Time-resolved dissociative intense-laser field ionization for probing dynamics: Femtosecond photochemical ring opening of 1,3-cyclohexadiene

Time-resolved dissociative intense-laser field ionization for probing

dynamics: Femtosecond photochemical ring opening of 1,3-

cyclohexadiene

W. Fuß, W. E. Schmid, and S. A. Trushin

Citation: J. Chem. Phys. 112, 8347 (2000); doi: 10.1063/1.481478

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JOURNAL OF CHEMICAL PHYSICS

VOLUME 112, NUMBER 19

15 MAY 2000

Time-resolved dissociative intense-laser ﬁeld ionization

for probing dynamics: Femtosecond photochemical ring

opening of 1,3-cyclohexadiene

W. Fuß, W. E. Schmid, and S. A. Trushin^a)

¨

Max-Planck-Institut fur Quantenoptik, D-85740 Garching, Germany

͑Received 20 December 1999; accepted 24 February 2000͒

The concerted photochemical ring opening of 1,3-cyclohexadiene was investigated in the gas phase

by low-intensity pumping at 267 nm and subsequent probing by high-intensity photoionization at

800 nm and mass-selective detection of the ion yields. We found ﬁve different time constants which

can be assigned to traveling times along consecutive parts of the potential energy surfaces. The

molecule is ﬁrst accelerated in the spectroscopic state 1B along Franck–Condon active coordinates,

then alters direction before changing over to the dark state 2A. All constants including that for

leaving the 2A surface are below 100 fs. These times are shorter than appropriate vibrational

periods. Such a maximum speed is evidence that the pathway is continuous leading from surface to

surface via real crossings ͑conical intersections͒ and that the molecule is accelerated right into the

outlet of the 2A/1A funnel. On the ground state it arrives as a compact wave packet, indicating a

certain degree of coherence. The experimental method promises a high potential for investigating

dynamics, since many consecutive phases of the process can be detected. This is because the

fragmentation pattern depends on the location on the potential energy surface, so that monitoring

several different ions permits to conclude on the population ﬂow through these locations. Ionization

at the intensities used is normally considered to be an effect of the electric ﬁeld of the radiation. But

in our case it is enhanced by resonances in the neutral molecule and in particular in the singly

positive ion, and it is not sensitive for the length of the molecule ͑different conformers of the

product hexatriene͒. The ionic resonances explain why hexatriene has a much richer fragmentation

pattern than cyclohexadiene. Coulomb explosion is observed from an excited state of a doubly

͓S0021-9606͑00͒00819-9͔

I. INTRODUCTION

correlation lines ͑Sec. III͒.

Pericyclic reactions are not only important for organic

chemistry, but they can also serve as model systems in reac-

tion dynamics since it is easy to ﬁgure out qualitative poten-

tial energy surfaces for them on the basis of the Woodward–

Hoffmann rules. An example is the photochemical

electrocyclic ring opening of 1,3-cyclohexadiene. It has re-

cently been investigated quantum chemically,^1–4by

resonance-Raman spectroscopy^5–9and by ultrafast spectros-

copy ͑transient absorption in solution^10–13and transient ion-

ization in the gas phase^14,15͒. The molecule is excited in the

Scheme 1

The energetic distance ⌬E of the 2A minimum ͑far from

the Franck–Condon region we drop the subscripts 1 and 2,

because of the reduced symmetry͒ from the 1A maximum is

more than 1 eV.¹According to the Landau–Zener formula

͑see, e.g., Ref. 16͒,

*

UV spectral range ͑267 nm in this work͒ in a ␲␲ transition

to the ͑‘‘bright’’͒ 1B₂state, which very rapidly decays to the

␲²⌬E²

*

͑‘‘dark’’͒ ␲␲ state 2A₁͑see also Sec. III and Fig. 2͒. The

Pϭexp Ϫ

,

͑1͒

ͩ

ͪ

h ⌬s

v

2A₁surface is higher than 1B₂in the Franck–Condon region,

but after a crossing with 1B₂reaches a minimum or station-

ary point along the reaction coordinate. This so-called peri-

cyclic minimum as well as a maximum of the ground-state

surface at a similar geometry are characteristic of photo-

chemically allowed, ground-state forbidden pericyclic

reactions.^16,17Both result from an avoided crossing of two

a molecule passing this geometry with a velocity will cross

over to the lower surface with a probability P; ⌬s is the

magnitude of the difference of the asymptotic slopes. The

v

larger ⌬s, the larger is P. Using the fairly high values

v

⌬sϭ5 eV/Å and ϭ2ϫ10¹³Å/s, one obtains with the

v

above ⌬E the very small Pϭ4ϫ10^Ϫ11. That is, the mol-

ecules will oscillate more than 10¹⁰times in the upper well

before reaching the lower surface. This is unrealistically

long. Times in the lower picosecond range for ring opening

a͒

Also at B. I. Stepanov Institute of Physics, Belarus Academy of Sciences,

220602 Minsk, Belarus.

0021-9606/2000/112(19)/8347/16/$17.00

8347

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8348

J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Fuß, Schmid, and Trushin

and internal conversion have been measured for the cyclo-

hexadiene derivative 7-dehydrocholesterol,¹⁸for cyclohexa-

diene itself and a dialkyl derivative.^8,9,19More recently evi-

dence has been presented for even shorter reaction times in

the gas phase^14,15and in solution.^10–13,20͑The discrepancy to

the previous work is resolved in Refs. 13 and 20.͒ Here, as

already in the brief account of this work,¹⁵we report a 2A

lifetime t_2Aϭ77 fs for cyclohexadiene in the gas phase. This

is shorter than an appropriate vibrational period. This means

that already the ﬁrst attempt to cross is successful. Thus,

according to ͑1͒ ⌬EϷ0; that is, there must be a real crossing

between the surfaces and there is a continuous pathway from

the upper to the lower surface. In fact, such a pathway pass-

ing through a conical intersection between the 2A and 1A

surfaces is just what quantum chemical calculations have

predicted.¹From the short t_2A, it was further inferred in Ref.

15 that the conical intersection is easily accessible, in par-

ticular without any barrier, and surmised that it is situated

near the line of steepest descent of the 2A surface. Here we

discuss this suggestion ͑Sec. VI C͒ in the light of recent

MCSCF calculations.³

The data were measured by transient ionization in the

gas phase with mass-selective detection, pumping by weak

frequency-tripled Ti-sapphire laser radiation ͑267 nm͒ and

probing by the fundamental ͑800 nm͒ at high intensity. The

nonresonant ionization has the advantage that there are no

dark states. The various ion signals showed time behavior

different from each other, thus providing more information

than with a single signal alone. In fact, we obtained time

constants for several consecutive ‘‘phases’’ of the ring open-

ing. This is an advantage over transient absorption which

normally only probes a single electronic transition.

used^25,26femtosecond pump-probe setup with transient

photoionization combined with mass-selective detection of

ion yields.

The radiation source is based on a Ti-sapphire laser os-

cillator ͑Spectra-Physics, Tsunami͒ followed by a one stage

Nd-YLF pumped ͑527 nm͒ Ti-sapphire stretcher–ampliﬁer–

compressor device ͑Quantronics, Series 100 and 4800͒,

which supplies ultrashort pulses at 800 nm with energy up to

700 ␮J at a repetition rate of 1 kHz. This beam is split by

means of a dichroic mirror into two. One part is used as input

for frequency doubling and tripling in a commercial fre-

quency converter ͑CSK Optronics͒ with 0.5 mm thick LBO

and 0.3 mm thick BBO crystals. The third harmonic ͑267

nm͒ serves for pumping and the remaining part of the fun-

damental radiation for probing.

The duration of the probe pulse, measured with an auto-

correlator by frequency doubling ͑APE, Pulsecheck͒, was

110 fs ͑full width at half maximum͒. The pump pulse had a

Gaussian shape with a length of 130 fs as determined by

difference frequency mixing with the 800 nm pulse in a 0.1

mm BBO crystal. The unfocused pump beam ͑diameter 1

mm͒ and the probe beam focused to a spot size of 100 ␮m

͑by a lens with a focal length of 50 cm͒ were colinearly

combined and guided into the photoionization chamber using

a dichroic mirror. The probe had a peak intensity in the focal

plane of about 2ϫ10¹³W cm^Ϫ2and the pump about

10⁹W cm^Ϫ2. The latter corresponds to 0.13 mJ cm^Ϫ2; this is

0.1% of the saturation energy (h␯/␴) of cyclohexadiene, so

that 0.1% of the molecules will be excited. In all the experi-

ments, the polarization of the probe laser was parallel to the

mass spectrometer axis. The polarization of the pump laser

could be rotated by a half-wave plate, selected for a small

wedge angle. In most of the experiments the polarization was

set to the magic angle of 54.7° relative to that of the probe

laser. The half-wave plate, however, lengthens the pump

pulse to 145 fs; therefore in some experiments ͑to be indi-

cated͒ this plate was not used.

The probe intensity used was in

a range (2

ϫ10¹³W cm^Ϫ2) where multiple ionization is observed and

where the ionization is considered to be caused by the elec-

tric ﬁeld of the laser light. This intense-laser ﬁeld ionization

͑IFI͒ depends on the length of a bond ͑which can expand

21–23

during the ionization process͒

or ͑comparing different

The delay between pump and probe pulses was varied

with a resolution of 6.7 fs by a motorized translation stage

under computer control. The time-zero was determined as

the maximum of the transient ion signal for Xe which is due

to pure nonresonant (2ϩ2) multiphoton ionization under the

given conditions. Two ion signals ͑normally a Xe peak and

one of the cyclohexadiene-related signals͒ were simulta-

neously recorded in each pulse using two boxcar integrators.

This method provided synchronization of different scans

with an accuracy of Ϯ2 fs. The pump and probe beams were

alternately blocked by two synchronized choppers. Ion sig-

nals were periodically measured with pump only (I_pu), probe

only (I_pr) and with both lasers together (I₂) to determine the

transient ion signal S at a given delay time t, S(t)ϭI₂(t)

ϪI_puϪI_pr. Each signal is averaged over 1000 pulses. The

resulting signal-to-noise ratio was better than 300. For a

given mass the background (I_puϩI_pr) was typically kept less

than 30% of the maximum of the signal by limiting pump

and probe intensities. The ion signals and the pump and

probe energies ͑measured by photodiodes͒, recorded by

gated integrators, were stored in a computer for further

analysis.

chemical species͒ on the length of the molecule.²⁴Therefore

we expected to detect in this way also the length changes of

the product Z-hexatriene resulting from a thermal single-

bond isomerization, following the photochemical step

͑Scheme 1͒. But although this process was detectable by

resonance-enhanced photoionization¹⁴͑see also Sec. V D and

Ref. 15͒, the IFI signal turned out to be insensitive for it.

