Cyclohexadiene ring opening observed with 13 fs resolution: Coherent oscillations confirm the reaction path

Article abstract of DOI:10.1039/b814201g

The third harmonic (270 nm, 11 fs), produced in a short argon cell from Ti-sapphire laser pulses (810 nm, 12 fs), was used to excite 1,3-cyclohexadiene to its lowest ππ* state (1B). Probing was done by transient ionization by the 810 nm pulses, measuring the yields of the parent and a fragment ion. As previously found with 10 times longer pulses, the molecule leaves in two steps (time constants τ₁, τ₂) from the spectroscopic (1B) to a dark (2A) state and from there (within τ₃) to the ground-state surface. In addition to slightly improved values for τ₁-τ₃, we found in all three locations (L₁-L₃) on the potentials coherent oscillations, which can be assigned to vibrations. They are stimulated by slopes (driving forces) of the potentials, and the vibrational coordinates indicate the slope directions. From them we can infer the path following the initial excitation: the molecule is first not only accelerated towards CC stretching in the π system but also along a symmetric C=C twist. The latter motion - after some excursion - also erects and stretches the CH₂-CH₂ bond, so that Woodward-Hoffmann interactions are activated after this delay (in L ₂). On leaving L₂ (the 1B minimum) around the lower cone of the 1B/2A conical intersection, the wave packet is rapidly accelerated along an antisymmetric coordinate, which breaks the C₂ symmetry of the molecule and eventually leads in a ballistic path to (and through) the last (2A/1A) conical intersection. The ring opening begins already on the 1B surface; near the 2A minimum it is already far advanced, but is only completed on the ground-state surface. the Owner Societies.

Full text of DOI:10.1039/b814201g

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www.rsc.org/pccp | Physical Chemistry Chemical Physics
Cyclohexadiene ring opening observed with 13 fs resolution: coherent
oscillations confirm the reaction path
K. Kosma, S. A. Trushin, W. Fuß* and W. E. Schmid
Received 14th August 2008, Accepted 13th October 2008
First published as an Advance Article on the web 6th November 2008
DOI: 10.1039/b814201g
The third harmonic (270 nm, 11 fs), produced in a short argon cell from Ti-sapphire laser pulses
(
810 nm, 12 fs), was used to excite 1,3-cyclohexadiene to its lowest pp* state (1B). Probing was
done by transient ionization by the 810 nm pulses, measuring the yields of the parent and a
fragment ion. As previously found with 10 times longer pulses, the molecule leaves in two steps
(
time constants t
to the ground-state surface. In addition to slightly improved values for t
three locations (L –L ) on the potentials coherent oscillations, which can be assigned to
1
, t
2
) from the spectroscopic (1B) to a dark (2A) state and from there (within t
3
)
1
–t , we found in all
3
1
3
vibrations. They are stimulated by slopes (driving forces) of the potentials, and the vibrational
coordinates indicate the slope directions. From them we can infer the path following the initial
excitation: the molecule is first not only accelerated towards CC stretching in the p system but
also along a symmetric CQC twist. The latter motion—after some excursion—also erects and
stretches the CH –CH bond, so that Woodward–Hoffmann interactions are activated after this
2
2
delay (in L
intersection, the wave packet is rapidly accelerated along an antisymmetric coordinate, which
breaks the C symmetry of the molecule and eventually leads in a ballistic path to (and through)
the last (2A/1A) conical intersection. The ring opening begins already on the 1B surface; near the
2 2
). On leaving L (the 1B minimum) around the lower cone of the 1B/2A conical
2
2
A minimum it is already far advanced, but is only completed on the ground-state surface.
1
1
1
. Introduction
‘‘turned on’’. From there the wave packet falls into a dark
2A or 2A) state; in doing so, it circumvents the 1B/2A
conical intersection (CI) along an antisymmetric (b or b,
-symmetry breaking) coordinate, as previously suggested.
Under C -constraint, the 2A potential has a ‘‘pericyclic
(
1
Photochemical ring opening of 1,3-cyclohexadiene (CHD) to
Z-hexatriene (HT) and its reverse is a prototype of pericyclic
1
reactions. The stereochemistry of such reactions with steroid
2
11
C
2
2
derivatives has played an important role in the derivation of
,3
the Woodward–Hoffmann (WH) rules.
hexatriene interconversion is also the basis of many photo-
minimum’’ half-way between the reactant and product. From
there, the same b distortion slightly lowers the 2A energy and
further leads to a CI, the minimum of the 2A/1A intersection
11
space. From this CI the path branches to the product HT
2
Cyclohexadiene/
2
4
,5
chromic dyes. The reaction was therefore much investigated
over the last two decades by quantum-chemical calcula-
and the reactant CHD. On the 1B surface the wave packet
11,33,34
travels E55 fs (a time consisting of two phases
departure from 2A takes E80 fs.
6
–21
22,23
tions,
time resolution,
by resonance-Raman spectroscopy,
in part with
29–31
by transient absorption in solution,
), and its
24–28
The early work
2
4–28
11,33–35
in the gas phase by transient ionization (time-resolved mass
35
spectroscopy),
and time-resolved electron diffraction.
36–39
and electron diffraction did not have sufficient time
resolution and only detected the ground-state products or
38,39
1
1,32–34
transient photoelectron spectroscopy
3
6–39
It may be the
those resulting from reactions in the hot ground state.
29–31
system, for which most details are now known on the reaction
path over the different surfaces (see, in particular, ref. 11). This
is probably also the reason, why the system has been studied
for application of shaped pulses for controlling the reaction,
The investigations in solution
(
found the correct total time
E200 fs) for the process, but could not monitor the
individual steps.
