Ultrafast Ring-Opening Reaction of 1,3-Cyclohexadiene: Identification of Nonadiabatic Pathway via Doubly Excited State

Identi ﬁ cation of Nonadiabatic Pathway via Doubly Excited State

Article

Ultrafast Ring-Opening Reaction of 1,3-Cyclohexadiene:

Shutaro Karashima, Alexander Humeniuk, Ryuta Uenishi, Takuya Horio, Manabu Kanno, Tetsuro Ohta,

Junichi Nishitani, Roland Mitric, and Toshinori Suzuki *

Cite This: J. Am. Chem. Soc. 2021, 143, 8034 −8045

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sı Supporting Information

ABSTRACT: The photoinduced ring-opening reaction of 1,3-

cyclohexadiene (CHD) to produce 1,3,5-hexatriene (HT) plays an

essential role in the photobiological synthesis of vitamin D in the

skin. This reaction follows the Woodward−Hoﬀmann rule, and C −

C bond rupture via an electronically excited state occurs with

conrotatory motion of the end CH groups. However, it is noted that

the photoexcited S (π,π*) state of CHD is not electronically

correlated with the ground state of HT, and the reaction must

proceed via nonadiabatic transitions. In the present study, we have

clearly observed the nonadiabatic reaction pathway via the doubly

excited state of CHD using ultrafast extreme UV photoelectron

spectroscopy. The results indicate that the reaction occurs in only 68

fs and creates product vibrational coherence. Extensive computational simulations support the interpretation of experimental results

and provide further insights into the electronic dynamics in this paradigmatic electrocyclic ring-opening reaction.

INTRODUCTION

1960s, van der Lugt and Oosterhoﬀ performed a theoretical

analysis of a related ring-closing reaction from butadiene to

cyclobutene, and they pointed out that the reaction is

mediated by a conical intersection (CoIn) of the potential

■

The photoinduced ring-opening reaction of 1,3-cyclohexadiene

CHD) to produce 1,3,5-hexatriene (HT) is a well-known

example of electrocyclic chemical reactions, and it plays a

central role in the photobiological synthesis of vitamin D in

the skin by facilitating photoisomerization of 7-dehydrocho-

lesterol to previtamin D . The ring-opening reaction of CHD

follows the Woodward−Hoﬀmann rule, and C −C bond

rupture via the electronically excited state occurs with

(

energy surface with a doubly excited state; the same

mechanism has been expected for the ring-opening reaction

of CHD. It is noted that the ground state of CHD with the

double occupancy of the 12a orbital is electronically correlated

with the doubly excited state of HT so that the two potential

energy surfaces indicated in black and blue in Figure 1 undergo

conrotatory motion of the end CH groups. The reaction

strong avoided crossing under the C symmetry, making the

starts from the S (π,π*) state of CHD reached by a

S −S energy gap to be prohibitively large for eﬃcient

HOMO(π)−LUMO(π*) transition in the ultraviolet (UV)

region, and the photoexcited state ultimately leads to the

nonadiabatic transition (it is seen in our ab initio calculations

shown in Figure 3). Therefore, the reaction has been predicted

to involve the symmetry-breaking nuclear motion to access the

ground electronic state (S ) of HT with the quantum yield of

−8

approximately 0.5.

However, it should be noted that the

S /S seam of crossing under non-C symmetry.

S₁(π,π*) state of CHD is not electronically correlated with the

S₀state of HT; therefore, the reaction must be facilitated by

nonadiabatic transitions among diﬀerent electronic states

Experimental attempts to observe the ring-opening reaction

of CHD in real time started decades ago, when Fuß and

3,11,12

colleagues

performed ultrafast photoionization mass

(

Figure 1).

spectrometry using strong ﬁeld ionization. Their experimental

results inspired a number of subsequent experimental and

The well-known feature of this paradigmatic ring-opening

reaction is that the energy ordering of the HOMO(12a) and

LUMO(11b) is reversed between the reactant and product.

Here, the notations a and b of the molecular orbital symmetry

are the irreducible representations in the C point group. We

Received: February 17, 2021

Published: May 24, 2021

(

employ these notations in order to explain the orbital

correlation between CHD and HT.) Consequently, the S₀

state of HT with double occupancy of the 11b orbital is

correlated with the doubly excited S state of CHD. In the

2021 American Chemical Society

J. Am. Chem. Soc. 2021, 143, 8034−8045

034

Article

ﬁnal states of the reaction products. High temporal resolution

of measurements is crucial for clear identiﬁcation of the

reaction path; therefore, a ﬁlamentation four-wave mixing

(

FFWM) deep UV (DUV) light source and a high-order

harmonic generation (HHG) EUV light source were combined

to achieve their cross-correlation time of 48 ± 2 fs in this

study. In Supporting Information section S6 , we also present

the results obtained using time-resolved photoelectron imaging

(

TRPEI) with UV pump and vacuum UV (6.3 or 7.4 eV)

probe pulses with a shorter cross-correlation time of 31−32 fs,

which fully support the results obtained with EUV probe

pulses presented below.

In the discussion presented below, we employ the following

nomenclature for the electronic states. We consider only the

valence singlet states and indicate them with the symbol S (n

0, 1, 2, ...), in which n starts from 0 in ascending order of

electronic energy. (The Rydberg states are conventionally

neglected in studies of the ring-opening reaction of CHD from

the S state because these states play a negligible role.)

