulses.
The direction of the polarization of the probe beam was
rotated by a half-wave plate, selected for a small wedge angle.
The energy of the probe pulses was monitored via beam
splitters and photodiodes before and after the reaction cell. The
diode signals were recorded via integrators and digital lock-in
amplifiers. A time constant of 300 ms was chosen to restrict
the signal fluctuation to 0.1%. All data were stored by the
computer.
Figure 4. Time-resolved transient absorption of dehydrocholesterol
3
(
0.4 mmol/dm ) in ethanol at 262 nm after excitation at the same
wavelength. The change of absorption ∆A ) -ln(T/T ) is plotted versus
the delay time between the femtosecond excitation and the probe pulse
points; T and T are the transmissions of the sample before and after
0
(
0
excitation, respectively). A fast and a slow recovery component are
readily seen. The solid line is the best fit of a doubly exponential
form (eq 1). The total absorption change of the sample including the
two-photon absorption in the solvent is depicted in the inset.
3
. Results
We report two series of measurements of the electrocyclic
ring opening: (1) the transient absorption kinetics of dehydro-
cholesterol after excitation at room temperature and (2) its
temperature dependence.
estimate that the pump pulse promotes approximately 40% of
the molecules in the irradiated volume to the electronically
excited state. Within the correlation width of pump and probe
beam, there is a rapid transient absorption peak (see inset of
Figure 4), which allows us to determine the width of our UV
pulses. This peak, also observed in pure ethanol at all three
wavelengths, can be attributed to a two-photon absorption
primarily in the solvent and (to a small extent and with opposite
sign) to a degenerate four-wave mixing process in the CaF2
(1) Transient Absorption at Room Temperature. The
absorption spectrum of dehydrocholesterol (D) dissolved in
ethanol
absorption band between 250 and 310 nm, which shows some
vibrational structure, is due to the ππ* transition (1A1 f 1B2)
of D. We used pump pulses at three different wavelengths (262,
2
2,23
is presented in Figure 3 (solid line). The strong
2
67, 272 nm) to excite dehydrocholesterol to this state.
A typical trace of the time evolution of the transient
2
5
windows. The two-photon absorption in ethanol also results
in a small residual increase of the absorption, which lasts longer
than the effects we are interested in. We subtracted it from the
measured absorptions.
absorption ∆A ) -ln(T/T0) after excitation, probed by a weak
delayed pulsesat the same wavelength as the pump pulsesis
shown in Figure 4 for a wavelength of 262 nm (filled circles;
T, T0, transmission of the sample with and without excitation).
The polarization of the probe beam relative to the pump beam
encloses the (“magic”) angle of 54.7° to eliminate the influence
In Figure 4 the excitation of dehydrocholesterol results in a
maximum absorption decrease of 3%. The following recovery
of ∆A shows a double-exponential behavior. ∆A increases at
first with a time constant t1 ) 5.2 ( 0.5 ps and then more slowly
2
4
of orientational relaxation on the observed transients. We

9
24 J. Phys. Chem., Vol. 100, No. 2, 1996
Fuss et al.
Figure 6. Suggested reaction steps of the photochemical ring opening
of dehydrocholesterol after UV excitation. The figure shows the
reaction center only.
present some further evidence for our assignment. After that,
we will discuss the temperature dependence of the observed
rates.
(
1) Kinetic Model. The experimental time-dependent ab-
Figure 5. Picosecond absorption change ∆A (normalized to 1 at time
3
sorption change ∆A(t) can be well fitted by
0
) of dehydrocholesterol in ethanol (0.4 mmol/dm ) at 272 nm after
excitation at the same wavelength for three different temperatures T )
47 (triangles), 281 (circles), and 315 K (squares). The solid lines are
∆
A(t) ) A + A exp(-t/t ) + A exp(-t/t )
(1)
2
0
1
1
2
2
doubly exponential fits. The inset shows that the fast recovery time is
temperature independent. The second (slow) decay time is clearly
temperature dependent.
This indicates that there are at least two consecutive reactions.
