# Time-Resolved X-Ray Spectroscopy of Phenanthridine: Elucidating the Photodynamics of a Nitrogen-Containing Polycyclic Aromatic Hydrocarbon

Dorothee Schaffner, Kira Diemer, Xincheng Miao, Emil Karaev, Marco Flock, Katharina Theil, Constant Schouder, Audrey Scognamiglio, Lou Barreau, Lionel Poisson, et al.

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Dorothee Schaffner, Kira Diemer, Xincheng Miao, Emil Karaev, Marco Flock, et al. Time-Resolved X-Ray Spectroscopy of Phenanthridine: Elucidating the Photodynamics of a Nitrogen-Containing Polycyclic Aromatic Hydrocarbon. Chemical Science, 2025, 16, pp.22711. 10.1039/D5SC03745J. hal-05357684

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# Time-Resolved X-Ray Spectroscopy of Phenanthridine: Elucidating the Photodynamics of a Nitrogen-Containing Polycyclic Aromatic Hydrocarbon†

Dorothee Schaffner,ª Kira Diemer,ª Xincheng Miao,ª Emil Karaev,ª Marco Flock,ª Katharina Theil,ª Constant Schouder,ᵇ Audrey Scognamiglio,ᵇ Lou Barreau,ᵇ Lionel Poisson,ᵇ Denis Mayer,ᶜ Andre Al Haddad,ᵈ Antoine Sarracini,ᵈ Gregor Knopp,ᵈ Xinhua Xie,ᵈ Patrick Hemberger,ᵈ Kirsten Schnorr,ᵈ Roland Mitric,\*ª and Ingo Fischer\*ª

Received Date
Accepted Date

DOI: 00.0000/xxxxxxxxxx

The photophysics and photochemistry of isolated phenanthridine have been investigated by time-resolved UV pump/X-ray probe spectroscopy at the SwissFEL free-electron laser combined with computations. Phenanthridine serves as the example for a polycyclic aromatic nitrogen-containing hydrocarbon (PANH), a class of molecules of considerable interest in material science and astrochemistry. It was excited at 268 nm into the bright 2ππ\* state. The dynamics was subsequently probed by time-resolved X-ray photoelectron (TR-XPS) and X-ray absorption (TR-XAS) spectroscopy at the nitrogen 1s edge. Two time constants of τ₁ ≈ 0.3 ps and τ₂ ≈ 3 ps were determined. The excited-state dynamics was simulated using the trajectory surface hopping method and computed TR-XAS to support the band assignments. The study reveals a sequential decay to the electronic ground state via internal conversion. Spectra recorded over longer delay times indicate a dissociation on a time scale of several hundred picoseconds.

## 1 Introduction

In this manuscript, we present a time-resolved X-ray photoelectron and photoabsorption spectroscopy study of the nitrogen-doped polycyclic aromatic hydrocarbon (PANH) phenanthridine 1, see Figure 1. PANHs currently attract considerable attention due to their role in several scientific areas. In astrochemistry, PANHs are considered as potential carriers of the Unidentified Infrared Bands (UIBs) that are observed in the interstellar medium.¹ In particular, the characteristic emission band around 6.2 µm cannot be assigned to pure hydrocarbons,² thus PANHs are currently investigated as alternative carriers. Furthermore, they are also assumed to be formed in the atmospheric chemistry of Titan, a moon of Saturn.³ In materials science and optoelectronics, PANHs are investigated as potential electron conductors,⁴

because the substitution of carbon by nitrogen allows the electronic properties of acenes to be modified.⁵ Thus, they potentially complement their pure hydrocarbon counterparts (PAHs), which are employed as hole conductors. Substitution of carbon by heteroatoms also permits modulating excited electronic state energies and thus finding new candidates for singlet fission materials, a process that has the potential to improve the efficiency of solar cells.⁶,⁷ Recent theoretical studies on the dinitrogen-doped N,N'-dihydroanthracenes and phenanthrenes have identified a number of PANHs as promising candidates for this process.⁸ First studies on aza-substituted TIPS-pentacene confirmed the assumption.⁹

The rich photophysics and photochemistry of PANHs challenge both the experimental and computational investigation of the excited-state dynamics. Only limited experimental data are available for PANHs, mainly originating from studies in solution or cold matrices.¹⁰⁻¹² Accurate gas phase data that provide insight into the intrinsic properties of these molecules are even more scarce. Compared to their pure hydrocarbon counterparts, their photochemistry is significantly complicated by the presence of additional low-lying nπ\* states due to possible excitation of the nitrogen lone pair electrons. These states open additional pathways for nonradiative deactivation. For example, nπ\* states can potentially enhance internal conversion rates and could lead to more efficient intersystem crossing (ISC) according to the El Sayed rules.¹³

<footnote>ª Institute of Physical and Theoretical Chemistry, University of Würzburg, Am Hubland, 97074 Würzburg, Germany. E-mail: roland.mitric@uni-wuerzburg.de; ingo.fischer@uni-wuerzburg.de</footnote>

<footnote>ᵇ Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405 Orsay, France.</footnote>

<footnote>ᶜ Deutsches Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany.</footnote>

<footnote>ᵈ Laboratory for Femtochemistry and Synchrotron Radiation, Paul Scherrer Institut (PSI), 5232 Villigen, Switzerland.</footnote>

