Ab-Initio Molecular Dynamics Simulation of Condensed-Phase Reactivity: The Electrolysis of Ammonia and Ethanimine in Aquatic Carbon Dioxide Solutions

: The re-use of wastewater is an increasingly important subject. Most recently, several attempts were reported to convert wastewater in harmless or even valuable substances by the use of electrical current. Electrochemistry is an old approach. The renewed interest stems from the fact that electrical current is often available in abundance, for example from solar energy in arid regions, while clean water is not. Experimentally, one has to deal with very many products which are the result of many reaction steps. Here, theory can help. Using Car–Parrinello molecular dynamics, we simulate the ﬁrst few reaction steps of the electrolysis of wastewater. On the basis of previous studies, we investigate the reaction of carbon dioxide and nitrogen compounds. The results show a great variety of reaction steps and resulting products. Some of them are technologically interesting, such as hydrogen and formic acid.


Introduction
The removal of wastewater is an industrial process in all regions of the world. The reasons for this are manifold. There are huge amounts of municipal wastewater in regions with high population density as metropolitan areas. Additionally, agricultural and industrial plants produce contaminated water in their processes [1].
One way to get rid of bioorganic and inorganic contamination in wastewater is the electrolysis of the pollutants. Thereby, different strategies are pursued. One way is the degradation of all chemicals to gaseous, harmless species like H 2 , N 2 , O 2 and CO 2 . The second way is to produce different chemicals which contain higher energies in concepts such as "power to fuel" [2][3][4] and "power to gas" [5][6][7][8] or summarized as "power to chemicals" [9,10]. The electrolytic conversion of wastewater pollutants has the benefit of combining two advantages. While electrolytic reactions can lead to desired products, the degradation simultaneously taking place can lead to further synthesis routes, e.g., Fischer-Tropsch synthesis [11,12], with H 2 and CO 2 . Experimentally, the number of compounds which may be generated is vast. Theoretical studies may help to find the most important intermediates and products [13]. The reactivity of biomolecules, such as peptides and urea, that are likely to be found in municipal and agricultural wastewater were studied in previous publications [14,15]. The outcomes of these studies in the picosecond timescale were solutions containing ammonia, ethanimine, and carbon dioxide which are going to be investigated in this work. For the electrolytic reaction of ammonia several mechanisms were stated in the past [16][17][18]. These results were mainly derived from experimental data, which focus on the products of the reaction, determined with the help of various methods.
In this work the ultra-fast reactions taking place under electrolytic conditions are investigated for their mechanism with focus on intermediate products and their energetics. 2 of 22 In contrast to other studies [19,20], we focus on the outer Helmholtz layer only. That is, we investigate the reactions which occur without direct contact with the surface of an electrode. Conditions at a distance from the electrode surface are simulated by creating OH or H radicals solvated in the aquatic environment of the simulation. The performance of our approach for such a system was investigated in reference [21]. In our simulations the radicals are created via simply removing nuclei and electrons from water molecules after an equilibration phase [14,15,22]. This approach models the situation immediately after the electron transfer. The electron transfer itself is not part of our simulations. Simulating this electron transfer would be difficult because our simulation boxes are small, and we use self-consistent field theory. Ionic species would be discharged by electronic tunneling already at a distance from the electrode surface. The radicals resulting from our simulations are reactive open shell molecules, which attack the molecules in the solution in different ways. The reactions are taking place in the picosecond timescale, so for investigations on the reaction mechanism, Car-Parrinello molecular dynamics (CPMD) [23][24][25] with up to 0.1 femtosecond timesteps can be used for the simulation. The use of the CPMD method has various advantages. CPMD describes the movement of all parts of a system in a limited timestep. This on-the-fly approach offers the advantage that reaction pathways can be found and not only known ones can be analyzed. CPMD describes the movement of both, the nuclei and the electrons of the system which leads to a good description of the reaction path and the mechanism [26]. However, the simulation of the movement of the whole molecular system leads to the disadvantage of high computing times. And as a result of these high computational efforts the strength of this molecular dynamics method causes also its limitation on a relative low number of timesteps. This makes CPMD only useful for the description of very fast reactions.
