Decomposition of 2,4,6-trinitrotoluene (TNT) and 5-nitro-2,4-dihydro-3H-1,2,4-triazol-3-one (NTO) by Fe13O13 nanoparticle: density functional theory study

To obtain more insight into the mechanisms of the decomposition of energetic compounds, we performed a computational study of the interaction of Fe13O13 nanoparticles with two energetic molecules such as 2,4,6-trinitrotoluene (TNT) and 5-nitro-2,4-dihydro-3H-1,2,4-triazol-3-one (NTO). The density functional theory using M06-2X, B3LYP, and BLYP density functionals was applied. We found that the reactivity of these molecules strongly depends on the place of adsorption (so-called top and bottom planes of Fe13O13). Namely, only the interaction with the bottom plane results in the thermodynamic characteristics of the decomposition that provide a medium reaction rate for the studied processes. Several pathways for such decomposition were found. One of them is the inter-complex oxygen transfer of nitro-group oxygen to Fe13O13. This pathway results in the formation of adsorbed nitroso compounds. The second pathway describes a more complex decomposition that includes the transfer of the nitro-group oxygen accompanied by the hydrogen transfer. In all cases, the interaction of energetic molecules with Fe13O13 nanoparticles takes place along with a barrier-less electron transfer from Fe13O13 to TNT or NTO species.


Introduction
The interest in the reactivity of nitro-compounds is caused by the wide involvement of such compounds in industrial activities. They are used as antioxidants, (de Resende et al. 2019; Alegria et al. 2018;Castonguay and Van Vunakis 1979;Díaz-Araya et al. 1998), dyes (Castonguay and Van Vunakis 1979), insecticides (Ooth et al. 1988;Becker et al. 2001;López et al. 2005;Ju and Parales 2010), and energetic compounds (Bretherick 1989;Li 2010;Salter-Blanc et al. 2015;Chang et al. 2020). Our interest in the properties of the compounds of this class has been mainly related to natural and designed ways of their utilization, i.e., decomposition and degradation. This is mainly because nitro-compounds are used as energetic materials. Let us give just one example. In 2010, more than 12 million pounds of energetic materials were released into waterways by the US Army's Radford Ammunition Plant (Mahbub and Nesterenko 2016). Investigations of the decomposition products of toxic species (including nitro-compounds) require the application of reliable techniques. Therefore, in addition to different experimental methods, computational modeling has been applied to study the transformations of energetic materials.
The application of efficient computational methods allows the prediction of a wide spectrum of properties and processes, starting from calculations of environmentally important physicochemical characteristics of a  (Qasim et al. 2007), followed by an estimation of the rate of its decomposition (Sviatenko et al. 2014(Sviatenko et al. , 2015. Currently, the predictions of reactivity mainly cover the area of the gas phase and water solution reactions. Let us illustrate this statement by just two of the most striking examples. Computational modeling was able to predict an aqueous solubility of more than 2500 environmental pollutants (Kovdienko et al. 2010) and temperature dependence of the solubility for a few hundreds of them (Klimenko et al. 2016). Another example demonstrates the ability of computational methods to model the rate of the alkaline hydrolysis of such pollutants as TNT and HMX (one of the modern energetic materials) with an accuracy comparable with experimental data (Sviatenko et al. 2014(Sviatenko et al. , 2015. Modeling the decay of any chemical species on the surface of minerals is usually a much more complicated task, compared to similar modeling in water solutions. Nevertheless, such processes are of environmental concern. Not surprisingly, the reactivity of Fe(II) containing minerals is one of the most complex topics among the research studies related to surface chemistry. This is due to the number of theoretical and computational problems associated with the open-shell electronic structure of these systems. To our knowledge, there was only one attempt to study the reactivity of nitro-compounds with Fe(II) species (Zilberberg et al. 2004). However, the models used in that study very crudely described the state of Fe(II) in the considered minerals. In addition, the situation was complicated by the lack of reliable experimental data on the structure of the active site(s) that can catalyze the decomposition of nitro-compounds on the surface of iron-containing minerals.
