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1 Prebiotic NH 3 formation: Insights from simulations András Stirling 1, Tamás Rozgonyi 2, Matthias Krack 3, Marco Bernasconi 4 1 Institute of Organic Chemistry, Research Centre for Natural Sciences of the Hungarian Academy of Sciences, POB 286, Budapest, 1519, Hungary 2 Institute of Materials and Environmental Chemistry, Research Centre for Natural Sciences of the Hungarian Academy of Sciences, POB 286, Budapest, 1519, Hungary 3 Laboratory for Reactor Physics and Systems Behaviour, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland 4 Department of Materials Science, University of Milano-Bicocca, Via R. Cozzi 55, Milano, Italy Supporting Information S1

2 Contents 1 Optimization of NO 3 and NO 2 on pyrite surfaces S3 2 NEB calculations S3 3 Maximally localized Wannier functions S6 4 Metadynamics simulations S7 5 Error Sources S8 5.1 Issues of the quantum chemical method S8 5.2 Issues of the free energy samplings S8 6 Representative snapshots of transition states S11 7 Free energy surfaces S12 References S14 S2

3 1 Optimization of NO 3 and NO 2 on pyrite surfaces We have identified a large number of possible minima on the potential energy surfaces of the adsorption of NO 3 and NO 2 on perfect and defective pyrite surfaces without water. For the optimization we have used the same quantum chemical setup as in the MD simulations. The main conclusions of the optimizations are the following: NO 3 : on the perfect and defective surfaces the optimal molecular adsorption is an O,O bidentate coordination mode to two neighbour iron sites. Monodentate modes are not found. Interestingly, the reverse is true in the presence of hot-pressurized water where an O-monodentate mode became the preferred coordination. This can be explained by the favorable interaction of the ion with the H 2 O molecules of the water layer. NO 2 : on the perfect surface the most stable adsorption form is the O,O bidentate coordination mode to two neighbour iron sites. However, the N-monodentate coordination is only 2.5 kcal/mol less stable. The presence of water has an important effect: beside these two coordination forms, the O-monodentate form also becomes accessible, because this provides the easiest contact with the water layer. On the defective surface the most stable form is the N,O-bidentate coordination on the defective iron sites. In the presence of water both this coordination form and the N-monodentate form could be observed during the unbiased simulations. 2 NEB calculations Climbing image nudged elastic band (CI-NEB) calculations 1 were performed to investigate NO x dissociation on dry pyrite surfaces using the same quantum chemical method and parameters and the same periodic pyrite slab as in the MD simulations but without water. The spring parameter was 0.6 au for all the calculations. The convergence criteria on the band were the following: maximum value of displacement was au, maximum value of forces was au, root mean square (rms) of displacement was au and rms of forces was au. In case of multistep dissociation processes each step was optimized separately. For each individual step (i.e., featuring only one transition state (TS)) 8 or 12 images were used and the two end-point configurations for each steps were freely optimized. Figures S1 and S2 depict the initial, the transition and the final states of the dissociation reactions for the perfect and the defective surfaces, respectively. The dissociation of NO 3 turned out to be a two-step process on the perfect surface and a threestep process on the defective surface. The first step is the breaking of one of the N-O bonds followed by the barrierless transfer of this O atom to a neighboring sulfur site. The second step of the process is the coordination of the dangling O atom to the surface iron site which has a much lower energy barrier. The dissociation of NO 3 on the defective surface is similar but the O atom fills the vacancy site. The reaction energy is considerably larger and the overall barrier is considerably smaller for the NO 3 dissociation on the defective than on the perfect surface (see Tables 1 and 2 ). The dissociation of NO 2 on both perfect and defective surfaces is a single step process. The S3