To accelerate the reactions and to observe as many reactions as possible, we use a very high density of active species. This may lead to reaction mechanisms that are not relevant under conditions that are closer to experiment. However, it is possible to monitor if, for a certain reaction, the simultaneous attack of two reactive species is needed. Hence, we must discuss in the end which reactions are overestimated due to the high number of reactive species. The products depend strongly on the initial conditions after equilibration; hence, we must perform as many simulation runs as possible.
Under such highly reactive conditions as they are to be found during electrolysis, many different reactions are taking place so that a selection which ones to discuss had to be made. For this reason, the selected reactions which are discussed in this work, was limited to stable products. The complete simulation data including the unstable open shell products can be found in the Supplementary Materials.
To limit the amount of CPU time used for the molecular dynamic simulations, we are restricted to GGA functionals such as BLYP-D3 [27][28][29] which has an incredible accuracy/cost relation, but also has well-known weaknesses. Hence, while the molecular dynamics runs were performed using CPMD in combination with BLYP-D3, the energetic properties of the products have been calculated with various methods as implemented in the Gaussian program code [30]. Wave-function, DFT and hybrid methods were used, further detail is given in the Methods section. The electronic energies ∆ r E and the heat of reaction ∆ r H were calculated and compared to the experiment. The complete results are summarized in the Supplementary Materials.
for the BLYP functional were employed for describing the core electrons [34,35]. The plane-wave cutoff, which determines the size of the basis set, was set to 70.0 Rydberg. The simulation cells were 20 × 20 × 20 a.u. 3 or 10.6 × 10.6 × 10.6 Å 3 . For the reactive simulations, the unrestricted version of Kohn-Sham theory was employed [36,37].
The density of the created solutions is higher than that of pure water (1.00 g/cm 3 ) because several water molecules are substituted with CO2, which has a higher molecular weight. Solutions with a density of roughly 1.22 g/cm³ were generated (8 ammonia, 9 carbon dioxide and 19 water molecules named system 1 or 7 ammonia, 9 carbon dioxide and 19 water molecules named system 2). Additionally, solutions with ethanimine were generated (4 ethanimine, 9 carbon dioxide, and 21 water molecules named system 3 or 4 ethanimine, 9 carbon dioxide and 22 water molecules named system 4). The solutions of systems 3 and 4 had a density of roughly 1.34 g/cm³. After the equilibration of stable, neutral, closed-shell systems, reactive species were generated in two ways: by removing eight hydrogen radicals, leading to OH radicals in order to simulate anodic conditions and by removing eight OH radicals, leading to eight hydrogen radicals in order to simulate cathodic conditions. For the reactive simulations, the spin-unrestricted version of Kohn-Sham theory was employed. To check the radical character of the observed species, we computed Mulliken charges.
The geometry optimizations were performed with the Gaussian 16 program package [30]. All geometry optimizations and vibrational frequency calculations were performed using the BLYP-D3 [31][32][33] functional, the B3LYP-D3 [38,39] hybrid functional, the B2PLYP-D3 [39] double hybrid functional, the Hartree-Fock method, the second order Møller-Plesset perturbation method MP2 [40], and the coupled cluster CCSD method in combination with the 6-311G(d,p) basis set [41]. Additionally, further calculations were performed using the CCSD method with the aug-cc-pVTZ basis set which will be referred to as CCSD/aug. In all calculations solvent effects for water were taken into account with the PCM continuum solvation model [42]. The thermodynamic data were calculated using the freq keyword function of the Gaussian 16 program.