Also in our previous transient-ionization work
11,33,34
and
1
2,15,40,41
42,43
both theoretically
As is typical for photoinduced pericyclic reactions
Fig. 3 and 6 below), the molecule is first excited to a ‘‘spectro-
scopic’’ state (1B in C2v, 1B in C ), from where it is
initially accelerated along Franck–Condon active coordinates
and experimentally.
35
the time-resolved photoelectron spectroscopy deconvolution
was necessary, because in particular the UV pump pulses had
durations of 130–150 fs. Recently we developed a simple
1
,44
(see
45
2
2
source of UV pulses with duration r10 fs and demonstrated
its use for time-resolved spectroscopy of metal carbonyl
46
dissociation. It seemed suggestive to measure also the times
1
1
(
stretches and twists of the p system ). Then also the
CH –CH2 s bond is stretched and the WH rules are
2
of the different phases of CHD ring opening directly. Even
more interesting is the possibility to resolve coherent oscilla-
tions. They cannot be revealed by deconvolution. We pre-
viously demonstrated, how much information of the reaction
Max-Planck-Institut fu¨r Quantenoptik, D-85741 Garching, Germany.
E-mail: w.fuss(mpq.mpg.de; Fax: +49-89-32905-200
1
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path can be deduced from them, if the corresponding vibra-
4
6–52
tional coordinate can be identified.
For their observation
a certain degree of coherence is necessary in the molecule.
A coherence seems to survive over a long time in CHD, as we
concluded from the compactness of the wave packet, when it
3
4
arrives at the ground state surface. The main goal of the
present work was therefore to detect coherent oscillations,
in the hope that the corresponding vibrations indicate the
(
varying) directions of the path on the excited-state surfaces.
In fact, we detect such oscillations. They also provide evidence
of the details (e.g. symmetry breaking), for which there
have only been suggestions before, and support the idea of
describing the process by driving forces.
2
. Experimental
3
4
As in our previous work, CHD was excited by the third
harmonic (270 nm) of a 1-kHz Ti-sapphire laser, and the
fundamental (810 nm) was used to probe the molecules by
1
3
ꢁ2
ionizing them at high intensity (E10 W cm ). The ion yield
was detected mass-selectively in a time-of-flight mass spectro-
meter. As compared to ref. 34, the pulse duration of the laser
system was shorter (45 fs) and was further shortened to 12 fs
by self-phase modulation of the radiation focused (f = 2 m)
into argon (500 mbar) and reflection from chirped
4
5,53,54
mirrors.
For third-harmonic generation, most (up to
E0.7 mJ) of this radiation was then refocused (f = 1 m) into a
small steel cell (length 18 mm) with pinholes, filled with Ar
(E250 mbar) and embedded in vacuum (o4 mbar). The beam
further propagated in vacuum through apertures (for differ-
ential pumping), via two dielectric mirrors (to isolate the
270 nm, collimate and focus the beam to the mass spectro-
meter) and through the hole of a mirror, serving to merge it
with the probe beam (E0.03 mJ). The duration (11 fs) of the
2
70-nm pulses was determined by cross correlation with
4
5
the fundamental in the mass spectrometer by ionizing Xe.
The detailed setup is described in ref. 45, 54 and 55.
3
. Results
The yields of the parent ion (mass 80 u, Fig. 1) and one
fragment (79 u, Fig. 2) were recorded versus the pump–probe
delay. According to ref. 34, these two masses are sufficient to
monitor the wave-packet motion on the excited-state surfaces:
the mass spectrum from 1B contains both, although in
different ratio from an earlier (L , Franck–Condon region)
1
and a later location (L , near the 1B minimum). From 2A
2
Fig. 1 Time dependence of the parent ion signal. (a) Full signal
(symbols) and its decomposition into contributions from L1 and L2
(without and with modulation, curves without symbols). The sum of
3
4
(
location L ) only mass 79 is observed, so that the parent ion
3
does not provide any information on this state. (The assign-
ment to 1B and 2A has recently been confirmed by time-
resolved photoelectron spectroscopy by Kuthirummal et al.,
these contributions is the simulation curve for the full signal. (b) L
1
contribution to the parent ion signal (symbols) with exponential and
modulated simulations. Division of these two curves (diminished by 1)
results in the modulation function at the bottom, whose Fourier
3
5
who found the same time constants. )
In a first step the signals are analysed by a sum of
exponentials (convoluted with the laser pulse shapes, if
necessary; i.e., for the shortest times), whose time constants
2
transform is shown in the inset. (c) The corresponding L contribution.
ionization probability, caused by a vibration of the wave
packet in location Li. The modulating function has the form
i
t correspond to the lifetimes of the population in the locations
L . This is a description of the population flow by rate
i
equations. In the present case, all signals showed also a
periodic modulation. It is interpreted as a modulation of the
f
osc = 1 + A cos(2pnct ꢁ j)
(1)
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Table 1 Lifetimes (t ) and oscillation wavenumbers (nia and nib)
i
1 3
found for the locations L –L in the excited states. The estimated
error limits are ꢂ5%
i
1
2
3
t
n
i
/fs
ia, nib/cm
21
950, 1430
35
310, 630
80
140, 270
ꢁ1
clear signatures of wave packet motion such as oscillations or
the ballistic motion introduced below.