Briefly and simplistically, the initial step of the decomposition (reduction) of nitro-compounds is considered a donation of two electrons from Fe(II)-containing species to the nitro-group of a nitro-compound with further formation of the nitroso-group. The simplest scheme, which is most appropriate for Fe(II)-containing water solutions or for Fe(II) ions adsorbed on the surface of different minerals, can be described as follows: It is important to highlight that the two protons in this equation come from the water solution. However, as follows from the results presented in Zilberberg et al.'s study (2004), there is a pathway of the nitro-group reduction, which at least at the initial step does not need the participation of protons. Such a mechanism includes an intra-complex transfer of one of the oxygen atoms of the nitro-group to Fe(II) containing species. The study (Zilberberg et al. 2004) considered the following reaction: The successful thermodynamic execution of the chemical reaction (2) requires the ability of a mineral surface to compensate for the value of energy necessary for the breaking of the N-O bond by the formation of an oxo ferrous iron bond. As follows from the data presented in Zilberberg et al.'s 2004 study, the elucidation of this issue at the computational level is not certain. Namely, calculations using pure DFT functionals such as BLYP and BPW91 reveal the thermochemical data quite close to the exothermic effect of this reaction. In contrast, calculations that use such a hybrid functional as B3LYP, which has been found quite successful in the studies of numerous physicochemical properties of Fe x O y systems [9], result in quite significant endothermicity of the reaction (2).
Two more important findings are described in the literature. First, a study using B3LYP functional predicts the highest value of activation energy for the considered process to be 29.7 kcal/mol. Such a value corresponds to a rather slow chemical reaction rate. In contrast, calculations applying such a pure DFT functional as BLYP predict just 12.0 kcal/ mol of activation energy for the same process. This classifies the reaction (2) as proceeding at a medium rate. Second, the initial stage of the interaction of nitrobenzene and FeO results in a non-barrier one-electron transfer from the d-shell of iron into the antibonding LUMO localized mostly on the nitro group of nitrobenzene. This transfer results in the formation of the open-shell electronic configuration of the NB-FeO intermediate with a pair of α and β electrons occupying the d δ (Fe) and π*(-NO2) orbitals, in addition to the unpaired four α electrons on the d(Fe) orbitals. Interestingly, the transferred electron is an addition to the remaining unpaired four α electrons on the d(Fe) orbitals. In other words, the adsorption of the nitro-compounds on ferrous iron could be accompanied by a non-barrier one-electron reduction of nitro-compounds. Similar to the topics explored in Zilberberg et al.'s 2004 study, here we investigate the initial steps of the reduction of energetic materials. For this purpose, we have designed nanoparticles possessing the composition of Fe 13 O 13 as presented in Fig. 1.
Such Fe 13 O 13 species could be considered an approximate but certainly more complex and realistic model of Fe(II)containing minerals, compared to the one considered by Zilberberg et al. (2004). The current study will provide new data on the interaction between nitro-compounds and Fe(II)containing species in the gas phase.
To study the nitro-to-nitroso conversion on the Fe 13 O 13 surface, we have chosen genuine energetic molecules belonging to two different classes of energetic materials. NTO (5-nitro-2,4-dihydro-3H-1,2,4-triazol-3-one) belongs to a relatively new class called insensitive munition, and TNT (2,4,6-trinitrotoluene) represents a traditional energetic (2) R − NO 2 + FeO → FeO 2 + R − NO material, which is the standard component for most military loads. Both compounds have been shown to be resistant to degradation under environmentally relevant conditions and are therefore recognized as persistent contaminants. Twodimensional structural formulas of TNT and NTO are presented in Scheme 1.

Computational details
The structure of Fe 13 O 13 drawn in Fig. 1 was chosen to mimic a cubic closed packed array since most Fe(II)-containing minerals crystallize in such a manner (Zhang 1999). The nanoparticle shown in Fig. 1 has specific featuresits top and bottom planes are not equivalent. The top plane (TP) has 4 iron and 9 oxygen atoms, and the bottom plane (BP) has an inverted structure-9 iron and 4 oxygen atoms (see Fig. 1). In addition, since all iron and oxygen atoms of Fe 13 O 13 lay on the surface, they downgraded the coordination numbers (lower than six, which is the coordination number of each bulk ion of a face-centered cubic arrangement). This is one of the reasons for elevated reactivity that we expected for the considered nanoparticle.