4 Figure S1: Initial, transition state and final geometries of the oxygen transfer reactions occuring on the perfect FeS 2 surface as obtained from NEB calculations. First row: NO 3 NO 2 + O, the transition state with the highest barrier is shown. ; second row: NO 2 NO + O ; third row: NO N + O. For color code see Fig. 1 of the article. Table 1: Reaction energies and barrier heights for the dissociation of NO x surface. Energies are in kcal/mol. species on perfect pyrite process reaction energy barrier height NO 3 NO 2 + O NO 2 NO + O NO N + O dissociation of NO 2 on perfect surface starts with the breaking of one of the N-O bonds and then the O atom is transferred to a neighboring sulfur site, while the product NO reorients to an Fe-NO configuration without barrier resulting in an overall slightly endotherm process. The dissociation of NO 2 from its most stable N,O bidentate coordination on the defective surface is slightly exotherm whereas a significant barrier arises for the N-O bond breaking which is followed by the movement of the dissociated O atom into the vacancy. The dissociation of the NO on perfect surface is a single step process. The TS configuration is an NO coordinated with the N and O to surface Fe and S atoms, respectively. The stable S4

5 Figure S2: Initial, transition state and final geometries of the oxygen transfer reactions occuring on the defective FeS2 surface as obtained from NEB calculations. First row: NO 3 NO2 + O, the transition state with the highest barrier is shown; second row: NO 2 NO + O ; third row: NO N + O, occurring in the presence of a vacancy filled by an O atom. For color code see Fig. 1 of the article. Table 2: Reaction energies and barrier heights for the dissociation of NO x species on defective pyrite surface. Energies are in kcal/mol. process NO 3 NO 2 NO 2 NO NO N reaction energy barrier height +O O O dissociated form is then a surface iron-nitride species and a neighbor monoxidized surface sulfur site. Similarly, on the defective surface the dissociating O atom forms a bond with a neighbor sulfur atom. The dissociation of NO2 and NO on perfect FeS2 surface has been evaluated also by Sacchi et al.2 using Linear Synchronous Transit and Quadratic Synchronous Transit methods.3 They obtained 46.1 and 61.3 kcal/mol activation barriers for the O abstraction from NO2 or from NO, respectively, in reasonable agreement with our results. S5

6 3 Maximally localized Wannier functions In order to have a chemically meaningful picture about the valance electron distributions we have localized the Kohn-Sham orbitals according to the maximal localization criteria by Marzari and Vanderbilt 4 and analyzed the centers of these Wannier orbitals. These orbitals are analogous of the localized molecular orbitals of clusters in the traditional quantum chemistry. Figure S3 illustrates this analysis for four selected examples of the adsorbed species. Note that our methodology treats explicitely only the outer electrons whereas the core electrons and the nuclei are replaced by pseudopotentials. In particular, we use an iron pseudopotential which corresponds to an extended valence state: 3s 2 3p 6 4s 2 3d 6. For the other atoms the number of valence electrons are: 6 for O and S, 5 for N and 1 for H. Panel A shows an NO 3 adsorbed on a surface iron site. The iron is in its 2+ state therefore it has 14 valence and semicore electrons, as shown by the 7 WCs. The NO 3 unit features 12 WCs, which clearly indicate a nitrate anion (a neutral NO 3 would have 23 valence electrons, whereas the 12 WCs represent 24 electrons). On panel B an NO anion adsorbed on an iron site is depicted. Again the iron is in its Fe(II) state with seven WCs. The NO unit features 6 WCs which indicate a NO charge state (neutral NO has 11 valence electrons). Panel C shows an Fe(VI)-nitrido species. 5 WCs surround the iron ion, 3 WCs constitute the triple Fe-N bond and a Wannier center rests on the nitrogen. This is the bonding mechanism given for this high-valent iron state. 5, 6 The Fe-N unit has a positive charge (in neutral state it would have 14+5=19 electrons, whereas the 9 WCs represent 18e charge). On panel D an adsorbed NH 2 O species is seen. The iron ion is surrounded by 7 WCs indicating Fe(II) state. Another 7 WCs can be found around the NH 2 O species, which indicates a negatively charged state (neutral NH 2 O would have 13 valence electrons). A B C D Figure S3: Centers (green balls) of the maximally localized Wannier functions. For the further colors see Fig. 1 of the article. A: NO 3 adsorbed on an iron site. B: NO anion adsorbed on an iron site. C: iron(vi)-nitrido state. D: NH 2 O adsorbed on iron. S6