Another surprise was that the intense-laser ﬁeld ionization

seems to be enhanced by intermediate resonances ͑Sec.

VI B͒.

After presenting the experimental method, in Sec. III we

will brieﬂy introduce the potential energy surfaces and in

Sec. IV intense-laser ﬁeld ionization and its potential for

probing dynamics. In Sec. V we present the results with

some conclusions being drawn in each subsection separately.

II. EXPERIMENTAL METHODS

All the experiments were conducted in a gas-phase reac-

tion chamber at room temperature, employing the widely

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J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Femtosecond photochemical ring opening

8349

thermal dissociation of some ionic precursor in less than

about 1% of the extraction time cannot be distinguished from

prompt ions produced immediately by the probe pulse.

If the ions generated in the focal zone have an initial

kinetic energy with a horizontal component, they will be

forced on parabolic trajectories which may end at the sepa-

rating wall outside the slit area and therefore are lost. This

favors ions with vertical initial speed and favors the detec-

tion of double peaks from Coulomb explosions.

All the experiment was performed at a gas temperature

of 293 K. Diffusion ͑molecular velocityу100 m/s͒ and gas

ﬂow were sufﬁcient to replenish the irradiated volume in the

millisecond between the pulses and avoid any accumulation

of products.

Cyclohexadiene ͑Fluka͒ was used after degassing with-

out further puriﬁcation. According to gas-chromatography

mass-spectrometry it contained about 1% of impurities,

which did not disturb the measurements, however, since they

either absorb at shorter wavelengths than the pump radiation

͑1,4-cyclohexadiene͒ or only contribute a time independent

signal ͑benzene, i.e., the dehydrogenation product͒.

Hexatriene ͑product of ring opening͒ was present in concen-

trations of less than 0.3%. Z-Hexatriene used for some com-

parison experiments was recovered from the commercial

͑Fluka͒ mixture of Z- and E-isomers by scavenging

E-hexatriene with maleic anhydride.²⁷

FIG. 1. Setup for photoionization and mass-selective detection. The upper

part is equipped with CaF₂windows ͑W͒ for the laser beam ͑LB͒, two grid

electrodes ͑GR1, GR2͒ to accelerate the ions generated in the focal region

and a gas feed ͑GF͒ through precision needle valves. A wall ͑SW͒ separates

the gas cell ͑upper part͒ from the high vacuum chamber ͑lower part͒ with

the microchannel plate ͑MCP͒. The slit helps to maintain the pressure dif-

ference. DT is the ﬁeld-free drift tube and MS a magnetic shielding ͑mu

metal͒.

III. QUALITATIVE POTENTIAL ENERGY SURFACES

The electrocyclic ring opening of cyclohexadiene is a

prototype of the more general class of photochemical pericy-

clic reactions. It is easy to construct general, though qualita-

tive, potential energy surfaces for them ͑Fig. 2͒: According

to the Woodward–Hoffmann rules in the interpretation of

van der Lugt and Oosterhoff ͑see, e.g., Ref. 16͒, we have the

following.

The ionization chamber combined with a linear time-of-

ﬂight mass spectrometer is sketched in Fig. 1. In its upper

part the ions generated in the focal region of the laser beam

are accelerated in two steps by the ﬁelds between the two

grid electrodes ͑GR1, GR2͒ and the separation wall ͑SW͒.

Then, in the lower part, the ions travel through a drift tube

͑DT͒, which has a slit at its upper end and is closed by a grid

at the lower end, and are detected by a two-stage

microchannel-plate ͑MCP, Galileo͒. The gases were inde-

pendently fed through precision leak valves into the upper

part of the chamber. The gas ﬂow is set to provide a pressure

in the range 3ϫ10^Ϫ5–3ϫ10^Ϫ7mbar in the upper part and

10^Ϫ7–10^Ϫ9mbar near the MCP. The pressure ratio is

roughly given by the ratio of cross sections of the slit and of

the pump. The background pressure is Ͻ10^Ϫ9mbar. The

spacing between the grids is 10 mm, the ﬁeld strength 600

V/cm. The focus is centered between the grids. The spacing

of SW and GR2 is 5 mm and the ﬁeld strength between them

4800 V/cm. The ratio of the electric ﬁelds is 1:8, which is

optimum for spatial focusing. The ﬁeld-free drift tube is 250

mm long. The ion of mass 80 has a signal peaked at 3.6 ␮s

time of ﬂight with a pulse width of 8 ns. To pass the accel-

eration region between the focal zone and slit, such ions

require about 450 ns ͑extraction time͒. Ions produced by

͑1͒ The ﬁrst excited state ͑1B͒ of the educt correlates with

the ﬁrst excited state of the product.

͑2͒ The ground state ͑1A͒ of the educt correlates with a two-

electron excited state ͑2A in the ﬁgure͒ of the product,

and vice versa.

͑3͒ An avoided crossing of the correlation lines between 1A

and 2A creates a high barrier in the ground state ͑which

justiﬁes the denotation ‘‘ground-state forbidden’’ for the

reaction͒ and a collection well for the excited states. The

latter is called pericyclic minimum. It is biradicaloid in

character and has the same nature for all photochemical

pericyclic reactions, no matter which was the primary

excited state.

Figure 2 represents this general scheme. But the crossing

is not avoided everywhere. In a suitable section ͑different

from the drawing plane͒ of the potential surfaces there will

be a real crossing with the shape of a double cone ͑broken

lines in Fig. 2͒, and for the cyclohexadiene/hexatriene case¹

and several other pericyclic reactions²⁸it has been localized

by ab initio calculations. In contrast to the biradicaloid struc-

ture at the pericyclic minimum with its two decoupled elec-

trons, at the subsequent conical intersection ͑CI͒ four elec-

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8350

J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Fuß, Schmid, and Trushin

kind of potential energy surfaces. Such surfaces are, how-

ever, not known. The horizontal broken line only indicates

the minimum energy ͑2 eV ³¹͒ for fragmentation to C₆H^ϩ₇.

IV. DISSOCIATIVE INTENSE-LASER FIELD

IONIZATION FOR PROBING MOLECULAR DYNAMICS

Femtosecond time-resolved multiphoton ionization com-

bined with mass selective detection has proved to be a pow-

erful tool in time-resolved studies of chemical reaction

dynamics.^25,26,32,33But it was not recognized before³³that, as

we show here, the different ions can represent different lo-

cations on the potential energy surface; instead, it was often

supposed that the different ionic fragments reﬂect a dissocia-

tion of the neutral molecule. Originally we chose nonreso-

nant ionization at long wavelength ͑800 nm͒ expecting that

there will thus be no dark states since the process will not

depend on resonances. Indeed we detect signals from all

states theoretically expected to be populated. On the other

hand, ions sometimes have absorptions at very long wave-

lengths. By such a resonant ionic excitation with photode-

composition we interpret ͑Sec. VI B͒ why hexatriene has a

fragmentation pattern which is drastically different from that

of the reactant cyclohexadiene. This is another great advan-

tage over UV photoionization where the two isomers show

mass spectra which are practically indistinguishable.³⁴

A third advantage turned out in the course of this work:

Most of the many ions differ in their time behavior. Hence

there must be a number of different neutral precursors of the

ions. ͑All signals generated from a single precursor must be

proportional to each other, since one entity can only have

one time behavior, even if it contains several time constants.͒

These precursors cannot be chemical species since only two

͑reactant and product͒ are present. Hence they must be loca-

tions on the potential energy surface. The many signals thus

permit us to deduce the population ﬂow through a number of

such locations. Note that this conclusion does not depend on

the interpretation of the ionization mechanism presented be-

low. It is also worth mentioning that the many time constants

are not extracted from a single signal ͑multiexponential de-

cay͒; but most signals contain only one or two time con-

stants; each time constant is contained in several signals, so

that there is redundant information.

FIG. 2. Schematic potential energy surfaces of cyclohexadiene/hexatriene

C₆H₈and of the parent ion C₆H^ϩ₈. The arrows indicate pumping with one

*

267 nm photon and nonresonant 800 nm probing. The asterisk ͑ ͒ indicates

the position of the conical intersection ͑outside the drawing plane͒. Ioniza-

tion of the molecule from the 2A state results in the formation of a ground-

state ion but with an excess vibrational energy of about 2.5 eV, which is

partly due to the difference in the energies of the 1B and 2A states of the

neutral and partly due to the release of energy when the ion runs downhill

from the crossing region. This excess energy is enough to overcome the 2

eV barrier for dissociation of the parent ion C₆H^ϩ₈into C₆H₇^ϩϩH.³¹The

horizontal broken line with arrows indicates the threshold for this fragmen-

tation.

trons are decoupled, and the manner of recoupling decides

between formation of different products and the educt.²⁸So

the CI not only provides a fast outlet of the funnel to the

ground state, but is also a branching point determining quan-

tum yields ͑product formation versus internal conversion͒

and the probability of the different photoproducts.

The upper part of Fig. 2 also shows potential energy

curves for the ions. The ground states of the two ions belong

to different symmetry species ͑just as the highest occupied

orbitals of the neutral molecules͒ and therefore do not corre-

late with each other. The two states are above the neutral

ground state by about 8.3 eV ͑ionization energy 8.25 eV for

cyclohexadiene²⁹and 8.32 eV for hexatriene³⁰͒. According

to the photoelectron spectra, the ﬁrst excited state is higher

by 2.5 eV²⁹or 1.7 eV³⁰in the case of cyclohexadiene and

hexatriene, respectively. The next higher state can also be

inferred from the absorption spectra of the ions.³¹As in Ref.

31 they are correlated in Fig. 2 with the ground states of the

complementary ion.