It is suggestive to assume the first step to be the photoinduced
ring opening of dehydrocholesterol (D) to the s-cis,Z,s-cis
conformer of previtamin D (P0), which then in a second step
rearranges thermally to the s-trans,Z,s-cis conformer (P). Figure
with t2 ) 125 ( 20 ps. The absorption does not completely
restore even at long delay times. Similar time evolutions of
the transient absorption were observed at 267 and 272 nm,
indicating that the time constants are independent of the specific
wavelength within the experimental accuracy. This was also
supported by tuning the probe wavelength to 304, 306, or 316
nm, after pumping at 267 nm. In this case, we observed a
transient increase of absorption, since dehydrocholesterol does
not noticeably absorb beyond 300 nm. So the longer wavelength
component exhibits the same temporal behavior, and for
example, the 5.2 ps exponential is not the result of a superposi-
tion of several decays with similar, but different, lifetimes. The
same time constants were also observed when the excitation
was at 292 nm (near the 0-0 transition of the dehydrocholesterol
band) and the probe at 267 nm. This indicates that the rate
constants do not depend on the initial vibrational excess energy.
Orientational relaxation cannot be seen in the applied,
6
summarizes in more detail the relevant reaction steps.
Dehydrocholesterol is excited by the pump pulse from the
ground state D to the electronically excited state D*, whose
nature will be discussed in section 5. This excited molecule
can undergo either the ring opening (rate constant kD*P ) or an
0
internal conversion (rate constant kic) to the ground state. The
sum of the two rate constants is kD*, the rate constant of the
overall depopulation of D* (see Figure 6). The primary product
P0 then converts to the final product P by a cis-trans
isomerization around a single bond with a rate constant kP P.
0
After photoexcitation all the time-dependent population densities
of the four involved species D, D*, P0, and P can contribute to
the absorption. The solution of the rate equations results in a
time dependence of the form of eq 1 with
“
magic” orientation of pump and probe polarizations and can
be ignored under these conditions. Using the method of ref
4, we deduced from the difference of the transient absorptions
t1-1 ) k , t2 ) k
-1
(2)
D*
P P
0
2
In the latter equation, an additive term kPP for the back reaction
0
with parallel and perpendicular polarization (pump versus probe)
an orientational relaxation time of 240 ( 60 ps for dehydro-
cholesterol dissolved in ethanol. This value is in the same range
as for molecules with a comparable size, e.g. rhodamine 6G.
2) The Effect of Temperature on the Transient Dynamics.
The transient absorption at different temperatures between 217
and 323 K was measured at the pump and probe wavelength
2
temperatures. The normalized absorption change is plotted
versus the delay time between pump and probe pulses. All
measurements show a sudden change of absorption at t ) 0 ps.
The following increase is found to be double exponential. The
first time constant is 5.2 ( 0.5 ps at all temperatures. This is
clearly shown in the magnified inset of Figure 5.
Quite different is the temperature dependence of the second
time constant t2 of the double exponential decay. In Figure 5,
the first rapid decrease of the transient absorption change is
seen to be followed by a slower one, whose time constant varies
between 60 ps at 315 K and 1300 ps at 247 K.
has been neglected. At all investigated wavelengths and
wavelength combinations we found t1 ) 5.2 ( 0.5 ps for the
ring opening (depopulation of D*, appearance of P) and t2 )
26,27
1
25 ( 20 ps for the single-bond cis-trans isomerization at room
(
temperature.
In the quantitative evaluation of the amplitudes Ai in eq 1
we have assumed that kD*P /kic ) 0.34/0.66 ) 0.52. (0.34 is
the reported quantum yield for the reaction).
