# Predicting energy-dependent transformation products of environmental contaminants: the case of ibuprofen

Grégoire Salomon, Mathias Rapacioli, J Christian Schön, Nathalie Tarrat

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Grégoire Salomon, Mathias Rapacioli, J Christian Schön, Nathalie Tarrat. Predicting energy-dependent transformation products of environmental contaminants: the case of ibuprofen. Physics, inPress. hal-05368451

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Article

# Predicting energy-dependent transformation products of environmental contaminants: the case of ibuprofen

Grégoire Salomon<sup>1,2,3,4</sup>, Mathias Rapacioli<sup>2,*</sup> and J. Christian Schön<sup>3</sup> and Nathalie Tarrat<sup>4,*</sup>

## Abstract

The environmental pollution caused by emerging organic contaminants - such as ibuprofen - is becoming increasingly a cause for alarm. New treatments for their removal are currently being developed, but the nature and toxicity of the transformation products (TPs) formed during the processes cannot be easily assessed experimentally. Atomistic simulations are thus of great interest in predicting the chemical structure of these TPs. In this work, we have demonstrated that the transformation of a contaminant molecule under irradiation can be studied using the threshold algorithm combined with the density functional based tight-binding (DFTB) method. The fragmentation pathways of an ibuprofen molecule under irradiation have been studied as a function of the energy added to the system. Specifically, the chemical structures of ibuprofen's TPs, the paths between them, their stabilities, probabilities of occurrence, and the related mass spectra were obtained as a function of the amount of energy absorbed. We also simulated the evolution of the ibuprofen molecule as a function of the number of pulses, i.e., for a sequence of energy depositions. A dominant fragmentation scheme was identified, where first the OH group is released, followed by the loss of the CO group. The photon energy and the number of pulses were found to be key parameters for the selection of this degradation route among all identified fragmentation pathways.

**Keywords:** Ibuprofen; Irradiation energy; Transformation Products; molecular fragmentation; threshold algorithm; DFTB; probability flows; mass spectra

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**Citation:** Salomon, G.; Rapacioli, M.; Schön, J. C.; Tarrat, N. Predicting energy-dependent transformation products of environmental contaminants: the case of ibuprofen. *Physics* **2025**, *1*, 0. https://doi.org/

**Copyright:** © 2025 by the authors. Submitted to *Physics* for possible open access publication under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## 1. Introduction

A major source of environmental pollution are the so-called emerging organic contaminants (EOCs) [1–4], which encompass a large variety of chemical compounds, including e.g. pharmaceuticals, hormones, endocrine disruptors, industrial chemicals, pesticides, personal care products, surfactants or plasticizers. Many of these compounds are not properly removed in conventional waste water treatments and are thus released into the environment, leading to environmental and health issues, prioritizing the development of highly controlled water treatment methods [5–9]. One of the major EOCs is the ibuprofen molecule (C₁₅H₁₈O₂, 2-(4-isobutylphenyl) propionic acid), which ranks third on the list of the world's most widely-consumed drugs [10–12]. This drug is often prescribed for pain relief, arthritis, non-rheumatic inflammation, fever and dysmenorrhea [13]. Its accumulation

<footnote n="1">1 CEMES, Université de Toulouse, CNRS, 29 Rue Jeanne Marvig, Toulouse, 31055, France</footnote>

<footnote n="2">2 Laboratoire de Chimie et Physique Quantiques LCPQ/FERMI, UMR 5626, Université de Toulouse (UPS) and CNRS, 118 Route de Narbonne, Toulouse, F-31062, France</footnote>

<footnote n="3">3 Max Planck Institute for Solid State Research, Heisenbergstr. 1, Stuttgart, 70569, Germany</footnote>

<footnote n="4">4 Present address : Univ. Grenoble Alpes, CEA-LETI, MINATEC Campus, 17 Avenue des Martyrs, Grenoble, 38000, Isère, France</footnote>

<footnote>* Correspondence: rapacioli@irsamc.ups-tlse.fr (M.R.) ; nathalie.tarrat@cemes.fr (N.T.)</footnote>
in soils and waste waters is of great concern because of its significant toxicity, particularly with respect to reproduction and other physiological implications [11,12,14]. Its removal or degradation has thus become a high priority.

Various strategies for ibuprofen removal based on physical, chemical or biological methods are available or under development [10]. Among them, molecular degradation schemes appear to be appealing alternatives. However, this approach presents a major risk, linked to the lack of knowledge about the nature of degradation products (often called Transformation Products - TPs), which can be even more toxic than ibuprofen [15]. It is therefore crucial to determine which TPs will be generated, depending on the method and the degradation environment.

Ibuprofen's degradation has been extensively studied in water environment via, e.g., photon absorption based processes [16–20], possibly assisted by metal-based catalytic surfaces or nanoparticles [18,21,22], thermal treatments [23,24], bacteria-based biodegradation [11] or electro-oxidation [25]. Note that various environmental parameters can affect the degradation; examples are the pH value, the ion concentration, the presence of other organic materials or humus, and the level of dissolved oxygen [26]. Some authors have also investigated the behavior at the water/atmosphere interface of semi-volatile ibuprofen TPs, such as the 4-Isobutylacetophenone (IbaP) [27] or the degradation of ibuprofen in the gas phase [28].