Results and Discussion
The most complex and important processes were observed during simulations of anodic conditions, that is why it makes more sense to begin the discussion with their detailed description. In order to better simulate the real systems, two new cells were created for each neutral equilibrated system, which differed only in the positions of created OH radicals. As expected, the formation of various reactive oxygen-based species was observed (e.g., hydrogen peroxide HOOH, HOO radical, O2). Furthermore, ammonia molecules were oxidized to several inorganic compounds, such as NHO, NO, NH2OH, NH2O, and NH2. Furthermore, ethanimine molecules were oxidized to several organic compounds, such as RNHO, nitrene radical, RNO radical, oxime. R is equal to ethylidene group.

Anodic Reactions
The first reaction observed is the formation of an HNO molecule out of NH3. The mechanism is shown in Figure 1. Its first reaction step corresponds to the abstraction of hydrogen radical from ammonia by OH radical which results in the formation of NH2 radical after 0.16 ps of Figure 1. Sequence of elementary reaction steps that lead to the formation of HNO molecule in system 1. The initial temperature of the system was set to 250 K.
Its first reaction step corresponds to the abstraction of hydrogen radical from ammonia by OH radical which results in the formation of NH 2 radical after 0.16 ps of simulation. The formed reactive intermediate is attacked further by a second OH radical within 0.02 ps. As a result, the stable closed-shell hydroxylamine molecule is formed. Key bond lengths for first and second reaction steps are depicted in Figure 2. Afterwards the hydrogen atom simulation. The formed reactive intermediate is attacked further by a second OH radical within 0.02 ps. As a result, the stable closed-shell hydroxylamine molecule is formed. Key bond lengths for first and second reaction steps are depicted in Figure 2. Afterwards the hydrogen atom of the hydroxyl group is attacked by a third OH radical which results in the formation of an NH2O radical and a water molecule. The new reactive intermediate is stabilized during the last step of the reaction via hydrogen radical abstraction, which is performed by the fourth OH radical. The closed-shell stable HNO molecule is formed after 0.35 ps. Key bond lengths for the third and fourth reaction steps are depicted in Figure 3 and Figure 4.        Among the reactions observed another mechanism for the formation of HNO was found for system 2, and it is depicted in Figure 5. The first reaction step corresponds to the attack of a hydroxyl radical on ammonia, which results in the formation of an NH3OH radical after 0.15 ps of simulation. The formed reactive and very unstable intermediate is attacked further by a second OH radical within less than 0.01 ps resulting in the formation of the closed-shell NH2OH product and a water molecule. Key bond lengths for the first and second reaction steps are depicted in Figure 6. During the third step the highly reactive hydroxylamine reacts with a second NH3 molecule yielding the NH2O radical intermediate and a neutral ammonium radical reactive and very unstable intermediate is attacked further by a second OH radical within less than 0.01 ps resulting in the formation of the closed-shell NH 2 OH product and a water molecule. Key bond lengths for the first and second reaction steps are depicted in Figure 6. During the third step the highly reactive hydroxylamine reacts with a second NH 3 molecule yielding the NH 2 O radical intermediate and a neutral ammonium radical after 0.02 ps. The reaction step is depicted in Figure 7. The last step is the attack of a hydroxyl radical, which abstracts a hydrogen radical yielding a stable closed-shell NHO molecule and water. The reaction is completed within 0.39 ps. Key bond lengths for the fourth reaction step are depicted in Figure 8. Figure 5. Sequence of elementary reaction steps that lead to the formation of an NHO molecule in system 2. The initial temperature was set to 300 K.
The first reaction step corresponds to the attack of a hydroxyl radical on ammonia, which results in the formation of an NH3OH radical after 0.15 ps of simulation. The formed reactive and very unstable intermediate is attacked further by a second OH radical within less than 0.01 ps resulting in the formation of the closed-shell NH2OH product and a water molecule. Key bond lengths for the first and second reaction steps are depicted in Figure 6. During the third step the highly reactive hydroxylamine reacts with a second NH3 molecule yielding the NH2O radical intermediate and a neutral ammonium radical after 0.02 ps. The reaction step is depicted in Figure 7. The last step is the attack of a hydroxyl radical, which abstracts a hydrogen radical yielding a stable closed-shell NHO molecule and water. The reaction is completed within 0.39 ps. Key bond lengths for the fourth reaction step are depicted in Figure 8. Figure 6. Sketch of the first and second reaction step (system 2). In the first step ammonia is attacked by an OH radical which leads to the formation of an NH3OH radical. In the second step, almost simultaneously, another OH radical is attacking, leading to the elimination of water and the formation of hydroxylamine. Color-code: blue-nitrogen, red-oxygen; white-hydrogen. Figure 6. Sketch of the first and second reaction step (system 2). In the first step ammonia is attacked by an OH radical which leads to the formation of an NH 3 OH radical. In the second step, almost simultaneously, another OH radical is attacking, leading to the elimination of water and the formation of hydroxylamine. Color-code: blue-nitrogen, red-oxygen; white-hydrogen.  . Figure 8. Sketch of the fourth reaction step (system 2). The attack of another OH radical on the NH2O radical and the following elimination of water leads to the formation of the closed-shell HNO molecule. Color-code: blue-nitrogen, red-oxygen; white-hydrogen.  Another reaction observed for system 1 is the formation of NO out of NH 3 with HNO as intermediate product, as depicted in Figure 9. Another reaction observed for system 1 is the formation of NO out of NH3 with HNO as intermediate product, as depicted in Figure 9. Figure 9. Second sequence of elementary reaction steps that lead to the formation of an NO molecule in a second simulation run for system 1. The initial temperature was set to 250 K.
