# Investigating dissociation pathways of nitrobenzene via mega-electron-volt
ultrafast electron diffraction

Kareem Hegazy1,2 James Cryan2,3,5 Renkai Li4 Ming-Fu Lin5 Brian Moore6 Pedro
Nunes6 Xiaozhe Shen5 Stephen Weathersby5 Jie Yang4 Xijie Wang5 Thomas
Wolf2,3,5 1Department of Physics, Stanford University, Stanford, California
94305, USA  2Stanford PULSE Institute, SLAC National Accelerator Laboratory,
2575 Sand Hill Road, Menlo Park, California 94025, USA  3Linac Coherent Light
Source, SLAC National Accelerator Laboratory, Menlo Park, California 94025,
USA  4Department of Engineering Physics, Tsinghua University, Beijing 100084,
China 5SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park,
California 94025, USA  6Diamond Light Source Ltd, Didcot, UK.

(August 30, 2024)

###### Abstract

As the simplest nitroaromatic compound, nitrobenzene is an interesting model
system to explore the rich photochemistry of nitroaromatic compounds. Previous
measurements of nitrobenzene’s photochemical dynamics have probed structural
and electronic properties, which, at times, paints a convoluted and sometimes
contradictory description of the photochemical landscape. A sub-picosecond
structural probe can complement previous electronic measurements and aid in
determining the photochemical dynamics with less ambiguity. We investigate the
ultrafast dynamics of nitrobenzene triggered by photoexcitation at 267 nm
employing megaelectronvolt ultrafast electron diffraction with femtosecond
time resolution. We measure the first 5 ps of dynamics and, by comparing our
measured results to simulation, we unambiguously distinguish the lowest
singlet and triplet electronic states. We observe ground state recovery within
160 $\pm$ 60 fs through internal conversions and without signal corresponding
to photofragmentation. Our lack of dissociation signal within the first 5 ps
indicates that previously observed photofragmenation reactions take place in
the vibrationally “hot” ground state on timescales considerably beyond 5 ps.

##  I Introduction

Nitroaromatics exhibit an intriguing and diverse photochemistry enabled by the
availability of fast intersystem crossing (ISC) channels due to the presence
of the nitro functional group (NO2). Therefore, they are ideal benchmark
systems for both experimental and simulation methods and have been extensively
studied [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. Nitrobenzene (NB)
represents the simplest nitroaromatic and is depicted in Fig. 1. Its gas-phase
photochemistry following excitation in the 200-280 nm range has been
investigated by various methods on timescales ranging from femtoseconds to
microseconds [15, 10, 9, 13, 7, 8, 6].

The three main photofragmentation pathways according to previous photolysis
experiments are (1) NO2, (2) NO, and (3) O abstraction (see associated
fragment structures in Fig. 1) [10, 15]

$\displaystyle\text{C}_{6}\text{H}_{5}\text{N}\text{O}_{2}+h\nu$
$\displaystyle\rightarrow\text{C}_{6}\text{H}_{5}+\text{N}\text{O}_{2}$ (1)
$\displaystyle\text{C}_{6}\text{H}_{5}\text{N}\text{O}_{2}+h\nu$
$\displaystyle\rightarrow\text{C}_{6}\text{H}_{5}\text{O}+\text{N}\text{O}$
(2) $\displaystyle\text{C}_{6}\text{H}_{5}\text{N}\text{O}_{2}+h\nu$
$\displaystyle\rightarrow\text{C}_{6}\text{H}_{5}\text{N}\text{O}+\text{O}.$
(3)

whereas contributions from channel 3 are minor. The branching ratio between
channels 1 and 2 is excitation energy dependent with NO2 dominating the
distribution at higher photon energies [15].

Channel 2 is of particular interest, since the NO reaction product cannot
result from a simple photodissociation reaction but must involve a more
complicated mechanism involving both bond formation and cleavage. Proposed
mechanisms include isomerization through an oxizaridine ring [6, 11, 16, 12,
15, 17, 18] or a roaming-type reaction [18, 13].