Nonresonant ionization requires high intensity. We used

about 2ϫ10¹³W cm^Ϫ2. Under such conditions ionization is

usually assumed to be caused by the electric ﬁeld of the laser

radiation ͑amplitude about 1.3 V Å^Ϫ1͒.^35,36It is often accom-

panied by extensive fragmentation. It can be called dissocia-

tive intense-laser ﬁeld ionization ͑DIFI͒. In a classical

model^35,36the Coulomb potential for the electron and the

ﬁeld of an intense laser superimpose to create an ionization

barrier which for strong ﬁelds is low enough to cause efﬁ-

cient ionization of an atom or molecule. This model predicts

the threshold intensity I_BSIfor ionization of atoms by barrier

suppression:³⁵

I_BSIϭA IE͒⁴Z^Ϫ2

,

͑2͒

͑

where Aϭ4ϫ10⁹W cm^Ϫ2eV^Ϫ4is a numerical constant, IE

the ionization energy, and Z the charge of the resulting ion.

Following DeWitt and Levis,³⁶we also use it for molecules.

The fragmentation energy of the ions is also expected to

depend on coordinates, so that it could be represented by

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J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Femtosecond photochemical ring opening

8351

9

͑According to Schroder et al., Aϭ2.3ϫ10 W cm^Ϫ2eV^Ϫ4

for diatomic molecules.³⁷͒ For cyclohexadiene with IE

ϭ8.25 eV for the ground state, the threshold intensity calcu-

tion can serve to roughly determine the vibrational energy

and thereby help to distinguish different electronic states.

It may be asked why the excess vibrational energy does

not cause dissociation of the neutral molecules before it is

transferred to the ion. In fact hot-ground-state reactions have

often been observed, in the case of cyclohexadiene, for in-

stance, a H migration and H₂elimination.⁴³But they take a

time of the order of nanoseconds,^14,43,44much beyond the

time scale of the pump–probe delay. In other words, single-

photon excitation at 267 nm does not cause prompt dissocia-

tion of cyclohexadiene ͑two-photon excitation ionizes it͒, so

that all fragmentation observed must have occurred in the

ion. Although in the ion it may also be slow, only its result

will be monitored by the probe, since all processes taking

place after ionization, but within a time much shorter than

͑e.g., Ϲ 1% of͒ the time needed for extraction ͑about 450 ns

for mass 80, 280 ns for mass 30͒, will not be time-resolved.

Another consequence of the Franck–Condon principle is

that at some locations of the potential energy surface the ion

is generated with excess electronic energy. ͑The minimum

number of probe photons required is then, of course, larger.͒

This situation is typical of a photochemical reaction where

the molecule runs down a descending excited-state surface

͑its slope drives the reaction!͒, whereas the ionic ground-

state surface rises, being usually more similar to the ground-

state surface of the neutral. For example, ionization from the

pericyclic minimum of cyclohexadiene/hexatriene leads to

the top of a barrier ͑Ϲ 1.5 eV ³¹͒ in the ion ͑Fig. 2͒. ͑It may

be worth noting that, despite the increased distance of ionic

and neutral surfaces, the ionization energy from the pericy-

clic minimum is still smaller and the ionization probability

larger than in the ground state.¹⁴͒ The excess electronic en-

ergy plus the vibrational energy transferred from the neutral

͑about 1 eV, the calculated energy difference between the

Franck–Condon region and the 2A minimum͒ exceed the

ﬁrst fragmentation threshold ͑2 eV³¹͒ of the ion. Hence the

parent ion will not be generated from the 2A minimum.

Besides the excess electronic and vibrational energy, an-

other source of fragmentation is photodissociation of the ion.

Resonances in the ion will, of course, depend on its geom-

etry ͑see also Sec. VI B͒ and hence—to the degree to which

ionization is vertical—also on the position on the surface of

the neutral. Usually the absorption of long-wavelength pho-

tons is more probable in ions than in neutrals due to the

higher density of electronic states in the ions. Ionic photof-

ragmentation is operative in experiments with both nanosec-

ond and femtosecond pulses ͑see the review of Weinkauf

et al.⁴⁵and the discussion in Ref. 46͒.

¨

lated from ͑2͒ is I_BSIϭ1.8ϫ10¹³W cm^Ϫ2

.

If the ionization efﬁciency mainly depends on the ion-

ization energy, we can expect an enhanced ion signal from

every electronically excited state independent of its elec-

tronic and vibrational nature ͑no dark excited state, as men-

tioned above͒. Since IE changes along the reaction path ͑be-

cause the ionic and neutral surfaces are not parallel͒, the

ionization probability will depend on the location on a po-

tential surface. This interpretation—as also the model on

which Eq. ͑2͒ is based—tacitly assumes that the ionization

process is vertical. A position dependence is even expected if

the process is only vertical in a ﬁrst step ͑as often in multi-

photon processes͒, and such a dependence is sufﬁcient to

allow measuring time constants. In the following four para-

graphs we consider three reasons ͑excess vibrational and

electronic energy, photochemistry of the ion͒ why also the

fragmentation pattern depends on the location on the PES.

The Franck–Condon principle which is valid for vertical

transitions implies that most of the vibrational energy of the

neutral precursor is transferred to the ion. This is immedi-

ately obvious for the fraction of the energy contained in the

many Franck–Condon inactive modes ͑selection rule ⌬

v

ϭ0͒. In case of a compact wave packet running down along

the potential energy surface, the kinetic energy is even com-

pletely conserved during ionization; this is a consequence of

the original Franck principle³⁸which postulates conservation

of nuclear position and momentum in a vertical electronic

transition. The case of the wave packet is probably appropri-

ate for the ultrashort processes described here. One source of

the excess energy is transformation of electronic to vibra-

tional energy when a molecule runs down a potential energy

surface or when during internal conversion or chemical re-

action it crosses from an initially excited state to a lower

state. ͑Note that the total energy is conserved since collisions

are negligible in the gas phase in the fs time scale.͒ A similar

situation has already been found in alkylbenzenes, where

ionization from the vibrationally hot triplet state primarily

produced fragments, but not the parent ions.³⁹This picture is

also supported by the recent femtosecond photoelectron/

photoion coincidence studies of benzene, where after the

S₂→S₁internal conversion the photoelectron spectrum only

indicated high-energy ions,⁴⁰just as expected if the excess

vibrational energy of the neutral molecule is transferred to

the ion. Similarly, the photoelectron spectrum of hexatriene

only indicates ions with excess energy, if it is measured at a

delay ͑after UV excitation͒ after which some of the initial

electronic energy has already been converted to

vibration.^41,42If the vibrational energy thus transferred to the

ion exceeds the threshold for fragmentation, the parent ion

will not be observed anymore, but a fragment instead. Thus

when the neutral molecule runs down the potential energy

surfaces, more and more electronic energy is converted to

vibration, and the ions observed will be lighter and lighter. In

fact, we observed the lightest fragments at the latest times,

i.e., after recovery of the ground state ͑Sec. V D͒. Hence, if

the fragmentation thresholds are suitable, ionic fragmenta-

To summarize this interpretation, the ionization prob-

ability depends on the location on the potential surface, be-

cause the ionization energy depends on it ͑due to the nonpar-

allel surface of neutral and ion͒, and the fragmentation

pattern changes with geometry for three reasons.

͑1͒ Due to the excess vibrational energy released on the way

down the potential energy surfaces. This energy is trans-

ferred in a vertical ionization to the ion and there causes

fragmentation.

͑2͒ Due to excess electronic energy in the ion, since typi-

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8352

J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Fuß, Schmid, and Trushin

cally a higher part of the ionic surface is reached in a

vertical transition from a reactive surface of the neutral.

͑3͒ Due to photochemistry of the ion. Its resonances ͑which

can be at long wavelengths͒ depend on its geometry, and

its ground-state surface is reached without geometry

change from the neutral by vertical ionization.

Whereas a dependence on the location on the potential

can also occur at lower intensities, a special feature of ﬁeld

ionization at laser intensities comparable or higher than I_BSI

is multielectron dissociative ionization, i.e., multiple ioniza-

tion followed by dissociation through Coulomb explosion of

the charged fragments.⁴⁷Organic molecules under these con-

ditions usually produce all possible fragment ions,

CH^ϩ,CH₂^ϩ,CH₃^ϩ,C₂H^ϩ,C₂H^ϩ₂, etc., including atomic carbon

and hydrogen ions.^47–50With appropriate resolution some

fragment ions show a doublet splitting corresponding to the

recoil energy acquired in the Coulomb explosion, and such a

splitting proves the formation by this process. Such a struc-

ture is easily observed with the light atomic ion H^ϩ. The

splitting arises, because in any Coulomb explosion which

takes place in the ionization zone between the acceleration

grids, some charged fragments are ejected toward and some

away from the detector. The two groups of ions will differ in

their arrival time, and from this difference the kinetic energy

of the ions can be calculated.

Recently it has been found that DIFI is dramatically en-

hanced in various molecular and cluster systems at some

critical internuclear distances, larger than equilibrium

ones.^{21,23,50–52}Corkum and co-workers proposed to use the

DIFI sensitivity to atomic distances as a probe in time-

resolved studies of a dissociative system.²²However, as ex-

plained above ͑see also Secs. V A and VI B͒ the DIFI frag-

mentation pattern not only changes along a dissociation

coordinate, but more generally depends on the position on

the potential energy surface and on structural changes which

the molecules experience during photoisomerization.

FIG. 3. Photoionization mass spectra of 1,3-cyclohexadiene ͑CHD, solid

lines͒ and tZt-hexatriene ͑tZt-HT, dashed lines͒ obtained by irradiation of a

gas sample with 110 fs laser pulses at 800 nm and intensity of about 2

ϫ10¹³W cm^Ϫ2. The spectra are normalized to the intensity of the parent

ion. They were recorded under identical conditions ͑sample pressure and

laser intensity͒ giving a similar parent ion yield in both cases. The arrow

marks a peak at M/Zϭ40.5 amu which is most likely due to the doubly

ionized isotopic species ¹³CC₅H₈^ϩϩ

.

a characteristic doublet shape; the splitting is due to recoil

energy originating from the Coulomb explosion of a doubly

charged precursor ion.^21,51Using the peak-splitting time ⌬t,

the kinetic energy E_kinof the ions can be calculated by the

following equation ͑see, e.g., Refs. 21 and 54͒:

E_kinϭC ⌬t²/m͒ ⌬U/d͒²q²,

͑3͒

͑

V. RESULTS

In this section we also present, besides results, some

immediate conclusions at the end of each subsection and a

model for evaluation in Sec. V D.