The first reaction step corresponds to the abstraction of hydrogen radical from ammonia by an OH radical which results in the formation of an NH2 radical after 0.06 ps of simulation. The formed reactive intermediate is attacked further by a second OH radical within 0.05 ps resulting in the formation of the NH2OH intermediate. Key bond lengths for the first and second reaction steps are depicted in Figure 10. During the third step hydroxyl amine reacts with a second NH3 molecule yielding an NH2O radical Figure 9. Second sequence of elementary reaction steps that lead to the formation of an NO molecule in a second simulation run for system 1. The initial temperature was set to 250 K.
The first reaction step corresponds to the abstraction of hydrogen radical from ammonia by an OH radical which results in the formation of an NH 2 radical after 0.06 ps of  Figure 10. During the third step hydroxyl amine reacts with a second NH 3 molecule yielding an NH 2 O radical intermediate and a neutral ammonium radical after 0.14 ps of simulation. The NH 2 O radical reacts further with an OH radical resulting in the formation of a water molecule and closed-shell HNO The last step is represented by the attack of a third OH radical on formerly formed HNO, which yields NO and a water molecule. The reaction is completed within 0.20 ps. Key bond lengths for the third and fourth reaction steps are depicted in Figures 11 and 12 and for the last step in Figure 13. . Second sequence of elementary reaction steps that lead to the formation of an NO molecule in a second simulation run for system 1. The initial temperature was set to 250 K.
The first reaction step corresponds to the abstraction of hydrogen radical from ammonia by an OH radical which results in the formation of an NH2 radical after 0.06 ps of simulation. The formed reactive intermediate is attacked further by a second OH radical within 0.05 ps resulting in the formation of the NH2OH intermediate. Key bond lengths for the first and second reaction steps are depicted in Figure 10. During the third step hydroxyl amine reacts with a second NH3 molecule yielding an NH2O radical intermediate and a neutral ammonium radical after 0.14 ps of simulation. The NH2O radical reacts further with an OH radical resulting in the formation of a water molecule and closed-shell HNO The last step is represented by the attack of a third OH radical on formerly formed HNO, which yields NO and a water molecule. The reaction is completed within 0.20 ps. Key bond lengths for the third and fourth reaction steps are depicted in Figure 11 and Figure 12 and for the last step in Figure 13.       In addition to HNO and NO, hydroxylamine NH2OH is formed during the simulation of reactions in system 2, depicted in Figure 14 hydroxylamine is also an intermediate of the mechanism shown in Figure 9. The first reaction step of the first mechanism corresponds to the homolytic dissociation of the N-H bond, which results in the formation of NH2 and H radicals after 0.15 ps of simulation. The formed hydrogen radical is coordinated by a second equivalent of ammonia. To be more specific, a hydrogen atom is located between two nitrogen centers. The second step is represented by the recombination of OH radical with NH2 yielding closed shell hydroxyl amine within 0.04 ps. The key bond lengths for the first and second reaction steps are depicted in Figure 15. During the third step hydroxyl amine reacts with a second OH radical yielding an HNOH radical intermediate and a water molecule after 0.01 ps. The last step is the recombination of NHOH radical with H radical and simultaneous loss of coordination by a second equivalent of ammonia, which leads to the formation of stable closed-shell hydroxylamine. The reaction is completed within 0.23 ps. Key bond lengths for the third and fourth reaction steps are depicted in Figure 16. In addition to HNO and NO, hydroxylamine NH 2 OH is formed during the simulation of reactions in system 2, depicted in Figure 14 hydroxylamine is also an intermediate of the mechanism shown in Figure 9. In addition to HNO and NO, hydroxylamine NH2OH is formed during the simulation of reactions in system 2, depicted in Figure 14 hydroxylamine is also an intermediate of the mechanism shown in Figure 9. The first reaction step of the first mechanism corresponds to the homolytic dissociation of the N-H bond, which results in the formation of NH2 and H radicals after 0.15 ps of simulation. The formed hydrogen radical is coordinated by a second equivalent of ammonia. To be more specific, a hydrogen atom is located between two nitrogen centers. The second step is represented by the recombination of OH radical with NH2 yielding closed shell hydroxyl amine within 0.04 ps. The key bond lengths for the first and second reaction steps are depicted in Figure 15. During the third step hydroxyl amine reacts with a second OH radical yielding an HNOH radical intermediate and a water molecule after 0.01 ps. The last step is the recombination of NHOH radical with H radical and simultaneous loss of coordination by a second equivalent of ammonia, which leads to the formation of stable closed-shell hydroxylamine. The reaction is completed within 0.23 ps. Key bond lengths for the third and fourth reaction steps are depicted in Figure 16. The first reaction step of the first mechanism corresponds to the homolytic dissociation of the N-H bond, which results in the formation of NH 2 and H radicals after 0.15 ps of simulation. The formed hydrogen radical is coordinated by a second equivalent of ammonia. To be more specific, a hydrogen atom is located between two nitrogen centers. The second step is represented by the recombination of OH radical with NH 2 yielding closed shell hydroxyl amine within 0.04 ps. The key bond lengths for the first and second reaction steps are depicted in Figure 15. During the third step hydroxyl amine reacts with a second OH radical yielding an HNOH radical intermediate and a water molecule after 0.01 ps. The last step is the recombination of NHOH radical with H radical and simultaneous loss of coordination by a second equivalent of ammonia, which leads to the formation of stable closed-shell hydroxylamine. The reaction is completed within 0.23 ps. Key bond lengths for the third and fourth reaction steps are depicted in Figure 16.