Figure 1: We show nitrobenzene and the primary photofragments after
dissociation from a 267 nm source. Here we denote carbon, nitrogen, oxygen,
and hydrogen by the colors black, blue, red, and white, respectively.

The photochemical dynamics triggered by photoexcitation at 267 nm into the
lowest absorption band of NB have been investigated in a number of time-
resolved studies employing different observables. The photolysis study by Lin
et al. finds a fragmentation timescale of 59 ns [15]. Saalbach et al. employ
time-resolved photoelectron spectroscopy (TRPES) and observe dynamics in the
femtosecond to picosecond range. They assign a relaxation mechanism involving
efficient ISC to the triplet manifold based on the strong spin-orbit coupling
observed in NB. However, the TRPES spectra do not provide an unambiguous
signature of the ISC. In agreement with the previous photolysis study, no
evidence of photofragmentation was observed in the TRPES spectra within the
first 200 ps after photoexcitation.

In contrast, a study by He et al. using ultrafast electron diffraction (UED)
with picosecond time resolution found photofragmentation to take place within
8.8 ps [6]. However, the limited temporal resolution of the study did not
permit a detailed investigation of the structural dynamics leading to
photofragmentation.

Additionally, the electronic structure and photochemistry of NB was subject to
several theoretical investigations [11, 19, 14, 12, 17, 9, 13]. These studies
predict reaction pathways on the potential energy surfaces of both the lowest
singlet and triplet states.

With our present study, we address the disagreement in the literature with
respect to the timescale of photofragmentation of NB. We employ ultrafast
electron diffraction at megaelectronvolt kinetic energies (MeV-UED), which
results in femtosecond temporal resolution. The sub-picosecond time resolution
has enabled MeV-UED studies to make important contributions to the elucidation
of elementary photochemical reaction mechanisms [20, 21, 22, 23, 24, 25, 26,
27, 28]. Using MeV-UED we address the question of the photofragmentation
timescale of NB. Additionally, we revisit the question about the multiplicity
of the electronic state the photofragmentation takes place in.

##  II Methods

We imaged the sub-picosecond structural dynamics of excited NB using
megaelectronvolt gas-phase diffraction at the SLAC UED facility. Reference
[29] describes the experimental setup in detail. Briefly, a pulsed nozzle
(Parker) operating at 180 Hz delivered the gas phase NB sample to the chamber.
To deliver gaseous NB, which is a liquid at room temperature, we heated the
sample to ~410 K with a corresponding vapor pressure of 0.12 bar [30, 31]. The
sample was excited at 267 nm with an intensity of $6.74\times 10^{11}$ W/cm2.
The intensity dependence of the diffraction signal with respect to the pump
intensity was investigated to confirm that photoexcitation was in the linear
regime. We probed the ensuing structural dynamics with a 3.7 MeV electron
probe pulse. We determined the overlap between the 267 nm pump laser pulse and
the electron probe using a solid-state sample independent from the gaseous NB.
The temporal resolution of the experiment was approximately 150 fs full width
at half maximum (FWHM) [20]. Our measurement focused on the first 1.1 ps of
the pump-probe delay and a single measurement at a 5 ps delay. Within the
first 1.1 ps, we sampled pump-probe delays below 400 fs with 67 fs temporal
intervals, and for delays beyond 400 fs we sampled with 100 fs intervals. The
maximum momentum-transfer of diffracted electrons was limited by signal-to-
noise to 8 Å-1. Due to a hole in the detector that transmits undiffracted
electrons and contamination of the scattering angles close to the edge of the
hole, the minimum momentum-transfer was 2 Å-1.