0
72 nm. Figure 5 presents the results for three different
2
8,29
We checked
whether this value is unchanged also for femtosecond excita-
tion: We determined the number of product molecules P by
measuring the UV spectra before and after irradiating under the
same conditions as in the pump-probe experiment; comparing
this value with the number of absorbed photons calculated from
the cross section, we found for this ratio 0.39-0.47, in
reasonable agreement with the literature value. In the spectral
region between 240 and 350 nm, we have not observed any
other products, e.g. those resulting from photoexcitation of P0
or P (such as tachysterol). However, more D molecules were
consumed in this experiment than P molecules produced. This
3
0
4
. Discussion
has already previously been observed at high intensity, and
the corresponding product has been identified as toxisterol B,
resulting from the addition of a solvent molecule to the double
First we will consider here which species can contribute to
the observed transient absorption (i.e. a kinetic model) and then

Ring Opening in the Dehydrocholesterol-Previtamin D System
J. Phys. Chem., Vol. 100, No. 2, 1996 925
3
0
bonds; it absorbs only at shorter wavelengths. This reaction
A first consideration is that there might be a barrier, but that
the molecules might not be in thermal equilibrium with the
solvent, so that its temperature would have a negligible influence
30
can be attributed to two-photon absorption (although this has
also been doubted ), giving rise to radical cations, which can
3
1
add a solvent molecule.32
only. The vibrational cooling can take several picoseconds.
36
The initial excitation at 267 nm is more than 4100 cm- ≈ 50
kJ/mol above the vibrational band origin (probably near 300
nm), so that a small initial barrier could be overcome.
Therefore, we employed in one experiment a pump wavelength
of 292 nm, which leaves a vibrational excess energy of only
about 900 cm- in D*. But the time constants did not change.
Another source of vibrational excess energy might be the fact
that, during the movement on the potential surface 2A1,
electronic energy is converted to nuclear motion (vibration).
So a late barrier could be overcome, because the molecule might
1
The radical cations themselves might, however, have a UV
absorption with a time dependence of its own. The reactions
of such species, such as ring opening3
3-35
or addition of the
solvent, would be ground state reactions (unless a third photon
is absorbed). They will be associated with an activation energy
and therefore be slow (nanoseconds or longer). So they will
not have any influence on the observed time constants. In fact,
when we varied the pump intensity by a factor of 2, we did not
observe any change of rates. However, the radical cations lead
to an uncertainty in the evaluation of the absorption cross section
of D* and P0, which are contained in the amplitudes A1 and A2
1
5
,6
be internally hot (as in cyclohexadiene ), independent of the
temperature of the surroundings. This possibility seems to infer
that we cannot exclude a late barrier. A barrier of 4 kJ/mol
-17
in eq 1. Thus, our values (e.g. at 267 nm σ(D*) ) 2.1 × 10
2
-17
2
cm and σ(P0) ) 1.7 × 10
cm ) are only preliminary.
1
5
(
2) Evidence for the Assignment. Although this model
has been predicted just before the conical intersection.
A
appears plausible, further evidence for the assignment would
be desirable, since other processes with similar time constants
are conceivable. For example, the vibrational cooling will occur
in a few picoseconds.36 Note that around 267 nm we do not
excite the 0-0 transition and that the electronic energy is
converted to nuclear motion during the reaction. On the other
hand, with excitation at 292 nm (near the 0-0 transition) t1
was again measured as 5 ( 1 ps. The strongest support that
the first time constant is due to the ring opening comes from
two independent methods, which found similar values for this
process.
certain excess energy might, however, be unimportant for
another reason: The redistribution of vibrational energy within
the molecule can be much faster than the cooling. According
to ref 37, it requires between 200 and 500 fs. Even with an
excess energy of 100 kJ/mol (the calculated energy release
before the conical intersection ), for each vibrational degree
of freedom there would be less than 1 kJ/mol (or a correspond-
ingly small temperature rise), not sufficient to climb a barrier.
So a late barrier of much larger magnitude is not probable.
1
5
Furthermore, the vibrational excess energy cannot explain the
slowness of the rate. According to the RRKM theory, much
above a barrier the reaction rate would be equal to the frequency
factor A, which is identical to the preexponential factor A in eq
(i) By investigating the yield ratio of the product P to the
secondary product, tachysterol (T), (produced by excitation of
P0 or P) as a function of the pulse duration, we found previously
a time constant of 4.3 ( 0.5 ps.2 This number depends on the
values for the quantum yields of the photoreactions P0 f T
and P f T. Only the latter one is known.28 If the former is
assumed to be slightly smaller, the agreement would be even
better.
3
.