<footnote>† Supplementary Information available: [details of any supplementary information available should be included here]. See DOI: 00.0000/00000000.</footnote>
To distinguish electronic states in the cascade of nonradiative
relaxation processes, time-resolved photoionization and photo-
electron spectroscopy (TR-PES) combined with high-level theory
have become the gold standard for investigating molecular dy-
namics in the gas phase.<sup>14–17</sup> However, employing visible or UV
probe pulses comes with a drawback: The relaxation process of-
ten includes transient structures with electronic configurations
that correspond to inner valence excitations, which are preferen-
tially ionized to excited electronic states of the cation. Since the
ionization energy increases strongly for accessing excited ionic
states, intermediate states can no longer be ionized and the sub-
sequent steps in the deactivation cannot be identified experimen-
tally. In particular, singlet or triplet $n\pi^*$ states that correspond to
excited ionic states in photoionization, as well as the vibrationally
highly excited electronic ground state, cannot be efficiently ion-
ized with UV pulses. Usually, the probe is chosen to limit reso-
nant ionization from the neutral ground state, so Franck-Condon
(FC) factors for photoionization to the cationic ground state are
small. Thus, a UV probe usually does not provide full informa-
tion on the transiently populated excited states. In contrast, the
use of extreme ultraviolet (XUV) or soft X-ray probe pulses cir-
cumvents these issues, with the additional advantage that inner-
shell electrons are highly sensitive to local structural and elec-
tronic changes.<sup>18</sup> Recent years have seen a growth in soft X-ray
probe techniques, concomitant with the increasing availability of
free-electron lasers (FELs) as well as table-top X-ray sources based
on high-order harmonic generation. Time-resolved X-ray absorp-
tion spectroscopy (TR-XAS) is a rather general method and has
been applied in a number of studies in the gas phase and in solu-
tion.<sup>19–22</sup> Time-resolved X-ray photoelectron spectroscopy (TR-
XPS) on the other hand acquired popularity, especially when a
heteroatom is present in the molecule.<sup>23–27</sup> With this method, a
change in the electron binding energy $E_B$ upon ionization from
electronically excited states (excited state chemical shift, ESCS)
has been reported, and serves to gain insight into the dynam-
ics.<sup>28</sup> This shift is caused by the dependence of $E_B$ on the local
charge density and its variation in the excited electronic state. In
thiouracil<sup>28,29</sup>, ionization of the sulfur 2p electrons was shown
to be sensitive to the change in electronic character at the sul-
fur atom as a function of time. The experiments outlined the
role of the <sup>1</sup>(nπ*) state, which acts as a doorway state for ISC
to the triplet manifold. As a further probe method, time-resolved
Auger-Meitner spectroscopy is particularly useful when investi-
gating dissociation processes and was employed in studies of the
dynamics of thymine and CS<sub>2</sub>.<sup>20,30,31</sup>

Phenanthridine 1 is an excellent model to investigate PANH
dynamics, because some prior information is available. We
recently reported multiphoton ionization spectra of three aza-
phenanthrenes, including 1 as well as benzo[f]quinoline and
benzo[h]quinoline, combined with simulations based on ab initio
computations.<sup>32</sup> It was found that two ππ* and one nπ* states lie
within 0.3 eV or less. In the present work, we employ TR-XPS and
TR-XAS at the N 1s edge to monitor the deactivation processes
in 1 after excitation at 268 nm and support the experiments by
trajectory-based nonadiabatic dynamics simulations along with
computed TR-XAS. This permits us to probe the changes occuring

<figure><img src="image_2.png" /><figcaption>Fig. 1 Scheme of the electronic processes in phenanthridine 1 inves-
tigated in this work. In the pump step (left), the molecule is valence
excited into the S₃ state. In the probe step (right), a N 1s electron is
subsequently either ionized (TR-XPS, solid blue line) or excited (TR-
XAS, dashed and dotted green lines) into a half filled or empty molecular
orbital (MO). Note that the orbital energies are not drawn to scale. The
depicted MOs are obtained at ωB97X-D/def2-SV(P) level of theory.</figcaption></figure>

at the nitrogen site and to assess in particular the role of low-lying
$n\pi^*$ states, which have a small ionization probability to the ionic
ground state in valence photoionization probe experiments.

## 2 Results

In the X-ray probe experiments discussed below, 1 is excited at 268 nm (4.63 eV). In agreement with our previous work,<sup>32</sup> time-dependent density functional theory (TDDFT) calculations revealed that the lowest three excited singlet states are energetically accessible, see Table 1a). To characterize the adiabatic states S<sub>1</sub> to S<sub>3</sub>, the natural transition orbitals (NTOs) for each state and the oscillator strengths were determined. As depicted in Figure S1 in the supporting information (SI), the S<sub>1</sub> and S<sub>3</sub> states have mixed ππ* character, whereas S<sub>2</sub> is a pure nπ* transition. Consistent with this characterization, the computed oscillator strengths *f* indicate a dark S<sub>2</sub> state (nπ*), and bright S<sub>1</sub> and S<sub>3</sub> states. These findings were supported by a high-level equation-of-motion coupled-cluster calculation with singles and doubles (EOM-CCSD), see Table 1b). As is evident from the ensemble spectrum shown in Figure S3, the S<sub>2</sub> state acquires intensity due to vibronic interaction outside the Franck-Condon region. Previous REMPI (resonance-enhanced multiphoton ionization, see Figure S4) work showed a vibrationally resolved electronic spectrum with an origin at 3.67 eV that was assigned to the S<sub>1</sub> ← S<sub>0</sub> transition.<sup>32,33</sup> At about 4.2 eV, a second transition sets in which is broad and unstructured, assigned to the second bright ππ* state.<sup>32</sup> However, intensity perturbations in the spectrum have been identified by comparison with simulations, which indicate mixing of electronic states.

Initially, ps- and fs-time-resolved photoelectron spectroscopy
(TR-PES) experiments using valence photoionization as a probe
were carried out, as described in Figures S5 and S6 in the SI. In
the ps-experiments, previously identified S<sub>1</sub> vibronic bands were
excited with tunable radiation and ionized using either 351 nm or
263 nm probe light. While a ns-lifetime was observed at the ori-
gin at 3.670 eV (337.8 nm), a rapid decay on the ps-scale is visible
for excited vibronic states. Time constants ranging from 100 ps
<table><caption>Table 1 Vertical excitation energies *E*<sub>exc</sub> and oscillator strengths *f* for the lowest excited singlet states and the corresponding dominant transition characters.</caption><caption>(a) ωB97X-D/def2-SV(P)</caption><thead><tr><th>state</th><th><i>E</i><sub>exc</sub> / eV</th><th><i>f</i></th></tr></thead><tbody><tr><td>S<sub>1</sub> (ππ*)</td><td>4.40</td><td>0.0146</td></tr><tr><td>S<sub>2</sub> (nπ*)</td><td>4.53</td><td>0.0017</td></tr><tr><td>S<sub>3</sub> (ππ*)</td><td>4.73</td><td>0.0456</td></tr><tr><td>S<sub>4</sub> (ππ*)</td><td>5.37</td><td>0.1112</td></tr></tbody></table>