In most of the former studies, the TPs are identified in the experiment through mass spectrometry, and their structures as well as the transformation paths among them are inferred from chemical intuition. However, due to the size of the molecule, the number of TPs that could be formed as well as the various fragmentation and recombination routes can be huge, and there is a need for support from quantum chemical theoretical methods.

In the case of a limited number of competitive dissociation paths, *ab initio* calculations, employing, e.g., wave function based methods, can be used to provide energetic dissociation profiles along cuts in the potential energy surfaces. Minimum Energy Paths (MEPs) including the identification of transition states can be obtained from methods like the nudged elastic bands approach [29,30]: these require the computation of energy gradients, which is mostly performed at the Density Functional Theory (DFT) level [31]. Beyond the identification of the MEPs, entropic contributions can be deduced from biased dynamical simulations, like umbrella sampling [32] or metadynamics [33].

Identifying the dominant dissociation routes for extended molecules presents additional challenges due to the large number of degrees of freedom and consequently of possible fragmentation channels, greatly complicating or ruling out the use of chemical intuition to identify and select the relevant ones. To address this challenge, unbiased exploration schemes are most suitable, usually relying on molecular dynamics or Monte Carlo based approaches to move on the energy landscape of the system [34]. Among them, the threshold algorithm [35–39] has become a popular tool as it allows to obtain a detailed map of the dominant isomerisation and dissociation processes available below a given energy, incorporating entropic contributions to the probability of the various dissociation pathways. The broad and statistically relevant overview over the accessible region of the landscape provided by such unbiased exploration schemes is obtained at the price of a large number (typically millions) of single point energy/force calculations, preventing the use of wave function and DFT schemes. Thus, the use of semi-empirical schemes is appealing since they are several orders of magnitude faster than *ab initio* calculations. In particular, the Density Functional based Tight Binding (DFTB) scheme [40,41] can be very useful. The DFTB scheme inherits, from Tight Binding models, a computationally efficient mathematical formalism, whereas it inherits from DFT the ability to address chemical reactivity, i.e., the bonds breaking and forming, and therefore can provide a valid descrip-
tion of dissociation processes. Its applications range from clusters, solid state physics, nanomaterials, to environmentally relevant biological molecules [42–47]. We have recently combined the threshold algorithm with the DFTB energy function, and we have reported its ability to map the competitive isomerisation processes within a gold cluster [48] or within a naphthalene molecule [49].

In the present work, we report, for the first time, the use of the coupled DFTB-threshold algorithm to investigate the competition between dissociation pathways for an ibuprofen molecule at various molecular internal energies. This scheme is also used to simulate the evolution of ibuprofen undergoing successive photon absorptions. This exploration was performed in absence of a water environment as a proof of concept of the general approach, allowing us to directly compare our TPs with those observed in vacuum by Zayed et al. [28]. The identification of the main TPs is expected to contribute to unravel the structures and dissociation pathways of the experimentally observed TPs, regardless of the specific ibuprofen degradation method and the medium where the degradation occurs.

In the next section, computational details regarding the threshold exploration and the DFTB energy function are given, as well as the strategy followed to simulate the evolution of a population of ibuprofen molecules as a function of their internal energy. The results are presented in section 3, including a detailed description of the TPs, a mapping of the dominant degradation fluxes and the simulation of the evolution of the mass spectra induced by sequential energy deposition. Finally, the results are compared with the literature and critically discussed.

## 2. Methods

### 2.1. *The DFTB Potential Energy*

The potential energy calculations were conducted with the DFTB method. In this approximated DFT scheme, all integrals are tabulated and the molecular orbitals are expressed in a minimal valence atomic basis. This results in computational costs hundreds to thousand times smaller than those of its DFT equivalent. More information about the method and its approximations can be found in the original papers or recent reviews [40–44]. In the present work, we make use of the original formulation of DFTB which is derived from DFT through a first order expansion of the electronic density with respect to a reference density, also known as DFTB0. Higher-order DFTB has not been used, in order to avoid issues during the fragmentation (self-consistent loop convergence and partial charges on fragments). This approximation is expected to have a minor impact on both relative energies and barrier heights, as chemical bond energy is reasonably well-described at the DFTB0 level. All calculations have been performed with the developer version of the deMonNano code [50] with the DFTB parameters developed by Frenzel et al. [51].