So we prefer to assume an activation entropy (∆Sa ≈ -3.4kB),
in spite of the preliminary consideration above. Celani et al.
calculated ∆Sa ≈ -2kB for the passage through an activated
1
5
state immediately before the conical intersection. A negative
entropy of activation means that some vibrations, which initially
are thermally excited, are not excited anymore in the activated
state, because their frequency has increased. An equivalent view
is that the exit channel is very narrow. The exit valley is
generated by the electronic stabilization due to the Woodward-
Hoffmann principle. So this stabilization seems to be very
sensitive to small distortions of the geometry.
(ii) Time-resolved resonance Raman studies of the electro-
cyclic ring openings in 1,3-cyclohexadiene and its 2-methyl-
5
-isopropyl derivative gave time constants of 6 and 11 ps,
4
,5
respectively.
For the second step, the orientational relaxation has already
been excluded as an alternative, since it cannot be observed at
the magic angle. The assignment as a thermal cis-trans
isomerization is also confirmed by the dependence on the
temperature and the viscosity of the solvent (see below).
(4) t2 and Its Temperature Dependence. In Figure 4 after
the rapid ring-opening reaction a slower process is observed
with a time constant of 125 ( 20 ps. We attributed it to the
thermal s-cis f s-trans isomerization P0 f P. This time
dependence allows for the first time a ready distinction between
the two molecular conformers P0 and P. This is in contrast to
cyclohexadiene, where the cooling rate appeared to be not fast
enough to prevent an immediate (7 ps) isomerization of the
(3) Temperature Dependence of t1. According to transition
state theory, a unimolecular rate constant k can be written as a
function of the enthalpy ∆Ha and entropy ∆Sa of activation:
k ) A exp(-∆H /k T)
(3)
(4)
a
B
5
,6
5
initially produced conformer. It has been suggested that the
cooling rate during a reaction is fast if the moving parts of the
molecule experience a strong friction in the solvent (see the
following paragraph), as in cis-trans isomerization of stilbenes
and certainly also in our example, and is slower if the friction
is weaker, as in the cyclohexadiene ring opening. As another
reason for the rapid conformational isomerization in the
A ) (k T/h) exp(∆S /k )
B
a
B
where kB and h are the Boltzmann and Planck constant,
respectively. At T ) 295 K, the first factor in eq 4 equals 6 ×
12 -1
1
0 s . There is no obvious reason why the activation entropy
of the ring opening should be large. (An example where it
would be large and negative would be the back reaction: In
the transition state, several torsional degrees of freedom must
be frozen, which in the open-chain molecule correspond to
coordinates of isomerization to other conformers.) From the
temperature independence of k (Figure 5) and from our limit of
accuracy, we could conclude that ∆Ha < 1 kJ/mol, a very small
value. So k should be equal to kBT/h. However, according to
our results, it is 30 times smaller. What can be the reason?
6
unsubstituted system, Reid et al. suggested steric hindrance in
the starting molecule, which would reduce the energy of
activation. However, the slower reaction in our more highly
substituted system (as well as the activation energy; see below)
rules out this interpretation.
To verify that this reaction is an isomerization around a single
bond as sketched in Figure 6, we measured the dependence of

9
26 J. Phys. Chem., Vol. 100, No. 2, 1996
Fuss et al.
divided into two consecutive steps, the ring opening itself and
the rearrangement from the primary conformer (P0) to the stable
one (P). P0, whose geometry is still ringlike, has repeatedly
been postulated as the precursor for the photochemical ring
closure of previtamin D and explains the wavelength dependence
of this reaction (see, for example, refs 45 and 46; for another
interpretation see ref 47. The conformational isomerization
proceeds in the electronic ground state over a barrier of 15.5
kJ/mol, with a time constant of 125 ps in ethanol at room
temperature. This is in contrast to the analogous reaction of
1
,3-cyclohexadiene, where the energy released in the photo-
chemical ring opening carries the molecule almost without delay
(
time constant 7 ps, i.e. similar to the ring opening; cooling
5,6
time 9 ps) over the barrier to the final conformer of hexatriene.