<table><caption>(b) EOM-CCSD/cc-pVDZ</caption><thead><tr><th>state</th><th><i>E</i><sub>exc</sub> / eV</th><th><i>f</i></th></tr></thead><tbody><tr><td>S<sub>1</sub> (ππ*)</td><td>4.29</td><td>0.0072</td></tr><tr><td>S<sub>2</sub> (nπ*)</td><td>4.80</td><td>0.0020</td></tr><tr><td>S<sub>3</sub> (ππ*)</td><td>5.11</td><td>0.0233</td></tr><tr><td>S<sub>4</sub> (ππ*)</td><td>5.28</td><td>0.0143</td></tr></tbody></table>

at +0.235 eV (317.5 nm) down to 10 ps at +0.677 eV (285.2 nm) have been found.³⁴ A signal offset at long delay times was visible, indicating that the final state of the deactivation can be ionized. In fs-TR-PES using 800 nm multiphoton ionization probe, a monoexponential decay with $\tau \approx 7$ ps was confirmed at 280 nm (not shown). However, at 266 nm excitation, the laser studies revealed a very different behavior. The time-resolved photoelectron signal could be adjusted by a biexponential decay. A sequential model was employed for the fit. We applied a two-step deactivation $A \to B \to C$, following the procedure outlined in section S10 in the ESI,³⁵ and obtained two time constants, $\tau_1 = 270 \pm 50$ fs and $\tau_2 = 4.35 \pm 0.15$ ps (see Figure S6 in the SI) No signal offset at long delay times was observed. However, only limited information on the electronic states involved in the deactivation could be deduced from these data, because the intermediate and final states of the deactivation cascade could not be identified with the 800 nm probe. We therefore switched to X-ray probe schemes to unravel the photophysics of the molecule.

## 2.1 TR-XPS

Figure 2a) shows the TR-XPS spectrogram obtained by ionization of a N 1s electron in the probe step with $h\nu_{probe} = 499$ eV (blue arrow on the right hand side of Figure 1). The 2D map displays the intensity of the difference photoelectron signal as a function of both electron kinetic energy (eKE, left ordinate) and binding energy $E_B$ (with $E_B = h\nu_{probe} - eKE$, right ordinate), and the pump-probe delay $\Delta t$ on the abscissa. The time-independent background signal (pump laser off) due to the XPS probe alone has been subtracted. Red bands in the 2D map indicate a signal increase upon interaction with the pump laser, while the blue color indicates a signal that decreases with respect to the background signal after pump excitation. The most pronounced feature is associated with a depleted photoelectron signal centered at eKE = 94.5 eV. It is assigned to a ground state bleach (GSB). From the static XPS in Figure 2b), a N 1s ionization energy (or $E_B$) of 404.5 eV is deduced, which is in line with the value for related

<figure><img src="image_3.png" /><figcaption>Fig. 2 (a) Time-resolved X-ray photoelectron spectrum of phenanthridine displayed as a 2D map (difference spectrum), using $h\nu_{pump} = 4.63$ eV (268 nm) and $h\nu_{probe} = 499$ eV. The bands in the map correspond to N 1s ionization. (b) Static XPS spectrum of phenanthridine (UV off). (c)–(f) Delay traces for selected kinetic energies (eKE) in the 2D map. A ground state bleach signal is visible around eKE = 94.5 eV (d). Two weaker transients around 93.4 eV (e) and 95.6 eV (c) are assigned to the excited-state dynamics of phenanthridine. The absorption band at eKE = 90 eV (f) shows no decay and is due to two-photon ionization of phenanthridine with subsequent N 1s ionization of the cation.</figcaption></figure>

molecules like pyridine (404.82 eV).³⁶ On the time scale of the experiment, the GSB does not fully recover. In addition, three photoelectron bands are recognized after $t_0$ at $E_B = 409.0$ eV, 405.6 eV and 403.4 eV (eKE = 90.0 eV, 93.4 eV and 95.6 eV). For these three bands and for the GSB, the corresponding delay traces are given in Figures 2c)–f). The one at eKE = 90 eV (Figure 2f) shows no decay and the chemical shift $\Delta E = 5$ eV is too large to be reasonably assigned to an excited electronic state of 1. In addition, the signal intensity depended sensitively on the pump laser pulse energy which was varied between 10 and 30 $\mu$J. A spectrum recorded at 20 $\mu$J is given for comparison in Figure S7 the SI. All bands are present, but the analysis is hampered by the low signal/noise ratio. Therefore, we assign the feature at eKE = 90 eV to the phenanthridine cation $1^+$, formed by a two-photon ionization in the pump step. Unsurprisingly, N 1s ionization of $1^+$
is associated with higher binding energies, because more energy
is required to remove a 1s electron from the cation. The latter
two absorption bands, however, are assigned to the intermedi-
ate state dynamics of 1. Qualitatively, the band at eKE = 93.4eV
(Figure 2e) appears directly after excitation and decays rapidly.
The band at eKE = 95.6eV (Figure 2c) seems to appear slightly
later in time and exhibits a pronounced component with a longer
lifetime. A global fit using the model outlined in section 2.0 (see
also section S10 for details) reveals two time constants, τ₁ ≤ 100 fs
and τ₂ = 3.3 ± 0.8 ps. Constant τ₁ seems to govern the decay of the
93.4 eV band (trace e) and the risetime of the 95.6 eV band (trace
c), while τ₂ describes the decay of the 95.6 eV band and the re-
covery time of the GSB (trace d). The determination of more
accurate values is impeded by the signal-to-noise (S/N) ratio of
the data.

To fully understand the processes in the S₀ state, TR-XPS spec-
tra were recorded up to 500 ps, using the same experimental con-
ditions. As can be seen from Figure S8, the signal attributed to
the GSB starts to increase again after 10 ps. A further transient
appears with time, broadens and starts to shift to lower kinetic
energies. This band has a temporal profile that is similar to the
GSB. In isolated molecules, such a change indicates either disso-
ciation or isomerization in the S₀ state and formation of a new
species with a slightly lower E<sub>B</sub> of 406.4 eV. Interestingly, this
value matches the E<sub>B</sub> of HCN of 406.69 eV quite well.<sup>37</sup> We there-
fore tentatively assign this band to the formation of a HCN pho-
toproduct from the electronic ground state of the neutral. The
rise time on the order of several 100 ps is commensurate with a
unimolecular dissociation that can be described by statistical rate
theory. At least in PANH cations this process (HCN loss) is well
documented.<sup>38</sup> RRKM calculations were not carried out, because
reasonably accurate barriers are necessary, which requires a com-
prehensive calculation of all possible reaction pathways leading
to HCN loss.

2.2 TR-XAS

To complement TR-XPS, time-resolved X-ray absorption spectra were recorded at the N 1s edge starting from UV valence excited 1 ($\lambda_{pump}$ = 268 nm). As illustrated on the right hand side of Figure 1, the N 1s electron can be promoted into the half-filled (green dashed and dotted lines) or empty orbitals (green dash-dotted line) of the optically excited molecule, i.e., transitions such as 1s → n and 1s → $\pi$ occur. The static X-ray absorption spectrum (Figure 3a) shows an intense band at 398.3 eV that is due to excitation of the N 1s electron into the $\pi^*$ orbital (LUMO). A second band at 401.3 eV is due to a transition into a higher unoccupied level (vide infra). In accordance with the XPS data above, the ionization limit is reached between 404 eV and 405 eV and leads to an increase of the XAS signal.