Cathodic Reactions
Under cathodic conditions, reactions with CO2 in the solution were also observed. The most promising reaction which took place is the formation of formic acid, which is depicted in Figure 17.

Cathodic Reactions
Under cathodic conditions, reactions with CO2 in the solution were also observed. The most promising reaction which took place is the formation of formic acid, which is depicted in Figure 17.

Cathodic Reactions
Under cathodic conditions, reactions with CO 2 in the solution were also observed. The most promising reaction which took place is the formation of formic acid, which is depicted in Figure 17. The first reaction step corresponds to the attack of hydrogen radical on carbon in CO2, which results in the formation of an HCOO radical after 0.05 ps of simulation and the formation of the H-C bond. The second reaction step is the hydrogen radical transfer Figure 17. Elementary reaction steps that lead to the formation of an HCOOH molecule in system 2. The initial temperature was set to 300 K.
The first reaction step corresponds to the attack of hydrogen radical on carbon in CO 2 , which results in the formation of an HCOO radical after 0.05 ps of simulation and the formation of the H-C bond. The second reaction step is the hydrogen radical transfer from an H 3 O radical to the formerly formed intermediate yielding closed-shell formic acid after 0.32 ps of simulation. Key bond lengths for the first and second reaction steps are depicted in Figures 18 and 19. Figure 17. Elementary reaction steps that lead to the formation of an HCOOH molecule in system 2. The initial temperature was set to 300 K.
The first reaction step corresponds to the attack of hydrogen radical on carbon in CO2, which results in the formation of an HCOO radical after 0.05 ps of simulation and the formation of the H-C bond. The second reaction step is the hydrogen radical transfer from an H3O radical to the formerly formed intermediate yielding closed-shell formic acid after 0.32 ps of simulation. Key bond lengths for the first and second reaction steps are depicted in Figure 18 and Figure 19.

Anodic Reactions
Additionally, the reactions of ethanimine under electrolytic conditions in systems 3 and 4 are under investigation. The chemically most interesting reactions took place under anodic properties, that is, with the participation of OH radicals. The first two reactions observed led to the formation of the stable zwitter-ionic species nitrosoethane, shown in Figure 20.
The first reaction step of mechanism 1 corresponds to the attack of a hydroxyl radical on the nitrogen atom of ethanimine, which results in the formation of an RNHOH radical after 0.09 ps of simulation. The formed reactive intermediate is attacked further by a second OH radical within 0.02 ps. As a result, a stable closed-shell zwitter-ionic species is formed. Key bond lengths for the first and second reaction steps are depicted in Figure 21. The process of zwitter-ion formation takes 0.27 ps in the Car-Parrinello MD simulation.
The single reaction step shown in Figure 22 corresponds to the hydrogen radical transfer between the unstable open-shell intermediate, the formation mechanism of which was part of the reaction shown in Figure 20, and a second ethanimine molecule. Figure 19. Sketch of the first and second reaction steps of the reaction of hydrogen radical with carbon dioxide. The most relevant bonding interactions deduced from Car-Parrinello simulations is highlighted. Color-code: red-oxygen; black-carbon; white-hydrogen.