Obviously, in the D/P system, the cooling is much faster than
ps. For interpreting this difference, one should notice that
9
the moving molecular parts in the s-cis f s-trans isomerization
P0 f P are much larger than in the unsubstituted hexatriene, so
that the coupling to the solvent will be stronger.
1
Figure 7. Plot of ln(kη
isomerization P
T
/ηref) versus T- for the conformational
0
f P in ethanol (open circles) and methanol (closed
circles). ηref ) 1.1 mPa s (viscosity of ethanol at 295 K). The solid
line is the best fit of the form of eq 5.
During the first step, the ring opening and the crossover from
the excited potential surface to the ground state surface occur
in 5.2 ps. This time constant is temperature independent. It
was also unchanged when the excitation was near the band
origin, so that there was nearly no excess vibrational energy.
So one can infer that there is no barrier higher than 1 kJ/mol
for the ring opening. It is worth noting that the photochemical
electrocyclic ring closure of s-cis dienes to cyclobutenes has
t2 on the solvent viscosity and on the temperature. The latter
gives information about the activation energy, which can be
compared to similar isomerizations, whereas the dependence
on the viscosity η is typical for reactions in which large parts
of the molecule move within the solvent with friction.3
8,39
From
studies in alcoholic solvents, the rate constant k of isomerization
reactions was found to be proportional to η with 0 e a e
-
a
3
8,40
48
1
.
a ) 1 corresponds to the strong coupling case between
been observed in a matrix at 15 K. So this reaction also seems
the solute and the solvent molecules, which is typical if the
moving parts of the solute are bulky. Including the temperature
dependence, the rate constant of the isomerization reaction can
then be described by an Arrhenius-type expression:38
to have no activation energy. The barrierless ring opening is
in contrast to the expectation on the basis of a qualitative
14
consideration and to the early quantum mechanical calculation,
whereas the deviation from ref 15 is only minor. A more serious
contrast, however, exists with the fluorescence, which can be
k ) (η295K/η )A exp(-∆H /k T)
(5)
T
a
a
2
observed at 77 K in a matrix, but not at room temperature. So
there seems to be a barrier which makes the radiationless
depopulation of the initially excited state at 77 K slow enough
that the fluorescence (time constant in the nanosecond range)
can compete with it, at least in the matrix. We believe that an
additional barrier is generated by the matrix, which can prevent
the movement or large amplitude vibrations of bulky groups.
The fluorescence requires such an effect near the Franck-
Condon region, where all atoms have experienced only very
little displacement. The associated activation volumes can be
where ηT is the temperature dependent solvent viscosity, A is
the Arrhenius preexponential factor, and ∆Ha is the thermal
intramolecular activation enthalpy for the isomerization reaction.
Transient absorption measurements of dehydrocholesterol
were carried out at different temperatures ranging between 247
and 315 K. Two different alcohols, ethanol and methanol,
served as solvent. Figure 5 shows three examples of the
measurements in ethanol. The isomerization rate of P0 varied
by a factor of 20 in this range. According to eq 5, we plotted
-1
3
in Figure 7 ln(kηT/ηref) versus T , where ηref is η295K for ethanol.
ηT was taken from ref 41. At room temperature, methanol has
half the viscosity of ethanol. Obviously at all temperatures,
estimated to several cm /mol, which would yield a reasonable
matrix-induced barrier of several kJ/mol, if the compressibility
-1
of the matrix is around 1 GPa .
-1
the rates in the two solvents lie on the same line. So k ∝ η .
This is just the strong coupling case, which is expected for such
an isomerization.
Other barrierless processes in photochemistry are some Z f
E (or cis f trans) isomerizations. For example, octatetraene
49
can isomerize at 4.2 K in a hexane matrix. In larger molecules
such as stilbenes (see, for example, ref 50) or cyanines (see for
example, ref 51), the process is slowed down by the solvent
viscosity.
From the slope in Figure 7 we can derive an internal
activation energy of ∆Ha ) 15.5 ( 1 kJ/mol. This value is in
good agreement with barriers for isomerizations about single
4
2,43
bonds in polyenes, which are on the order of 16 kJ/mol.