Diffraction patterns were simulated within the independent atom model using a
publicly available code [32] based on form factors evaluated with the ELSEPA
program package [33]. Structures of expected dissociative states were
calculated by solving for the ground state structures of each fragment using
the Firefly package [34]. The ground state NB structure was taken from Ref.
[11]. For simulations of the vibrationally “hot” ground state and triplet
state, all quantum chemical calculations were performed in the ORCA 5.0
program package [35, 36]. Stationary points and vibrational frequencies were
performed using B3LYP/def2-SVP [37, 38, 39, 40]. For the structural
signatures, we adapted a procedure, which was previously used for spectroscopy
applications [41, 42], for electron diffraction signatures. In short, we
approximate the distribution of the photoabsorbed energy over the vibrational
degrees of freedom as statistical, which can be in turn approximated by a
canonical ensemble of a specific vibrational temperature using evaluated
vibrational frequencies. In the case of the electronic ground state, the
vibrational energy is identical with the excitation photon energy of 4.65 eV,
which corresponds to a vibrational temperature of 2940 K. For the triplet
state, we evaluate the energy difference between the ground state minimum and
the triplet state minimum using CCSD/aug-cc-pVDZ, [43, 44] correct it by the
zero point vibrational energies of both states, and subtract it from the
absorbed photon energy. The remaining excess vibrational energy is 2.25 eV,
which corresponds to a vibrational temperature of 1335 K. We use these
temperatures to simulate molecular dynamics trajectories for both states using
PBE0/def2-SVP [45]. The starting geometries of the trajectories are the
respective minimum geometries. The trajectories are propagated for 10 ps. To
evaluate diffraction signatures, 5000 geometries are randomly sampled from the
last quarter of the trajectory.

When working with the data, we use the modified molecular isotropic scattering
pattern, which removes the strong $s$ dependence in the atomic scattering
factors [46].

$\text{sM}(s,t)=s\frac{\int I(s,\theta,t)\sin\theta
d\theta}{\sum_{i}|f_{i}(s)|^{2}}.$ (4)

Here, $I(s,\theta,t)$ is the measured diffraction pattern, $\theta$ is the
azimuthal angle on the detector, and $f_{i}(s)$ is the atomic scattering
amplitude of the $i^{\text{th}}$ atom calculated with the ELSEPA program
package [33]. We highlight the molecular dynamics through the difference in
modified diffraction intensity ($\Delta$sM($s,t$)), by subtracting the
$\text{sM}(s,t)$ before the arrival of the 267 nm pump pulse. Taking this
difference also removes the constant atomic scattering and most time-invariant
detector artifacts from our measurement.

In the following analysis, we examine the rise of the observed signal and the
subsequent molecular state NB occupies. Our method and detailed results for
extracting the rise time are given in Section VII and briefly below. For each
time point, we sum over the absolute value of the ratio between
$\Delta$sM($s$) and its standard deviation:
$\sum_{s}|\Delta\text{sM}(s)/\sigma_{\Delta\text{sM}(s)}|$. The rise time is
determined by fitting these dynamics to an error function.

##  III Results

Figure 2: We show the measured time-dependent diffraction signal
$\Delta$sM($s,t$) as a function of delay in panel a. The blue bands signify
one standard error of the mean. In panel b we show the rise in the signal
amplitude (points) and the rise time fit (blue line). The black error bars
also signify one standard error of the mean.

Nitrobenze’s absorption spectrum between 215–285 nm is dominated by a strong
absorption band associated with excitation to S4 and centered at 248 nm [15,
47, 48]. It exhibits a weak shoulder associated with a transition to S3 and
centered at 280 nm [15, 48]. Our 267 nm pump pulse is redshifted from the
stronger S4 and blueshifted from the much weaker S3 band. Thus, we primarily
photoexcite NB into the S4 state, but the simultaneous preparation of minor
amounts of population in the S3 state cannot be ignored.