7 4 Metadynamics simulations We have selected various functions of coordination numbers 7 (CNs) as CVs. Table 3 summarizes these CN-s and their functions as CVs. Table 3: Coordination numbers applied in the present study and their action. Distances are in Å. A B r c p q role of the CV CN1 N O NOx N-O bond breaking CN2 N O NOx N-O bond breaking CN3 Fe surf, S surf O NOx O interaction with the surface CN4 Fe surf, S surf O NOx O interaction with the surface CN5 Fe surf, S surf O NOx, N NO 2 adsorption, O transfer CN6 N H water proton interaction with N CN7 Fe surf, S surf O water, water adsorption on surface CN8 O water H water O-H bond breaking functions of CNs CV9 CN4-CN2 O transfer from NO x to the surface CV10 CN8-CN7 O-H bond breaking upon adsorption Most of the CVs involves many degrees of freedom which implies that they are truly collective in nature and the corresponding biasing potential makes a large variety of reaction channels accessible. We have used metadynamics in its direct approach without introducing auxiliary variables for the CVs. In exploring a reaction route we have first performed an exploratory run using Gaussian biasing potentials with a height of k B T and width of 0.1 (in coordination number units). Then in subsequent refinements we started the simulations from a situation where the first free energy well was filled roughly half-way and continued the metadynamics exploration with lower Gaussian hills. A similar strategy has been successfully employed in previous studies on the simulation of the peptide synthesis at the FeS 2 surface. 8, 9 With this strategy the expected error of the metadynamics sampling is of the order of k B T (see further discussion below). Inspection of the temperature of the individual atoms has shown that thermal equilibration during the metadynamics runs was sufficient in most of the cases and that in less efficient cases refinement of the simulations enhanced the temperature homogeneity. In the present study, we have focused on the forward paths. This implies that a full free energy profile cannot be constructed. For the barrier of a given step several runs have been performed and the average barriers are presented. We did not seek to obtain relative stabilities of the intermediates and backward free energy barriers. As shown in the main article the thermodynamic force is very large toward the NH 3 formation which indicates that the overall exergonic reaction can be analyzed and interpreted by the barriers obtained from metadynamics. S7

8 5 Error Sources 5.1 Issues of the quantum chemical method The methods employed in the present study have their own limitations. In the article we have already discussed the performance of the PBE functional in reproducing the properties of bulk FeS 2. The same functional has been shown to perform well in modeling reaction occurring at the pyrite-water interface 8, 9, 10 and also in bulk water as well. 8, 9, 11 Nevertheless it is important to keep in mind that semilocal functionals yield somewhat underestimated barriers because they tend to overstabilize delocalized states (transition states usually feature more delocalized electron distribution than intermediates) due to the uncomplete correction of the self-interaction in the exchange-correlation energy. 12 An important issue is the inclusion of empirical dispersion corrections. 13 Such corrections are highly important when long range interactions play an important role. In our systems the reactive events are localized, therefore we do not expect large improvements from disperion corrections. In addition we have found that including dispersion correction has negative effect on the pyrite cell constant. In the light of the above discussion we have not used empirical dispersion corrections in the calculations. Additional errors may arise from the finite basis sets used to expand the orbitals and densities. To this end, test calculations have been performed on small molecules and on bulk pyrite. On the basis of these results we selected the MOLOPT basis set of double-zeta quality and augmented it with polarization functions for the S, O, N, and H atoms. This basis set yielded nice agreement between theory and either experiment or other calculations for structural properties of the surface and individual molecules and for bulk properties (cell parameter, bulk modulus, band-gap). In the simulations we have considered reaction paths featuring closed shell configurations. Certainly the extreme conditions and the presence of the iron may initiate open shell (radical) routes. However, their exploration requires far more computational efforts. In this regard it is necessary to note that the barriers found in the present simulations represent upper bounds for the NO x NH 3 reaction because possible more favorable radical routes will necessarily have lower barriers. 5.2 Issues of the free energy samplings The statistical error of the free energies obtained from metadynamics depends on the various parameters of the metadynamics simulations. For ideal cases Laio et al. derived suitable formulas which can be, however, extremely time-consuming to evaluate in real cases. 14, 15, 16 For example in a domain of the CVs with cubic shape the error can be estimated by the following equation: ( ) π2 k 2 δs 2 2S 2 ɛ 2 ( = S2 w βdτ g δs ) d 2π exp S k 0 π 2 k 2 (1) S8