A
The fluorescence spectrum of 7-dehydrocholesterol overlaps
with the absorption spectrum, whereas in lumisterol (which has
only a slightly different geometry) there is a small gap between
molecular mechanics calculation of the previtamin D conformers
found about 33 kJ/mol;44 this deviation is still acceptable for
such a calculation. The preexponential factor A equals (6 ( 2)
21
the two. As argued in ref 10, this means that in the latter the
1
2
-1
×
10
s
in ethanol. This is just equal to kBT/h. That is,
1
B2 state relaxes to the slightly lower lying 2A1 state before
according to eq 4, ∆Sa ) 0, not unexpected for such a reaction.
In summary, the temperature and viscosity dependence of t2
strongly supports our assignment that this process is the
isomerization P0 f P (Figure 6).
emission, whereas in the dehydrocholesterol the 2A1 state seems
to lie higher than the 1B2 state (in the Franck-Condon region).
Nevertheless, the relaxation 1B2 f 2A1 will not be a bottleneck
for the reaction, which is assumed to proceed initially on the
2
A surface. The crossover to the ground state surface 1A in
5
. Summary and Concluding Remarks
the region of the conical intersection will also be extremely
fast. If there is no electronic bottleneck, one expects for
1
5
We found that the electrocyclic ring-opening reaction of
dehydrocholesterol (D) to previtamin D (P) can clearly be
energies above a barrier (or if there is no barrier) a rate of kBT/h

Ring Opening in the Dehydrocholesterol-Previtamin D System
J. Phys. Chem., Vol. 100, No. 2, 1996 927
12
)
6 × 10 s-1, unless there is an activation entropy ∆Sa. Since
(7) MacDiarmid, R.; Sablji c´ , A.; Doering, J. P. J. Chem. Phys. 1985,
8
3, 2147.
8) Kohler, B. E. J. Chem. Phys. 1990, 93, 5838.
9) MacDiarmid, R. Int. J. Quantum Chem. 1986, 29, 875.
(10) Hudson, B. S.; Kohler, B. E.; Schulten, K. In Excited States; Lim,
K., Ed.; Academic Press: New York, 1982; Vol. 6, p 1.
11) Buma, W. J.; Kohler, B. E.; Song, K. J. Chem. Phys. 1990, 92,
622.
12) Buma, W. J.; Kohler, B. E.; Song, K. J. Chem. Phys. 1991, 94,
4691.
the observed ring opening is 30 times slower, there must be a
Sa of about -3.4kB. A negative ∆Sa means that the electro-
cyclic reaction with its aromatic transition state can easily be
perturbed by some thermally excited vibrations.
Surprisingly, this value of ∆Sa is about the same as for the
thermal) ring closure of hexatriene to cyclohexadiene and
derivatives,
open-chain compound, one expects for the ring closure much
more change of order than for the ring opening. ∆Sa is slightly
(
(
∆
(
4
(
(
5
2-54
although due to free internal rotation in the
(
13) Klessinger, M.; Michl, J. Excited States and Photochemistry of
Organic Molecules; Verlag Chemie: Weinheim, 1995.
14) Share, P. E.; Kompa, K. L.; Peyerimhoff, S. D.; van Hemert, M.
C. Chem. Phys. 1988, 120, 411.
(15) Celani, P.; Ottani, S.; Olivucci, M.; Bernardi, F.; Robb, M. A. J.
Am. Chem. Soc. 1994, 116, 10141.
16) Bernardi, F.; De, S.; Olivucci, M.; Robb, M. A. J. Am. Chem. Soc.
990, 112, 1737.
17) Bernardi, F.; Olivucci, M.; Ragazos, I. N.; Robb, M. A. J. Am.
Chem. Soc. 1992, 114, 8211.
(
1
5
more negative than calculated by Celani and co-workers for
a place on the surface, before the molecule turns to the conical
intersection.
(
An experimental hint that the (entropy) bottleneck for the
reaction is not close to the starting point of the reaction along
the 2A1 potential surface, but close to a much lower minimum,
comes from the very low fluorescence yield at room temperature
1
(
(
(
(
18) Klessinger, M. Angew. Chem. 1995, 107, 597.