Furthermore, we use single and double asterisks to indicate

predominantly singly and doubly excited electronic characters,

respectively. Therefore, when the ﬁrst excited singlet state with

a singly excited electronic character undergoes avoided

crossing with the doubly excited electronic state, the notation

changes from S * to S **. We will later discuss the doubly

Figure 1. Experimental setup and schematic diagram of ring-opening

reaction of CHD. Deep UV pump (3ω, 267 nm, 4.6 eV) and extreme

UV probe (14ω, 57 nm, 21.7 eV) pulses were employed (TM,

toroidal mirror; CoIn, conical intersection; CHD, 1,3-cyclohexadiene;

HT, 1,3,5-hexatriene). The orbital symmetries are indicated assuming

excited electronic characters of the S and S states more fully

based on quantum chemical calculations. Since the C₂

symmetry of CHD is lifted during the reaction, we use the

irreducible representation in the C point group only when it is

the C symmetry to illustrate the correlation of the orbitals between

indispensable for explaining the character of molecular orbitals

and the propensity of electronic transitions. Figure 1 employs

CHD and HT. C symmetry holds only between the Franck−Condon

region and S /S CoIn. The symmetry-breaking motions play an

both the nomenclature S (n = 0, 1, 2, ...) with asterisks and the

important role to access the S /S seam of crossing under non-C

molecular orbital symmetries under the C symmetry in order

symmetry.

to explain the correlation of electronic states between CHD

and HT.

−8,10−21

theoretical studies on this reaction.

photoelectron spectroscopy (TRPES),

Time-resolved

,18,19

RESULTS AND DISCUSSION

Figure 2A shows a two-dimensional (2D) map of EUV

photoelectron spectra measured as a function of the pump−

probe delay time. The pump pulses excited CHD to the S *

ultrafast near-edge

■

X-ray absorption ﬁne structure spectroscopy and ultrafast

electron diﬀraction experiments have been performed to

study the reaction. Nevertheless, the reaction pathway via the

doubly excited state has yet to be unambiguously identiﬁed.

One of the diﬃculties with these previous experiments was

their relatively low temporal resolution. As described in the

present paper, the nonadiabatic transition occurs within 30 fs

after photoexcitation, and it is therefore crucial to have a

suﬃciently high time-resolution to clearly capture the non-

adiabatic transition. In this regard, the cross-correlation time

state, and the EUV probe pulses induced photoemission from

all transient species in all electronic states. The spectra are

plotted against the electron binding energy (eBE), given by the

diﬀerence between the EUV photon energy and the measured

electron kinetic energy (eKE). The three negative-intensity

bands indicated in violet in Figure 2A are the ground-state

bleach (depopulation) induced by the UV pump pulses, which

can be conﬁrmed by comparing with an EUV photoelectron

spectrum of CHD at room temperature shown in the same

ﬁgure. The positive signals at short pump−probe delay times

(<100 fs) are primarily from the excited electronic state of

CHD, while those at longer delay times are from the reaction

products.

(

typically 100−150 fs) of the pump and probe pulses in past

ultrafast spectroscopy experiments on this system was

insuﬃcient except for the experiment by Fuß and colleagues

using 13 fs pulses. Furthermore, mass spectrometry and X-

ray/electron diﬀraction experiments are generally insensitive to

the electronic character of a molecule so that they are not best-

suited for observation of nonadiabatic transitions.

Figure 2B shows an enlarged view of the rectangular region

outlined by the white dashed lines in Figure 2A. The

The objective of the present study is to perform real-time

observation of the electronic dynamics of the ring-opening

reaction of CHD and to establish a mechanistic picture of this

paradigmatic ring-opening reaction. To this end, TRPES was

photoelectron signal for S * starts from three eBE values of

3.8, 6.2, and 7.1 eV at time zero. The lowest eBE band is

associated with the D ← S * ionization transition; the initial

employed with extreme UV (EUV) probe pulses (21.7 eV).

The EUV pulses ionize all the chemical species involved in the

eBE value of 3.8 eV at the time origin agrees well with the

vertical ionization energy of CHD of 8.4 eV measured using

our apparatus. The photoabsorption spectrum of matrix-

reaction; therefore, EUV photoelectron spectroscopy enables

complete observation of the dynamics from the Franck−

isolated CHD cations exhibits two bands at around 2.62 and

Condon (FC) region in the S (π,π*) state of CHD until the

3.20 eV, which can be assigned to the ﬁrst and second

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J. Am. Chem. Soc. 2021, 143, 8034−8045

Article

opening reaction path, while the energy of the stable cationic

ground state D increases along the path (Figure 4B). The S *

signal intensity integrated over an energy range of 3.0−5.5 eV,

as shown with red open circles in Figure 2C, exhibits a single

exponential decay. The time proﬁles shown in Figure 2C were

determined with experimental uncertainties of 1%. As

described in Supporting Information section S2, the high

ﬁdelity of our measurement enabled estimation of the time

constants with a standard deviation of about 10%, which

corresponds to several femtoseconds. The proﬁle of S * was

reasonably well expressed with a latency time and exponential

decay time constant of 10 ± 3 and 21 ± 2 fs, respectively, from

which the 1/e lifetime of S * was determined to be 31 fs. As

presented in Supporting Information section S6-2, we also

performed TRPEI experiments using vacuum UV pulses, which

provided slightly diﬀerent estimates of the latency time and

decay time constant of 17 ± 4 and 17 ± 6 fs, respectively;

however, these values also provide an S * lifetime of 34 fs.

Thus, we conclude that the S * population decreases to 1/e in

approximately 31−34 fs.