Anodic Reactions
Additionally, the reactions of ethanimine under electrolytic conditions in systems 3 and 4 are under investigation. The chemically most interesting reactions took place under anodic properties, that is, with the participation of OH radicals. The first two reactions observed led to the formation of the stable zwitter-ionic species nitrosoethane, shown in Figure 20. The first reaction step of mechanism 1 corresponds to the attack of a hydroxyl radical on the nitrogen atom of ethanimine, which results in the formation of an RNHOH radical after 0.09 ps of simulation. The formed reactive intermediate is attacked further by a second OH radical within 0.02 ps. As a result, a stable closed-shell zwitter-ionic species is formed. Key bond lengths for the first and second reaction steps are depicted in Figure 21. The process of zwitter-ion formation takes 0.27 ps in the Car-Parrinello MD simulation.   The single reaction step shown in Figure 22 corresponds to the hydrogen radical transfer between the unstable open-shell intermediate, the formation mechanism of which was part of the reaction shown in Figure 20, and a second ethanimine molecule. The reaction yields the zwitter-ionic closed-shell species and an ethylamine radical after 0.25 ps of simulation. Key bond lengths for the single reaction step are depicted in Figure 23.  The single reaction step shown in Figure 22 corresponds to the hydrogen radical transfer between the unstable open-shell intermediate, the formation mechanism of which was part of the reaction shown in Figure 20, and a second ethanimine molecule. Figure 22. Sequence of elementary reaction steps that lead to the formation of zwitter-ion in system 3. The initial temperature of the system was set to 250 K.
The reaction yields the zwitter-ionic closed-shell species and an ethylamine radical after 0.25 ps of simulation. Key bond lengths for the single reaction step are depicted in Figure 23. The reaction yields the zwitter-ionic closed-shell species and an ethylamine radical after 0.25 ps of simulation. Key bond lengths for the single reaction step are depicted in Figure 23.
Furthermore, the formation of (E)-acetaldehydeoxime has been observed during the simulation, which is depiceted in Figure 24.
There are two different possible mechanism for this reaction, which are shown in Figures 23 and 25. The first reaction starts with the attack of a hydroxyl radical on the nitrogen atom of ethanimine, and this results in the formation of an RNHOH radical after 0.08 ps of simulation. The formed reactive intermediate is attacked further by a second OH radical within 0.01 ps, so the reaction is completed within 0.11 ps. As a result, two stable closed-shell species are formed: oxime and water. Key bond lengths for the first and second reaction steps are depicted in Figure 25. Furthermore, the formation of (E)-acetaldehydeoxime has been observed during the simulation, which is depiceted in Figure 24. There are two different possible mechanism for this reaction, which are shown in Figure 23 and Figure 25. The first reaction starts with the attack of a hydroxyl radical on the nitrogen atom of ethanimine, and this results in the formation of an RNHOH radical after 0.08 ps of simulation. The formed reactive intermediate is attacked further by a second OH radical within 0.01 ps, so the reaction is completed within 0.11 ps. As a result, two stable closed-shell species are formed: oxime and water. Key bond lengths for the first and second reaction steps are depicted in Figure 25.  Furthermore, the formation of (E)-acetaldehydeoxime has been observed during the simulation, which is depiceted in Figure 24. There are two different possible mechanism for this reaction, which are shown in Figure 23 and Figure 25. The first reaction starts with the attack of a hydroxyl radical on the nitrogen atom of ethanimine, and this results in the formation of an RNHOH radical after 0.08 ps of simulation. The formed reactive intermediate is attacked further by a second OH radical within 0.01 ps, so the reaction is completed within 0.11 ps. As a result, two stable closed-shell species are formed: oxime and water. Key bond lengths for the first and second reaction steps are depicted in Figure 25. Not only the formation of the (E)-isomer of acetaldehydeoxime can be observed, but also the formation of (Z)-acetaldehydoxime, which is depicted in Figure 26.
In the second reaction the first step corresponds to the hydrogen radical abstraction by hydroxyl radical after 0.05 ps of simulation. The first step is completed after 0.01 ps and yields a nitrene radical. The second step is represented by the addition of a second hydroxyl radical to the previously formed open-shell intermediate. The reaction is completed after 0.36 ps of simulation. Key bond lengths for the first and second reaction steps are depicted in Figure 27. Not only the formation of the (E)-isomer of acetaldehydeoxime can be observed, but also the formation of (Z)-acetaldehydoxime, which is depicted in Figure 26. In the second reaction the first step corresponds to the hydrogen radical abstraction by hydroxyl radical after 0.05 ps of simulation. The first step is completed after 0.01 ps and yields a nitrene radical. The second step is represented by the addition of a second hydroxyl radical to the previously formed open-shell intermediate. The reaction is completed after 0.36 ps of simulation. Key bond lengths for the first and second reaction steps are depicted in Figure 27.  Not only the formation of the (E)-isomer of acetaldehydeoxime can be observed, but also the formation of (Z)-acetaldehydoxime, which is depicted in Figure 26.