19) Manthe, U.; K o¨ ppel, H. J. Chem. Phys. 1990, 93, 1659.
20) Trulson, M. O.; Dollinger, G. D.; Mathies, R. A. J. Chem. Phys.
-
6
20
(
2 × 10 for cyclohexadiene ): If the molecule would remain
in the Franck-Condon region for 5 ps, either in the 1B2 state
1989, 90, 4274.
20
(
radiative lifetime 6 ns ) or in the 2A1 state (radiative lifetime
(21) Havinga, E.; de Kock, R. J.; Rappoldt, M. P. Tetrahedron 1960,
11, 276.
22) Sternberg, J. C.; Stillo, H. S.; Schwendeman R. H. Anal. Chem.
960, 32, 84.
(23) Gliesing, S.; Reichenb a¨ cher, M.; Ilge, H.-D.; Fassler, D. J. Prakt.
Chem. 1987, 329, 311.
(24) Lessing, H. E.; Jena, A. v. Chem. Phys. Lett. 1976, 42, 213.
25) Laubereau, A. In Ultrashort Laser Pulses; Kaiser, W., Ed.;
Springer: Berlin, 1988.
(26) Fleming, G. R.; Morris, J. M.; Robinson, G. W. Chem. Phys. 1976,
7, 91.
27) Myers, A. B.; Hochstrasser; R. M. IEEE J. Quantum Electr. 1986,
QE-22, 1482.
28) Gliesing, S.; Reichenb a¨ cher, M.; Ilge, H.-D.; Fassler, D. Z. Chem.
1989, 29, 21.
29) Jacobs, H. J. C.; Gielen, J. W. J.; Havinga, E. Tetrahedron Lett.
981, 22, 4013.
1
4
about 15-55 times longer, depending on the geometry ), it
(
-
3
-5
should fluoresce with a quantum yield of 10 to 2 × 10 . If
it, however, proceeds rapidly (e.g. in 10 fs) to a much lower
energy state on the potential surface, as suggested by the
1
1
5
calculations, then the low quantum yield of UV fluorescence
is understandable. So probably, the molecule moves in a very
short time on a purely repulsive surface to the pericyclic
minimum, from where it proceeds within 5.2 ps through an
entropic bottleneck (probably again without barrier) down to a
conical intersection and from there to the product P0 or the educt
D.
In any case, the D* observed by us by excited state absorption
corresponds to a state with a lifetime of 5.2 ps. This state would
be ionized by a UV photon if its energy is still close to the 1B2
or 2A1 state; but if it is much lower in energy (e.g. near the
pericyclic minimum, as suggested above), the UV photon would
not be sufficient for ionization. Since the spectral dependence
of σ(D*) is probably different for the two cases, extending the
measurements of σ(D*) can probably distinguish between them
and thus help to locate the reaction bottleneck.
(
1
(
(
(
1
(
30) Bogoslowskii, H. A.; Berik, I. K.; Gundorov, S. I.; Terenetskaya,
I. P. High Energy Chem. 1989, 23, 218.
(31) Terenetskaya, I. P.; Gundorov, S. I.; Kravchenko, V. I.; Berik, I.
K. SoV. J. Quantum Electron. 1988, 18, 1323.
(
32) Orlov, A. I.; Mikhailova, N. P.; V’yunov, K. A. Khim. Prirod.
Soedin. 1989, 225.
(33) Shida, T.; Egawa, Y.; Kubodera, H.; Kato, T. J. Chem. Phys. 1980,
3, 5963.
7
(
(
34) Shida, T.; Kato, T.; Nosaka, Y. J. Phys. Chem. 1977, 81, 1095.
35) Bondybey, V. E.; English, J. H.; Miller, T. A. J. Mol. Spectrosc.
Whereas the ring opening is slow compared to the expectation
for a barrierless unimolecular process, it is worth noting that it
is much faster than any bimolecular reaction, caused by
collisions between two solute molecules. Nevertheless, pho-
todimers have been observed for dehydrocholesterol as well as
for cyclohexadiene, in particular with excitation at long
1
980, 80, 200.