The photoemission band intensity in the next eBE region of

.5−6.8 eV exhibits diﬀerent temporal behavior. As shown in

Figure 2C, the integrated intensity in this energy range appears

time-delayed with respect to the signal in the 3.0−5.5 eV range

and decays more slowly. If only the D ← S * transition occurs

in the 5.5−6.8 eV region, the time proﬁles observed for the two

regions of 3.0−5.5 and 5.5−6.8 eV are expected to be the

same. However, the observed diﬀerence between the time

proﬁles indicates that another photoemission band corre-

sponding to D ← S ** transition exists in the 5.5−6.8 eV

region. We will conﬁrm this assignment later using quantum

chemical calculations. The individual contributions of the D₁

←

S * and D ← S ** transitions in the 5.5−6.8 eV region are

separated as follows. The S * population proﬁle was already

determined from the D ← S * signal in the 3.0−5.5 eV

region; therefore, it can be employed to estimate the D ← S *

time proﬁle in the 5.5−6.8 eV region, except for its absolute

intensity. The formation curve for the S ** population must be

the same as the decay curve for S * because the overall

population in the S manifold is maintained in this time range.

Thus, what are unknown here are the relative ionization cross-

sections for the D ← S * and D ← S ** transitions and the

decay time constant for S **. By assuming latency and rise

times of 10 and 21 fs for S **, respectively, the decay time for

S ₁ ** was estimated to be 37 ± 2 fs. (As described in

Supporting Information section S6-2, TRPEI estimates the

Figure 2. Experimental photoelectron spectra. (A) 2D map of EUV

photoelectron spectra with the photoelectron spectrum of the ground-

state CHD shown on the right. The negative signals correspond to the

ground-state bleach. (B) Enlarged 2D map of the area indicated with

dashed lines in (A). (C) Time proﬁles of the photoelectron signal

intensities integrated over 3.0−5.5 and 5.5−6.8 eV regions (open

circles) and their least-squares ﬁtting (solid lines). Dashed lines

indicate the deconvoluted components of S * and S **. The residues

lifetime of S ** to be 27 ± 10 fs.) Figure 2D shows spectral

features of the separated D ← S * and D ← S ** bands (the

details of the spectral ﬁ tting method are described in

Supporting Information section S5 ). The intensity of the D₁

←

S₁* band is stronger than expected from the electron

conﬁguration shown in Table 1, for the reason explained later.

An important point raised by van der Lugt and Oosterhoﬀ

regarding the electrocyclic reaction is the involvement of the

of the least-squares ﬁtting are shown with dots above the proﬁles.

These time proﬁles were measured with the experimental

uncertainties of 1%. (D) 2D maps of the contributions from S₁*

doubly excited state. However, the character of each

electronic state possibly varies with nuclear displacements so

and S **. See Supporting Information section S5 for details.

that one may ask whether the S ** and S ** states really have

a doubly excited electronic character. It would be of interest to

investigate this point using conﬁguration interaction (CI)

calculations in order to establish this concept more ﬁrmly.

Figure 3A shows one-dimensional potential energy curves

calculated for CHD using the extended multistate complete

active space second-order perturbation theory (XMS-

excited cationic states (D and D ). The observed eBE values

of 6.2 and 7.1 eV agree reasonably well with those expected for

D ← S * and D ← S *, respectively. As the delay time is

increased, the D ← S * band shifts rapidly to higher eBE

because the electronic energy of S * decreases along the ring-

036

J. Am. Chem. Soc. 2021, 143, 8034−8045

Journal of the American Chemical Society

Optical and electron energy loss spectroscopies.

Article

Table 1. Electronic Energies of CHD Calculated Using XMS-CASPT2 under C Symmetry and Corresponding Experimental

Values (eV)

at 1 A equilibrium geometry

at 2 A equilibrium geometry

state

leading conﬁguration(s)

calcd

exptl

leading conﬁguration(s)

calcd

3²

2²

(9b) (11a) (10b) (12a) (11b)

11.78

11.60

11.8

(10a) (10b) (11a) (11b) (12a)

13.72

13.09

(9b) (11a) (10b) (12a) (11b)

(10a) (10b) (11a) (11b) (12a)

(

10a) (10b) (11a) (11b) (12a)

2²

(9b) (11a) (10b) (12a) (11b)

11.11

11.3

(10a) (10b) (11a) (11b) (12a)

13.16

(

10a) (10b) (11a) (11b) (12a)

1²

2¹

(9b) (11a) (10b) (12a) (11b)

10.70

8.37

6.06

10.7

(10a) (10b) (11a) (11b) (12a)

9.98

10.00

3.80

(9b) (11a) (10b) (12a) (11b)

8.25

(10a) (10b) (11a) (11b) (12a)

(9b) (11a) (10b) (12a) (11b)

(10a) (10b) (11a) (11b) (12a)

(

9b) (11a) (10b) (12a) (11b)

(10a) (10b) (11a) (11b) (12a)

s Rydberg state

5.87

4.88

5.39

4.94

1¹

(9b) (11a) (10b) (12a) (11b)

(10a) (10b) (11a) (11b) (12a)

4.21

2.83

(9b) (11a) (10b) (12a) (11b)

(10a) (10b) (11a) (11b) (12a)

(

10a) (10b) (11a) (11b) (12a)

This work. The details of computational method are described in the Computational Simulation section. The absorption spectrum of the CHD

cation in a freon matrix suggests 11.5 eV. The 3 B and 2 B are almost degenerate, and their energetic orders are diﬃcult to determine. He I

PES.