Figure 3b) shows ΔXAS recorded at various time delays, with
ΔXAS = XAS(t) – XAS(probe only). At several probe photon ener-
gies, marked as colored lines in the experimental spectrum, the
signal was subsequently measured as a function of time delay.
The time-dependence of these traces is shown in Figure 4. An
initial qualitative discussion will be based on Figure 3. Exciting

1 at 268 nm results in a depletion of population in the electronic
ground state, and subsequently a time-dependent bleach of the
1s → LUMO signal (green line at 398.3 eV). A further bleach is
apparent for the second band at 401.3 eV. As it is also due to de-
population of the S₀ state, its time-dependence is very similar to
the 1s → LUMO signal. Several transient absorption (TA) features
appear towards lower energies. The lowest energy transient fea-
ture at 394.8 eV (black line) appears immediately after the pump
pulse and is therefore assigned to TA from an electronic state that
is either populated upon excitation or very rapidly thereafter. It is
shifted by ca. -3.5 eV relative to the 1s → LUMO ground state ab-
sorption and reaches its highest intensity in the 80 fs trace, before
it decreases again. The second band at 396.1 eV (red line) appears
slightly later and decreases on a ps-time scale. It is therefore as-
sociated with a transiently populated electronic state. Finally, the
band at 397.8 eV (blue line) starts to appear between 80 fs and
680 fs and increases on a ps-time scale. As it is very close in en-
ergy to the GSB, we assign this band to absorption of vibrationally
excited molecules in the S₀ state. Alternatives to hot ground state
formation would be an excited state dissociation, which should
be visible in the TR-XPS at short delay times, and radiative de-
cay, which would occur on a longer time scale. Thus, after non-
radiative deactivation, energy is instead redistributed among the
vibrational degrees of freedom, forming a hot ground state. This
band assignment is confirmed by computations, as described be-
low. There are several further TA bands in between the two GSB
features at 398.3 eV and 401.3 eV. At the high energy side of the
major band (398.3 eV) we also expect hot ground state absorp-
tion. However, there is an overlap with transitions terminating in
higher unoccupied orbitals, so it becomes increasingly difficult to
disentangle the various contributions. Therefore, these features
are not further discussed.

In addition to the transitions in neutral phenanthridine, we also
expect a transition in the phenanthridine ion 1⁺, corresponding

<figure><img src="image_4.png" /><figcaption>Fig. 3 Experimental X-ray absorption spectra of phenanthridine measured as total electron yield (TEY): (a) static XAS and (b) ΔXAS at different pump-probe delay times. Vertical lines indicate probe photon energies where delay traces were recorded.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 4 Time delay traces of the XAS experiments. The color code represents the lines given in Figure 3. The band at 394.8 eV (a), black line, circles) shows a rapid decay, whereas the band at 396.1 eV (b), red line, squares) decays more slowly. The band at 397.8 eV (c), blue line, triangles) shows a monoexponential rise and is assigned to hot ground state absorption. The bottom trace (d), green line, reverse triangle) finally depicts the GSB. The time constants $\tau_1 = 0.45 \pm 0.18$ ps and $\tau_2 = 3.1 \pm 1.8$ ps were determined in a global fit.</figcaption></figure>

to the band at $E_B=409$ eV in the XPS, which was assigned to two-photon ionization of **1**. The XAS of $1^+$ has not been studied, but for some small molecules, including $N_2^+$ XAS of the cations are available.³⁹ In that case, the $1s \rightarrow$ SOMO peak of the ion appears at an energy that corresponds to the binding energy in the XPS minus the IE of the neutral. Inserting the values for **1**, we obtain 396.2 eV for the likely transition in $1^+$. This value is very close to the band at 396.1 eV. Thus, a contribution from $1^+$ can be expected for the latter band.

Figure 4 shows the time delay traces obtained for absorption energies of 394.8 eV (a), 396.1 eV (b) and 397.8 eV (c), as well as the GSB at 398.3 eV (d), corresponding to the bands labeled with lines in black, red, blue and green in Figure 3. The top trace (Figure 4a) shows a rapid rise within the instrument response function (irf) of ca. 100 fs, followed by a fast decay. In contrast, the band at 397.8 eV (Figure 4c) shows a monoexponential rise on the ps-scale, which matches the formation of a hot ground state. The GSB itself (Figure 4d) shows a slight recovery, but increases again after ca. 10 ps, cf. Figure S8. The band in Figure 4b), corresponding to a probe photon energy of 396.1 eV (red), is more difficult to interpret and has an unusual appearance. After a rapid increase, the absorption signal decreases in a complicated fashion and seems to show multiple components. The signal also does not

decrease to zero, but rather reaches a finite value. As outlined above, the band is most likely perturbed by the time-independent absorption of $1^+$. Both contributions are independent, because they originate from different processes. Their presence nevertheless renders the determination of time constants more difficult. We therefore assume that the signal is composed of a quickly rising contribution of $1^+$ that remains constant on the time scale of the experiment and a contribution from **1** with a few ps decay.

The solid lines in Figures 4a)–c) represent a global fit of all three traces, again employing the previously described model, which yields two time constants, $\tau_1 = 0.45 \pm 0.18$ ps and $\tau_2 = 3.1 \pm 1.8$ ps.

## 2.3 Nonadiabatic dynamics

To gain further insight into the electronic states involved in the photodynamics, trajectory surface hopping simulations over 1 ps were performed on a set of 50 trajectories of **1** launched from their brightest excited states: 26 were started from the $S_2$ state, while the other 24 were started from the $S_3$ state.

The time evolution of the populations in the adiabatic picture is shown in Figure 5a). The excited state deactivation of **1** from $S_2$ or $S_3$ to $S_1$ takes place within the first ca. 60 fs. The population transfer from $S_3$ to $S_2$ is essentially completed within 10 fs, while the decay from $S_2$ to $S_1$ is slower. All trajectories remain in this lowest excited singlet state from roughly 100 fs on; occasionally, some trajectories hop between $S_1$ and $S_2$ (and $S_3$). After about 500 to 700 fs, nine trajectories have returned to the electronic ground state. However, the switch to the electronic ground state is not well represented in the framework of TDDFT, because the multi-reference character of $S_0$ in the region of the conical intersection between $S_1$ and $S_0$ is not taken into account.