(36) Seilmeier, A.; Kaiser, W. In Ultrashort Laser Pulses; Kaiser, W.,
Ed.; Springer: Berlin, 1988.
(37) Weiner, A. M.; Ippen, E. P. Chem. Phys. Lett. 1985, 116, 656.
(38) Keery, K. M.; Fleming, G. R. Chem. Phys. Lett. 1982, 93, 322.
(39) Hicks, J. M.; Vandersall, M. T.; Sitzmann, E. V.; Eisenthal, K. B.
Chem. Phys. Lett. 1987, 135, 413.
3
45,55
(40) Nikowa, L.; Schwarzer, D.; Troe, J.; Schroeder, J. J. Chem. Phys.
wavelengths and at high concentrations (40 mmol/dm ).
In
1
992, 97, 4827.
41) Lide, D. R., Ed. Handbook of Chemistry and Physics, 74th ed.;
the products, the ring has not been opened. The obvious
explanation is that the photodimers are formed by excitation of
van der Waals dimers, which will be in equilibrium with the
monomers at higher concentrations.
(
CRC Press: Boca Raton, 1993.
(42) Ackermann, J. R.; Kohler, B. E. J. Chem. Phys. 1984, 80, 45.
(
(
(
(
43) Carreira, L. A. J. Chem. Phys. 1975, 62, 3851.
44) Dauben, W. G.; Funhoff, D. J. H. J. Org. Chem. 1988, 53, 5070.
45) Jacobs, H. J. C.; Havinga, E. AdV. Photochem. 1979, 11, 305.
46) Pfoertner, K. HelV. Chim. Acta 1972, 55, 937.
Acknowledgment. We thank F. Bernardi and M. Olivucci
(Bologna) and I. P. Tereneckaja (Kijev) for helpful comments.
(47) Dauben, W. G.; Disanayaka, B.; Funhoff, D. J. H.; Kohler, B. E.;
Schilke, D. E.; Zhou, B. J. Am. Chem. Soc. 1991, 113, 8367.
(
(
48) Squillacote, M.; Semple, T. C. J. Am. Chem. Soc. 1990, 112, 5546.
49) Granville, M. F.; Holtom, G. R.; Kohler, B. E. Proc. Natl. Acad.
References and Notes
(
1) Woodward, R. B.; Hoffmann, R. The ConserVation of Orbital
Symmetry, 3rd ed.; Verlag Chemie: Weinheim, 1981.
2) Gottfried, N.; Kaiser, W.; Braun, M.; Fuss, W.; Kompa, K. L. Chem.
Phys. Lett. 1984, 110, 335.
3) Trulson, M. O.; Dollinger, G. D.; Mathies, R. A. J. Am. Chem.
Soc. 1987, 109, 587.
4) Reid, P. J.; Doig, S. J.; Mathies, R. A. Chem. Phys. Lett. 1989,
56, 163.
5) Reid, P. J.; Doig, S. J.; Wickham, S. D.; Mathies, R. A. J. Am.
Chem. Soc. 1993, 115, 4754.
6) Reid, P. J.; Lawless, M. K.; Wickham, S. D.; Mathies, R. A. J.
Phys. Chem. 1994, 98, 5597.
Sci. U.S.A. 1980, 77, 31.
(50) Waldeck, D. H. Chem. ReV. 1991, 91, 415.
(51) A° berg, U.; A° kesson, E.; Alvarez, J.-L.; Fedchenia, I.; Sundstr o¨ m,
V. Chem. Phys. 1994, 183, 269.
(52) Marwell, E. N.; Caple, G.; Schatz, B.; Pipin, W. Tetrahedron 1973,
29, 3781.
(
(
(
(53) Gaasbeek, C. J.; Hogeveen, H.; Volger, H. C. Recl. TraV. Chim.
Pays-Bas 1972, 91, 821.
1
(
(
(
54) Lewis, K. E.; Steiner, H. J. Chem. Soc. 1964, 3080.
55) Havinga, E. Experientia 1973, 29, 1181.
(
JP952536Q