### 2.2. *The threshold algorithm*

The threshold algorithm [35,36,39] has been developed to explore the relevant low-energy regions of the energy landscape of complex systems with continuous state spaces such as molecules, clusters, or periodic approximants to crystalline and amorphous solids. Starting from a microstate of interest $\vec{R}_0$ of the system - typically a low-energy minimum corresponding, e.g., to a stable isomer of the molecule being studied -, the region of the landscape accessible from $\vec{R}_0$ below a given energy threshold $L_j$ is explored using a random walk; in the case of chemical systems, the moveclass used to select the next microstate corresponds to random small changes in the atom positions. During this random walk, every move from a microstate $\vec{R}_i$ to a neighbor state $\vec{R}_{i+1}$ is accepted as long as the state $\vec{R}_{i+1}$ lies below the energy threshold, i.e., $E(\vec{R}_{i+1}) \le E(\vec{R}_0) + L_j$. Along this path, the walker samples the local density of states $g(E; \vec{R}_0, L_j)$ of the landscape pocket accessible
from $\vec{R}_0$ below lid $L_j$. Furthermore, periodically the walker stops along its trajectory, and one or more stochastic quenches, followed by local gradient optimization, are performed from these stopping points into the accessible local minima, which can eventually be a fragmented system made of two or several TPs, and the frequency of occurrence of various local minima is registered as a function of time along the trajectory.

This procedure is repeated for an increasing sequence of energy lids $L_j$ ($L_{j+1} > L_j$), and from all relevant local minima obtained during the exploration. Analyzing these data yields the likelihood to reach neighbor minima as function of energy, and thus not only the height of the energy barriers between the low-energy minima can be ascertained but also the entropic barriers separating them. For more details, we refer to the literature [39].

In the specific study presented here, the lid energy $L_j$ corresponds to the energy of a photon absorbed by either the ibuprofen molecule or by a given TP. Analyzing the accessible minima associated with the TPs and the frequency of their occurrence when starting from the ibuprofen molecule or one of the other TPs, provides both the possible degradation pathways and their probability, as function of photon energy. In order to establish a sufficiently high statistics, many threshold runs are performed for every starting point and lid value.

## 2.3. Computational details

### 2.3.1. Lid energy range for fragmentation

In a preliminary set of threshold runs, the lid range of interest was established. As the lowest lid value of interest, a value of 0.20 Ha was chosen, because for the test runs at lower energies (from 0.01 to 0.10 Ha) no ibuprofen fragmentation was observed. Since for a lid of 0.5 Ha the ibuprofen molecule right away splits into many (small) fragments, making any chemical fragmentation path analysis impossible, only lids below 0.5 Ha were suitable. Thus, six lid energies, namely 0.20, 0.25, 0.30, 0.35, 0.40 and 0.45 Ha, were employed, in order to evaluate the effect of the energy given to the system on the various fragmentation pathways.

### 2.3.2. Scheme of investigation

For each lid value, the following exploration scheme was used: a total of 36 threshold runs were performed starting from the most stable ibuprofen isomer. Each individual threshold run consisted of 1 000 000 MC steps, with 100 stopping points separated by 10 000 MC steps along the trajectory. A MC step consisted of a random displacement of a single atom with a maximum amplitude of 0.1 Å. At each stopping point, one stochastic quench of 1000 MC steps was performed, followed by a gradient minimization. The structures of the resulting minimum atomic configurations were compared with the starting structure and other minima observed earlier.

Two types of transformations have been observed: the fragmentation of the starting molecule into fragments of smaller molar masses, and its isomerization leading to a different molecule with the same molar mass. A fragmentation test was carried out throughout the simulations, and each run was stopped as soon as a fragmentation was detected. In the absence of fragmentation, the possibility of an isomerization was tested by analyzing the final geometry. Each individual TP, arising from either fragmentation or isomerization, was stored in a TP structure library. For each stored TP $j$, its probability of occurrence $p_{i \to j}$ was calculated by averaging over the results of each set of 36 threshold calculations starting from the structure $i$, as well as its stability $p_{i \to i}$, i.e., its probability to either stay in or return to its starting configuration. The $p_{i \to j}$ values were used to build a cumulative probability of occurrence ($p_j^{cum}$), defined as the product of the probabilities $p$ leading to the TP $j$ from the initial ibuprofen molecule (labeled as 206 according to its molar mass in atomic units), e.g.,
$p_j^{\text{cum}} = p_{206 \to k} \cdot p_{k \to k'} \cdot p_{k' \to k''} \cdot p_{k'' \to j}$ for three intermediary TPs k, k' and k''. If several paths lead to the same TP, the $p_j^{\text{cum}}$ obtained for the different routes are summed. The stability of all significant TPs was also investigated by relaunching a set of 36 threshold runs from these fragments, and the process was repeated until only non-significant TPs were obtained. In practice, we have considered that a TP is non-significant (hereafter called negligible TP) at a given lid energy if its cumulative probability $p_j^{\text{cum}}$ is below a critical significance threshold $p_{\text{sig}}^{\text{cum}}$. In practice, we used $p_{\text{sig}}^{\text{cum}} = 1\%$ for lids up to 0.35 Ha and $p_{\text{sig}}^{\text{cum}} = 3\%$ at lids 0.35 Ha and above, due to the higher complexity of the accessible region of the energy landscape at high lid values. Analyzing the threshold runs performed at each lid yields (i) the chemical structure of the TPs encountered, (ii) the probability flows between them ($p_j^{\text{cum}}$) and ($p_{i \to j}$) represented in the form of a transition graph structure with ibuprofen as the root and (iii) the simulation of mass spectra of ibuprofen exposed to successive absorption of photons with similar energies, as encountered during a sequence of laser pulses [19]. To compute the latter, the probability flows are gathered in a transition matrix $P$ with $P_{ij} = p_{i \to j}$. We define $X_n$ as the probability distribution of the TPs once the ibuprofen has been exposed to $n$ laser pulses. $X_n$ is computed by the repeated application of the transition matrix $P$: $X_n = P^n X_0$ where $X_0$ corresponds to the initial state of the system; in particular as we start with ibuprofen only, we have $X_0 = (1, 0, \dots, 0, 0)$. A mass spectrum for the $n$th pulse can then be derived from $X_n$. We emphasize that with this approach, only one-step fragmentation processes are considered for each pulse; fragmentations that consist of a sequence of several separate fragmentation processes, which are induced by a single pulse are neglected. Indeed, we assume that most of the absorbed energy is dissipated during the first fragmentation via the breaking of the chemical bonds and acquisition of the kinetic energy by the fragments, leaving insufficient intramolecular energy in the TPs for a secondary fragmentation.