Classiﬁed as 4 A at the FC geometry. The leading conﬁguration is ...(9b) (11a) (10b) (12a) (11b) (13a) . The state energy was

calculated in the multistate-multireference scheme of XMS-CASPT2 with an active space of four electrons in eight orbitals, namely, two π and two

π* orbitals in addition to 3s, 3p , 3p , and 3p Rydberg orbitals. 13a is of 3s Rydberg character. Resonance enhanced multiphoton ionization.

lists the leading electron conﬁgurations of these states for

equilibrium geometries of 1 A and 2 A. It can be seen that the

electronic character of S (2 A) in the ground-state equilibrium

geometry contains a fair amount of [(10b) (12a) (11b) ]

conﬁguration in addition to the doubly excited conﬁguration of

[

(10b) (12a) (11b) ]. Is the fraction of the doubly excited

character of 2 A smaller than our expectation? In order to

clarify this point further, we evaluated the fraction of the

doubly excited characters of [(10b) (12a) (11b) ] and

[

(10b) (12a) (11b) ] in the electronic wave functions of 1 A

and 2 A using the CI coeﬃcients obtained using XMS-

CASPT2 calculations. Figure 3B shows the squared CI

coeﬃcients of the doubly excited conﬁgurations in the

electronic wave functions of the 1 A and 2 A states as a

function of the C −C distance. The results indicate that the

(

11b) doubly excited character in the 2 A state increases as

the C −C bond is elongated to 2.0 Å, where the 2 A potential

energy curve crosses the 1 B curve. Thus, the calculations

conﬁrmed that the second valence-excited singlet state has a

doubly excited electronic character near the S /S surface

crossing region. Since most of the nuclear trajectories from the

Franck−Condon region to the S /S minimum energy conical

intersection (MECI) pass the region close to the C symmetry,

the above argument assuming C symmetry is valid for an

ensemble of nuclear trajectories in this region of the potential

energy surface, even without the symmetry restriction assumed

here.

Previously, this reaction has been studied using UV two-

photon ionization from the excited state. Two-photon TRPES

studies revealed the sequential appearance of resonance-

enhanced two-photon ionization via Rydberg states from

Figure 3. (A) Potential energy curves of 1 A, 1 B, 2 A, 1 A, 1 B, 2 A,

B, and 3 B for CHD calculated assuming C symmetry. (B) Squared

CI coeﬃcients of the doubly excited conﬁgurations in the electronic

wave functions of the 1 A and 2 A states.

,19

high to low principal quantum numbers (n);

however, the

CASPT2) method as a function of the C −C distance by

origin of these signals was not well understood. In order to

revisit this problem, we performed two-photon UV-TRPEI

with a higher time-resolution (58 fs) than in previous studies

and obtained the results shown in Figure 4A. It is seen that the

6s Rydberg state has a maximum at a delay time of 13 fs, while

the 3p state has a maximum at 35 fs. One of the key criteria for

assuming that C symmetry is maintained. Under C symmetry,

the S (1 B) and S (2 A) potential energy curves are crossed

because they belong to diﬀerent irreducible representations.

On the other hand, the 2 A and S (1 A) states form a strong

avoided crossing at around a C −C distance of 2.3 Å. Table 1

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J. Am. Chem. Soc. 2021, 143, 8034−8045

here to present rather congested trajectories for diﬀerent

Article

the assignment of these Rydberg signals is their appearance

times; as the experimental results shown in Figure 2 revealed,

the photoexcited CHD is in the S * state within this time

range. Therefore, this clearly represents ionization from the S₁*

state. It is noted that the energy diﬀerence between the

Rydberg state and S * is expressed by

E_R_y_d− E(S *) = eBE(S *) − R/(n − δ)

where δ is a quantum defect and R is the Rydberg constant.

Thus, the excitation energies from S * to the Rydberg series

increases exactly with eBE(S *). We have already seen the

rapid increase in eBE(S *) in Figure 2. Consequently, the

Rydberg state in resonance with the UV probe photon energy

progressively shifts to lower Rydberg states with decreasing

values of n − δ (see Figure 4B). Presumably, part of the two-

photon ionization via 3p Rydberg states after 30 fs is from

S₁**.

In order to conﬁrm our interpretation of the EUV

photoelectron spectra and to gain further insight into the

dynamics, we employed two theoretical analyses. In the ﬁrst

approach, we selected the most probable ring-opening reaction

path estimated by geodesical interpolation among the

molecular geometries of FC, S /S MECI, S /S MECI

(

non-C -symmetry), and the equilibrium geometries of the

HT isomers, and we calculated the eBE values and photo-

ionization cross-sections along the path using the XMS-

CASPT2 method, as shown in Figure 5A. The highest cationic

Figure 4. TRPES with two-photon ionization. (A) 2D map of the

photoelectron spectra measured with the resonance-enhanced two-

photon ionization via Rydberg states using 394 nm probe pulses. (B)

state considered here is D . Superimposed with diﬀerent colors

in this ﬁgure are the ionization cross-sections estimated from

the norm of Dyson orbitals. The value on the horizontal axis is

the total arc length for nuclei to move along this reaction path

so that the value extends up to 25 Å. A semilog plot is used

Schematic diagram of photoionization from S * with EUV and UV

probe pulses.

Figure 5. Computational simulation of photoelectron spectra. (A) Variation of eBE calculated along the geodesically interpolated ring-opening

reaction path connecting the FC state, S /S MECI, S /S MECI, cZc, cZt, and tZt forms of HT. Ionization from S −S to D −D is considered.

Photoionization cross-sections estimated from the norm of Dyson orbitals for each ionization channel are superimposed. The value on the

horizontal axis, shown in a logarithmic scale, is the total arc length for nuclei to move along this reaction path. Molecular structures in FC, S /S

MECI, S /S MECI and the S minimum are illustrated on top with the bond length (Å). (B) Photoelectron spectra simulated based on trajectory

surface hopping calculations by Polyak et al. Both CHD and HT forming channels are included, and experimental temporal (48 fs) and energy

0.12 eV) resolutions are incorporated. (C) Experimental time energy map obtained by elimination of the ground-state bleach signal from the data

shown in Figure 2A.