Following photoexcitation to the S3 and S4 states, we observe the onset of a
transient diffraction signal, shown in Fig. 2, around time zero. This signal
is characterized by intensity increases between $4<s<5$ Å-1 and $7<s<8$ Å-1,
as well as a depletion between $5<s<6$ Å-1. We quantify the rise time of this
transient signal to be $160\pm 60$ fs (Fig 2b) by an error function fit. We do
not believe this result is due to our instrument response as previous PES by
Saalbach et al. are sensitive to sub-100 fs lifetimes and observe a similar
$195\pm 20$ fs lifetime [7].

Figure 3: We show the comparison between the measured average $\Delta$sM($s$)
signal after 700 fs when the signal has equilibrated. The error bars
correspond to the standard error of the mean. Panel a shows the best fits from
the vibrationally “hot” S0 and T1 states. The shaded portions correspond to
the standard error of the mean based on a selection of 5000 structures within
these “hot” ensembles. Panel b shows the best fits from previously observed
dissociative states.

Following the onset of the transient signal at time zero we do not observe
significant structural dynamics in Fig. 2 (panels a and b). We consider NB has
reached a steady state after undergoing either a photochemical reaction or a
redistribution of energy into vibrational degrees of freedom. To determine the
structural changes associated with the onset of the steady-state signal in
Fig. 2a we compare the averaged $\Delta$sM($s,t$) between 0.75–5.25 ps, where
we no longer observe changes, to simulations of different processes in Fig. 3.

Simulation | $\bm{\chi}^{2}$
---|---
S0 |  0.29
$\text{C}_{6}\text{H}_{5}\text{N}\text{O}+\text{O}$ | 0.30
T1 | 0.37
$\text{C}_{6}\text{H}_{5}+\text{N}\text{O}_{2}$ | 0.58
$\text{C}_{6}\text{H}_{5}\text{O}+\text{N}\text{O}$ | 0.91
Table 1: We provide the $\chi^{2}$ values from fitting the simulated responses
to the measured $\Delta$sM($s$) signal.

We employ two types of simulated $\Delta$sM($s$) in this comparison, those
based on the vibrationally “hot” molecules in the S0 and T1 states as well as
optimized product structures from the three photofragmentation channels (Fig.
3) [10, 15]. In the former case (Fig. 3a), the $\Delta$sM($s$) signal
originates from the substantial amount of energy, absorbed from the pump
photon, being redistributed into the vibrational degrees of freedom (see the
methods section). In the latter case (Fig. 3b), we expect the signal to be
dominated by the elimination of many pairwise distances and can therefore be
approximated by a single fragment structure.

In the comparison in Fig. 3a, the simulation of the vibrationally ”hot” S0
signature clearly agrees better with the experiment, specifically in the
regime above $s>5.5$ Å-1. In the comparison in Fig. 3b, the signature of the
$\text{C}_{6}\text{H}_{5}\text{N}\text{O}+\text{O}$ channel clearly shows the
best agreement.

We quantify the agreement between experimental and simulated $\Delta$sM($s$)
signatures by the $\chi^{2}$ values from linear fits of the simulations to the
experimental data. These values are listed in Table 1. The vibrationally “hot”
S0 simulation yields both the best qualitative and quantitative
($\chi^{2}=0.29$) agreement with the measurement. The $\chi^{2}$ value of the
$\text{C}_{6}\text{H}_{5}\text{N}\text{O}+\text{O}$ channel is slightly larger
and the $\chi^{2}$ values of the
$\text{C}_{6}\text{H}_{5}+\text{N}\text{O}_{2}$ and
$\text{C}_{6}\text{H}_{5}\text{O}+\text{N}\text{O}$ channels $\chi^{2}$ values
two and three times larger, respectively.