To analyse the character of the electronic states during deactivation, a diabatisation along the nuclear trajectories was performed as described in Section S6 of the SI. The results of the diabatisation are depicted in Figure 5b). The initial ensemble as excited into the $S_3$ and $S_2$ state has primarily $\pi\pi^*$ character. The $S_2$ state, although formally an $n\pi^*$ state, gains some $\pi\pi^*$ character due to vibronic coupling. The initial rise in the $S_2$ population within the first 10 fs correlates with the concomitant drop in the $\pi\pi^*$ population, indicating that molecules excited to $S_3$ convert into an $S_2$ of predominantly $n\pi^*$ character, whereas those directly excited to $S_2$ retain their $\pi\pi^*$ character. A short section of almost constant population observed for both $S_2$ and $\pi\pi^*$ between 5 and 15 fs signifies that the diabatic character of $S_2$ is preserved.

Subsequently, $S_2$ decays faster than the $\pi\pi^*$ population, showing that the nascent $S_1$ state carries a substantial $\pi\pi^*$ contribution. Once $S_2$ is depleted, the $S_1$ character continues to change from $\pi\pi^*$ to $n\pi^*$ character for some 100 fs. I.e. once the trajectory reaches $S_1$, it experiences an intrastate shift from $\pi\pi^*$ to $n\pi^*$ character. After ≈500 fs return to the electronic ground state sets in. To obtain a deeper insight into the dependence of the electronic structure of **1** on the nuclear geometry, the potential energy surfaces were scanned for selected vibrational modes. The normal modes that dominate the relaxation dynamics
starting from the $S_3$ state were identified by transformation of the time-dependent cartesian coordinates into time-dependent normal coordinates by means of a projection of the trajectories onto the normal modes of **1** in the FC structure.⁴⁰ For more details, see Section S7 of the supporting information. The investigation revealed that the vibronic coupling is mainly mediated by three in-plane bending modes (see Figure S10) along which the potential energy surfaces exhibit pronounced crossings, as can be seen from Figure S11.

<figure><img src="image_6.png" /><figcaption>Fig. 5 Time evolution of the populations in the (a) adiabatic states and (b) diabatic states, averaged over 50 trajectories.</figcaption></figure>

To support the interpretation of the experimental data, the X-ray absorption spectra were simulated based on EOM-CCSD computations that include core hole excitations and, to further aim for simulations of time-resolved XAS, employing the less expensive CASPT2/RASPT2 method (abbreviated as RASPT2 in the following) for which the chosen active space is depicted in Figure S2. This calculation type produces a set of orbitals by unitary transformation of the molecular orbitals, resulting in the so-called natural orbitals (NOs) which do not have physically meaningful energies, and are therefore arbitrarily ordered. The orbital labels used in this work, along with their corresponding characters, are provided in Table 2a). The vertical excitation energies $E_{exc}$ and the oscillator strengths $f$ given in Table 2b) are in good agreement with the TDDFT results (cf. Table 1a). When comparing computed with experimental intensities, their method-dependence should nevertheless be taken into account. The excited state composition at CASPT2 level of theory (Table 2b) is in line with the TDDFT calculation regarding the $S_1$ and $S_2$ states, whereas the mixed character of $S_3$ is not well reproduced. However, this state is populated only for a very short time, so its contribution to the TR-XAS simulated at RASPT2 level is expected to be of minor importance.

<figure><img src="image_7.png" /><figcaption>Fig. 6 (a) Comparison of the experimental static XAS with the simulated XAS for the electronic ground state computed using EOM-CCSD and RASPT2. All calculations were carried out at the equilibrium structure of **1** and the simulated stick spectra were broadened with a Gaussian profile with the width of $\sigma = 0.3$ eV. The EOM-CCSD (dashed) and RASPT2 (solid) spectra were shifted by -4.0 eV and -3.1 eV, respectively. (b) Simulated XAS of the ensemble used in the nonadiabatic dynamics, computed at the RASPT2 level. The magenta trace is the total ensemble-averaged XAS at time zero, while the yellow and black traces show the sub-ensemble contributions from molecules initially promoted to $S_3$ or $S_2$, respectively. All stick spectra were shifted by -3.1 eV and broadened with a Gaussian of width $\sigma = 0.1$ eV. The smaller Gaussian width in panel (b) reflects the fact that the ensemble's intrinsic distribution of molecular geometries already contributes to significant spectral broadening.</figcaption></figure>

Figure 6a) compares the simulated X-ray absorption spectra at the equilibrium structure of **1** in the electronic ground state computed at EOM-CCSD (dashed line) and RASPT2 (solid line) level of theory with the experimental spectrum (dotted line). The EOM-CCSD simulation was shifted by -4.0 eV so that the $1s \rightarrow$ LUMO absorption band (A) coincides with the most intense band in the experimental spectrum. The computed spectrum is in good agreement with the experimental one for the signal at ca. 401.3 eV (B), which can be assigned to the mixed transition involving $1s \rightarrow$ LUMO+1 (55%) and $1s \rightarrow$ LUMO+2 (22%) orbital excitations. The RASPT2 simulation was shifted by -3.1 eV analogously. Due to the absence of the LUMO+2 in its active space, the band B is not well reproduced in the RASPT2 spectrum and appears at 399.6 eV (B').

Figure 6b) displays the simulated XAS of the ensemble used in the nonadiabatic dynamics, computed at the RASPT2 level. The magenta trace is the total ensemble-averaged XAS at time zero, while the yellow and black traces show the sub-ensemble contributions from molecules initially promoted to $S_3$ or $S_2$, respectively. The band at 394.0 eV with the high-energy shoulder at 394.5 eV is attributed to the excited-state absorption (ESA) from
<table><caption>Table 2 (a) Labels and characters of the natural orbitals. (b) Vertical excitation energies $E_{exc}$ and oscillator strengths $f$ for the three lowest excited singlet states and the corresponding dominant transition characters along with the state compositions computed at the Franck-Condon geometry. The data were computed at SA4-RMS-CASPT2(6,5)/cc-pVDZ level of theory (for more details, see Section 5).</caption><thead><tr><th colspan="2">(a)</th><th colspan="3">(b)</th></tr><tr><th>label</th><th>character</th><th>state</th><th>composition</th><th>E<sub>exc</sub> / eV</th><th>f</th></tr></thead><tbody><tr><td>LUNO+1</td><td>π*</td><td rowspan="2">S<sub>1</sub> (ππ*)</td><td>54% HONO-1 → LUNO</td><td rowspan="2">4.09</td><td rowspan="2">0.0203</td></tr><tr><td>LUNO</td><td>π*</td><td>27% HONO-2 → LUNO+1</td></tr><tr><td>HONO</td><td>n</td><td rowspan="2">S<sub>2</sub> (nπ*)</td><td rowspan="2">90% HONO → LUNO</td><td rowspan="2">4.54</td><td rowspan="2">0.0066</td></tr><tr><td>HONO-1</td><td>π</td></tr><tr><td>HONO-2</td><td>π</td><td>S<sub>3</sub> (ππ*)</td><td>91% HONO-1 → LUNO+1</td><td>4.67</td><td>0.6965</td></tr></tbody></table>

$S_2$, because the intensity of the excitation from $S_3$ is very low at this energy window. The band around 395.2 eV results from absorptions of both $S_2$ and $S_3$ into higher core-excited states. As the excited population at time zero has mainly $ππ^*$ character the signals result from a $1s→π$ transition to a large extent, although a non-negligible contribution from $1s→n$ is present, cf. Figure 5b).