A. Mass spectra

Whereas with low-intensity photoionization ͑e.g., at 267

nm͒ the mass spectra of cyclohexadiene ͑CHD͒ and

Z-hexatriene ͑HT͒ are almost indistinguishable ͑also with

REMPI⁴⁸͒, they show a rather different fragmentation pattern

when the molecules are ionized by an intense-laser ﬁeld ͑Fig.

3͒: The yield of the parent ion is practically the same for

both isomers if ionized at 800 nm with an intensity around

2ϫ10¹³W cm^Ϫ2, but in HT the light fragments with masses

around 51, 39, and 27 are more abundant by about a factor of

10, and the atomic ions C^ϩand H^ϩby two orders of magni-

tude, than in CHD.

FIG. 4. Time-of-ﬂight spectra ͑H^ϩsignal͒ of CHD ͑solid line͒ and tZt-HT

͑dashed line͒ obtained under the conditions of Fig. 3. The intensities are

normalized. The actual H^ϩintensity in CHD is about 100 times smaller than

in HT. The asymmetry between the components of high and low kinetic

energy is just the other way around than in previous observations. This

difference can be attributed to the discriminating properties of the slit used

by us at the entrance of the mass-spectrometer ﬂight tube ͑Ref. 53͒.

Formation of the atomic ions C^ϩand H^ϩis typical of

intense-laser ﬁeld ionization of organic compounds. It is usu-

ally attributed to dissociative multielectron ionization.^21,51In

fact, the H^ϩsignal in the time-of-ﬂight spectrum ͑Fig. 4͒ has

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J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Femtosecond photochemical ring opening

8353

where Cϭ0.120 eV ␮s^Ϫ2amu cm²V^Ϫ2, m is the molecular

mass, ⌬U/d the electric ﬁeld across the ﬁrst pair of accel-

eration grids and q the charge in units of the elementary

charge. The splittings in Fig. 4 are ⌬t_CHDϭ11.3Ϯ0.3 ns and

⌬t_HTϭ15.0Ϯ0.3 ns. For the ⌬U/dϭ422 V cm^Ϫ1employed,

this corresponds to a kinetic energy of the H^ϩion of 2.74

Ϯ0.15 and 4.82Ϯ0.20 eV in case of CHD and HT, respec-

tively. Double ionization is conﬁrmed by the peak at mass 40

with its satellite at M/Zϭ40.5; the latter is due to HT^ϩϩ

with a single ¹³C and shows the correct abundance. This

signal is obviously due to a stable state of this ion, whereas

the H^ϩis launched from a dissociative electronic state. The

H^ϩpeak was also noticed in a recent work;^24,55but its origin

from a Coulomb explosion was not recognized and a differ-

ent interpretation was presented. Double ionization was also

observed in aniline, pyridine and furan.⁵⁶

We cannot exclude that some other light fragments such

as those with the masses 51, 39 and 27 are also due to double

ionization and subsequent Coulomb explosion. If so, their

recoil-energy splitting seems not to be resolved by our in-

strument. However, we assume that they are actually photo-

chemical products of the singly positive ion. Some of the

ions thus produced may have vibrational excess energy and

may be metastable; i.e., they decompose during the extrac-

tion time ͑100–500 ns͒, thus giving rise to broad peaks. The

broad group of peaks around mass 12 may be such a case,

too, although other workers^21,51prefer to assign it to Cou-

lomb explosion. Levis et al. ascribe the broadening to recoil

in some impulsive dissociation of the neutral;⁵⁵but such a

process seems to us less probable when many bonds have to

be broken, such as in this case.

FIG. 5. Transient time-of-ﬂight spectrum of CHD ͑dashed line͒ recorded at

400 fs delay after single-photon pumping at 267 nm with 145 fs laser pulses.

The spectrum is obtained with photoionization by delayed pulses at 800 nm

and intensity of about 2ϫ10¹³W cm^Ϫ2. The solid curve shows a spectrum

of static tZt-HT recorded under identical conditions but with 800 nm only

͑see Fig. 3͒. The spectra are normalized to the intensity of the H^ϩion in

each case. The numbers near the peaks indicate the mass values.

We will discuss in Sec. VI B why HT is more liable to

ionic photodissociation and multielectron ionization and thus

shows more light fragments than its isomer CHD. The ob-

served drastic difference between the DIFI mass spectra of

the two molecules ͑Fig. 3͒ has a practical consequence: It

allows us to monitor the appearance of the photoproduct and

its identiﬁcation. This expectation is conﬁrmed by Fig. 5

where the transient IFI mass spectrum, recorded at 400 fs

delay after one-photon excitation of CHD at 267 nm, is pre-

sented together with the DIFI spectrum of not pre-excited

HT. The two spectra are obviously very similar not only in

the presence of the light fragments and their pattern, but also

in their recoil structure ͑the lower part of Fig. 5͒. The only

difference is that the 400 fs spectrum also shows a strong

depletion ͑i.e., a decrease compared with negative delays͒ of

HT^ϩϩ. This is not unexpected, since it will be hot when

produced from hot neutral HT, so that the corresponding ions

will decompose. The similarity of the spectra clearly shows

the presence of some form of hexatriene at 400 fs. It can be

concluded that the ring opening is already complete at this

time.

constants do not depend on the ionizing probe energy, al-

though the relative height of the H^ϩpedestal decreases with

lowering of the probe energy. According to Sec. IV and Fig.

3, we can expect that the parent ion C₆H^ϩ₈͑mass 80͒ and the

fragment C₆H^ϩ₇͑mass 79͒, which is also the strongest one in

electron-impact⁵⁷and low-intensity photoionization³⁴mass

spectra, will contain information about the temporal history

of electronically excited states, whereas the light fragments

including atomic ions will reﬂect the product appearance and

processes in the ground state.

Typical transient signals for the former two ions are pre-

sented in Fig. 6 in a singly logarithmic scale. The broken

curve shows the response function calculated for

(1ϩ3)-multiphoton ionization ͑3 is the minimum number of

probe photons required to ionize the 1B state͒ on the basis of

the measured pulse shapes and time zero. The signals of the

masses 80 and 79 instantaneously grow with the pump pulse,

reach their maxima at 26 and 60 fs and then decay to values

near zero. After the pump–probe overlapping region both

ions show exponential decay over more than two orders of

magnitude with decay time constants of 43Ϯ3 fs for the par-

ent and 77Ϯ7 fs for the fragment ions. These values are

averaged over at least 10 independent scans. They do not

depend on the intensities and relative polarizations of the

pump and probe beams. Only at higher pump energies a

small negative pedestal at long delay can be seen for both

masses owing to a partial depletion of the educt. In order not

B. Time dependence

To monitor the dynamics of the photochemical ring

opening of CHD, we recorded the delay-time dependence of

various ion yields. All the transient ion signals were found to

be proportional to the pump energy, which conﬁrms that they

are produced by absorption of a single UV photon. The time

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8354

J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Fuß, Schmid, and Trushin

FIG. 6. Relative ion yield in CHD for the parent C₆H^ϩ₈and fragment C₆H^ϩ₇

ions versus the time delay between the 130 fs pump at 267 nm and the 110

fs probe at 800 nm. The symbols show the experimental data and the lines

represent singly exponential ﬁts to them. The broken curve is the response

function calculated for a pump pulse of 130 fs FWHM and a probe pulse of

110 fs FWHM assuming that three probe photons are used for ionization.

The shape of the transient signals for the parent and fragment ion at mass 79

does not depend on the relative polarizations of the laser beams. Note: The

data are slightly offset in such a way as to have a zero pedestal at long delay.

FIG. 8. Anisotropy r of the H^ϩsignal in CHD versus delay time t between

the 267 pump and the 800 nm probe. r has been calculated from the transient

H^ϩsignals recorded for parallel (S_ʈ) and orthogonal (S_Ќ) polarization by

using Eq. ͑3͒. For normalization, rϭ0 (S_ʈ/S_Ќϭ1) has been assumed for the

region of the minimum around 1700 fs. The solid curve shows a single-

exponential ﬁt to the data in the region 500–1300 fs, giving an anisotropy

decay rate of 1.72Ϯ0.22 ps^Ϫ1

.

fragments with the masses 39, 27 and 1 measured under

these conditions. These fragment ions C₃H^ϩ₃, C₂H₃^ϩand H^ϩ

show practically the same steep growth as the parent ion, but

delayed relatively to it. The delay is most pronounced for H^ϩ

where it is as large as 170 fs. H^ϩreaches a maximum at 200

fs and then drops to a positive pedestal value. The fragment

ions C₃H^ϩ₃,C₂H^ϩ₃behave similarly, but are less delayed and

more broadened as compared with H^ϩ. They reach their

maxima at 110 and 140 fs, respectively, and then decay to a

positive pedestal. A pedestal indicates that the end product

contributes to the signal. As shown in Fig. 7, the decaying

part of all three signals can well be approximated by a single

exponential with time constant of 77 fs, the same as for the

decay of the fragment ion C₆H^ϩ₇. After 400 fs none of the

monitored signals shows any change over at least 60 ps ͑with

probing under the magic angle͒.

to distort the singly exponential decay in the logarithmic

scale in such cases, the data presented in Fig. 6 have been

offset to have a zero pedestal at long delay.

In contrast to the masses 80 and 79, the signals at lighter

masses depend on the relative polarization of pump and

probe. Therefore their kinetics was studied with magic angle

͑54.7°͒ between pump and probe polarizations. Figure 7

shows the transient signals for the parent ion and the ionic

The polarization dependence was studied in detail for

the H^ϩsignal. It is typical of orientational relaxation of

freely rotating anisotropic molecules.^58,59Its kinetics is most

easily seen in a plot of the rotational anisotropy r,

rϭ S ϪS ͒/ S ϩ2S ͒,

͑4͒

͑

ʈ

Ќ

where S_ʈand S_Ќare the transient ion signals with the polar-

izations of the pump and probe parallel and perpendicular,

respectively. Figure 8 shows for H^ϩthe decay of r versus the

delay time t. Although the experimental conditions for one

given polarization were very stable, there is some uncertainty

of the absolute signal values in different runs, due to a varia-

tion of the spatial overlap for pump and probe beams after

realignment to change the polarization. Therefore in evaluat-

ing the anisotropy we set for simplicity rϭ0(S_ʈ/S_Ќϭ1) for

the region tϭ1.7 ps where r has a minimum, and normalized

the experimental data accordingly. This assumption can in-

ﬂuence only the absolute values of the anisotropy, but does

not change the rate constants. In the region 0ϽtϽ0.3 ps, the

FIG. 7. Relative ion yield in CHD for the parent C₆H^ϩ₈͑dashed curve͒ and

fragments C₃H^ϩ₃͑squares͒, C₂H^ϩ₃͑triangles͒ and H^ϩ͑circles͒ ions versus the

time delay between the 145 fs pump at 267 nm and the 110 fs probe at 800

nm. The solid lines show one-parameter single-exponential ﬁts to the tail of

fragment ions using a ﬁxed time constant of 77 fs. In this ﬁtting only the

pedestal values were varied; two-parameter ﬁtting gives for H^ϩ75Ϯ7 fs and

for the 27-amu and 39-amu fragments the little bit longer decay of 90

Ϯ10 fs. The data were recorded with a relative angle of 54.7° between

pump and probe polarization.