The parent-ion signal is shown in Fig. 1a. Its decay is
obviously doubly exponential (t = 21 fs, t = 35 fs), both
1
2
parts showing some modulation. Looking first to the later time
70–150 fs) and dividing by the exponential simulation, we
extract from it two modulation functions of type (1) with
(
ꢁ
1
ꢁ1
wavenumbers n2a = 310 cm and n2b = 630 cm (these
numbers result from the second iteration step, using Fig. 1c),
which represent vibrations in L
(
2
. The modulated signal part
, multiplied by the
i.e., an exponential with time constant t
2
modulation functions, the flatter pair of curves in Fig. 1a) is
extrapolated back to time 0 (with convolution) and subtracted
from the signal. The result is the signal contribution from L1
(
Franck–Condon region) shown in Fig. 1b. It also shows a
modulation (lower curve in Fig. 1b), whose Fourier transform
ꢁ
1
ꢁ1
(
inset) has two maxima (n1a = 950 cm , n1b = 1430 cm ).
Using these frequencies, the modulation of the L part of the
parent-ion signal can be well simulated (Fig. 1b). Subtracting
the thus obtained L contribution from the full signal (Fig. 1a)
yields the L contribution, which is shown in Fig. 1c, including
1
1
2
its oscillatory part (with its simulation) and its Fourier
transform (inset).
Fig. 2 shows the corresponding fragment-ion signal. It not
Fig. 2 Time dependence of the fragment ion signal. (a) Full signal
symbols) and its decomposition into contributions from L –L . The
sum of these contributions is the simulation curve for the full signal.
b) L contribution to the fragment ion signal (symbols) with
(
1
3
(
3
only contains contributions from L (in contrast to the parent
3
exponential and modulated simulations. The division of these two
curves (and subtracting 1) results in the modulation function at the
bottom, whose Fourier transform is shown in the inset.
ion) but also from L and L . The latter time dependence (time
1
2
constants and parameters of the modulation functions) are
known from the parent ion and are subtracted. The result
(
3
Fig. 2b) shows a decay (t = 80 fs) with a modulation
where the amplitude A, wavenumber n (frequency nc) and
phase j are fit parameters. To extract the frequencies, we
divide the signals (or the contributions to them from the
showing two frequencies in the Fourier transform (n3a
140 cm , n3b = 270 cm ). At early times (o60 fs) this curve
also exhibits a weak high-frequency modulation with the two
=
ꢁ1
ꢁ1
different L , see below) by their exponential simulations; the
i
frequencies observed in L ; the structure also disappears
1
result (diminished by 1) is then Fourier-transformed. As it
turned out, all three L required the product of two factors of
within about t . Therefore we ascribe it to a residue from
L , which is obviously not perfectly eliminated from the signal
1
1
i
the type (1), because each L exhibits two modulation frequen-
i
by our subtraction procedure.
cies. Details of the procedure are described in ref. 46 and 49.
It should be noted that, in contrast to previous cases (e.g., in
ref. 46 and 49), eqn (1) does not contain a dephasing term
4. Discussion
(
exponential decay) before the cosine; introduction of such a
4
.1 Assignment of time constants and oscillations
factor resulted in an only marginal improvement, so that we
neglected it. That is, all detected oscillations practically decay
with the lifetime of the population at the corresponding
location. It seems that there is not much opportunity for
dephasing of the oscillations within the short lifetimes.
In Fig. 3 we assign the measured time constants to three
locations on the excited-state surfaces. These surfaces are
schematic cuts of the potential along a C -preserving coordi-
2
nate. (Calculated potentials along the minimum-energy path,
that also includes antisymmetric deformation, are shown in
ref. 11) The assignment is taken over from our previous
Table 1 summarizes the wavenumbers and time constants
resulting from the evaluation of the two time-dependent
signals. The error limits are estimated to be near ꢂ5%, as
determined in our previous experiments. Near the end of
section 5 we also discuss why it is justified to use rate equations
and time constants for part of the analysis, although there are
1
1,33,34
work.
It is based on the idea that the change of the
electronic energy can be roughly estimated from the ionization
probability and degree of fragmentation: a lower-lying state is
harder to ionize at the long wavelength used; on the other
1
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Fig. 4 Gas-phase UV spectrum (absorption cross-section s(n) versus
wavenumber n) of CHD (bold line), measured with 50 mbar in a 10 cm
cell. For enhancing the vibrational structure and showing the 2A band,
the spectrum s was multiplied (result shown by the thin line) by a
4
factor F (dotted line), where F = s/hsi and hsi is the spectrum after
ꢁ1
applying a Fourier low-pass filter. The pump laser is near 37 000 cm
ꢁ1
and has a half-width of E2100 cm
.
Fig. 3 Potentials for CHD ring opening with assignment of the
excited-state time constants and motion directions. The second conical
intersection (CI) is out of the drawing plane, as is also the path around
the first CI.
that involves CH –CH stretching (see below). One can con-
2
2
clude that the detection windows are not defined by the
molecule alone but also by the probing process, so that the
observation window for fluorescence can be narrower than
our L , and the width of L can depend on the duration of the
hand, it has vibrational excess energy (because the total energy
is conserved), and such a hot molecule will give rise to a hot
ion, which can then dissociate in the long time (nanoseconds)
before acceleration in the ion source. As already mentioned,
the assignment was recently confirmed by time-resolved photo-
electron spectroscopy: the spectra showed the 2B state, which
is left within 55 fs (which is very near to our t + t = 56 fs)
1
1
probe pulse.