The time-resolved XAS shown in Figure 7a) is computed by subtracting the ground state XAS obtained at time zero from the XAS computed along the surface hopping trajectories (broadened with a two-dimensional Gaussian profile with $\sigma_{exc} = 0.1$ eV and $\sigma_t = 20$ fs). All computations are performed at RASPT2 level. Figure 7b) depicts the relevant time and energy region for the ultrafast decay of the $S_2$ state, where narrower two-dimensional Gaussian profiles were used. Again, the energies have been shifted by -3.1 eV to match the experimental static XAS. For enhanced visibility the individual contributions of the transient population in the $S_0$, $S_1$, $S_2$ and $S_3$ state are given separately in Figure S12.

The light blue feature at around 394.1 eV visible in Figure 7b) that appears already at time zero arises from ESA of the subensemble initially excited to $S_2$. This can be inferred from the ensemble XAS in Figure 6b) and the $S_2$ state-selective TR-XAS in Figure S12. Between 5 and 10 fs signals at 394.4 eV and 394.6 eV (two light blue stripes) grow in alongside a further intensification of the 394.1 eV band, reflecting the ultrafast decay of $S_3$ and concurrent rise of the $S_2$ population (cf. Figure 5). After about 20 fs, these $S_2$-related features weaken while a new broad signal between 394.6 and 395.3 eV appears and intensifies, which is caused by ESA from $S_1$ as recognised from Figure S12. Finally, as visible in trace a) beyond ca. 600 fs, the $S_1$ signature decays and a feature at 397.3 eV emerges, marking the recovery of the hot electronic ground state, accompanied by a hot ground state feature. This feature is best recognised in the $S_0$ state-selective TR-XAS shown in Figure S12.

Figure 7 supports the following assignments for the experimental time delay traces in Figure 4:

* The trace at 394.8 eV (black line in Figure 4a) follows the energy and kinetics of the $S_2$ ESA in the simulated TR-XAS.

* The trace at 397.8 eV (blue line in Figure 4c) coincides with the hot ground-state XAS.

* The trace at 398.3 eV (green line in Figure 4d) matches the GSB.

All three features are therefore assigned to ESA of $S_2$, hot ground state XAS, and GSB, respectively. The trace at 396.1 eV (red line in Figure 4b) follows the temporal profile of simulated $S_1$ ESA but is shifted by about 1.1 eV. This offset is attributed to the limited active space in our RASPT2 calculations; nonetheless, the qualitative agreement remains valid (see Section S9 in the supporting information). As noted above, the experimental band also contains contributions from $1^+$.

<figure><img src="image_8.png" /><figcaption>Fig. 7 (a) Simulated transient X-ray absorption spectrum of 1 computed using the RASPT2 method. The ensemble ground state spectrum was broadened with a Gaussian profile with the width of $\sigma_{exc} = 0.1$ eV, the transient TR-XAS was broadened with a two-dimensional Gaussian profile with the standard deviations of $\sigma_{exc} = 0.1$ eV and $\sigma_t = 20$ fs. (b) Close-up of the first 80 fs between 393.5–395.5 eV, where the spectrum was broadened with a two-dimensional Gaussian profile with $\sigma_{exc} = 0.05$ eV and $\sigma_t = 10$ fs.</figcaption></figure>

For a direct comparison with the experiment, the simulated counterparts of the four experimental time delay traces in Figure 4 are plotted in Figure 8 as dashed lines. Overall, the simulation reproduces the main temporal features, with the exception of the blue trace in panel c), which exhibits an elevated signal
at time zero. We attribute this initial offset to ESA from S₂ and S₃ into highly excited core-level states that are likely poorly described by the limited active space in our RASPT2 calculations and therefore deviate from the experiment. The transients in panels a), b) and c) were fitted with a sequential two-step deactivation model (solid lines in Figure 8), yielding time constants of τ₁ = 63 fs and τ₂ = 1.7 ps. These values are in reasonable agreement with the experimental lifetimes.

<figure><img src="image_9.png" /><figcaption>Fig. 8 Simulated time delay traces for selected bands in the computed transient X-ray absorption spectrum (Figure 7) using a temporal broadening of 20 fs.</figcaption></figure>

## 3 Discussion

The experimental and computational data presented above provide a detailed insight into the photodynamics of 1. In this section, we will put the various observations in context and derive a consistent interpretation of the data. At 268 nm, the molecule is excited into the 2ππ* state. Previous REMPI spectra (Figure S4) showed an intense band that is broad and unstructured.³² Although this study suggests that this band corresponds to the S₃ ← S₀ transition we prefer to describe it as a 2ππ* ← S₀ transition, because the 2ππ* character dominates the absorption of the ensemble.

Three different probe methods were employed, 800 nm multiphoton ionization using a femtosecond laser (Figure S6, time-resolution ≈150 fs), TR-XPS (Figure 2) and TR-XAS (Figure 3) with X-ray FEL radiation (time-resolution ≈100 fs, see below). In all three approaches, the time-dependence of the signal was fitted by a biexponential function. The fitting procedure is described in section S10 of the ESI, while the time constants obtained in the

experiments are summarized in Table 3. They deviate somewhat quantitatively, in particular τ₁ obtained by TR-XPS is smaller, possibly due to overpumping in the FEL experiments or due to an inferior signal/noise ratio, but agree qualitatively quite well. The first one, τ₁, is on the fs-scale and lies around 300 fs, while τ₂ is around 3 to 4 ps. Thus, the data agree with a two-step deactivation. In contrast, theory suggests a three-step process, with two sub-100 fs time constants and a third one on the ps-time scale. We therefore introduced a third time constant in the fit to the experiments, but this did not improve the fit further.