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J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Femtosecond photochemical ring opening

8355

anisotropy has a constant value of 0.33, then it drops to the

minimum around tϭ1.7 ps and thereafter recovers to about

0.02. Such oscillatory behavior is typical of orientational re-

laxation of freely rotating anisotropic molecules.⁵⁹A signal

beginning at a positive r ͑near 0.4͒ and then decaying means

that the dipole moments for the pump and probe transitions

͑the latter will be identiﬁed in Sec. VI B͒ are ͑nearly͒ paral-

lel, whereas with perpendicular transition moments r starts

from a negative initial value. The minor initial rise and

slightly delayed decay which were observed probably mean

that the two dipole moments form a small nonzero angle

with each other. In the decaying part ͑0.5–1.2 ps͒ the data

can be ﬁtted by a singly exponential decay with a rate of

k_rϭ1.72Ϯ0.22 ps^Ϫ1. Using the equation given in Ref. 59,

such a decay rate would be expected from a molecule of

moment of inertia ␪ϭ171 amu Å²rotating at room tempera-

ture. This ␪ is very near the values calculated for cyclohexa-

diene ͑184 amu Å²for an axis perpendicular to the ring; the

other two ␪ are half as large͒ and the cZc conformer of

hexatriene whose moments of inertia are certainly very simi-

lar. The tZt conformer would have ␪ϭ35, 321 and 356 amu

Å²along its three axes. Hence we can conclude that at least

a large fraction of the product identiﬁed in Sec. V B as

hexatriene (at 400 fs) is the cZc conformer. So at this time

this ͑expected͒ primary product has not yet undergone

single-bond isomerization to other conformers. From the ob-

servation of the cZc moment of inertia we can also infer that

the strong ﬁeld of the probe laser does not automatically

stretch the molecule during multiple ionization to its longest

͑tZt͒ conformer.

contributions from different precursor states. These contribu-

tions can be extracted by kinetic modeling, as done in the

following.

To derive information about the dynamics of cyclohexa-

diene ring opening from the kinetics of various ion signals,

we assume that the pathway is not branched and describe the

population at each location ͑level, observation window͒ by

rate equations. It is common to model the dynamics in fem-

tosecond transition-state spectroscopy by rate equations ͑see

Ref. 61 and references therein, and Ref. 62͒. Although such a

model ignores coherences,⁶³it is powerful in providing the

nature of population ﬂow. A justiﬁcation is that we observed

exponential decays ͑which are solutions of rate equations͒ in

some examples ͑Fig. 6͒ over 2.5 orders of magnitude. On the

other hand, signs of a coherent effect were observed, too

͑compactness of the H^ϩsignal; see the end of this section͒.

The ion signals are then calculated from these time-

dependent populations ͑resulting from the rate equations͒ by

convolution with the measured pump and probe pulse

shapes.^61,64According to Sec. II, the pump pulse is well de-

scribed by a Gaussian ͑full width ␶_puat half maximum͒. The

time-dependent population of the ith level N_i(t) produced by

this ﬁnite-length pump pulse is then given by

t

N t͒ϭ

n tϪt ͒I t ͒dt ,

͑5a͒

͑

Ј

pu

Ј

͵

i

Ϫϱ

where I_pu(t)ϭI⁰_puexp(Ϫ␣_put²) is the normalized intensity of

the pump pulse, ␣_puϭ4 ln 2/␶_pu; n_irepresents the population

2

resulting from the rate-equation calculations with an inﬁni-

tesimally short pump pulse, n_i(t) being a sum of exponen-

tials. Then convolution with a probe pulse of length ␶_prgives

the contribution of the ith level to the intensity of the ion

signal at mass M at a pump–probe delay time t:

Evidence has been presented that in solution the con-

former isomerization begins in the subpicosecond range; but

a time constant ␶

could not be given since this process

conf

ϱ

competes with vibrational cooling.^11,13,60So we expect ␶

^MS t͒ϭ^M␴

N t ͒I^mt Ϫt͒dt ,

͑5b͒

͑

Ј

i

͑

Ј

pr

Ј

conf

͵

i

Ϫϱ

between 1 ps and 400 fs in the gas phase. Therefore we

re-assign the time constant of 580Ϯ60 fs found in the gas

phase¹⁴by transient resonance-enhanced multiphoton ioniza-

tion ͑REMPI͒ to the single-bond isomerization. It is probably

the shifting of the UV spectra and increase of absorption

during this process^11–13which sensitizes REMPI for this

isomerization.

In the temporal regionм600 fs, the DIFI signals ͑Fig. 7͒

do not change. This is surprising, since the length of

hexatriene increases from its cZc to its tZt conformer by

nearly a factor of 2, and a length dependence was expected

for ﬁeld ionization. Obviously, with our intensities there is

no strong dependence of the DIFI signals on the length of

hexatriene. In Sec. VI B we point to the dominating inﬂuence

of resonances in the hexatriene ions.

where I_pr(t)ϭI⁰_prexp(Ϫ␣_prt²) is the normalized intensity of

the probe pulse, ␣_prϭ4 ln 2/␶², ^M␴ is the effective cross

i

pr

section to produce the ion of mass M from the i-th level and

m the effective order of the ionizing process. ͑Also in DIFI,

one ﬁnds that the ion yields are proportional to a power of

I.²⁴͒ It can be shown ͑using Heaviside’s step function to

match the integration limits, then invoking that convolution

is commutative and associative͒ that Eqs. ͑5a͒ and ͑5b͒ can

be contracted to

t

^MS t͒ϭ^M␴

n tϪt ͒I

t ͒dt ,

͑

Ј

instr

͑5c͒

͑

Ј

͵

i

Ϫϱ

where the instrumental function I_instrϭI⁰_instrexp(Ϫ␣_instrt²) is

the correlation of the pump with a suitable power ͑m͒ of the

probe pulse, ␣_instrϭ4 ln 2/␶_instr,␶_instrϭ␶_puϩm^Ϫ1␶_p²_r. The lat-

ter relation shows that the exact value of m practically does

not matter, as long as mм3: Inserting mϭ4 instead of 3 and

2

C. Simulation by a rate-equation model

It was explained in Sec. IV that different locations on the

potential energy surfaces have different ionization probabili-

ties and fragmentation patterns. In an ideal situation, each

region would give rise to just one ion. Then a decay of one

signal would be connected with the rise of another one with

the same time constant. Actually each fragment ion contains

the pulse lengths of Sec. II, ␶

just decreases by 2%.

instr

Therefore we did not determine this parameter, but chose it

͑see Scheme 2͒ according to energy considerations. Since the

solutions of the rate equations are a sum of exponentials, Eq.

͑5c͒ results in an analytical expression ͑containing the error

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8356

J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Fuß, Schmid, and Trushin

signal, giving a longer delay ͑a broken line in Fig. 10͒. The

assumption of a preceding short-lived (␶₁ϭ10 fs) level with

80

higher ionization probability ͑ ␴₁Ͼ⁸⁰␴₂, Table I͒ than in

the following 43 fs removes the deviation and perfectly re-

produces the parent ion signal. Only the levels 1 and 2 give

rise to the parent ion. The third time constant ␶₃ϭ77 fs is

mainly from the tail of the fragment ion C₆H^ϩ₇. The simula-

tion also reproduces the full temporal behavior of this signal,

in particular also its early appearance, if we assume a rather

high contribution from locations 1 and 2 ͑expressed by the

quantities ⁷⁹␴ and ⁷⁹␴ ͒. As mentioned, this is probably due

1

2

to photodissociation of the parent ion produced from these

early levels.

To describe the time behavior of H^ϩ͑Fig. 11͒, we must

introduce into the rate-equation model at least three more

levels. The ﬁrst of them, level 4 with lifetime ␶₄, does not

contribute intensity to the H^ϩsignal (¹␴₄ϭ0), but gives rise

FIG. 9. Time constants ͑in fs͒ resulting from the kinetic simulation of the

experimental data ͑see Figs. 10 and 11͒ of the cyclohexadiene ring opening

with assignments to regions or levels ͑their numbering is encircled͒ of the

potential energy surfaces. Note also the interpretation of these times as

traveling times in Sec. VI.

to a shift without broadening. The ﬁfth level with lifetime ␶

5

is responsible for the H^ϩspike and the sixth one with an

‘‘inﬁnite’’ ͑Ͼ50 ps͒ lifetime accounts for the H^ϩpedestal.

The steepness of the leading front of the H^ϩsignal is close to

the experimental response limit and the decay of the trailing

edge coincides with the lifetime (␶₃) of the third level. This

is expected if ␶₄,␶₅Ӷ␶₃. To reproduce the shift of the H^ϩ

signal, the model requires ␶₄ϩ␶₅ϭ55 fs. With ␶₄м35 fs and

␶₅Ϲ20 fs the model reasonably well reproduces both the

steep leading front and the decay of the H^ϩsignal ͑the solid

line in Fig. 11͒. However, the calculated signal is still

function͒ which can be directly used in ﬁtting to the mea-

sured data using commercial evaluation software. Parameters

resulting from the ﬁt are the time constants ␶ and the ion-

i

M

ization probabilities ␴_i.

It was found that the main features of the early kinetics

for all ions can be reproduced by the rate equations using six

levels connected by ﬁve time constants ͑Scheme 2; see also

Fig. 9͒. These ﬁve constants are a minimum set to achieve a

good ﬁt. Only two ͑43 and 77 fs͒ of them can be directly

read from the exponential tails of suitable signals ͑Figs. 6, 7

and Sec. V B͒. The smaller one is from the tail of the parent

ion. However, a simple convolution of an exponential func-

tion with a time constant of 43 fs with the instrumental func-

tion noticeably deviates from the experimental parent-ion

SCHEME 2. Levels ͑observation windows͒ used in the kinetic simulation.