The coherent oscillations in L1 are expected to be
Franck–Condon active vibrations, caused by the changed
bond properties in the p system after excitation. An obvious
assignment is the symmetric CQC stretch and the C–C stretch
ꢁ
1
ꢁ1
1
2
vibration for n1a = 1430 cm and n1b = 950 cm , respec-
tively (ground-state values 1579 and 945 cm , the latter
ꢁ
1
towards a lower-lying state (2A) with a lifetime of 84 fs (which
3
5
57,58
agrees well with our t = 80 fs); only one step on the 1B
strongly mixed with other vibrations
). They should also
3
surface was resolved with the long pulses in ref. 35.
be apparent in the UV absorption spectrum of CHD. In fact, a
weak modulation with four distinguishable peaks is detected in
3
3,34
Also our previously determined time constants
0 fs, t2old = 43 fs, t3old = 77 fs) agree well, if we compare the
sum t + t instead of the individual lifetimes. In fact, as said
(t1old =
ꢁ1
1
the spectrum (Fig. 4), converging from 1540 to 1360 cm
ꢁ1
1
2
(average 1440 cm ). The convergence is too rapid to be due to
anharmonicity, but is characteristic of superposition of two or
more progressions in the way as demonstrated in ref. 59. The
UV spectrum is much less well resolved than our Fourier
transform. Hence the broadening in the former (see the
simulations in ref. 59) is not only caused by the short lifetime
in ref. 33 and 34, the deconvolution method is more accurate
for the sum than for the individual constants; but also if we
compare the latter, the agreement is still satisfactory within
the standard deviation (ꢂ5 fs) quoted in ref. 33 and 34. On the
other hand, there might also be a physical reason behind the
small deviation: the limit between the detection windows
L and L will occur in a region, where the ionization energy
ꢁ1
(10 or 21 fs would give rise to a width of only 500 or 250 cm
)
1
2
but also by activity of additional vibrations that are not
active in ionization probing. A Franck–Condon activity of
the CQC vibration on ionization from the 1B state was
also found in the time-resolved photoelectron spectrum
(and hence the ionization probability) changes sufficiently; if
this change is not very sudden (i.e., if the ion potential rises
only gradually), it may be that our shorter pulses with their
1
ꢁ
1
35
0 times broader coherent bandwidth require a larger change,
(1350 cm in the ion).
ꢁ
1
so that t is lengthened at the expense of t
1
2
.
In L , we observed oscillations with n = 310 cm and
2
2a
ꢁ
1
From the fluorescence quantum yield a lifetime of the
emitting state of 10 fs was inferred in ref. 23 and 28, and it
was suggested that emission is stopped by depletion from
n2b = 630 cm ; the latter probably an overtone of the first.
Such low wavenumbers can only be due to ring puckering
(ring twisting); in the ground state they have wavenumbers of
2
3,28
ꢁ1
57,58
the spectroscopic 1B to the dark 2A state.
This would
199 (n ) and 506 cm
18
(n ),
ignoring antisymmetric
(b in C ) vibrations (which would appear only as overtones,
1
9
not be compatible with our t + t . We suggest that fluores-
1
2
2
cence fades much earlier, already on the 1B surface, by a
strong long-wavelength shift along the path. (The radiative
if active at all). They are outlined on the left of Scheme 1.
The lower-frequency vibration represents a twist of the
CH –CH group against the rest of the molecule, whereas
ꢁ3 56
rate depends on the emission wavelength l as l . ) In fact,
the S potential is expected to rise steeply along the path in L
2
2
0
2
,
n18 can be described as a conrotatory twist of the two CQC
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factor of 2–3 compared to observation. However, the calcu-
lated frequency is derived from the curvature in the minimum
(
harmonic approximation), whereas above the barrier of a
double-minimum potential a vibrational frequency usually
drops by a factor of two. The discrepancy is thus eliminated:
ꢁ1
the observed 140 cm then corresponds to a Dv = 2 overtone
of the calculated vibration, whose frequency is lowered by the
anharmonicity above the barrier. The higher wavenumber
Scheme 1 Vibrations in L
2
and L
3
, as discussed in the text. The
vibration observed in L (n
2
2
) is identified as n18. The right-hand
ꢁ
1
+
side shows the two symmetry-equivalent structures in the 2A minima;
the arrows indicate the coordinate (‘‘p*–CI’’ in the text) connecting
(n3b = 270 cm ) observed in the C
be the next higher overtone (Dv = 4). It would be unlikely
that n3b is just the same ring puckering as in L (wavenumber
2a = 310 cm ), since the geometric structure and bonding at
H
6 7
fragment may then
ꢁ1
them, which is also the coordinate of the 140-cm vibration (n3a).
2
ꢁ
1
n
bonds. If our observed n
2
corresponded to n19, it would imply
the two locations are very different.
that the n19 frequency was raised by 56% in 1B. This seems
unlikely; frequency lowering would be expected. In particular,
It may be worth noting that a frequency very similar to our
n3a was observed in optimal-control experiments: Carroll et al.
excited CHD by shaped 800 nm pulses, which implies three-
2
2,23
also because resonance Raman spectra
indicate an early
4
2,43
acceleration to the n18 direction but not to n , we compare our
photon excitation of the 1B or 2A state.
The hexatriene
19
ꢁ1
n2 in 1B (L ) with the 506 cm in the ground state. The
yield was highest with a pulse having a modulation with a
period of E250 fs (or a pulse train with this period), corres-
2
smaller wavenumber in 1B indicates that the restoring force in
this state is already strongly reduced along this coordinate. In
fact the calculation of ref. 11 for this vibration in the 1B
minimum (point ‘‘MEP(6)’’, which we identify with a point in
ꢁ
1
ponding to a wavenumber of E135 cm , very similar to our
n . Such pulses, which have side bands with a distance of
3
a
ꢁ
1
135 cm , efficiently excite via a Raman process vibrations of
such a frequency in the ground and/or excited state and in
such a way displace the molecule along the corresponding
ꢁ
1
our L
experimental n
As said above, the location L
2
) reports a value of 245 cm , not too far from our
2
.
6
1
3
is assigned to the 2A state.
direction. The ground-state frequencies are higher (and
would not be resolved by the long pulses in ref. 42 and 43).