9 where S is the size of the free energy well, δs is the hill width (assuming spherical hills), w is the hill height, τ g is the hill deposition frequency, β = 1/k B T, D is the diffusion coefficient of the CVs and d is the dimensionality of the CV space. k is a d dimensional vector with positive or null integers and k 2 is its square norm. The diffusion coefficient D can be calculated from the velocity-velocity autocorrelation function of the CVs. A more practical approach is to calculate the standard deviation of the free energy values obtained from repeated simulations with different initial conditions. In this study we have followed this strategy. For each barrier at least 3 independent estimates have been obtained. Table 4 summarizes the error estimates for the calculated barriers obtained in this way. Table 4: Free energy barriers and their standard deviations. Values are in kcal/mol. process activation free energy error perfect surface NO 3 NO NO 2 Fe-NO defective surface NO 3 NO NO 2 Fe-NO Fe-NO Fe N Fe-NO Fe-NHO Fe N Fe-NH Fe-NHO Fe-NH Fe-NHO Fe-NH 2 O Fe-NH Fe-NH Fe-NH 2 O Fe-NH Fe-NH 2 Fe-NH The finite size of the model system limits the accessible concentrations of the solute in water. In a real experiment the concentration of the reactants and products may be significantly different from those we could model in our simulation cell. The effect of this uncertainty on the barrier height can be estimated by F = F (c 2 ) F (c 1 ) = k B T ln c 1 c 2 (2) Even at a 100-fold concentration variation this translates to only 4.6 k B T (7.4 kcal/mol) stabilization, ie. the barrier heights may increase by this amount of energy. This increase should be taken into account only for the reactions of NO 3 and NO 2 surface. as the other intermediates prefer to stay at the Additional conceptual issues arise from the complexity of the real system that we wish to model. S9

10 Concentration range of the reactants, ph, fluctuations in temperature and pressure, various surface imperfections, different roles of possible radicals are not taken into account in the present models. However, the very large number of combination of these issues is presently not tractable with the available computational technology. Instead we focused on well-defined model reactions to address the NH 3 formation at a molecular scale. S10

11 6 Representative snapshots of transition states A B Figure S4: Representative configurations of the transition state ensembles for reactions occurring on the perfect FeS 2 surface. A: NO 3 NO 2. B: NO 2 NO. For color code see Fig. 1 of the article. A B C D E F G H I J Figure S5: Representative configurations of the transition state ensembles for reactions occurring on the defective FeS 2 surface. A: NO 3 NO 2. B: NO 2 NO. C: NO Fe N. D: Fe-NO Fe-NHO. E: Fe N Fe-NH. F: Fe-NHO Fe-NH. G: Fe-NHO Fe-NH 2 O. H: Fe-NH Fe-NH 2. I: Fe-NH 2 O Fe-NH 2. J: Fe-NH 2 Fe-NH 3. For color code see Fig. 1 of the article. S11

12 7 Free energy surfaces We present here the free energy surfaces (FES) for the most important routes which have not been shown in the main article. The CVs of the simulations are associated with the CVs of Table 3. Figure S6: FES of the NO 3 NO2 transformation occurring on a defective FeS2 surface. The label indicates the reaction stages according to the article. CV1 = CN1; CV2 = CN4. The energy values are in kcal/mol. Figure S7: FES of the NO transformation occurring on a defective FeS2 surface. The 2 NO label indicates the reaction stages according to the article. CV1 = CN1; CV2 = CN4. The energy values are in kcal/mol. S12

13 Figure S8: FES of the NO Fe N Fe-NH Fe-NH2 NH3 transformation occurring on a defective FeS2 surface. The labels indicate the reaction intermediates according to the article. CV1 = CV9; CV2 = CN6. The energy values are in kcal/mol. The double minima at the nitride intermadiate region correspond to the built-in of the dissociated O atom into a neighbour Fe and S atom in the uppermost pyrite layers. Figure S9: FES of the NO NHO NH2 O NH2 NH3 transformation occurring on a defective FeS2 surface. The labels indicate the reaction stages according to the article. CV1 = CV9; CV2 = CN6. The energy values are in kcal/mol. The double minima at the NH2 region correspond to the built-in of the dissociated O atom into a neighbour Fe and S atom in the uppermost pyrite layers. S13

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