<table><caption>Table 3 Time constants determined in the various experiments.</caption><thead><tr><th>Method</th><th>TR-PES</th><th>TR-XPS</th><th>TR-XAS</th></tr></thead><tbody><tr><td>τ₁ / ps</td><td>0.27 ± 0.05</td><td>≤0.1</td><td>0.45 ± 0.18</td></tr><tr><td>τ₂ / ps</td><td>4.3 ± 1.3</td><td>3.3 ± 0.8</td><td>3.1 ± 1.8</td></tr></tbody></table>

It is the main goal of the current study to unravel the detailed dynamics of the deactivation cascade and correlate the time constants with specific processes. The best information to this end is available from the TR-XAS. Here, a band shifted by 3.5 eV to lower energies (black line in Figure 3b) appears right after the excitation and might at first glance be assigned to TA from the S₃ 2ππ* state. However, the surface hopping simulations suggest very fast sub-100 fs time constants for both the S₃ → S₂ and S₂ → S₁ deactivation (cf. Figure 5). As we only extract one fast time constant from the experimental data, we conclude that it corresponds to the S₂ → S₁ transition, because the calculated oscillator strength for the ESA of S₂ is significantly larger than that for S₃. Therefore, the contribution from S₃ (cf. Figure 6b) is not visible in the experimental spectrum. The second time constant is then associated with return of population to the electronic ground state. This is evidenced by the GSB signal in the TR-XPS at E<sub>B</sub> = 404.5 eV (eKE = 94.5 eV), cf. Figure 2d), as well as the decay of the transient absorptions at 396.1 eV (red line in Figure 4b) and the rise at 397.8 eV (blue line in Figure 4c), formation of hot ground state). Thus, τ₂ is assigned to an internal conversion (IC) from the S₁ state to the electronic ground state. The experimental evidence is in line with the simulated excited state spectra (Figure 7 and Figure 8) and the computed time constants of 63 fs and 1.7 ps. As noted above, the XAS band at 396.1 eV likely contains a contribution from the time-independent absorption of the cation (Figure 4b). This increases the error in the determination of the time constants.

The bands in the TR-XPS spectrum (Figure 2) can in principle be assigned based on the local charges on the N-atom. A population analysis based on Löwdin charges revealed the highest positive charge density on the nitrogen atom in the nπ* state. This results in a higher E<sub>B</sub> (and lower eKE) for ionization from the nπ* state and suggests the band E<sub>B</sub> = 405.6 eV (eKE = 93.4 eV, Figure 2e), black line) to be associated with this processes. As both S₂ and S₁ have a mixed ππ* / nπ* character that evolves during deactivation, an assignment based on local charges only seems inadequate.

The surface hopping computations also provide information on the electronic character of the states. Over time, the initially
dominant $n\pi^*$ character in the $S_1$ state changes to $n\pi^*$ character. More precisely, the sub-ensemble originally excited to the $S_2$ state follows the deactivation cascade $2\pi\pi^* \rightarrow 1\pi\pi^* \rightarrow n\pi^* \rightarrow S_0^*$, while the sub-ensemble originally excited to the $S_3$ state decays according to $2\pi\pi^* \rightarrow n\pi^* \rightarrow 1\pi\pi^* \rightarrow n\pi^* \rightarrow S_0^*$. Note that the fast time constants are not commensurate with intersystem crossing, which is therefore not further considered.

Once back in the hot ground state $S_0^*$, 1 dissociates with a time constant of several hundreds of ps. As concluded from the TR-XPS data at longer delay times, dissociation is associated with HCN loss, cf. Figure S8. Dissociation in PAH is often associated with loss of H$_2$ or C$_2$H$_2$ and can usually be described in a statistical model. In PANH cations, loss of HCN constitutes an alternative to acetylene loss reaction and is often dominant,³⁸ its appearance in 1 would therefore not surprising. This possible loss of HCN in neutral PANH might also be of relevance for astrochemistry.

The data obtained here apply to deep UV excitation, but also permit to expand the interpretation to lower energies, i.e., the ¹(1ππ*) state. As shown in Figure S5 in the SI, a ns-lifetime has been found for $S_1$ 0º band, while decay times between roughly 10 and 100 ps have been observed for the well resolved excited vibronic bands. A signal offset at long delay times shows that the final state can be efficiently ionized. We therefore assign the decay to a ¹(1ππ*) → ¹(nπ*) internal conversion. At low energies, the ¹(nπ*) is long-lived. However, when the ¹(2ππ*) state is accessed, the dynamics accelerate dramatically, following the mechanism outlined above.

## 4 Conclusions

In this work, we studied the excited state deactivation of the polycyclic aromatic nitrogen-containing hydrocarbon phenanthridine after UV excitation at 268 nm into the bright $2\pi\pi^*$ state. The analysis was based on time-resolved X-ray photoelectron and X-ray absorption spectra at the nitrogen 1s edge as well as valence photoionisation with $\lambda_{probe}=800$ nm, along with trajectory surface hopping computations and time-resolved X-ray absorption simulations. The experimental data suggested two time constants of ca. 0.3 ps and 3 ps. Since the trajectory simulations predicted a very fast sub-10 fs time constant for the $S_3 \rightarrow S_2$ process, we conclude that it is too fast to be time resolved in the experiments. The $S_2 \rightarrow S_1$ transition appears in the TR-XAS as the lowest energy transient feature that rises immediately after the pump pulse and shows a rapid decay. All methods confirmed the return of the population to the electronic ground state, so the second time constant was readily assigned to the internal conversion from $S_1$ to $S_0$. This process is reflected in the TR-XAS by a transient absorption signal that decays more slowly along with a reduction of the ground state bleach. In addition, the formation of vibrationally excited molecules in the electronic ground state was observed. The TR-XPS data confirm the mechanism outlined above, but also provide additional information. They indicate the presence of a contribution from ¹⁺ that shows no fast dynamics and is difficult to isolate in the TR-XAS. Furthermore, on a time scale of several hundreds of ps, a unimolecular dissociation of 1 is apparent in the TR-XPS, possibly associated with loss of HCN.

Data using $\lambda_{probe}=800$ nm probably yield more accurate time

constants, but cannot identify the intermediate states in the deactivation process, while picosecond time-resolved experiments allow to extend the interpretation to lower excitation energies.