According to the calculations (e.g. ref. 11, 17 and 18), the 2A
potential has two symmetry-equivalent very flat minima, in
ꢁ1
However it is an open question whether the 135 cm in the
control experiment can belong to a vibration in 2A far from
the Franck–Condon region.
which the C symmetry is broken. The structures are shown on
2
the right in Scheme 1: in one, C-atom 6 forms a weak three-
electron three-center bond with atoms 4 and 5, whereas in the
other the three-center bond connects atoms 1, 5 and 6. The
arrows indicate the coordinate connecting the two minima via
4
.2 Conclusions on the potentials and the reaction path
the flat C
minimum’’ p*, i.e., the 2A minimum in the cut shown in
Fig. 3); it is hence the symmetry-breaking coordinate (b in C ).
2
-symmetric saddle point (the traditional ‘‘pericyclic
It was already mentioned that many features of the potentials
and the path were only deduced from calculations, some from
interpretation of experiments. More evidence can now be
deduced from the observed oscillations. As pointed out, e.g.,
in ref. 44, after excitation the molecules are guided by the
slopes on the potential, even if after some advance on its path
the wave packet may deviate from the minimum-energy path
due to accumulated momentum. Down-slopes are the driving
forces. Typically, their direction changes repeatedly along the
2
Proceeding further along this direction beyond the minima
leads to the 2A/1A CI. Therefore this coordinate is called
p*–CI.
The main oscillation observed in L has a very small
3
ꢁ1
wavenumber (n3a = 140 cm ). The corresponding vibration
must again have a small restoring force and (or) must move
large masses. Hence also in this case one should consider some
ring deformations. An obvious candidate is a vibration along
the symmetry-breaking coordinate (p*–CI) above, because the
potential is very flat in this direction. In fact, its wavenumber
has been calculated in the 2A minimum: Celani et al. report
1
1,34
path, as also in the case of CHD ring opening.
Accelera-
tion on a slope can also cause oscillations of the wave packet,
if it is reflected back by a rising slope. (A common description
is based on the superposition of stationary vibrational
states in the Franck–Condon region by the coherent width
ꢁ
6
1
ꢁ1
ꢁ1
1
35 cm (Fig. 5 of ref. 6), whereas 204 cm was found more
(E1400 cm ) of a pump laser, which gives rise to oscillating
0
recently (for the method of ref. 60, see ref. 15 and 16); in both
cases it is the lowest frequency in this state. The small restoring
force (flatness of the potential) is unique for the p*–CI
coordinate and would be higher for other directions. Therefore
wave packets. This is just an alternative description to the
acceleration mechanism.) It may happen that such an oscilla-
tion is stimulated in an early location and is only (or still)
observed later. This is another momentum effect. Examples
are discussed below. If the vibrational coordinate can be
identified, it provides information on the direction of
the slope.
ꢁ
1
we assign our n3a = 140 cm oscillation to a vibration in the
p*–CI direction.
2
However, this coordinate is antisymmetric (b) in C . The
molecule has enough excess energy to vibrate above the small
barrier between the minima, so that the effective symmetry is
As pointed out in ref. 11, the initial slope of every photo-
chemical reaction is towards Franck–Condon (FC) active
coordinates, as is already implied by their definition. They
involve only the p system. Only later, when the molecule is
enough distorted to allow also interaction of s bonds with the
2
C . One should then only observe overtones (Dv = 2,
4
8–51
4
The lowest calculated frequency seems thus too large by a
,ꢃ ꢃ ꢃ. . .,
2
because the ion is probably also C symmetric.
1
76 | Phys. Chem. Chem. Phys., 2009, 11, 172–181
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p system, the Woodward–Hoffmann (WH) rules are turned on
and the direction of motion changes (by modifying the s bond
length, for instance). This rule is relatively general, too: it
1
1
6
2
was also found in H migration in cycloheptatriene, for
example, and plays an important role in cyclobutene ring
opening, where it can explain the deviations from the WH
6
3
rules.
It was argued in ref. 11, and substantiated by calculation
and by substituent effects, that the FC active modes not only
involve bond stretching in the p system but also double-bond
torsion. The latter distorts all the backbone of the molecule,
erecting also the CH
2 2
–CH bond, so that after some excursion
Fig. 5 Surfaces and illustrations of acceleration forces (double
arrows) and directions of vibrations (wavy lines; actually the indicated
ranges only comprise a single period). For a calculated surface, see
ref. 11. Most of the wave packet falls down from the 1B to the lower
the WH (s–p) interactions can in fact set in (Fig. 3). A more
1
8
recent calculation by Tamura et al. finds the same path. The
initial motion and acceleration directions are now confirmed
by the oscillations: two CC stretch vibrations are found in L1
2
1
A surface near the first CI; a small fraction remains, however, on the
B surface and completes an oscillation (thin wavy line). For the final
(
the FC region) and a CQC torsion (n , Scheme 1) in L . The
1
8
2
CI, only the two (symmetry-equivalent) positions are indicated.
Vibrations in the Franck–Condon (FC) region follow different
coordinates (CQC and C–C stretch) and therefore cannot be indicated
in this figure.
latter (period 110 fs) cannot be observed in the short-lived
21 fs) L , but is certainly stimulated already there (in the FC
region), because according to calculation the lower part of the
B surface before the intersection with 2A (i.e., location L ) is
energetically very flat, so that there is also no slope towards
(
1
1
2
the fact that the 1B/2A and 2A/1A conical intersections
6
4
n18. The fact that n18 is actually FC active is confirmed by the
resonance Raman spectrum.
have very similar branching spaces, also in other examples. )
The observation of an oscillation in the p*–CI direction
now provides a neat experimental confirmation of this
antisymmetric deflection near the first CI.