Three density functional theory functionals in conjunctions with 6-311++G(d,p) basis set: M06-2X, BLYP, and B3LYP were used in this work. The B3LYP and BLYP functionals were also modified by a D3 version of Grimme's dispersion with Becke-Johnson damping (D3BJ) (Grimme et al. 2011). Fe 13 O 13 nanoparticle is constructed as an associate of 13 (FeO) molecules. According to the experimental and theoretical data (Bretherick 1989;Allen et al. 1996;Gutsev et al. 2000;Rollason and Plane 2000), each FeO molecule has a 5 ∆ ground state (S z = 2). Therefore, the initial electronic and spin states of a Fe 13 O 13 were assigned as having a spin equal to 26. In other words, the initial electronic state of Fe 13 O 13 was treated as a quintet of unpaired d-electrons located on each iron atom. Optimized geometry for such a system was obtained at the M06-2X level, keeping the molecular symmetry as C 4V . The equilibrium interatomic distance of Fe-O was found equal to 2.02 Å. Since it is not obvious that the final spin state for Fe 13 O 13 is just a simple sum of the spin states of FeO components, the The dependence of the total energy of Fe 13 O 13 on its spin state dependence of the total energy value in the vicinity of the state characterized by S = 26 was studied for a fixed Fe 13 O 13 C 4V -geometry, using BLYP, M06-2X, and B3LYP levels of theory (the addition of a dispersion correction is not necessary in such cases). Results presented in Fig. 2 illustrate the tendency that was established early (Zilberberg et al. 2004). Namely, the spin states that are higher than 26 are favored in the case of application of the hybrid type for functionals like B3LYP and M06-2X (the minimum was found in the area corresponding to S z = 28 or 29 (see Fig. 2). However, slightly lower spin states are favored in the case when BLYP functional was used. Still, as follows from the shape of the curves presented in Fig. 2, the situation is less clear in the case of BLYP. Therefore, in this work, we decided to study the decomposition of NTO and TNT only in the case of high-spin states of Fe 13 O 13 . Namely, we investigated the decay of NTO and TNT adsorbed by nanoparticle Fe 13 O 13 characterized by spin 29. Some of those adsorbed complexes were also checked for SCF instability (Seeger and Pople 1976;Bauernschmitt and Ahlrichs 1996) to ensure that all obtained solutions are stable.
Considering that the top and bottom planes of the Fe 13 O 13 (see Fig. 1) are not equivalent, the interaction of NTO and TNT with Fe 13 O 13 was probed for both planes.
The limited geometry optimization performed in this work for the interacting species included a fully relaxed geometry of NTO and TNT (C 1 symmetry was assumed) and a frozen geometry of Fe 13 O 13 . We perfectly understand that our choice of the optimal spin state for the Fe 13 O 13 moiety would be more convincing in the case of a full optimization of nitro-compound-Fe 13 O 13 complexes. However, all our attempts to include the geometry of Fe 13 O 13 into the optimization during the adsorption process were unsuccessful due to numerous SCF non-convergences. The local minima and transition states were verified by harmonic vibrational frequencies analysis. All calculations were carried out within the Gaussian-09 and 16 packages (Frisch 2009;Frisch et al., 2016).
To make the analysis of the obtained data more informative, the spin difference density was obtained for the complex formed between TNT and Fe 13 O 13 . The spin difference density ∆ρ(r) is defined as: where ρ(r) is the density for the complex; ρ TNT (r) is the density of TNT calculated for the geometry of the TNT moiety of the complex, using the "complete" basis set, i.e., including functions for the Fe 13 O 13 moiety of the complex. The ρ Fe13O13 (r) density of Fe 13 O 13 is calculated similarly to that of TNT.
To predict the ability of TNT and NTO to be reduced during the considered process, the value Gibbs free energy calculated as ΔH − TΔS at 293.15 K was used.

Electronic structure of TNT and NTO-adsorbed complexes
To understand the reactivity of TNT and NTO during the initial steps of reduction, it is appropriate to start with analyzing some electronic and geometrical parameters of adsorbed complexes. First, we would like to analyze the data related to the interaction of both TNT and NTO compounds with the Fe 13 O 13 . The interactions of the title compounds with Fe 13 O 13 are characterized by the formation of several adsorbed complexes that differ in the orientation of adsorbed molecules regarding the TP and BP planes of the nanoparticle. The molecular structures of those complexes are presented in ESI (see Fig. 1S and 1S and Table 1S). The complexes that are the most stable according to relative Δρ(r) = ρ(r) − ρ TNT (r) − ρ Fe13O13 (r)  Table 1 collects the most important parameters of charge distribution, spin state, and geometry, which are necessary for future discussion.
As follows from the data presented in Table 1, both TNT and NTO compounds are predicted to be chemosorbed on the surface of Fe 13 O 13 , since the intermolecular NO…Fe (R4 and R5) distances are virtually the same (sometimes even shorter) as the Fe-O distances in the isolated nanoparticle (2.02 Å). Therefore, the case of a very strong interaction between the nanoparticle and adsorption moieties is revealed.