(

038

J. Am. Chem. Soc. 2021, 143, 8034−8045

Article

Figure 6. Photoelectron spectra due to transitions from S state to diﬀerent cationic states simulated based on trajectory surface hopping

calculations by Polyak et al. Experimental temporal (48 fs) and energy (0.12 eV) resolutions are incorporated.

ionization channels in the range of small displacement along

the reaction path. The ﬁgure indicates a steep increase in the

eBE value for the D ← S * band, followed by a rather

transitions can clearly be seen in the panel for D −S . As

described earlier, one puzzling feature concerning the

experimentally observed D ← S * band is that it appeared

constant eBE value for D ← S ** and a large increase in eBE

with a greater intensity than expected (Figure 2). Since the

upon formation of the ground-state HT. These features are in

excellent agreement with the experimental results shown in

Figure 2. The eBE values calculated using the XMS-CASPT2

level of theory were highly accurate and in quantitative

agreement with the experimental values; however, we found

that the simulated spectra were being shifted by −0.4 eV with

respect to the experimental ones. Therefore, we adjusted the

simulated spectra by +0.4 eV for closer comparison with the

experimental results. In order to relate the eBE values and the

molecular structures, the calculated structures at the critical

points along the reaction path are also shown in Figure 5A.

The CHD molecule has two CC double bonds in the FC

geometry, while all carbon−carbon bonds except the

dissociating C −C become almost the same length in the

leading electron conﬁgurations for S * and D are respectively

[(10b) (12a) (11b) ] and [(10b) (12a) (11b) ] (see Table

1), the D ← S * ionization transition is expected to be very

weak; Figure 5A also predicts a low intensity for this transition

in accordance with this expectation. However, examination of

Figure 5B reveals that the spectral simulation based on the full-

dimensional surface hopping trajectory calculations reproduces

the strong appearance of the D ← S * band. What is the

reason for this diﬀerence? In order to ﬁnd the origin of this

enhanced ionization intensity, we examined the D ← S *

photoionization cross-section along the full-dimensional

nuclear trajectories in the S * state. We found that the D

← S * cross-section estimated from the Dyson norm is only

0.1 for the FC geometry, while it is 0.3 on average for an

ensemble of trajectories spreading out from the FC geometry.

Therefore, the higher intensity of the D ← S * band is

structures for S /S and S /S CoIn. The equilibrium

structures of HT isomers have three CC double bonds.

Greater structural change occurs on the ground-state surface of

HT. The actual nuclear motions are not restricted to this

geodesically interpolated path; therefore, the map shown in

Figure 5A only describes the principal part of the multidimen-

sional dynamics. Nonetheless, the one-dimensional analysis in

Figure 5A provided highly valuable insights into the reaction

and photoionization dynamics.

ascribed to a non-Condon eﬀect due to variation of the

electronic wave function caused by nuclear motions

perpendicular to the ring-opening reaction coordinate.

Meanwhile, the leading electron conﬁgurations for S ** and

D₀are [(10b) (12a) (11b) ] + [(10b) (12a) (11b) ] and

[(10b) (12a) (11b) ], respectively, in the ground-state equi-

librium geometry; therefore, photoionization from S ** to D

is unfavorable for this geometry. However, the leading electron

A clear limitation of the results shown in Figure 5A is that

they do not include a nonreactive internal conversion path to

c o n ﬁ g u r a t i o n s f o r S * * a n d D ₀c h a n g e t o

the S state of CHD or predict the reaction time. Therefore, in

[(11a) (11b) (12a) ] + [(11a) (11b) (12a) ] and

[(11a) (11b) (12a) ] and/or [(11a) (11b) (12a) ] for the

the second approach, we performed a thorough dynamical

simulation of the experimental results by a combination of the

full-dimensional surface hopping calculations performed by

equilibrium geometry of S **, respectively. This enables a

strong D ← S ** ionization transition. Examination of Figure

Polyak et al. and our own calculations of the ionization

5A reveals that the D ← S ** band is overlapping with the D

dynamics at the XMS-CASPT2 level of theory. The spectra

thus simulated are shown in Figure 5B, including both

pathways to form CHD and HT. The highest cationic state

← S ** band in the reaction coordinate range from 2 to 7 Å.

2 2

These are basically transitions to the cationic 1 A and 1 B

states. As seen in Figure 3A, the potential energy curves for

considered in this simulation is D , and the simulated spectra

S *(2 A) and D (1 B) are nearly parallel to each other;

1 0

are shifted by 0.4 eV as mentioned earlier. The experimental

temporal (48 fs) and energy (0.12 eV) resolutions were

incorporated. The simulated spectra are in excellent agreement

with the experimental results shown in Figure 5C.

therefore, the D ← S ** band exhibits a relatively constant

0 1

eBE value.

Although the accuracy of the computational simulations

presented in Figure 5B is among the highest reported, close

comparison between the computational and experimental

results reveals some discrepancies. First of all, the reaction

time is slightly longer for the computational results, which

points to small inaccuracies in the calculated potential energy

surfaces. Second, the photoemission intensity for the excited

For closer examination of the photoelectron spectra, we

present photoemission time−energy proﬁles for individual

photoionization channels from the S state to ﬁve cationic

states of CHD in Figure 6. In these panels, S * and S ** are

not diﬀerentiated; however, the D ← S * and D ← S **

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results, which suggests small inaccuracies in the ionization

Article

states of CHD appears slightly stronger in the computational

Figure 8. Representative trajectory leading to CHD. (A) Snapshots of

Dyson orbitals for ionization from current electronic state to D . (B)

Electronic energies along nuclear trajectory, where current state is

marked by purple circles.