2
2,23
It is worth noting that distortion in n18 direction conserves
the C symmetry; i.e., it is conrotatory. This does not mean
that the WH rules are active already in the FC region. Instead,
the conrotatory initial acceleration follows from the fact that
2
With Fig. 5 we try to illustrate how the oscillations n
2
and n
3
are stimulated: The symmetric CQC torsion n (n18) is already
2
n
whereas the corresponding disrotatory combination of the
18 is totally symmetric in C
2
and thus can be FC active,
excited in the FC region, but only a small part of the wave
packet completes a full period, whereas the dominant part
immediately falls down to the 2A surface. (Only the division
5
8
CQC torsions (n36, b symmetry ) is antisymmetric and FC
inactive. (If CHD were planar, symmetry group C2v, also n18
through the exponential decay, exp(–t/t
brings the small part to light. A full period of 110 fs corres-
ponds to 3.2t , so that only exp(–3.2) = 4% of the molecules
2
), in the evaluation
2
would by antisymmetric, symmetry type a . On the other
hand, disrotatory distortion as in some CHD derivatives
would render n36 FC active. In fact, the importance of pre-
distortion for the choice e.g. between con- and disrotatory
reactions was pointed out in ref. 64). The conrotatory twist
2
are expected to have survived without decay.) Around the
1B/2A CI, the wave packet is accelerated to an antisymmetric
direction (the partial wave packets always being in symmetry-
(
n ) of the CQC bonds also implies a torsion of the C–C bond
3
equivalent positions). This eventually leads to the n vibration
1
8
between them; this is just the coordinate j, identified in the
calculations of de Vivie–Riedle et al. as the direction of initial
along the p*–CI direction over the double minimum. Also in
this case, only a small part of the wave packet (again revealed
through division by the exponential decay) performs a full
period, whereas most of it immediately passes through the CI
region down to the ground-state surface.
1
2–16,40
motion.
The low-frequency oscillation (140 cm and its overtone
ꢁ
1
ꢁ
1
2
70 cm ) in L
vibration along the minimum-energy path; i.e., along the line
p*–CI (antisymmetric in C ) connecting the C -symmetric
stationary point of 2A (‘‘pericyclic minimum’’ p*) with the
3
(2A state) was assigned above to an (overtone)
An early acceleration (near the first CI) towards the last CI
was also invoked in ref. 11 to rationalize the short t . The
3
2
2
argument can now be quantified. In fact, on a flat potential
such as from p* to the CI, i.e., in the absence of a strong
acceleration, the wave packet would normally find the outlet
(the 2A/1A CI) only by a kind of a diffusive process
2
potential is very flat,
A minima and 2A/1A CIs (Scheme 1). Since this region of the
1,18
1
the vibration must again have been
stimulated before. It is not excited in the FC region, because it
is antisymmetric (also because it very much involves the
6
(as assumed in ref. 6), which would be slow. By contrast,
former CH
initially be affected by the excitation). However, it was pointed
2
–CH
2
bond—see Scheme 1, which should not
the fastest conceivable process would be a ballistic motion
from the initial symmetric structure to the antisymmetrically
distorted turning point; starting from p*, the wave packet
could then reach the CI region (which is near the turning
point) in a quarter of the period of the corresponding vibra-
1
1
out that 1B - 2A relaxation requires an antisymmetric
b type) distortion, so that the wave packet circumvents the
B/2A CI around its lower cone; thereafter, the wave function
even has a node along the symmetry line connecting this first
(
1
ꢁ
1
tion. This time would be 120 fs for the 140 cm vibration
(which we assign to an overtone, see above), longer than
1
8
CI with p* (Fig. 5), a consequence of the Berry phase. The
calculations say that this deflection is just in the p*–CI
t = 80 fs. However, the acceleration in this direction is much
3
faster near the first CI, because the negative curvature on the
1
1,17,18
direction.
(The background of this theoretical result is
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lower cone of this CI is very much larger than at the stationary
point p*. (Values are given in terms of imaginary frequencies
in Fig. 9 of ref. 10.) Hence in this interpretation a ballistic path
of the wave packet in an antisymmetric direction, leading
eventually to the outlet to the ground state, already begins
in the surrounding of the first CI.
An alternative or supplementary mechanism to explain the
short t
means the energy minimum of the 2A/1A intersection space
IS). The IS extends also to molecular structures closer to
-symmetric geometries. (A point in the IS with C -symmetry
3
was also offered in ref. 11: ‘‘The 2A/1A CI’’ actually
(
C
2
2
1,18
1
lies, however, higher than our excitation energy,
which is
in the long-wavelength wing of the UV spectrum (Fig. 4). By
contrast, quantum-dynamical calculations with higher
initial energy predict a preferential passage through the
1
2–14,16,40
Fig. 6 Correlation of wavenumbers of ring vibrations with the
11
C -symmetric CI.
) If energetically reachable parts of
the IS are, e.g., by 30% closer to a C -symmetric structure, a
2
2 2
calculated CH –CH distance d.
2
6
7
ballistic trajectory could arrive at it in about 30% less time
(0.95 ps), certainly also due to hindering of ring twisting
(along the antisymmetric coordinate in this case). Similar
3
than in 120 fs, i.e., in about the measured t . However, even in
this case an early and rapid acceleration is necessary to trigger
a ballistic motion. The observation of the antisymmetric
vibration makes it most likely that this acceleration leads to
a region of the IS, which involves asymmetric distortion of the
molecule and is energetically easily accessible, although not
the very minimum of the IS, as already suggested in ref. 11.