The ﬁrst level ͑L1͒ is the initially excited state 1B₂of cyclohexadiene in the

Franck–Condon ͑FC͒ region, and the sixth level ͑L6͒ is the primary photo-

product of the ring opening: the ground state 1A₁of cZc-hexatriene. To

account for the main features of the kinetics of all the fragments, we must

introduce at least four intermediate levels, L2–L5. L4 and L5 are two inter-

mediate regions on the ground-state surface; the former is near the conical

intersection ͑CI͒ and the latter location shows some resonance with the

probe laser. The parameter m_i, entering in Eq. ͑5b͒, indicates the order of

the ionization process. The simulation is not very sensitive for the value of

m_i͓м3, see near Eq. ͑5c͔͒. The m_ivalues used are indicated in the captions

of Figs. 10 and 11 which compare the experimental data with the simulation.

A set of parameters, for which the kinetics of all the ions within the 6-level

rate-equation model can be well simulated, is presented in Table I.

FIG. 10. A comparison of experimental data ͑from Fig. 6͒ for the parent

͑squares͒ and fragment C₆H^ϩ₇͑circles͒ ions with the results of the simula-

tion. The dashed curve shows a single exponential decay ͑time constant 43

fs͒ convoluted with a one-photon pump pulse ͑130 fs FWHM͒ and a three-

photon probe pulse ͑110 fs FWHM͒. The solid curves result from simulation

80

using the ﬁrst three levels of Fig. 9 and the ionization cross-sections

␴

i

79

and ␴ of Table I. The order m of the ionization process is assumed to be

i

3 for forming mass 80 and 5 for forming mass 79.

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J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Femtosecond photochemical ring opening

8357

TABLE I. Experimental results and simulation parameters for the six-level

rate-equation model. ␶ is the lifetime of level i ͑traveling time through

i

observation window i͒ and M the relative ionization cross-section to pro-

␴

i

duce an ion of mass M from this level. ␶

is the time ͑calculated from ␶

1

prod

and ␶ ͒ needed to form 63% of the product in its ground state ͑ring-opening

5

time͒, ␶_rotthe time constant for rotational anisotropy decay of the H^ϩsignal.

The inﬁnity sign stands for lifetimes Ͼ50 ps. ␶_prodand the level lifetimes ␶

1

to ␶ are also given in Fig. 9.

5

level ͑i͒

1

2

3

4

5

6

␶_i/fs

10Ϯ5

1.0

0

43Ϯ3 77Ϯ7 м35^a

Ϲ20^a

ϱ^b

0

80

␴

0.23

0.87

0

0.53

0

0.7

0.9

0

i

79

␴

i

39

␴

27

0.7 0.05

0.9 0.096

1.0 0.068

i

␴

0

i

1

␴

i

␶

_prod/fs

_rot/fs

205

580Ϯ75

a

␶₄ϩ␶₅Ϸ55 fs.

^bThis level comprises the conformers of Z-hexatriene, not distinguished by

probing at 800 nm. Relaxation from cZc hexatriene to a high-temperature

equilibrium of conformers proceeds with a time constant of ␶_confϭ580

Ϯ60 fs, as is detectable by REMPI at 280–300 nm ͑see Sec. V D͒.

FIG. 11. A comparison of experimental data ͑from Fig. 7͒ for the fragments

C₃H^ϩ₃͑squares͒, C₂H^ϩ₃͑triangles͒ and H^ϩ͑circles͒ with the results of the

simulation. The dashed curve shows the experimental signal for the parent

broader than the experimental one. This inconsistency can be

removed by simulating the H^ϩsignal with a modiﬁed six-

level kinetic model with a single bottleneck for the third

level ͑␶₃ϭ77 fs, lifetimes of all preceding levels assumed

Ͻ4 fs; note that the preceding levels do not contribute to the

H^ϩsignal͒ and with an artiﬁcial time offset of ϩ103 fs. The

ion C₆H^ϩ₈͑curve 1 of Fig. 10͒. The solid curves result from the simulation

M

using all six levels of Fig. 9 and the ionization cross-sections ␴ of Table

i

I. The order m of the ionization process is assumed to be 5 for ion formation

from the ﬁrst level and 6 from the others. The dotted curve shows the H^ϩ

signal simulated by the six-level rate-equation model with one single bottle-

neck of 77 fs for leaving the third level ͑lifetimes of all other levels are

1

results of the calculation for ␴₅:¹␴₆ϭ1:0.016 are shown

1

by the dotted line in Fig. 11. This description approximates a

‘‘coherent’’ motion of a nonbroadening wave packet on the

potential surfaces with only one bottleneck: the departure

from level 3. In photodissociation of iodobenzene Zewail

and coworkers observed a similar delay and ascribed it to a

coherent motion of the wave packet.⁶⁵

Fitting to the experimental data not only yields the time

constants for the various steps, but also their sequence. Spe-

cial considerations are then required to assign each level to a

deﬁnite location on the potential energy surfaces.

shorter than 4 fs͒ and ϩ103 fs temporal offset, assuming ␴₅:

␴

6

ϭ1:0.016. This model approximates a nonbroadening ‘‘coherent’’ motion

of a wave packet on the potential energy surfaces with the departure from

the 2A surface as the only bottleneck.

after which the conversion of electronic energy of the 1B

state to vibration is becoming substantial͒. Most likely this

region terminates near the crossing point between the 1B and

2A surface, where there is a sharp change in the slopes of

potential curves. So we assign this time of 43 fs to the de-

parture from the 1B state.

The ﬁrst level with its lifetime of ␶₁ϭ10 fs must corre-

spond to departure from the Franck–Condon region, because

the same lifetime was deduced from the ﬂuorescence quan-

tum yield,⁵and according to the spectrum the ﬂuorescence in

fact came from the Franck–Condon region. The second level

͑lifetime of ␶₂ϭ43 fs͒ then must be related with the later

parts of the 1B surface probably until the crossing between

1B and 2A.

VI. DISCUSSION

Some conclusions and interpretations were already given

at the end of the foregoing subsections and in Fig. 9.

A. Assignment of the time constants to the different

observation windows

The lifetimes resulting from the rate equations should

not be understood as times for passing a bottleneck ͑if there

is any͒ or for leaving a discrete level, since traveling times

are of the same order of magnitude. Therefore we wrote

them in Fig. 9 near some arrows meant to represent observa-

tion windows of nonvanishing extension and without sharp

limits.

The third time constant (␶₃ϭ77 fs) was determined from

the decay of the fragment ion C₆H^ϩ₇. As mentioned, a strong

contribution to this signal is expected from the 2A state, in

addition also from the shorter-lived 1B region. The slow de-

cay can therefore be attributed to departure from the 2A state

͑or more generally: a region following the 1B state͒. Quan-

tum chemistry supports this assignment since it predicts that

As explained in Sec. IV, an ion generated from the re-

gion of the 2A minimum will have sufﬁcient excess energy

͑м2 eV͒ that it will dissociate and will only be detected as

the 2A state has the longest lifetime;¹␶ is in fact the longest

3

ϩ

Ϫ1

the fragment C₆H₇. Therefore the rate ͑43 fs͒ deduced

from the exponential decay of the parent ion can be assigned

to the departure from the region before ͑or from a region

time in the sequence found ͑Fig. 9͒.

Much stronger fragmentation is already observed from

level 4 (␶₄м35 fs). ͑A column of the table roughly indicates

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8358

J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Fuß, Schmid, and Trushin

the fragmentation pattern of the level concerned.͒ This is

plausible if some electronic energy was again converted to

excess vibrational energy, as expected if the molecule has

already reached the ground-state surface. A similar statement

can be made about level 5 (␶₅Ϲ20 fs). The maximum of the

H^ϩsignal during this time will be attributed in Sec. VI B to

a resonance, which helps to localize this level more accu-

rately. We also recall that the mass spectrum measured dur-

ing this time requires that this level lies on the product side

͑end of Sec. V A͒, i.e., on the right-hand side ͑Fig. 9͒ of the

2A minimum and on the ground-state surface.

unimportant in view of the large widths and steep slopes

connected with the short lifetimes.

B. Interpretation of the enhanced multielectron

ionization in hexatriene and a comment on Coulomb

explosion

In Sec. V A we reported on strongly enhanced two-

electron ionization ͑followed by Coulomb explosion͒ in

hexatriene as compared with cyclohexadiene. It is respon-

sible for the drastically different mass spectra of the two

compounds ͑Fig. 3͒. The difference was unexpected, since

the two molecules have the same ionization energy. Let us

discuss possible mechanisms responsible for it. Recently it

has been found that the rate of multielectron dissociative

ionization in intense ﬁelds rapidly increases, by several or-

ders of magnitude, as the internuclear separation is extended

to a certain critical distance.^21–23A different phenomenon,

not involving bond stretching, is the observation that longer

hydrocarbons give higher ion yields than shorter ones ͑see

Ref. 24 and references therein͒. tZt-Hexatriene is nearly

twice as long as its ring-closed isomer cyclohexadiene ͑ter-

minal C–C distance 5.7 vs 3.1 Å͒. So we could expect an

enhanced multiple ionization of the longer molecule. How-

ever, our experimental ﬁndings disagree with this idea. First

of all, the anisotropy decay of the H^ϩsignal shows that the

hexatriene product rotates at a speed which is only consistent

with the moments of inertia of the cZc conformer, but not

with those of the tZt conformer ͑Sec. V B͒. The subsequent

CZc→tZt isomerization with the concomitant elongation

from 3.1 to 5.7 Å then proceeds with a time constant of 580

fs ͑Sec. V D͒ as determined by REMPI probing in the UV¹⁴

͑see Sec. V B͒. It is most remarkable that during this time the

H^ϩand other signals do not change. This means, the intense-

laser ﬁeld multielectron ionization is not sensitive for the

length of the molecule in this case! ͑We already concluded in

Sec. V B in the context of polarization dependence, that the

strong ﬁeld does not stretch the product hexatriene to its

longest conformer tZt.͒

Level 6, comprising the different conformers of

Z-hexatriene, shows no time dependence detectable by the

method of this work (␶₆Ͼ50 ps), because the conformers

seem to give the same signals. According to the end of Sec.