Figure 7. Representative trajectory leading to HT. (A) Snapshots of

Dyson orbitals for ionization from current electronic state to D . (B)

Electronic energies along nuclear trajectory, where current state is

marked by purple circles.

cross-sections obtained from the Dyson norms. Third, the

calculated photoemission bands are slightly shifted in energy

from the experimental ones, as described earlier.

To understand the electronic and structural dynamics more

clearly, Figures 7 and 8 present the time-evolution of the

Dyson orbital, which can be regarded as an electron hole

created by photoionization, and molecular geometry along the

two nuclear trajectories leading to HT and CHD products,

obtained using full-dimensional surface hopping calculations.

In Figure 7A, it can be seen that the Dyson orbital associated

Figure 9. (a) 11b and 12a molecular orbitals (as in Figure 1). (b)

Linear combination of 11b and 12a orbitals with equal amplitudes.

with photoionization from S * at delay times of 0 and 20 fs is a

orbitals with equal weights creates the orbital patterns 12a +

1b singly occupied molecular orbital. However, the 12a

1b and 12a − 11b, as shown in Figure 9, and these are clearly

character with a node between the C and C carbon atoms

seen at delay times of 32 and 39 fs in Figure 7A. When we take

these orbitals as the basis functions, the following relationship

is obtained:

emerges at 32 fs, and the Dyson orbital exhibits frustrated

ﬂickering until 50 fs when the 11b character dominates in the

ground state of HT. In Figure 8A, the Dyson orbitals at 0 and

0 fs also have an 11b character, while at 27 fs it has a 12a

[(12a + 11b) (12a − 11b) ]

character. The Dyson orbital at 55 fs is clearly 12a in the

ground state of CHD. The important contributions of both the

[(12a) (11b) ] − [(12a) (11b) ]

1b and 12a orbitals seen here are consistent with Figure 3B.

Thus, the same electronic state can be expressed either with a

singly excited electronic character with one basis (left) or with

a doubly excited electronic character with the other basis

(right). The aforementioned notion of a doubly excited state is

based on the latter standpoint; it should be kept in mind that

the description of the electronic wave function depends on the

Using these Dyson orbitals, we will further discuss the notion

of doubly excited state characters. The Dyson orbitals shown

in Figures 7 and 9 clearly indicate that the S and S electronic

wave functions in the avoided crossing region have equal 11b

and 12a characters. A linear combination of 11b and 12a

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Journal of the American Chemical Society

are that the electronic energies for both CHD and HT

Article

basis functions. The interesting features in Figures 7B and 8B

not exhibit any oscillation. An intense pump pulse can

generally induce impulsive Raman scattering to create

vibrational coherence in the ground state of the reactant;

however, the oscillatory features observed in the eBE region of

.7−10.4 eV are well separated from the photoelectron bands

of cold CHD (Figure 2A). Therefore, the observed beat signals

are clearly of the vibrational coherence in the products (hot

CHD or HT). We performed Fourier transform of these time

proﬁles for the temporal region indicated with blue dots in

Figure 10A, and we found the main quantum beat component

was centered at 270 cm in the unit of wavenumbers (see

Figure 10B). We have measured similar data for a shorter

pump wavelength of 250 nm and obtained essentially the same

oscillatory features albeit with slightly smaller amplitudes (see

Supporting Information section S4).

−

The deﬁnitive assignment of these quantum beats is diﬃcult

at this point. As shown in Figure 11 , the photoelectron spectra

Figure 10. Vibrational coherence in reaction products. (A) Time

proﬁle of photoelectron intensities integrated over eBE regions of

.0−8.0, 8.2−8.7, and 9.7−10.4 eV. Black lines are the experimental

data, and red lines are the population obtained by the analysis

described in section S3 of the Supporting Information . It is noted that

the phase of the oscillations is shifted by π between the traces of 7.0−

Figure 11. Photoelectron spectra of CHD and HT. (Top two panels)

.0 and 9.7−10.4 eV. The trace for 8.2−8.7 eV is for the

26,34

Experimental photoelectron spectra of CHD and HT(tZt)

photoelectron band center of the ground-state CHD, for which no

oscillatory component is identiﬁed. (B) Fourier transform of

oscillatory components in D ← S and D ← S transitions of the

measured at room temperature along with the band positions

predicted using XMS-CASPT2 quantum chemical calculations. The

calculated positions were not shifted. (Middle two panels) Photo-

electron spectra of CHD and HT produced by the ring-opening

reaction of CHD calculated using XMS-CASPT2 surface hopping

calculations. The calculated spectra were shifted by +0.4 eV to

compare with the experimental result. (Bottom panel) Experimental

photoelectron spectrum of reaction products. Solid and dashed lines

show the experimental results with pump pulses of 267 and 252 nm,

respectively. The negative signals in the experimental spectrum due to

the ground-state bleach of CHD were compensated by addition of the

photoelectron spectrum of cold CHD with an estimated pumping

eﬃciency.

reaction products. Fourier components were obtained from the

residues shown with blue dots in (A). A rectangular window function

was used in the Fourier transform. (C) Comparison of the observed

vibrational quantum beat and computed photoelectron intensities for

CHD and HT products in selected eBE regions of 7.0−8.0 eV (solid

line) and 9.7−10.4 eV (dashed line).

products vary between 1 and 3 eV, indicating that these

trajectories do not sample the potential region near the

ground-state equilibrium geometries of the products.