The time for departure from the 2A surface was calculated by
quantum dynamics to 130–180 fs after leaving the FC region
(though smaller) substituent effects on the individual L
i
lifetimes have been found for two dialkyl derivatives of
CHD and have been interpreted by mass effects (i.e., not by
1
1
activation energies). A barrier before the last CI may also
arise, if extension of the p system (such as in photochromic
substances) lowers the spectroscopic state very much, but does
much less so with the 2A state and hence the 2A/1A CI;
2
1
activation energies were in fact calculated for such systems
and relatively slow ring-opening and closing times were
1
8
(
the path leading through the asymmetric CI region). This is
6
8,69
in the range of our t + t + t = 136 fs.
1
2
3
found.
An instructive correlation of the observed wavenumbers of
The region of the outlet from 2A (the 2A/1A IS), where the
wave packet actually passes through, cannot be very extended.
1
1
the low-frequency vibrations with the calculated distances d
of the two CH groups is possible, even without detailed
knowledge of the nature of n . It is shown in Fig. 6. The low
Otherwise the arrival time at S
0
would be spread over a certain
3
2
4
range. This would be in conflict with the finding that the
wave packet is still very compact, when it arrives at a location
3
frequencies indicate that these vibrations must be delocalized
5 0
(L in ref. 34) on the S surface, characterized by a narrow
over the ring and have a small restoring force such as twisting
ꢁ
1
resonance in the ion at this geometry. Hence the wave packet
seems to leave the 2A surface in a narrow region near the
minimum of the IS (usually called ‘‘the CI’’), which is near the
turning point of the antisymmetric vibration. In this case we
can expect that the 2A population drops in a stepwise manner.
Indeed a first such step can be recognized from the data of
Fig. 2 (near 110–130 fs); a second step is probably washed out
by interference between the vibrational frequencies.
or bending. The lowered wavenumber of n2a (310 cm , 61%
1
ꢁ
of the ground-state value of n18 = 506 cm ) indicates that the
ring is already weakened (restoring force 37% of that in S ),
consistent with the calculated beginning of d lengthening near
the first CI (i.e., in L ). A more drastic decrease of the
0
2
wavenumber and force constant occurs on arrival at the 2A
minimum. This is consistent with the very long calculated d
2
and the only weak interaction of one CH group with the other
A more or less ballistic path is, of course, only conceivable,
if any barriers are negligible compared with the available
excess energy. This is practically consistent with the calcula-
tions (an energy difference of E0.09 eV was found between 2A
end of the ring. The wavenumbers hence demonstrate
(in agreement with theory) that the ring begins to be opened
near the 1B/2A CI (near the 1B minimum) but advances very
much more on the 2A surface. On the other hand, the reaction
is not completed in the excited state; otherwise a ring vibration
would not exist anymore.
1
8
minimum and the last CI ) but can primarily be inferred from
the short time constants and the fact that they are the same
3
5
in a cold supersonic beam. This result should not be
generalized to all derivatives of CHD. Thus, the steroid
derivatives 7-dehydrocholesterol and ergosterol fluoresce
For completeness, we should also consider here the possi-
bility that—despite the calculations—the ring would already
ꢁ1
be fully open in the 2A state and the 140 cm would be a
hexatriene vibration. Indeed, in the ground state, Z-hexatriene
6
5
65,66
(
quantum yield 0.19 ) in a matrix at 80 K,
probably
7
0
because the initial conrotatory twist is hindered by the sub-
stituents, giving rise to a minor barrier. (This is another
confirmation that a ring twist such as n18 is FC active and is
required to reach the 1B outlet, i.e., the first CI: stretching of
CC bonds alone could not be hindered by bulky substituents
or the matrix.) Also the departure from the 2A state is slower
has vibrations of such low wavenumbers. They correspond
to hindered free rotation around the C–C bonds and to CCC
bending. However, they would both not be Franck–Condon
active in the probing transition, since the respective angles in
the ion would not (or not much) differ from those in the
neutral molecule. Hence these hexatriene vibrations would not
1
78 | Phys. Chem. Chem. Phys., 2009, 11, 172–181
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be observed, and the observed oscillation must be due to the
intermediate structure discussed above. Furthermore, it was
shown in ref. 34 by means of an ionic resonance that a
structure corresponding to Z-hexatriene is only reached after
(and probably more) examples, the acceleration direction
in the FC region controls, which of several WH-allowed
reactions are initiated later on.
On the basis of the calculated lengthening of the CH –CH
2
2
arrival on the S surface.
0
distance (Fig. 6), it was suggested that the ring opening is
7
already more or less complete before leaving the 1B surface.
,10
The ring vibrations observed by us, however, demonstrate that
the ring is still intact, though weakened, even in the dark state.
In principle, in the latter case most of the restoring force could
be located in the rest of the backbone, not in the weak three-
electron three-center bond (Scheme 1). However our previous
investigation shows that the geometrical structure of hexa-
5
. Concluding remarks
2
,3
For photochemical reactions, Woodward and Hoffmann
primarily considered the orbitals and the spectroscopic state
1B), i.e., the state resulting from excitation of one electron
from the highest occupied (HOMO) to the lowest unoccupied
LUMO) molecular orbital. Whereas in this way one could
(
(
0
triene is only reached on arrival on the S surface, some
rationalize, for instance, the ring opening of cyclobutene to a
diene, the backward reaction would be very endothermic
distance after the last CI (location L5 in ref. 34). This is
probably characteristic of all nonadiabatic photochemical pro-
cesses: the reaction already begins on the excited surface(s) but
is only half completed near the location of the radiationless
transition (through a CI) to the ground-state surface.