### 2.3.3. Transformation tests and library construction: technical details

An atom-atom bond-based connectivity matrix representing the bond connectivity graph was built for each optimized structure. Its comparison to the connectivity matrix of the initial structure allows to detect transformations. A bond between two atoms was considered to be present if the distance $d$ between them did not exceed the typical DFTB equilibrium distance $d_0$ for these two atoms by more than 5% ($d_0^{C-C} = 1.55$ Å, $d_0^{C-O} = 1.39$ Å, $d_0^{C-H} = 1.12$ Å and $d_0^{O-H} = 0.98$ Å). Else, the bond between the two atoms was considered to be broken or non-existent. If a fragmentation was detected, i.e., the bond graph consisted of two or more disconnected pieces, the smallest fragments were disregarded in the further analysis of the fragments, since the experimental studies mostly focus on the identification of TPs exhibiting large masses (typically above a hundred a.u.). Note that in our protocol the fragments have the lowest multiplicity compatible with their number of electrons, allowing for the consideration of the radical character of some of them. If the connectivity matrix was modified but did not exhibit fragmentation, we visually checked whether the structure had remained chemically the same (with permutation of atoms of the same types) or had isomerized. This allowed to compute the stability probability of the TPs identified. In order to avoid redundancy when adding a new TP to the library, it was visually compared to all the previously identified ones.

## 3. Results

### 3.1. Main transformation products

The 24 significant (i.e., non-negligible) TPs identified during the explorations at the different lids are depicted in Fig. 1. The TPs are arranged in decreasing order for molar
mass, starting with the parent ibuprofen molecule which has a molar mass of 206 a.u.
The name of a TP is a combination of its molar mass and of a 2<sup>nd</sup> number to discriminate
molecules presenting the same mass but different structures. For simplicity, we will label
C1 the ring carbon atom attached to the isobutyl group in the ibuprofen molecule and C4
the ring carbon atom attached to the propionic acid group (see Fig. 1 for illustration). Note
that in all TPs of Fig. 1, we have kept the C1 atom at the top and the C4 atom at the bottom
of the central ring. For simplicity's sake, the chains associated with these carbon atoms will
be referred to as C1 and C4 chains.

It appears that the ring remains unbroken in the 24 significant TPs. We mention,
however, that the breaking of the ring was observed in the benchmark simulations at the lid
energy of 0.5 Ha. We first note that (a) for all the 24 TPs, the OH hydroxyl is gone, and that
(b) for 13 of the TPs, the isobutyl chain remains unchanged. The heaviest TP is therefore
TP 189-1, which differs from ibuprofen only by the absence of the OH group, leading to a
propan-1-one group (O=C-CHR-CH3) attached to C4. All the TPs can be roughly classified
into two groups, depending on whether they do or do not contain an oxygen atom:

* The 8 TPs containing an oxygen atom exhibit a carbonyl group (189-1, 188-1, 187-1, 174-1, 174-2, 173-1, 173-2 and 132-1) and they correspond to the heaviest TPs, except for the TP 132-1. In 5 of them, the C4 atom is attached to a propan-1-one group (189-1, 187-1, 174-2, 173-1 and 132-1). In the 3 other TPs, the C4 chain differs from the propan-1-one group by the loss of a hydrogen atom (188-1), a methyl group (174-1) or both (173-2). In the C1 chain, the isobutyl group is retained in 4 TPs (189-1, 188-1, 174-1, and 173-2) and modified in the others (187-1, 174-2, 173-1, 132-1). Note that 187-1 also presents the loss of a hydrogen atom on the ring.

* The 16 other TPs are oxygen free. The isobutyl group is retained in the C1 chain for 9 of them (161-1, 161-2, 161-3, 160-1, 160-2, 159-2, 159-3, 146-1, 133-1) and is modified in the 7 other TPs (159-1, 146-2, 145-1, 119-1, 119-2, 118-1 and 104-1). One notices that 4 oxygen free TPs exhibit either an addition (161-2 and 119-1) or a removal (159-1 and 159-2) of a hydrogen atom on the ring.