There are at least two reasons for such strong adsorption. First, all atoms of Fe 13 O 13 are characterized by downgraded coordination numbers. Second, as follows from the data presented in Table 1, adsorption of both considered species is accompanied by a barrier-less electron transfer from Fe 13 O 13 to TNT and NTO (actually, this is a typical case of chemical reduction). A similar effect was observed in our early study (Zilberberg et al. 2004) devoted to the interaction of nitrobenzene and FeO. However, there are also some specifics due to the different nature of the two adsorbed species. Namely, since the electron affinity of TNT is much stronger than that of nitrobenzene (−2.2 eV and −1.04 eV, respectively, at the M06-2X level of the theory), the former molecule can accept up to two electrons from Fe 13 O 13 . The indication of this ability is the values of electron charge transfer to TNT, which approaches −2 a.u. depending on the type of DFT approximation and values of spin density (which in the case of BLYP and B3LYP functionals even exceeds 2 a.u.). We would also like to mention that most of this spin-density is located on the nitrogen and oxygen atoms of the nitro-groups of TNT (see Figs. 3S and 4S, where the shape of TNT LUMO, LUMO+1, and LUMO+2 orbitals, along with spin difference density, is presented). Additional evidence of the nature of redistribution of electron density after adsorption of TNT on Fe 13 O 13 is provided by a mean value of <S 2 > operator. The data presented in Table 1 suggest that all three considered DFT approximations predict it as 870 a.u. This corresponds exactly to an eigenvalue of S(S + 1), S = 29 and means that more than six of the d-electrons located on each Fe atom are unpaired. During the adsorption of TNT, up to two unpaired electrons are transferred to the TNT molecule. This is in full correspondence with our recently published results (Zilberberg et al. 2004) where we also established that more than six unpaired electrons per Fe atom participate in the electron transfer to a molecule of nitrobenzene. Adsorbed NTO demonstrates behavior similar to that of TNT. However, since it has an electron affinity lower than TNT (1.84 eV, M06-2X), only up to one electron is transferred from Fe 13 O 13 . There is one more important conclusion. In the case of the nitrobenzene-FeO interaction, we stated that pure and hybrid functionals behave differently. Namely, a pure functional (BLYP) does not reveal a profound effect regarding electron transfer, but it demonstrates quite good correspondence with the experiment related to the thermodynamics of the reaction: nitrobenzene + FeO. The calculations carried out using hybrid functional B3LYP demonstrated the opposite trends that disagree with an experiment that approaches −2 a.u. depending on the type of DFT approximation and values of spin density (which in the case of BLYP and B3LYP functionals even exceeds 2 a.u.). Additional evidence of the nature of redistribution of electron density after adsorption of TNT on Fe 13 O 13 is provided by the mean value of <S 2 > operator. Analyzing the data collected in Table 1, one can conclude that all three functionals qualitatively describe similar trends in the electronic structure of TNT and NTO complexes adsorbed by Fe 13 O 13 . Namely, both molecules interact tightly with the surface of Fe 13 O 13 . The adsorption initiates a transfer

Pathways of TNT decomposition
More complex and representative structures of both iron-containing moiety and species adsorbed on its surface, as considered in the current work, could generate pathways that could be different than the ones found for oversimplified models (Zilberberg et al. 2004). The thermodynamical parameters related to the computationally generated pathway computed in this study are collected in Tables 2, 3, and 4. Let us start from the analysis of pathways similar to those found in the earlier study (Zilberberg et al. 2004). As we already mentioned in the Introduction, such a model describes an intra-complex transfer of one of the oxygen … of the nitro-group to Fe(II)-containing species. We found that TNT adsorbed on both considered planes of Fe 13 O 13 is able to participate in such a type of decomposition. The corresponding thermodynamical parameters are collected in Table 2. However, the thermodynamical parameters that characterize the course of this reaction on the top plane could be considered ineffective from the practical point of view (high activation barrier and endergonicity). For the corresponding energetic profile, see ESI Fig. 5s.
Much more interesting for the analysis are the results presented in Fig. 4. Namely, the BLYP-D3BJ and M06-2X level calculations predict low enough values of activation barriers to consider that the transfer of oxygen to the Fe 13 O 13 could be carried out with an observable chemical rate. Also, according to the B3LYP-D3BJ and BLYP-D3BJ level data, the breaking of one of the nitrogen-oxygen bonds of the nitro-group is quite satisfactorily compensated by the formation of two additional oxo ferrous iron bonds in Fe 13 O 13 . This results in significant exergonicity of this reaction. However, the M06-2X level calculations predict this reaction to be just slightly endothermic. To explain this difference, we assumed that in the case of B3LYP-D3BJ and BLYP-D3BJ the oxygen atom transfer includes a more significant transfer of charge and electron density than in the case of M06-2X. However, we did not find a convincing explanation since both electronic characteristics are virtually the same at the B3LYP-D3BJ, BLYP-D3BJ, and M06-2X levels of theory.