V B, isomerization from the cZc hexatriene to a high-

temperature equilibrium of conformers takes place within

580 fs ͑measured previously¹⁴͒. The population of level 6

calculated from ␶ to ␶ reaches 63% (ϭ1Ϫe^Ϫ1) of its

1

5

maximum after 200 fs. This time can be denoted the time of

photochemical ring opening of cyclohexadiene.

The H^ϩsignal, mostly generated from level 5, deserves a

special comment: Its delay and compactness was not pos-

sible to model well enough by rate equations; instead we

introduced an artiﬁcial delay which is probably a manifesta-

tion of the coherent motion of a wave packet after leaving

the 2A state down through the conical-intersection region

and further on the ground-state surface to a region ͑level 5͒

where multiple ionization is maximal. The existence of a

compact wave packet around 200 fs implies that equiparti-

tion of internal energy cannot yet be complete at this time.

On the other hand, around 600 fs is the molecule already

isomerized to the other conformers with a rate as statistically

expected with equipartition.¹³So intramolecular vibrational

redistribution seems to proceed in this interval.

The ion signals in Figs. 10 and 11 are complementary to

each other and together result in a complete picture of the

reaction: Whereas mass 80 ͑parent ion͒ monitors the 1B state

alone and mass 79 reﬂects the populations of 2A and 1B with

no contribution from the ground state, H^ϩappears only when

the ground state of the product is reached. The other frag-

ments C₂H^ϩ₃and C₃H^ϩ₃are produced from both the Franck–

Condon region of the 1B state and the ground state of the

product. It is noteworthy that the 2A state contributes to only

one ion, C₆H^ϩ₇.

The possibility of determining a time constant as short as

␶₁ϭ10 fs requires a special justiﬁcation: It was the only time

constant deduced from data during the overlap of the pump

with the strong probe radiation, and the latter could in prin-

ciple modify the potential energy surfaces via intensity-

induced level shifts. But as already mentioned in Sec. V B,

the time constants do not depend on varying the probe inten-

To explain the enhanced yield for multiple ionization in

hexatriene, we instead invoke an intermediate resonance in

the singly charged positive ion. The ﬁrst allowed transition

2

(²B₁→ A₂; see Fig. 2͒ in the hexatriene cation (HT^ϩ) has a

cut-off at about 700 nm and probably at even longer wave-

lengths in the hot ion, while in the cyclohexadiene ion

(CHD^ϩ) the cut-off for the corresponding band ͑²A₂

31

2

→ B₁; Fig. 2͒ is at shorter wavelengths ͑about 530 nm͒.

Thus the probe wavelength of 800 nm is close to resonance

with HT^ϩwhich will not only enhance the ionic photofrag-

mentation, but also seems to help reaching the second ion-

ization limit. The corresponding resonance in CHD^ϩis far-

ther away. It is rather unusual to postulate an intermediate

resonance for intense-laser ﬁeld ionization, a process which

has been believed to be a ﬁeld-induced process which is

insensitive for resonances. ͑Resonances with Rydberg states

have previously been seen in DIFI of H₂.^67,68͒ Note, how-

ever, that the resonance in HT^ϩconcerns the second elec-

tron, which has already a rather high ionization energy, so

that the intensity for barrier-suppression ionization ͓Eq. ͑2͔͒

sity. Furthermore ␶ was also independently determined

1

from the ﬂuorescence quantum yield.⁵Another justiﬁcation

comes from measurements with Mo͑CO͒ and W͑CO͒₆,

6

where the lifetimes of initially excited state ͑30 and 46 fs͒

could not only be extracted from within, but also from out-

side the pump–probe overlapping region.⁶⁶Probably shifts

of levels relative to each other, or changes of slopes, are

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J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Femtosecond photochemical ring opening

8359

terms of geometries instead of energies: Because HT^ϩis in

resonance with the probe laser and CHD^ϩis not and because

the HT geometry is reached only after arrival of the neutral

at the ground state.

might not be reached. ͑Also for the ﬁrst electron, our inten-

sity is just only at the threshold, since we are now dealing

with ionization from the ground state.͒

Strong evidence for the suggested resonance is the rota-

tional anisotropy ͑Sec. V B͒: Ionization without any interme-

diate resonance will either not depend at all on the molecular

orientation or, if a length dependence is assumed, will be

sensitive for anisotropy of the molecular shape. In the latter

case, it is the rotation around an axis in the ‘‘ring plane’’ of

the nearly ring-like molecule cZc-hexatriene which should

show up in the signal. However, the rotation around an axis

perpendicular to the ring was observed. This is just what is

expected for a resonance whose transition dipole moment is

Resonances in the neighborhood of a conical intersec-

tion, tuned through the 800 nm probe wavelength, were al-

ready used to explain a number of observations including

coherent oscillations in metal carbonyls, for instance

Cr͑CO͒ produced by photodissociation of Cr͑CO͒₆.⁶⁹

5

We can conclude that level 5 is not characterized by a

property of the ground-state surface alone, but it corresponds

to a position on it where the distance to the 1B surface is

around 1.55 eV ͑probe photon͒ and where there is a similar

resonance in HT^ϩ. The existence of this ‘‘label’’ on the

ground-state surface allowed us to determine the time needed

after departure from the 2A surface through the conical in-

tersection until this position, which itself cannot be very far

from the intersection as to conclude from the small energetic

distance to the 1B surface ͑Sec. V D͒. It also permitted us to

detect the compactness of the wave packet ͑Sec. V D͒.

The resonance in HT^ϩexcites a ␲ electron. This is only

the very ﬁrst step for reaching the ionization limit of the

second electron, and many additional photons have to fol-

low. If it is the ␲ electron which continues to be excited until

ionization, the product will be the ground states of HT^ϩϩand

CHD^ϩϩ. They are observed ͑Figs. 3 and 5͒ and hence are

both stable enough, unless they have excess vibrational en-

ergy ͑Sec. V A͒. ͑The properties of HT^ϩϩin its ground and

some excited states have been calculated in Ref. 70.͒ Cou-

lomb explosion must hence originate from an electronically

excited state. We suppose it is a state ͑1͒ in which both

electrons have been removed from a single CH bond, ͑2͒

which is populated by transition from a precursor state with

a single hole in the CH bond and the second hole probably

delocalized in the ␲ system ͑Fig. 12͒; the transition can ei-

ther be photon-induced ͑by excitation of the last CH electron

into the other hole͒ or induced by curve crossing. This as-

sumption can explain the following observation: The H^ϩre-

coil energy ͑2.7 eV, Sec. V A͒ due to Coulomb explosion of

CHD^ϩϩindicates a distance between the two charges of 5.3

Å before ejection of the H^ϩion, whereas for HT^ϩϩwe cal-

culate from 4.8 eV the smaller distance 3.0 Å using Cou-

lomb’s law. The suggested assumption predicts that this ejec-

tion distance only depends on the CH bond strength and

length in the precursor state and on its energy; the Coulomb

repulsion curve is always the same ͑Fig. 12͒. In fact, in

CHD^ϩϩwith a single hole in a CH bond of a CH₂group the

remaining electron can delocalize in the ␲ system and the

CH bond will therefore be long and weak ͑see the ﬂat poten-

tial curve with its minimum at a large CH distance in Fig.

12͒. In HT^ϩϩsuch a delocalization is not possible since the

␴ orbital of the CH bond is in the nodal plane of the ␲

orbitals.

2

in the ring plane. The suggested B₁→ A₂transition of the

hexatriene ion in fact has just a polarization nearly in this

plane: Its direction is near the line connecting the two termi-

nal carbons. This is parallel to the dipole moment of the

pump transition in cyclohexadiene. In Sec. V B we found in

fact that pump and probe transitions are nearly parallel. A

small angle between the two can be rationalized by assuming

that the cZc-hexatriene is slightly distorted from C₂symme-

try due to steric crowding.

In principle it would be consistent with this interpreta-

tion that the two signals C₆H^ϩ₈and C₆H₇^ϩformed from the

excited states do not depend on the polarization: To form

these ions, no resonance is involved. But a more trivial ra-

tionalization of this insensitivity is that the rotational anisot-

ropy does not strongly change before about 500 fs ͑Fig. 8͒,

i.e., at a time when both ion signals have already decayed to

near zero.

It is tempting also to interpret by a resonance why there

is a location ͑level 5͒ on the potential energy surface giving

rise to a transient maximum yield of doubly charged ions and

the consecutive products such as H^ϩ. In this case one needs

a resonance which is tuned by the ring-opening coordinate.

Such a feature exists in the ion and in the neutral: The

ground state of HT^ϩcorrelates with the second excited state

͑2²B₁around 4 eV͒ of CHD^ϩand vice versa, and along the

ring-opening coordinate there is an allowed crossing.³¹

Hence the ͑strongly allowed͒ ionic transition 1²A→2²B is

tuned through zero and through the laser frequency during

ring opening of the neutral molecule; the end is the imperfect

resonance discussed above for static HT^ϩ. For the neutral,

the 1A→2A transition grows from zero energy at the conical

intersection to several eV; but its oscillator strength is very

small. The much stronger transition 1A→1B begins with

little above 1 eV at this point ͑as to conclude from the

calculation²͒ and will pass the laser frequency ͑correspond-

ing to 1.55 eV͒ soon after the conical intersection. We sug-

gest that it is this resonance, further enhanced by the one in

HT^ϩ, which gives rise to the transient peak of two-electron

ionization probability. An enhancement by this resonance

from the neutral ground state can simultaneously explain

why the double ionization is much more efﬁcient from this

ground state than from the 2A level. The opposite could have

been expected, since the 2A state contains a substantial per-

centage of a two-electron excited conﬁguration, so that both

electrons could be detached with little ionization energy.

Why a resonance is more important can be understood in

So the process begins with ionization of a ﬁrst ␲ electron

and continues with excitation of a second such electron; but

later-on it can branch: It either continues in this direction

until reaching a stable doubly charged ion or it begins to

involve one and eventually even two ␴ electrons to lead to

Coulomb explosion.