(
van der Lugt and Oosterhoff
42 eV) in this excited state. This problem was solved when
71,72
found that the dark state 2A
can have a low-lying minimum, the pericyclic minimum (p*),
resulting from an avoided crossing of the potentials correlating
the reactant ground state and a two-electron excited product
state and the corresponding pair for the backward reaction.
The observed coherent oscillations also confirm the previous
(e.g. ref. 11) ideas on the reaction path: initial motion along
FC-active coordinates (CC stretch and conrotatory CC
torsion), which after some excursion still on the 1B surface
(
Two recent calculations with time-dependent density-
functional theory for technical reasons also considered the
2 2
activates WH interactions (because the CH –CH bond is now
1
side.
B state alone and found a CI with S on the hexatriene
more parallel to the p orbitals); then on surrounding the
1B/2A CI, acceleration to a symmetry-breaking direction that
leads directly to a part (probably not the minimum) of the
2A/1A IS. The wave packet moves in ‘‘record time’’, i.e.,
within a small fraction of the periods of the torsional vibra-
tions along the local reaction coordinates; this is ascribed to
early acceleration in regions of the potential, where it is still
steeper. The largest part of the wave packet is transmitted
through the two CIs at the first attempt; only a smaller part
(revealed in the evaluation by division by the exponential
decay) passes by, oscillates and returns to the CI. This part
is small enough, so that on arrival at the ground-state surface,
the wave packet is still compact.
0
1
9,20
11,32–35
However the present and previous
time-
resolved spectroscopy shows clear evidence that the path
passes via the 2A state.) However, the calculations usually
show two 2A minima, a lower one in the WH-allowed and a
higher one in the WH-forbidden direction, both easily
accessible (see, e.g., ref. 72 for cyclobutene or Fig. 3 of
ref. 73 for butadiene); continuing in anti-WH direction, the
exit of the latter has a barrier. According to our results, the
molecules in the ‘‘wrong’’ minimum cannot simply go back
and then find the allowed minimum in the second attempt; this
path would imply an activation energy, and therefore this
process would be too slow to be compatible with our observed
short times.
In view of this more or less ballistic motion, one may ask
whether the analysis by rate equations (modified by periodic
modulation functions, eqn (1)) is justified. If the observation
windows, associated with the probing technique, were very
narrow, then the signal would reflect the shape of the wave
packet passing by the window; it would not be exponential.
However, these windows are broad (symbolized by the lengths
of the arrows in the figures), and the ionization probability
continuously varies within them. This may contribute to wash
out in the signals some signatures of a coherent or ballistic
The problem is solved by considering more than one reac-
tion, taking also into account that the initial acceleration is
towards the FC-active coordinates, whereas the WH rules are
turned on only later. In CHD, most molecules (those excited
2
from the lower-energy chair-like conformer with C symmetry)
initially follow a conrotatory path; thereafter, the WH-type
interactions facilitate its continuation via the first CI to the 2A
minimum and the last CI towards the allowed ring opening.
But a small fraction of the molecule (those excited from a
higher-energy boat-like conformer with C symmetry) are
s
motion. A similar suggestion, applied to dissociation reac-
75,76
6
4
accelerated towards a disrotatory direction. However, then
probably only in the 2A state, if the calculations for
tions, is due to Møller, Hendriksen and Zewail.
A closer
(
theoretical analysis would be desirable, however. It is a related
idea that we write the time constants besides the arrows, not to
localized points (‘‘states’’): if these times are as short as in
CHD, they mostly reflect the travelling times of the wave
packet, not any time for transmission through a bottleneck.
As already pointed out, breaking of the molecular symmetry
is necessary to render the radiationless (symmetry non-
conserving) 1B - 2A transition possible. The calcula-
7
3
butadiene can be generalized) a barrier resulting from WH
interactions hinders continuation towards disrotatory ring
opening. Instead, from there the molecules (such as many
dienes) can follow a nearly barrierless WH-allowed path to
the disrotatory ring closure to a cyclobutene derivative
(
bicyclo[2,2,0]hexene-2). (The fact that the diene - cyclobutene
path is nearly barrierless and ultrafast, was found for
cycloheptadiene and cyclooctadiene in ref. 74.) It was pointed
out in ref. 64 that CHD derivatives favoring the C -symmetric
1
0,11,18
tions
find substantial down-slopes in such a direction
near the 1B/2A CI, which are now confirmed by the observa-
s
conformer in fact prefer this disrotatory path. Hence in these
tion of the antisymmetric vibration (n ) after the radiationless
3
a
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transition. It is worth mentioning that the loss of molecular
symmetry also withdraws the basis for the ‘‘conservation of
orbital symmetry’’, which was the initial interpretation of the
28 M. K. Lawless, S. D. Wickham and R. A. Mathies, Acc. Chem.
Res., 1995, 28, 493–502.
2
3
3
3
9 S. Pullen, L. A. Walker II, B. Donovan and R. J. Sension, Chem.
Phys. Lett., 1995, 242, 415–420.
0 S. H. Pullen, N. A. Anderson, L. A. Walker II and R. J. Sension,
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2
,3
WH rules. The crucial property of the orbitals is the relative
sign on surrounding a full perimeter, i.e., the corresponding
bonding or antibonding properties.
Acknowledgements
33 S. A. Trushin, W. Fuß, T. Schikarski, W. E. Schmid and
K. L. Kompa, J. Chem. Phys., 1997, 106, 9386–9389.
34 W. Fuß, W. E. Schmid and S. A. Trushin, J. Chem. Phys., 2000,
This work was supported by the Deutsche Forschungsge-
meinschaft (project FU 363/1). We thank Regina de
Vivie-Riedle for providing the unpublished information on
the lowest-frequency vibration in 2A.
1
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