As we already mentioned, a more complex structure of Fe 13 O 13 considered in this study could, in principle, generate the pathways that are different from a simple oxygen transfer from the nitro-group to a Fe(II)-containing mineral or species. An example of such a pathway is presented in Fig. 5.
The main feature of this pathway is the participation of the hydrogen atom of the CH 3 -group in the decay of the ortho-nitro-group of TNT. The structures of located transition state and product are presented in Fig. 5. Intuitively, one expects the appearance of an intermediate on the path from the transition state to the product. However, we did not locate such a structure at any of the DFT approximations considered here. We would also like to highlight that the predicted decay of the ortho-nitro-group is kinetically less effective than a simple oxygen transfer that characterizes the decay of the para-nitro-group of TNT. However, it is characterized by an even more pronounced exothermic effect that is predicted in the case of the ortho-nitro-group.

Pathways of NTO decomposition
In the case of NTO, only the pathway that is very similar to the one characterizing the decay of the ortho-nitrogroup of TNT was predicted. As follows from the Gibbs energy profile presented in Fig. 6, the first step, in this case, is a transfer of the closest NH proton in the direction of the nitro-group oxygen. Since the mobility of this hydrogen is greater than in the case of the mobility of the hydrogen from the CH 3 -group (it is more acidic (Golius et al. 2015), the observable reaction barriers are smaller than the ones that relate to TNT transformation. Similar to TNT, the reaction is characterized by high exothermicity effects. Finally, we would like to convey two details of the computational challenges of this project.
First, during the performed calculations, for several initial geometries, we faced multiple cases of SCF nonconvergences. Due to such failures of calculation procedures, we cannot assure that there are no additional minima corresponding to reactive intermediates in addition to the structures presented in the profiles in Figs. 4, 5, and 6. This relates especially to the cases of the decay of the ortho-nitro-group of TNT and to the decay of NTO. For example, we found an intermediate that corresponds to an intramolecular proton transfer in NTO (see Fig. 6s of ESI). This pathway starts from another adsorption state, which is less effective than the one presented in Fig. 6. However, it has approximately the same values of Gibbs free energy barriers as the profile presented in Fig. 6.
Second, one may argue that the relaxation of the Fe 13 O 13 nanoparticle could quantitatively change the results described above. We tried to perform full optimization of the Fe 13 O 13 nanoparticle with and without the adsorbed NTO molecule. However, we met even more problems than already described. Therefore, we present here just two trustworthy results.
1. The geometry of the optimized cluster did relax significantly compared to … considered in this work (compare the structures presented in Fig. 1 and Fig. 7s). The structure with the lowest energy corresponds to the spin equal to 26 compared to the structure having S = 29 and studied in this work. 2. During the optimization, we were not able to locate a transition state of NTO decomposition. However, we found that the product (see Fig. 8s) of such decomposition is similar to the one presented in Fig. 5. We concluded that most probably the relaxed structure has a similar electron donor ability to transfer barrierless electron(s) to the adsorbed species. Therefore, we believe that the electron-donor properties of the relaxed structure of Fe 13 O 13 and its decomposition ability are similar to the one considered in this work.

Conclusion
We performed a computational analysis of the spin states of Fe 13 O 13 nanoparticles in a wide range of spin states. We found that in the case of B3LYP and M06-2X DFT functionals, the state with the lowest total energy corresponds to S z = 29. The computational analysis of the decomposition pathways of TNT and NTO adsorbed by Fe 13 O 13 nanoparticle that has the abovementioned S z suggests that both molecules will undergo a chemical reduction under investigated conditions. In the case of TNT, we found two possible routes for that decomposition: an intra-complex transfer of one of the para-nitrogroup oxygen atoms and a synchronous movement of one of the CH 3 -group hydrogen and nitro-group oxygen. In the case of NTO, the predicted pathway included a synchronic movement of the NH hydrogen and nitro-group oxygen. Generally, the values of activation Gibbs free energy indicated a medium reaction rate for the considered decomposition of TNT and NTO. It is important to highlight that all considered DFT approximations predicted that the interaction between TNT and NTO was accompanied by a barrierless electron transfer from the Fe 13 O 13 nanoparticle to the energetic material molecule.