##  IV Discussion

According to our fit results, the “hot” ground state and the
$\text{C}_{6}\text{H}_{5}\text{N}\text{O}+\text{O}$ dissociation channel
signatures describe the experimental $\Delta$sM($s$) signal almost equally
well. However, the $\text{C}_{6}\text{H}_{5}\text{N}\text{O}+\text{O}$
dissociation was previously observed to be a minor channel [15]. Thus, the
corresponding experimental signature must represent a weighted superposition
of $\text{C}_{6}\text{H}_{5}\text{N}\text{O}+\text{O}$ with different
signatures of higher weight, e.g. other photofragmentation channels or
vibrationally “hot” signatures. However, fits of such superpositions to the
experimental signature either yield weights incompatible with
$\text{C}_{6}\text{H}_{5}\text{N}\text{O}+\text{O}$ being a small channel or
trivial results (superposition with “hot” S0 signature). Thus, our time-
resolved structural probe of NB indicates the molecule relaxes from the S3 and
S4 states to the vibrationally “hot” S0 state, with a $160\pm 60$ fs rise
time. This is in agreement with Saalbach et al. who do not observe time-
dependent fragmentation, from ion yields, within the first 200 ps [7].

The observed timescale is consistent with the previous TRPES work by Saalbach
et al. which observed NB relaxation from S3 and S4 with a $195\pm 20$ fs
lifetime [7]. Saalbach et al. interpret the lifetime differently, as
relaxation to the “hot” T1, but admit that their probe is not particularly
sensitive to the multiplicity of the final state of the relaxation. Previous
theoretical works [11, 16, 19, 14] propose relaxation channels leading to both
S0 and T1.

Our results disagree with this scenario in two ways. Firstly, fits of the
experimental signature with a superposition of the vibrationally “hot” S0 and
T1 simulations yield either comparable or significantly larger $\chi^{2}$
values than with S0 alone. This can be seen in Fig. 3a where adding the T1
signature to S0 deviates the S0 signature away from the data except within the
small regions between 2.5-3 Å-1 and 3.5-4.25 Å-1. That is, we would expect
such a superposition to improve the fit within a ~1.25 Å-1 range while
worsening the fit in the remaining ~4.75 Å-1 fit range. Secondly, despite a
growing body of evidence for the existence of ultrafast, even sub-picosecond
ISC in molecules exclusively comprised of light elements [49], the assignment
of the observed $<$200 fs timescale to ISC would require strong additional
evidence. However, our analysis of the measured time-dependent diffraction
signal aided by simulated signals from thermalized molecular dynamic
simulations clearly points to population of the vibrationally “hot” S0 via
internal conversion.

The observation of the repopulation of S0 and the absence of additional
structural dynamics within the first 5 ps after excitation indicates, in
agreement with previous studies [15, 7, 10], that photofragmentation reactions
must occur on larger timescales. These results are, however, in disagreement
with the previous picosecond time-resolved UED study, which reported
$\text{C}_{6}\text{H}_{5}\text{O}+\text{N}\text{O}$ photofragmentation with a
time constant of 8.8 ps [6]. The previously observed $\Delta$sM($s$) signature
is in reasonable agreement with our observations. Thus, we hypothesize that
the previously observed time constant represents the experimental time
resolution (6 ps [6]) rather than the reaction dynamics of the molecule.

The disagreement in the interpretation of the $\Delta$sM($s$) signals might
lie in the employed models. He et al. simulated the signature of the
vibrationally “hot” S0 under the assumption that it can be described by a
single geometry through the incorporation of effects from the vibrational
excitation [6]. However, a statistical distribution of the absorbed photon
energy in the vibrational modes corresponds to a vibrational temperature of
2940 K (see methods). It is likely that at this high vibrational temperature
the experimental signature is not well described anymore by a single geometry
and, therefore, the employed model is not valid anymore. An ab initio
trajectory explicitly exploring the phase space, as performed in the present
study and likely computationally infeasible at the time of the previous study,
can easily overcome this limitation.