3.2. *Transition graphs*

3.2.1. Transition graphs description

The ibuprofen fragmentation pathways are represented through their transition graphs
in Figs. 2 and 3. On these graphs, the significant TPs, i.e. those matching the criterion of
cumulative probability p<sub>j</sub><sup>cum</sup> to be above 1% for lids L<sub>j</sub> &le; 0.35 Ha on Fig. 2 and 3% for
lids L<sub>j</sub> &ge; 0.35 Ha in Fig. 3, respectively, appear as green ellipses while the negligible ones
appear as yellow rectangles. The green ellipse contains the identifier of the corresponding
TP, and the value of the cumulative probability of reaching this TP from ibuprofen p<sub>j</sub><sup>cum</sup> is
indicated in red. The yellow rectangles represent all the negligible TPs with a given molar
mass, and are labelled with *other* when at least one significant TP has the same mass. The
stability probability (p<sub>i&rarr;i</sub>) of each significant TP is indicated by the thickness and the type
of the contour of the ellipse. The very thick full lines correspond to p<sub>i&rarr;i</sub> > 70%, the thick
dashed lines to 70% > p<sub>i&rarr;i</sub> > 42%, the thin full lines to 42% > p<sub>i&rarr;i</sub> > 11% and, finally,
the very thin dashed lines to p<sub>i&rarr;i</sub> < 11%. We note that, as the negligible TPs have not been
used as starting geometries for threshold explorations, the corresponding p<sub>i&rarr;i</sub> could not be
computed and the corresponding rectangles contours have thus no meaning. The value
of the transition probability p<sub>i&rarr;j</sub> from TP i to TP j is indicated by 4 possible arrow types
using the same visual code. The corresponding intervals from the thickest to the thinnest
arrows are: p<sub>i&rarr;j</sub> > 70% (very thick full lines), 70% > p<sub>i&rarr;j</sub> > 42% (thick dashed lines),
42% > p<sub>i&rarr;j</sub> > 11% (thin full lines) and p<sub>i&rarr;j</sub> < 11% (very thin dashed lines).
### 3.2.2. Main degradation channel: 206 → TP 189-1 → TP 161-1

The probability of ibuprofen fragmentation increases with the energy given to the system, from 11% at lid 0.20 Ha to 64% at lid 0.25 Ha and 100% at and above lid 0.30 Ha. The dominant fragmentation channel starting from the ibuprofen molecule is the loss of the hydroxyl group leading to TP 189-1 (206 → TP 189-1). As can be seen from Fig. 2, up to lid 0.35 Ha, it is the only possible dissociation channel. TP 189-1 is unstable ($p_{189-1 \to 189-1} = 0$) for all the lids investigated. It mainly transforms into TP 161-1 via the loss of a carbonyl function (TP 189-1 → TP 161-1) with $p_{189-1 \to 161-1} = 95\%$ for lids 0.20/0.25/0.30 Ha, 81% for lid 0.35 Ha, 72% for lid 0.40 Ha and 58% for lid 0.45 Ha. The main degradation channel is thus 206 → TP 189-1 → TP 161-1.

Interestingly, the creation of TP 161-1 must involve TP 189-1 as an intermediary fragment only up to lid 0.35 Ha. For higher lids, it can also come from the direct degradation of ibuprofen (206 → TP 161-1). One might suspect that at such a high lid energy, the molecule fragmentation might first have reached TP 189-1 and then continued to TP 161-1. But we recall that the protocol of our exploration stops at the first detected fragmentation; thus, at this higher energy lid there is either a direct degradation of ibuprofen to TP 161-1 (i.e. the loss of the carboxyl group does not follow a sequential scheme but involves a single, possibly concerted, reaction coordinate) or a very fast, stepwise process that the algorithm does not resolve, i.e. an evolution of the system so rapid that the walker has already passed "through" the TP 189-1 state before even the first stopping point of the exploration has been reached. But that is only possible, if the walker never enters the intermediary local minimum region and stays above it on the landscape, which precisely means that the transformation pathway avoids this intermediary TP 189-1 region and proceeds directly to TP 161-1.

The very high cumulative probability of TP 161-1 of being obtained from 0.25 Ha to 0.45 Ha (with $59\% < p_{161-1}^{cum} < 94.4\%$) and its high stability make it the main TP observed in our study. We finally note that, at lid 0.45 Ha, ibuprofen can also directly degrade into TP 190, but with a low transformation probability ($p_{206 \to 190} < 3\%$). Moreover, the stability of TP 161-1 drops at this lid and it can give birth to numerous transformation products, opening routes toward new significant TPs (TP 161-1 → TPs 161-3/160-2/159-3/119-2/118-1/133-1).