Cathodic Reactions
In another reaction taking place, an imine molecule is attacking a CO 2 molecule under cathodic conditions. The product of the reaction is the radical and zwitter-ionic species of a carbamic acid derivative. The mechanism of the reaction is depicted in Figure 28.
Its first reaction step corresponds to the hydrogen radical abstraction by a free hydrogen radical after 0.04 ps of simulation. The first step is completed after 0.01 ps and yields an imine radical. The second step is represented by the addition of the previously formed reactive open-shell intermediate to carbon dioxide molecule, so a new C-N σ-bond was formed.

Cathodic Reactions
In another reaction taking place, an imine molecule is attacking a CO2 molecule under cathodic conditions. The product of the reaction is the radical and zwitter-ionic species of a carbamic acid derivative. The mechanism of the reaction is depicted in Figure 28. Its first reaction step corresponds to the hydrogen radical abstraction by a free hydrogen radical after 0.04 ps of simulation. The first step is completed after 0.01 ps and yields an imine radical. The second step is represented by the addition of the previously formed reactive open-shell intermediate to carbon dioxide molecule, so a new C-N σ-bond was formed.
Key bond lengths for the first and second reaction steps are depicted in Figure 29. Figure 27. Sketch of the two reaction steps taking place. The first step shows the attack of an OH radical on the ethanimine molecule and the elimination of water. This reaction leads to the formation of a reactive nitrene radical which is attacked by another OH radical in the second step, forming the closed-shell oxime. Color-code: blue-nitrogen, red-oxygen; white-hydrogen. Figure 27. Sketch of the two reaction steps taking place. The first step shows the attack of an OH radical on the ethanimine molecule and the elimination of water. This reaction leads to the formation of a reactive nitrene radical which is attacked by another OH radical in the second step, forming the closed-shell oxime. Color-code: blue-nitrogen, red-oxygen; white-hydrogen.

Cathodic Reactions
In another reaction taking place, an imine molecule is attacking a CO2 molecule under cathodic conditions. The product of the reaction is the radical and zwitter-ionic species of a carbamic acid derivative. The mechanism of the reaction is depicted in Figure 28. Its first reaction step corresponds to the hydrogen radical abstraction by a free hydrogen radical after 0.04 ps of simulation. The first step is completed after 0.01 ps and yields an imine radical. The second step is represented by the addition of the previously formed reactive open-shell intermediate to carbon dioxide molecule, so a new C-N σ-bond was formed.
Key bond lengths for the first and second reaction steps are depicted in Figure 29. Key bond lengths for the first and second reaction steps are depicted in Figure 29.

Energetics
The electronic energies and enthalpies of formation were calculated using various methods in Gaussian 16 as stated in the method section. The complete results are to be found in the Supplementary Materials. For comparison, experimental data from literature are provided. From these electronic energies and enthalpies of formation the energies for the corresponding reactions were calculated. The results are shown in Tables 1 and 2 for comparison of methods. The best results are provided using the BLYP-D3 functional, certainly a fortuitous agreement. It shows the lowest deviation values from the experimental data. Second best results are given by the Møller-Plesset perturbation method, MP2. The B2PLYP-D3 double-hybrid functional and the B3LYP hybrid functional yield comparable results. Comparable results to the previously mentioned hybrid functionals are provided by the CCSD functional with the aug-cc-pVTZ basis set. The coupled cluster CCSD method with a small basis set provides higher deviations from the experimental data. In contrast to the basis set, the use of an implicit solvent hardly affects the results. Finally, the worst results are obtained by the Hartree-Fock method, the deviations are in the order of magnitude of the reaction enthalpies.