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8360

J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Fuß, Schmid, and Trushin

In view of the strong difference in the fragmentation

patterns of hexatriene and cyclohexadiene which we found

under conditions of intense-laser ﬁeld ionization it is inter-

esting to discuss the recent results of Levis and DeWitt

et al.^24,71They studied dissociative photoionization of aro-

matics and alkyl substituted derivatives using intense 780 nm

radiation and found ionic fragmentation increasing with the

number of atoms⁷¹or ␴ bonds²⁴in the molecule. For expla-

nation, the authors invoke superexcited states⁷¹͑i.e., states of

the neutral parent molecule with internal energy exceeding

the ionization potential͒ and ﬁeld-induced dissociation.²⁴We

think that these two mechanisms alone would not explain all

the details reported above, such as the H^ϩoriginating from a

Coulomb explosion or the resonances, etc. Rather one should

consider also in these cases ionic transitions enhanced by

near resonance. Note that according to photoelectron spectra

the lowest ionic states of higher aromatics and of alkyl sub-

stituted benzenes have a smaller distance than those of ben-

zene, and that radical ions with a ␴ hole always have very

low-lying excited states.²⁹The same can be said about

aniline, furane and pyridine studied in Ref. 56. The degree of

fragmentation depends on the relative rates of further excita-

tion versus decomposition of an excited ion.

FIG. 12. Suggested potential energy curves for the Coulomb-repulsive state

͑repulsive curve, right-hand side͒ and precursor states of CHD^ϩϩand

HT^ϩϩ. Open and solid circles indicate holes and electrons, respectively. The

creation of the last ␴ hole from a ␲ hole probably takes place at a curve

crossing at the CH distances indicated in the ﬁgure. The transition to the

Coulomb-repulsive curve can either be purely diabatic ͑e.g., after the ab-

sorption of the last photon͒ or optical ͑by absorption from a lower state͒. In

a dressed-states description, the latter case involves a curve crossing, too.

In this work, a number of features were observed which

are normally considered to be typical of multiphoton pro-

cesses. Among them are several resonances and nonvertical

steps such as the geometrical relaxation before Coulomb ex-

plosion ͑Sec. VI C͒. It may therefore be surprising why we

keep speaking about ﬁeld ionization ͑DIFI͒. The main reason

is that the intensity is clearly beyond the limit of Eq. ͑2͒ ͑or

an analog for molecules͒, if excited states are concerned.

Nevertheless, the singly positive ion is below the limit, ow-

ing to the high energy for removing the second electron, and

ionic resonances play an important role in this work. So,

obviously a combination of ﬁeld ionization with subsequent

multiphoton processes is possible. It is also conceivable that

resonances which are important at low intensities can still

facilitate excitation at intensities typical of ﬁeld ionization.

Franck–Condon active coordinates, a ﬂatter region which is

crossed by the 2A surface ͑schematically shown in Figs. 2

and 9͒. Only in this second region the ␴ bond ͑C1-C6, num-

*

bering as in hexatriene͒ initially not affected by the ␲␲

excitation begins to open. That is, the direction of the path

changes. In Sec. VI A we assigned the ﬁrst two time con-

stants to these two regions on the basis of energetic and

spectroscopic arguments. Recently we also found a conﬁr-

mation of the direction change in the effect of substituents on

␶ and ␶₂.⁷²

1

On the 2A surface the initial calculations¹showed a

minimum energy path ͑MEP͒ ﬁrst leading to the 2A mini-

mum and then changing direction toward the 2A/1A conical

intersection ͑CI͒. Whereas in the 2A minimum the molecule

has a geometry similar to cZc-HT, with the C₂symmetry

conserved, in the CI ͑more precisely, the energy minimum of

the CI space͒ the symmetry is broken, one of the terminal C

atoms forming a triangular structure ͑three-electron three-

center bond͒ with the other two terminal C atoms. According

to the calculation, the time to ﬁnd this special geometry is

C. Comparison with calculated potential energy

surfaces and pathways

All the lifetimes given in Fig. 9 are so short that it must

be concluded from the Landau–Zener consideration in the

Introduction that the pathway is continuous all the way down

the different potential energy surfaces. There can be no sig-

niﬁcant gap between the surfaces, and in particular there

must also be a real crossing between the 2A and 1A surfaces.

So the experiment directly supports the conical intersection

predicted for this case.¹Figure 9 is one of the most detailed

descriptions of the dynamics of a reaction. The assignment

of all these numbers would not have been possible without at

least the qualitative ideas about the potential energy surfaces

presented in Sec. III. Recent progress in quantum chemistry

now permits to calculate more accurate potential energy sur-

faces and to predict details of the pathway. Examples are the

work of the groups of Bernardi, Olivucci and Robb.^1–3,28The

results can be compared with the experiments.

lengthened by

a

negative activation entropy (⌬S^a

ϭϪ2.0k_B). The minor activation energy found (⌬E^a

ϭ0.04 eV͒ was at the limit of accuracy and is not conﬁrmed

by recent calculations.³Its inﬂuence on the 2A lifetime could

anyway be neglected in view of the large excess energy ͑Ϸ1

eV͒ released along the path from the Franck–Condon region

down to the 2A minimum. With ⌬S^aand transition-state

theory, one estimates a 2A lifetime of 1200–450 fs using in

the pre-exponential factor (k_BT/h) a temperature of 300–

800 K, the latter calculated from the assumption that the

excess energy is equipartitioned. So the experimental rate

͑77 fs͒^Ϫ1seems to be faster, though not much, than the maxi-

mum predicted by statistics. This is conceivable if the mol-

ecule is accelerated by the slope of the potential energy sur-

The calculations of the 1B surface²showed, after a steep

initial slope accelerating the molecule in the direction of

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J. Chem. Phys., Vol. 112, No. 19, 15 May 2000

Femtosecond photochemical ring opening

8361

faces directly to the funnel and its outlet, so that statistical

energy redistribution is not required to ﬁnd the direction.

The same conclusion can be drawn from comparison of

the 2A lifetime with the period of a vibration much contrib-

uting to the reaction coordinate. The MEPs before and after

the 2A ͑symmetric͒ minimum have large components of

nonplanar torsions, all of which having wavenumbers of the

order of 100 cm^Ϫ1͑in the ground state; magnitudes of cur-

vatures are, however, not drastically different in excited

states͒. 77 fs correspond to only a fraction of their periods

before the last step a bond must be extended, as suggested in

Sec. V B to explain the difference of Coulomb recoil energy

for the two isomers.

DIFI usually gives a signal for every part of the potential

energy surface being passed, and it gives rise to many dif-

ferent ions which often differ in temporal behavior, thus pro-

viding more information than methods based on only one

transition such as transient absorption or ﬂuorescence. This

is the reason why we obtained an unprecedented number of

details on the dynamics of the ring opening of cyclohexadi-

ene. A similarly detailed picture was obtained for H migra-

tion in cycloheptatriene⁷⁵and for dissociation of some tran-

sition metal carbonyls and subsequent isomerization.^66,69,76

With low-intensity photoionization or with REMPI, this non-

selectivity and generation of many ions is not common.

Whereas photoionization with mass-selective detection

is often used for time-resolved probing, it was apparently not

recognized before, that different ions monitor different loca-

tions on the potential energy surface; instead, it was often

attempted to correlate the ionic fragments with a supposed

dissociation of the neutral, an assumption which at least for

cyclohexadiene is invalid. Reference 77 shows that transient

DIFI is consistent with transient absorption, although the lat-

ter would probably provide comparably rich information

only if it were measured at many different wavelengths.

As already pointed out, the levels used in the kinetic

equations actually represent observation windows, each char-

acterized by a set of probabilities ͑␴͒ to produce the observed

ions. Traveling times required to cross each window are ex-

pected to be of the same order of magnitude as the observed

times. It is even probable that all the time is used for travel-

ing and there is no bottleneck anywhere on or between the

surfaces. It seems that a new observation window can open

not only when the molecule enters another electronic state,

but also if it changes direction on a given surface ͑note the

two times assigned to the 1B surface͒. This phenomenon

probably occurs if the difference of slopes of ionic and neu-

tral potentials abruptly changes.

^Ϫ1ˆ

(100 cm ϭ 333 fs͒. This suggests that the funnel outlet is

just somewhere early along the line of such a vibration.

Hence also this consideration infers that the molecule does

not have to search around.

Since the direction changes along the reaction path, the

idea of the steepest slope directly leading the molecule to the

funnel infers a valley which guides the molecules around a

smooth curve to the new direction. They would not follow a

sharp curvature, due to the momentum in the direction of

initial acceleration. Recent calculations³indeed conﬁrm this

idea: Already early on the path which appeared to be a MEP

before¹there is a large negative curvature towards the fun-

nel. The deﬂection of the path even seems to begin before

the ﬁrst conical intersection.⁷²This is probably characteristic

for pericyclic reactions,⁷²whereas two examples of cis–trans

isomerizations showed a less smooth or even abrupt change

of direction.³

A recent study investigates the quantum dynamics on the

2A surface of cyclohexadiene and ﬁnds broadening or con-

traction of the wave packet depending on the initial width

near the 1B/2A intersection.⁷³The narrow wave packet ob-

served after passing the 2A/1A conical intersection ͑the end

of Sec. VI A͒ probably also infers a small width immediately

before.

VII. CONCLUDING REMARKS

Originally Corkum and coworkers suggested using dis-

sociative intense-laser ﬁeld ionization ͑DIFI͒ for ultrafast

spectroscopy.²²The idea was to proﬁt from the extreme sen-

sitivity of multiple ionization for the dissociation ͑Coulomb

explosion͒ coordinate, which thus provides an observation

window for motion along this direction. Recently Castleman

and coworkers studied the proton transfer in the hydrogen-

bonded dimer of 7-azaindole by DIFI;⁷⁴depending on the

progress of reaction of the neutral dimer, Coulomb explosion

after ionization separated the monomers either with or with-

out a transferred hydrogen. Our work demonstrates that the

potential of DIFI to study dynamics is even broader: The

DIFI signals can also be sensitive for reaction coordinates

͑such as the ring opening of cyclohexadiene͒ which have

nothing to do with the direction of Coulomb explosion ͑the

ejection of H^ϩfrom a doubly charged ion͒. This sensitivity

has various origins which were discussed in the text. All of

them are, however, related to the Franck–Condon principle,

which rationalizes why the ionization probability and frag-

mentation pattern depend on the location on the potential

energy surface. For this mechanism to hold, only the ﬁrst

step must be ͑more or less͒ vertical; it does not matter if

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Article Doi

Time-resolved dissociative intense-laser field ionization for probing dynamics: Femtosecond photochemical ring opening of 1,3-cyclohexadiene

DOI: 10.1063/1.481478

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