### 3.2.3. Secondary degradation channels

We now address the secondary degradation paths by analyzing the routes between the significant TPs as a function of the lid values. These channels always present small cumulative probabilities ($p^{cum} < 8.1\%$) and are therefore minor routes with respect to the main channel. Although the corresponding transition probabilities are small, and consequently more subject to statistical convergency issues, it makes sense to analyze the possible degradation routes and their significant TPs. In particular, those presenting a high stability criterion are of interest, since they might be observed despite their low formation probabilities. Four secondary degradation channels can be identified, for which, as in the main degradation channel, the first step consists in the ibuprofen → TP 189-1 transition.

A first secondary channel appears from lid 0.25 Ha with the release of one or two H atoms leading to TPs 188-1 and 187-1, respectively. TP 188-1, which exhibits an unchanged C1 group and a ketene function in its C4 chain, appears to be very stable with $p_{188-1 \to 188-1} = 100\%$ at lid 0.25 Ha and 78% at lid 0.35 Ha. In contrast, TP 187-1 is only observed at lid 0.30 Ha and turns out to be very unstable ($p_{187-1 \to 187-1} = 0\%$). From lid 0.30 Ha, this degradation can be followed by a CO release (leading to TPs 160-1 and 159-1). Furthermore, from lid 0.30 Ha, a second secondary channel opens, with the release of a CH₃ group from the C4 chain (TP 174-1) which is followed by a CO release at lid 0.35 Ha (TP 146-1). The third and fourth secondary channels appear only for lids $L_j \ge 0.35$ Ha. The
third one consists in the loss of the whole C4 chain (TP 133-1). Interestingly, we note that all the significant TPs in the formerly discussed degradation routes maintained an intact carbon skeleton for the C1 chain. The fourth secondary channel consists in a degradation path involving the C1 breaking with the loss of a CH₃ group leading to TP 174-2 followed by either (i) the sequential removal of one hydrogen atom (TP 173-1) and a CO group (TP 145-1), (ii) the sequential removal of the remaining atoms from the C1 chain (TP 132-1) and a CO group (TP 104-1) or (iii) the sequential a removal of a CO group (TP 146-2) followed by removal of one hydrogen atom (TP-145-1) or of the remaining C1 chain (TP 104-1).

At the highest lids, the number of the possible degradation pathways strongly increases, leading to plenty of TPs and the multiplication of accessible routes. Clearly, the dominance of the main dissociation channel decreases, as can be seen, e.g., by considering that $p_{161-1}^{cum}$ decreases from 94.4 to 59 % between lids 0.30 and 0.45 Ha.

Finally, we notice some general trends regarding the patterns associated with low or high stability (i.e., those shown with thin or thick ellipse contours in Figs. 2 and 3). All the structures presenting a C4 chain with a RR'-CH-CO pattern (TPs 189-1, 187-1 and 173-1) exhibit a very low stability, as they can all easily lose the CO group. In addition, TP 189-1 can also lose a hydrogen atom (TP 189-1→ TP 188-1) to recover a pure ketene function. Moreover, we noticed that, apart from TP 145-1 in which the C1 chain turned to a vinylidene form, all the very stable structures possess an unchanged C1 chain.

### 3.3. Multiple-pulse-induced degradation products mass spectra

The evolution of mass spectra computed as outlined in section 2.3.2 is shown for the 4 first pulses in Fig. 4. In addition to the main TPs spectra, the left subplots collect the number of negligible TPs. A first look at this figure shows that a significant fraction of ibuprofen molecules remains unbroken even after four pulses at lid 0.20 Ha, whereas at lid 0.30 Ha and above ibuprofen completely disappears at the first pulse. In all spectra, significant contributions are only found for molar masses 206, 189 and 161, highlighting the already identified main degradation channel (see section 3.2.2). The evolution of the TPs associated with the main channel is represented in Fig. 5 for a larger number of pulses. It can be seen that at lid 0.20 Ha, the ibuprofen transformation is slow, requiring at least twenty pulses before being fully eliminated (mostly transformed into TP 161-1). In contrast, this transition takes about 4 pulses at lid 0.25 Ha. From lid 0.30 Ha onwards, ibuprofen is converted to TP 189-1 at the first pulse and to TP 161-1 at the second pulse. At lids below 0.35 Ha, 161-1 is a dead end for this channel with an efficiency above 90 %. At lid 0.35 Ha, negligible TPs start to appear (we note that this observation is not due to the change of $p_{sig}^{cum}$ from 1% to 3%, as shown in Fig. S1). At and above an energy of 0.40 Ha, we obtain mixtures of numerous TPs, as shown by the increase in the amplitude of the peak corresponding to negligible TPs in Fig. 4. This is in agreement with the degradation of TP 161-1 at such high lid energies, and also with the appearance of secondary channels with increasing lid energies as already discussed in section 3.2.3. We finally note that the analysis of the evolution of the mass spectra of significant TPs, for all secondary channels, shows that none of them exceeds a 7% probability of existence, and when they do, it is only for a short time, as they disappear during subsequent pulses. We note that, at such high lid energies, sequential fragmentation induced by a single pulse could start to occur, possibly leading to the appearance of several new fragments, reinforcing the present observation that numerous fragmentation channels coexist, leading to a very complex mixture.