Theory and experiment together conclude that the ultrafast excited state deactivation of phenanthridine takes place according to $2\pi\pi^* \rightarrow 1\pi\pi^* \rightarrow n\pi^* \rightarrow S_0^*$ for the sub-ensemble originally excited to the $S_2$ state and according to $2\pi\pi^* \rightarrow n\pi^* \rightarrow 1\pi\pi^* \rightarrow n\pi^* \rightarrow S_0^*$ for the sub-ensemble originally excited to the $S_3$ state. The interpretation was supported by investigating the potential energy surfaces of the lowest three excited singlet states along the dominant normal modes responsible for the relaxation dynamics (in-plane bendings). They exhibit pronounced crossings, allowing for an ultrafast internal conversion in phenanthridine. Three general conclusions are derived from the present work: a) As expected, the photochemistry of phenanthridine is significantly more complex than in the pure hydrocarbon PAH and involves $n\pi^*$ states in addition to $\pi\pi^*$ states. b) Based on previously observed similar electronic spectra of other aza-phenanthrene isomers,³² a related deactivation mechanism is expected to govern their photochemistry. Finally, c) time-resolved X-ray spectroscopy at the N 1s edge is an excellent tool to unravel the detailed photochemistry of N-heterocycles, in particular when combined with high-level computations that properly represent the time-resolved X-ray absorption spectrum.

## 5 Methods

### 5.1 Experimental

The experiments were performed at the soft X-ray beamline Athos of the SwissFEL free-electron laser,⁴¹ using the Maloja endstation. The experiment operated at a repetition rate of 100 Hz. The 30–40 fs pump pulses centered at 268 nm (FWHM ≈ 4 nm) were derived from the third harmonics of a Ti:Sa laser system and the pulse energy was varied between 10 and 200 µJ by tuning a waveplate. In the experiments described above, an energy of 30 µJ was employed. The instrument response function was around 100 fs. The FEL is operated in self-amplified spontaneous emission (SASE) mode. Using the Athos monochromator, a photon bandwidth of 0.4 eV is cut out of the original 1% energy bandwidth SASE pulses. This value also determines the energy resolution of the spectra to $\Delta E \approx 0.1\%$. The undulators and the monochromator were aligned to a fixed photon energy of 499 eV for the TR-XPS experiments, while for the TR-XAS experiments the photon energy of the FEL was tuned between 393 eV and 405 eV. The X-ray pulse energy at the sample was around 50 µJ, a focus size of 100 x 100 µm is estimated, assuming a Gaussian beam profile. The X-rays and the optical laser beams were overlapped by a drilled mirror. For every fifth FEL pulse, the pump laser was delayed and the probe-only signal was recorded for background subtraction. The FEL pulse energy was constantly monitored by detecting the Ar ion signal in a time-of-flight mass spectrometer for every pulse, permitting to normalize all data to the FEL pulse energy. The time intervals between the points varied between 45 fs close to the pump-probe overlap and up to 1.3 ps far away from it, the points being measured randomly. Typically, in each run 2000 pulses were averaged per data point and four (sixteen)
runs were averaged for the XAS (XPS) spectra shown above.

A Specs PHOIBOS 150EP hemispherical analyzer was employed for electron detection. For TR-XPS, it was operated at a pass energy of $E_P = 240$ eV (photoelectrons were accelerated appropriately) and calibrated by ionizing $N_2$ with the FEL. For TR-XAS, conditions in the analyzer were changed to detection of Auger electrons and X-ray absorption spectra of $N_2$ were recorded for photon energy calibration.

The sample was obtained from Sigma Aldrich and used without purification. It was slightly heated in an oven source kept at 60 to 65 °C, the pressure in the experimental chamber was kept at $p \approx 1 \cdot 10^{-6}$ mbar.

## 5.2 Theory

Computations on 1 were carried out using time-dependent density functional theory (TD-DFT) employing a long-range corrected hybrid functional $\omega B97X-D$42 combined with the def2-SV(P)43 basis set, as implemented in the Q-Chem software package44. For trajectory-based nonadiabatic dynamics simulations with four electronic states, Tully's fewest-switches surface hopping45 procedure was applied using the $\omega B97X-D/def2-SV(P)$ electronic structure method.46,47 For more details, see Section S5 of the supporting information. A total of 50 initial structures were generated by sampling a harmonic canonical Wigner distribution48,49 at 330 K and were subsequently relaxed by propagating for 100 fs in the electronic ground state without any thermostats. The relaxed geometries were launched from the brightest electronic state and the trajectories were propagated for 1 ps with a time step of 0.25 fs. For simulating the X-ray absorption spectra, the equation-of-motion coupled-cluster formalism with singles and doubles (EOM-CCSD)50 combined with the cc-pVDZ51 basis set was employed. The core-level states were included by the core-valence separation (CVS) scheme.52 Additionally, the state-averaged complete active space self-consistent field method53 (SA-CASSCF) including the first four singlet states using the cc-pVDZ basis set was applied, as implemented in the OpenMolcas v23.02 software package54. Second-order multiconfigurational perturbation theory was added employing the rotated multistate approach (SA-RMS-CASPT2).55 As an active space, six electrons in five orbitals were selected, labeled as SA4-RMS-CASPT2(6,5). This procedure was extended to the state-averaged restricted active space self-consistent field method56, followed by multiconfigurational perturbation treatment (RMS-RASPT2).55 The nitrogen 1s orbital was chosen as the RAS1 space and the RAS2 space included six electrons in five orbitals as before. Hence, the resulting restricted active space consisted of eight electrons in six orbitals, labeled SA-RMS-RASPT2(8,6). Because state mixing of the SA-CASSCF wavefunction becomes significant upon geometric distortion, we included the first six singlet states in the SA-CASSCF to ensure correct state ordering for both ensemble XAS and TR-XAS. Valence excited states calculated using SA6-RMS-CASPT2(6,5) then served as reference configurations for the promotion of exactly one electron from the nitrogen core orbital forced within the subsequent SA10-RMS-RASPT2(8,6) calculation considering the lowest ten X-ray excited states. For reasons of computational

efficiency, the spectrum along the trajectories was determined every femtosecond within the first 20 fs, then every 5 fs up to 100 fs and then every 10 fs.

## Conflicts of interest

There are no conflicts to declare.

## Data availability

The data supporting this article have been included as part of the Supplementary Information. Further data is available from the corresponding authors upon reasonable request.

## Acknowledgements

This work was financially supported by the Deutsche Forschungsgemeinschaft, contracts FI575/16-1 and MI1236/6-1. We are indebted to the SwissFEL staff for their experimental support and acknowledge the Paul Scherrer Institute, Villigen, Switzerland for provision of free-electron laser beamtime at the Maloja instrument of the SwissFEL ATHOS branch. We thank Sonia Coriani for her advice on EOM-CCSD calculations of the excited state XAS. DS acknowledges a fellowship by the Fonds der Chemischen Industrie. XM acknowledges a fellowship by the Studienstiftung des Deutschen Volkes. Travel grants from the CNRS (Go To XFEL program) are also gratefully acknowledged.

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