Energetics
The electronic energies and enthalpies of formation were calculated using various methods in Gaussian 16 as stated in the method section. The complete results are to be found in the Supplementary Materials. For comparison, experimental data from literature are provided. From these electronic energies and enthalpies of formation the energies for the corresponding reactions were calculated. The results are shown in Tables 1 and 2 for comparison of methods. The best results are provided using the BLYP-D3 functional, certainly a fortuitous agreement. It shows the lowest deviation values from the experimental data. Second best results are given by the Møller-Plesset perturbation method, MP2. The B2PLYP-D3 double-hybrid functional and the B3LYP hybrid functional yield comparable results. Comparable results to the previously mentioned hybrid functionals are provided by the CCSD functional with the aug-cc-pVTZ basis set. The coupled cluster CCSD method with a small basis set provides higher deviations from the experimental data. In contrast to the basis set, the use of an implicit solvent hardly affects the results. Finally, the worst results are obtained by the Hartree-Fock method, the deviations are in the order of magnitude of the reaction enthalpies.

Conclusions
The electrolytic reactions of ammonia and ethanimine in a carbon dioxide enriched aquatic solution were investigated by the use of Car-Parrinello molecular dynamics. A variety of reaction mechanisms and products was determined. In the considered timescale of 0.5 ps, the formation of both open-and closed-shell products was observed, among the most important being consecutive products of hydroxylamine and formic acid. At this point, it should be emphasized that our approach with many reactive species overestimates reactions that demand the simultaneous attack of two reactive species. An example is the NH 2 OH formation where the two reaction steps are nearly simultaneous. Additionally, our picture is not complete in the sense that we cannot perform a sufficient number of simulation runs to observe all the reactions that are possible in a system.
While we found a variety of reaction pathways, there are some characteristic patterns. Under anodic conditions, typically the first reaction step is a simple hydrogen abstraction by OH radicals. In the case of ammonia this attack is sometimes almost simultaneous with the formation of an N-O bond corresponding to a radical recombination. Similarly, water and hydroxylamine are formed. Further simple abstractions of hydrogen by OH radicals lead to products like HNO. Under cathodic conditions the formation of molecular hydrogen is predominant. Additionally, we observed the addition of nascent hydrogen at the carbon atom of CO 2 . In the case of ethanimine two initial reactions predominate under anodic conditions: the attachment of OH radicals to the nitrogen atoms and the abstraction of the hydrogen atom bound to nitrogen. Under cathodic conditions it is one of the hydrogen atoms of the methyl group which is abstracted by an OH radical. We observe interesting further steps involving CO 2. How does this compare to the experiment? In contrast to the experiment [16][17][18], we observe predominantly the formation of an N-O bond, but we never observe the formation of an N-N bond, even if we use high ammonia concentrations. This supports the mechanism assumed on the basis of experimental data, where the formation of N-N bonds is postulated to be, at least in part, an effect of surface catalysis. Experimentally, NH 2 OH and consecutive products are obtained at high voltages.
The energetic calculations that were performed show that all reactions observed are energetically favored in good agreement with experimental data. The best values in comparison to the experimental heats of formation are obtained using the BLYP-D3functional and the MP2 method. Under the aspect of "power to chemicals", it is interesting to note that the formation of formic acid and a carbamic acid species from CO 2 were observed. It is an interesting finding that CO 2 can be converted into formic acid without a particular surface catalysis. The cathodic formation of molecular hydrogen is, of course, interesting under the aspect of "power to fuel". For the decontamination of wastewater via the degradation of harmful substances, further investigation is necessary. Even if we started from a relatively simple model (no electrolyte, no electrodes) a large number of intermediates and products were observed. In view of the renewed interest in electrolysis experiments, it makes sense to systematically enter this vast field stepwise from a theoretical side, starting with systems that are as simple as possible.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/en14206510/s1. Author Contributions: Methodology, software, visualization, data curation and writing-review and editing, I.G.; data curation, visualization and writing-original draft preparation, L.S.; conceptualization, methodology, validation, writing-review and editing, project administration and funding acquisition, I.F. All authors have read and agreed to the published version of the manuscript.