In terms of degradation efficiency, we can thus conclude that the degradation of all ibuprofen molecules requires a large number of pulses at low lids, i.e., photon energies, while at high photon energies a very wide variety of TPs is observed starting already at the 2^nd^ pulse. At intermediate lids, i.e., for energies in the range of 0.30/0.35 Ha, a total
degradation of most ibuprofen is obtained already at the first pulse and the degradation products are relatively pure, i.e., we obtain mainly TP 189-1 after one pulse and TP 161-1 after the 2^nd^ pulse.

These results suggest that an appropriate choice of photon energy would allow the complete degradation of ibuprofen after a few pulses, leading to a limited number of TPs, with the number of pulses providing a means to control the major degradation product(s).

## 4. Discussion

Most of the studies available in the literature have investigated the fragmentation of ibuprofen in water. A direct comparison with our pathways and degradation products, investigated in the gas phase context, is of limited value as fragment recombination and reactivity with ionized solvent molecules are expected to occur in water. Fortunately, the experimental results of Zayed et al. [28] can be directly compared with our simulations, since these authors have investigated unimolecular fragmentation pathways either through electron ionization mass spectrometry (EI-MS) in vacuum or through thermal analysis (TA) in an inert argon atmosphere.

The mass spectrum resulting from TA is dominated by a peak at 161 a.u. and the thermal fragmentation pathway proposed by the authors is 206→TP 161→TP 119→TP 92. This is in agreement with the fact that TP 161-1 is the terminus of the main degradation channel in our explorations for lids up to 0.30 Ha. Furthermore, TP 189-1 is found to be a very unstable intermediate in our simulations which explains why it is not observed experimentally. Note that the subsequent degradation paths suggested by Zayed et al. [28], leading to TP 92 via TP 119 as an intermediary product, are also present in our simulations at higher energies.

The mass spectra resulting from EI-MS (shown in figure 2 in [28]) can also be compared with our results: Here one should keep in mind that the experiment involves the degradation of ionized ibuprofen instead of the neutral ibuprofen molecule in our study, and as detailed theoretical studies of similar size organic molecules such as sucrose and trehalose have shown, the presence of such charges can lead to massive changes in the stability of a molecule against dissociation processes [52]. Masses at 161 and 119 a.u. are clearly visible, in agreement with the degradation pathway suggested by the TA experiments. Four other features at 91, 107, 117 and 163 a.u. are also noticeable in the measurements. In our explorations at high lids, we find that TPs 91 and 117 can be reached via several pathways. Concerning TP 107, it was only obtained in our simulations at the highest lid 0.45 Ha via the degradation of TP 133-1, which can be reached along several degradation routes starting from TP 161-1, TP 161-3, TP 189-1 or TP 159-3. Only the fragment with mass 163 a.u. was not observed in our simulations. However, we note that, in the experiment, each dominant peak in the mass spectrum is surrounded by smaller peaks differing by a few mass units, suggesting that many fragments can be present with a lack or excess of hydrogen atoms. This even applies to the ibuprofen parent peak at mass 206, where a small contribution of under- and overhydrogenated ibuprofen is visible. Such a variability in the composition of the fragments regarding their number of hydrogen atoms is also present in our calculations: many TPs with very similar masses only differ in the number of hydrogen atoms or their organization on a given carbon skeleton. This also holds for the TPs 159, 160 and 161, suggesting that the peak at 163 a.u. could be interpreted as an overhydrogenated variation of the main degradation channel, possibly favored by the fact that fragments in the EI-MS experiment are ionized.

We finally recall that our exploration protocol probes only the fragmentation channels in the electronic ground state for various lid energies, as defined in the threshold algorithm and the multiple-pulse-induced degradation process only describes an arbitrary evolution
scheme (all fragmentation simulations for the various TPs performed with the same lid energy). Obviously, it does not exactly map the energy deposition and relaxation of a real experiment. For instance, in EI-MS, the total energy is deposited in a single initial step, and in photofragmentation experiments, one should also consider the absorption cross section for each fragment. Moreover, for both methods, dissociation might happen in electronic excited states. Furthermore, in TA, the thermalisation should be represented by an energy distribution rather than a fixed lid energy. Nevertheless, the agreement between our predictions and the experimental observations suggests that our simulation protocol is a powerful tool to identify the dominant degradation pathways.

## 5. Conclusion

In this work, we have demonstrated that the transformation of a contaminant molecule under irradiation can be studied using the threshold algorithm to explore a potential energy landscape provided by the density functional based tight-binding (DFTB) method. This approach allowed us to investigate the possible degradation pathways of an ibuprofen molecule exposed to a sequence of laser pulses in the gas phase and to compare the simulated mass spectra with their experimental counterparts. The six chosen threshold energies, ranging from 0.20 to 0.45 Ha, correspond to the energies of the photons absorbed by the system. We have identified the main degradation route of gas phase ibuprofen as 206 → TP 189-1 → TP 161-1, corresponding to a sequential loss of the hydroxyl and carboxyl groups. This sequence of transformation products was the dominant one for all lids investigated, and the main transformation product observed is TP 161-1. Our theoretical results agree with the available experimental data, explaining the main peaks observed in the mass spectrometry analyses. Investigating the toxicity of the main transformation product TP 161-1 would allow to determine the benefit/risk balance associated with the appearance of this contaminant during the degradation process of ibuprofen.