Returning to the photoelectron spectra in Figure 2A, it can

be seen that the photoelectron signals from the nascent

reaction products exhibit sinusoidal intensity modulation.

These are vibrational coherence in the reaction products

created by this ballistic ring-opening reaction. Figure 10A

shows the time proﬁles of these photoelectron signal intensities

integrated over selected eBE regions. The signals in the 7.0−

of hot CHD and HT computed based on the aforementioned

full-dimensional trajectory calculations and ionization cross-

sections were quite similar to each other and their spectral

separation was diﬃcult. Alternatively, we examined the

computed photoelectron spectra for CHD and HT and

extracted the oscillatory features as shown in Figure 10C.

Both of the calculated photoelectron spectra for CHD and HT

products exhibit oscillatory features, although the amplitude

was greater for HT. Therefore, the experimentally observed

vibrational coherence is most likely of the HT product;

.0 and 9.7−10.4 eV regions exhibit clear intensity oscillations.

Furthermore, the phase of the oscillation diﬀers by π between

these two regions. For comparison, the signal integrated for

.2−8.7 eV is of the ground-state bleach of CHD, and it does

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Article

however, quantum mechanical analysis is necessary for more

single harmonic (14ω: 57 nm, 21.7 eV) was selected with a grating-

based time-preserving monochromator. The pump pulses were

generated using FFWM in Ar gas using the fundamental (ω, 0.5

mJ) and 2ω (0.3 mJ) pulses. The output pulses were reﬂected and

monochromatized using multilayer mirrors designed for 3ω. The

optical path length of the 3ω pulses was controlled using a translation

stage with 5 nm resolution. The temporal width and energy of the

pump pulses were sub-30 fs and 800 nJ/pulse, respectively. The cross-

correlation time between the pump and probe pulses was determined

to be 48 fs using nonresonant ionization of Xe.

deﬁnitive assignment in the future. An ultrafast electron

diﬀraction study on this system indicated an oscillatory

feature of the diﬀraction signal of HT with an interval of 0.25

and 0.29 ps. The period of the vibrational quantum beat shown

in Figure 10 is about 100 fs and ascribed to a diﬀerent type of

vibrational motion.

Vibrational coherence in the photochemical reaction

product has been observed for the cis−trans photoisomeriza-

tion of rhodopsin by Mathies and co-workers using stimulated

CHD vapor seeded in He carrier was injected into a photoelectron

spectrometer through a pinhole (⌀0.1 mm) at a stagnation pressure of

0−32

Raman spectroscopy

and by Miller and co-workers using

.06 MPa at room temperature. The eKE distribution was measured

transient grating spectroscopy. The product vibrational

coherence observed in the ring-opening reaction of CHD is

attributed to strong electronic coupling and an extremely short

reaction time, which are similar to the case of rhodopsin.

using a magnetic bottle time-of-ﬂight (TOF) spectrometer. The

photoelectrons traveled through a 1300 mm long ﬂight tube were

detected using a microchannel plate detector (⌀42 mm) at the end of

the ﬂight tube. A retardation voltage of −6.0 V was applied to the

ﬂight tube in order to reject low-energy electrons produced by one-

color two-photon ionization of CHD with the pump pulses. The

energy calibration of the photoelectron spectrometer was performed

SUMMARY

■

The present study ﬁrmly established the reaction pathway

mediated by the doubly excited state for the paradigmatic ring-

opening reaction of 1,3-cyclohexadiene and also uncovered its

extremely short reaction time (68 ± 7 fs). Our estimate of the

reaction time is based on the decay of the excited state of

CHD, which corresponds to formation of the cZc form of HT.

Formation of the tZt involves rotational isomerization around

C−C single bonds, and it will be slightly delayed. The

ultrashort reaction time is comparable with the cis−trans

photoisomerization of retinal in rhodopsin for which product

using the P and P peaks in the photoelectron spectrum of Xe.

1/2

The energy resolution was estimated to be 0.12 eV. The pressure in

−5

the photoionization chamber and TOF analyzer was 4.0 × 10 and

−

1.0 × 10 Torr, respectively, during the measurements. Further

information on the experimental setup is described in the Supporting

Information section S1.

Computational Simulation. The ring-opening reaction of CHD

proceeds by breaking its C symmetry. However, the potential energy

curves calculated under C symmetry provide information regarding

the correlation of the electronic states between CHD and HT. The

eﬀective potential energy curves for the ring-opening reaction of CHD

were computed using the Roos atomic natural orbital (ANO) basis

30−33

vibrational coherence has been observed.

The computed

eBE map along the geodesically interpolated reaction pathway

reproduced the general features of the experimental photo-

electron spectra well, and the full-dimensional computational

simulation of the photoelectron spectra based on the XMS-

CASPT2 surface hopping dynamics calculation reproduced the

experimental results semiquantitatively. Rigorous assignment

of the observed vibrational quantum beat was diﬃcult in the

framework of this study, and it awaits more thorough quantum

mechanical analysis of nuclear motions. At this point, we

speculate that it is most likely of HT products. We estimated

the photoelectron spectra of hot CHD and HT from the

trajectory data and photoionization cross-sections and

concluded that clear diﬀerentiation of the CHD and HT

products is not feasible with photoelectron spectroscopy. For

this reason, reliable experimental evaluation of the CHD/HT

branching ratio in this reaction was diﬃcult in the present

study. Estimation of the branching ratio is expected to be

set contracted to 4s3p2d functions for carbon and 2s1p functions

for hydrogen using the ab initio quantum chemistry software

40,41

MOLPRO.