##  V Conclusion

We investigated the complex photochemistry of the simplest nitroaromatic,
nitrobenzene, in the first sub-picosecond resolved study with specific
sensitivity to the structural evolution of the compound, using MeV-UED. Our
results reveal, aided by simulations, that after excitation to the S4 and S3
excited states at 267 nm, NB relaxes to the vibrationally “hot” S0 state
within $160\pm 60$ fs. Due to the global sensitivity of MeV-UED to structural
changes, we preclude previously proposed channels (e.g. relaxation via ISC to
the triplet manifold and photofragmentation) from receiving a significant
amount of population within the observed 5 ps after photoexcitation. Our
results point to the previously observed photochemistry happening on longer
timescales through statistical mechanisms on the S0 potential energy surface.
Thus, our results present an important contribution to the elucidation of
photochemical reaction mechanisms in nitrobenzene and nitroaromatic compounds
in general.

###### Acknowledgements.

We thank the 2018 SLAC MeV-UED gas-phase team and the ASTA team for their help
in running our MeV-UED experiment. We also thank our funding agencies for
supporting this work. This work is supported by the U.S. Department of Energy
Office of Science, Basic Energy Sciences, Chemical Sciences, Geosciences, and
Biosciences Division. The UED work was performed at SLAC MeV-UED, which is
supported in part by the Department of Energy Basic Energy Sciences’
Scientific User Facility Division Accelerator and Detector research and
development program, the LCLS Facility, and SLAC under contract Nos. DE-
AC02-05-CH11231 and DE-AC02-76SF00515.

english

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Supplemental Materials

##  VI Static Nitrobenzene Signal

To validate the delivery of ground state nitrobenzene in the gas phase, we
recorded static diffraction images taken without the 267 nm pump pulse. To
remove the atomic scattering and contributions from the experimental response
function we fit the measurement using the five expected zero-crossings, from
simulation. These zero-crossings were found at 1.76, 4.99, 6.82, 9.01, and
11.74 Å-1. Each zero-crossing was fit with an exponential to guarantee that
the signal at these points are equal to 0, as expected by the ground state
simulation. After subtracting these exponentials, the results were fitted with
the simulated ground state molecular diffraction signal (sM($s$)). Figure S1
shows the delivered sample is in good agreement with ground state nitrobenzene
and that the sample was not damaged upon delivery.

Figure S1: We show the measured static signal after subtracting the atomic
scattering and measurement background. The black line corresponds to the best
fit of the calculated ground state of nitrobenzene to the data.

##  VII Rise Time Measurement

We isolate the temporal dynamics from the two-dimensional $\Delta$sM($s,t$) by
summing over $s$. However, the $\Delta$sM($s,t$) amplifies the signal at
higher $s$ that suffers from poor signal-to-noise, while the raw diffraction
intensity is dominated by low $s$ contributions. To account for the strong
$s^{-4}$ dependence in the raw diffraction intensity and weight data points
based on their signal to noise, we normalize the $\Delta$sM($s,t$) by its
standard deviation $\sigma_{\Delta\text{sM}}(s,t)$.

$R(t)=\sum_{s}\left|\frac{\Delta\text{sM}(s)}{\sigma_{\Delta\text{sM}}(s)}\right|$
(S1)

This temporal signal $R(t)$ is shown as data points in Fig. 2b.

Figure S2: We show the $\chi^{2}(t)$ distribution and its parabolic fit that
is used to retrieve the optimal rise time and its uncertainty.

To retrieve the rise time, we fit $R(t)$ to an error function. We
simultaneously fit the mean, standard deviation, and amplitude of the Gaussian
that is integrated within the error function. The rise time corresponds to the
fitted standard deviation. To further resolve the optimal rise time and
calculate its error, we fit the mean and amplitude of the error function while
varying the standard deviation around the region of the first fit. This
produces a quadratic distribution of $\chi^{2}(t)$ values, shown in Fig S2,
where the minimum corresponds to the optimal rise time and the width
corresponds to its error [50]. We retrieved a rise time of $160\pm 60$ fs.