This successful comparison with experimental data, and the unraveling of the degradation process leading to the experimental mass spectra peaks, not only validates our method for investigating molecular degradation as a function of the energy given to the system, but also paves the way for its use to reveal the fragmentation products of all types of molecular environmental contaminants. Our approach provides essential information, namely the molecular structure(s) that can be associated with each mass, helping toxicologists to assess the toxic or non-toxic nature of the degradation products of a given pathway. Extracting data regarding the dependence of the TP nature on the energy and pulse number may also help in establishing a proper decontamination strategy. In particular, the information obtained via the threshold exploration runs can be used to model the multi-pulse degradation process as a stochastic Markov process. Such a model can serve as the basis for an optimal control analysis of the degradation of the contaminant molecule, similar to studies of the controlled evolution of phases in solids [53]. Specifically, by varying the energy and number of laser pulses, it is possible to optimize the degradation process, both with regard to the types of molecular fragments produced, their quantitative distribution, and the amount of total energy required to achieve a degradation of the contaminant to a non-toxic set of transformation products which might serve as possible inputs in future chemical applications. Such an optimized procedure should prove to be an efficient and sustainable way for dealing with environmental contaminants not only from the point of view of their removal from the environment but also with respect to opening possible avenues towards an energy efficient combination of the degradation with the recycling of the material.
**Supplementary Materials:** Mass spectra of the TPs as a function of the number of pulses for lid 0.35
Ha and cartesian coordinates of the ibuprofen molecule and of the 24 significant TPs

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**Author Contributions:** Grégoire Salomon: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Resources, Software, Validation, Visualization, Writing – Original Draft, Writing – Review & Editing.

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Mathias Rapacioli: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Resources, Software, Supervision, Validation, Visualization, Writing – Original Draft, Writing – Review & Editing.

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J. Christian Schön: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Resources, Software, Supervision, Validation, Visualization, Writing – Original Draft, Writing – Review & Editing.

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Nathalie Tarrat: Conceptualization, Data Curation, Formal Analysis, Investigation, Methodology, Resources, Software, Supervision, Validation, Visualization, Writing – Original Draft, Writing – Review & Editing.

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**Data Availability Statement:** The data supporting this article have been included as part of the Supplementary Information.

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**Acknowledgments:** The authors thank Germán Francisco de la Fuente for fruitful discussion and Louise Rapacioli for drawing the graphical abstract. This work was granted access to the HPC resources of CALMIP supercomputing center under the allocation p18009.

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**Conflicts of Interest:** The authors declare no conflicts of interest.

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<figure><img src="image_2.png" /><figcaption>**Figure 1.** Molecular structure of ibuprofen and the 24 identified significant TPs sorted by decreasing molar mass (in a.u.). The name of each TP is a combination of its molar mass and of a second number to distinguish molecules with the same mass but different structures. Oxygen, carbon and hydrogen atoms are depicted by red, green and white balls, respectively. C1 and C4 identify the ring carbon atoms, respectively attached to the isobutyl group and to the propionic acid group.</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Transition graphs for ibuprofen degradation for lids 0.20, 0.30 and 0.35 Ha. Significant TPs are depicted in green ellipses and negligible ones in yellow rectangles (selection criterion: $p_{sig}^{cum} = 1\%$). The stability probability ($p_{i \to i}$) of each significant TP is shown by its ellipse contour type and the value of the transition probability ($p_{i \to j}$) from TP i to TP j is indicated by the corresponding arrow type. The four intervals for arrows and ellipse contours are from the thinnest to the thickest: [0:11%] (very thin-dashed), [11:42%] (thin-full), [42:70%] (thick-dashed) and [70:100%] (very thick-full).</figcaption></figure>
<figure><img src="image_4.png" /></figure>

lid 0.35

<figure><img src="image_5.png" /></figure>

lid 0.40

<figure><img src="image_6.png" /></figure>

lid 0.45

**Figure 3.** Transition graphs for lids 0.35, 0.40 and 0.45 Ha. Significant TPs are depicted in green ellipses and negligible ones in yellow rectangles (selection criterion: $p_{sig}^{cum} = 3\%$). The notation is the same as in figure 2.
<figure><img src="image_7.png" /><figcaption>**Figure 4.** Mass spectra of the TPs as a function of the number of pulses at various lids. The cumulative probability of reaching negligible TPs is depicted in the left boxes. The selection criterion $p_{sig}^{cum}$ for significant vs negligible TPs is 1% up to lid 0.35 Ha and 3% above (see text).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 5.** Main degradation scheme proposed for ibuprofen 206 → TP 189-1 → TP 161-1. The corresponding probability flows $p_{i→j}$ as a function of the lid energy are presented on top of each transition arrow. Below each TP structure, a graph depicts the dependence of its probability of existence as a function of the number of pulses, for the various lid energies.</figcaption></figure>