For neutral CHD, static electron correlation was

treated at the complete-active-space self-consistent ﬁeld (CASSCF)

42,43

level of theory

with an active space composed of six electrons

distributed among six orbitals, i.e., two π and two π* orbitals in

addition to one σ and one σ* orbital initially localized at the breaking

C −C bond. The CASSCF orbitals were averaged over the states of

interest (1 A, 1 B, and 2 A) with equal weights. Dynamic electron

correlation was then taken into account at the level of the extended

multistate CAS second-order perturbation theory (XMS-

44,45

CASPT2)

with a level shift of 0.3 hartree adopted to avoid

intruder state problems. The geometry of CHD was optimized in

the 1 A and 2 A states under C symmetry constraints. Along the path

linearly connecting the two optimized geometries, the three neutral

states were evaluated using the multistate multireference (MS-MR)

scheme of XMS-CASPT2. A number of cationic states accessible from

the neutral states by a 21.7 eV photon were also obtained using the

single-state single-reference (SS-SR) scheme of XMS-CASPT2 with a

larger active space of thirty-one electrons in seventeen (fourteen σ,

two π, and one π*) orbitals. The results thus obtained are presented

in Figure 3 and Table 1.

possible with diﬀraction experiments. The time-resolution of

EUV photoelectron spectroscopy can be further improved by

shortening the driving laser pulse duration and the use of a

time-compensated EUV monochromator; the cross-correla-

tion time of the laser system in the present study was

predominantly determined by the temporal width of an EUV

pulse. It is of great interest to explore various photochemical

reactions using EUV-TRPES with a higher temporal resolution.

The ionization energies (vertical eBEs) for three isomers of cold

HT, shown in Figure 11, were computed in a similar manner. The

geometry optimization of neutral HT in the 1 A state was conducted

at the CASPT2 level with an active space consisting of six electrons in

six (three π and three π*) orbitals. The resultant equilibrium

geometries of the cZc, cZt, and tZt isomers were of C , C , and C

symmetry, respectively. Cationic states reachable from the 1 A state

for each isomer were evaluated using the SS-SR scheme of XMS-

CASPT2 with an active space of thirty-one electrons in seventeen

(thirteen σ, three π, and one π*) orbitals.

EXPERIMENTAL SECTION

■

Experimental Setup. A one-box 1 kHz Ti:sapphire regenerative

ampliﬁer (35 fs, 800 nm, 1 kHz, 6 mJ) was used as a driving laser for

nonlinear optical processes to generate the DUV pump (267.5 nm)

and EUV probe (57.1 nm) pulses. The probe pulses were produced

using HHG in Kr gas with the second harmonic (2ω, 0.29 mJ) of the

Ti:sapphire laser as a driving pulse. The 2ω laser pulses were

produced with a 0.3 mm thick β-barium borate crystal and focused

using a quartz lens (f = 500 mm) into a Kr gas cell. The 14th order

For simulations of photoelectron spectra shown in Figures 5−8, we

evaluated the electronic structures of CHD and HT in a similar

manner as that used by Polyak et al. For singlet (doublet) cases, the

XMS-CASPT2/cc-pVDZ calculations with an active space of eight

(seven) electrons in eight orbitals were performed including the S −

S (D −D ) states with the BAGEL software. An energy shift of 0.5

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orcid.org/0000-0002-4941-0436

Article

hartree was introduced. The photoionization cross-section was

estimated from the norm of the Dyson orbitals, i.e., the overlap

between CASPT2 wave functions for the initial (S ) and the ﬁnal (D )

Roland Mitric

Chemie, Universität Wu

− Institut fu

r Physikalische und Theoretische

rzburg, Wurzburg 97074, Germany;

states, by neglecting the dependence on the electronic continuum.

Dyson orbitals were computed with the help of a recent

implementation by one of the authors (A.H.) in a development

version of BAGEL. The molecular orbitals in the S and D wave

Complete contact information is available at:

https://pubs.acs.org/10.1021/jacs.1c01896

functions diﬀer due to orbital relaxation and are therefore non-

Funding

orthogonal. The Dyson orbitals between Slater determinants built

This research was supported by JSPS KAKENHI Grant

from nonorthogonal orbitals were evaluated as previously described.

5H05753, Mitsubishi Foundation, and the Japan-Belgium

The calculated energy structures of the cation are slightly diﬀerent

between Figures 3 and 5 owing to the diﬀerence in the active space

considered in the calculations.

Research Cooperative Program between JSPS and F.R.S.-

FNRS Grant JSBP120192201.

The minimum energy path that led to diﬀerent isomers of HT in

the ring-opening reaction of CHD was calculated at the XMS-

CASPT2/cc-pVDZ level of theory. The reaction path from the FC

region in S through S /S and S /S MECIs to cZc, cZt, and tZt-HT

Notes

The authors declare no competing ﬁnancial interest.

ACKNOWLEDGMENTS

■

was considered. The stationary points and MECIs were optimized,

and the intermediate segments joining these points were calculated by

The authors thank Dr. I Polyak and Professor P. J. Knowles for

generously making the results of their surface hopping

trajectory calculations available for comparison with our

experimental results. M.K. gratefully acknowledges fruitful

discussions with Professor F. Remacle and Dr. B. Mignolet on

electronic structure computations.

geodesic interpolation using a previously presented algorithm. The

time-resolved photoelectron spectra were calculated using previously

obtained trajectory data (geometries and current electronic states).

The eBE values and Dyson norms were computed for ionization from

each S to ﬁve D states along each trajectory with a time interval of 1

fs. The contributions from all trajectories were summarized in a 2D

map and convoluted with the instrumental function for comparison

with the experimental data.

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