Nucleation of mercury sulfide by dealkylation

Metal sulfide minerals are assumed to form naturally at ambient conditions via reaction of a metallic element with (poly)sulfide ions, usually produced by microbes in oxygen-depleted environments. Recently, the formation of mercury sulfide (β-HgS) directly from linear Hg(II)-thiolate complexes (Hg(SR)2) in natural organic matter and in cysteine solutions was demonstrated under aerated conditions. Here, a detailed description of this non-sulfidic reaction is provided by computations at a high level of molecular-orbital theory. The HgS stoichiometry is obtained through the cleavage of the S-C bond in one thiolate, transfer of the resulting alkyl group (R’) to another thiolate, and subsequent elimination of a sulfur atom from the second thiolate as a thioether (RSR’). Repetition of this mechanism leads to the formation of RS-(HgS)n-R chains which may self-assemble in parallel arrays to form cinnabar (α-HgS), or more commonly, quickly condense to four-coordinate metacinnabar (β-HgS). The mechanistic pathway is thermodynamically favorable and its predicted kinetics agrees with experiment. The results provide robust theoretical support for the abiotic natural formation of nanoparticulate HgS under oxic conditions and in the absence of a catalyst, and suggest a new route for the (bio)synthesis of HgS nanoparticles with improved technological properties.


Evaluation of the Gibbs free energy
Stationary points of the reaction pathway were identified by scanning the potential energy surface (PES) against the location of all atoms in the system without water molecules. The Gibbs free energy in aqueous solution (Gaq) for the molecular state (M) at each stationary point was evaluated according to: Gaq(M) = ECCSD(T)(M) + ΔGcorr(M), (1) where ECCSD(T)(M) is the total electronic energy (i.e., potential energy) including the solvent effects, and ΔGcorr(M) is the thermal and entropic contributions to G calculated at 298 K and 1 atm. The thermal and entropic contributions were obtained by performing frequency calculations. The Gaq(M) values were corrected for the difference between the standard molar concentrations in solution and gas phase. Since the CPCM solvation energy does not include the energy of formation of solvent cavities, we evaluated this contribution separately for the final structures using the SMD version 1 of the polarizable continuum dielectric model (PCM). The correction for this effect on the calculated energy barriers was small, in the range of 1-2 kcal mol -1 . The conformational degeneracy of the transition state was taken into account by adding to G the term -RT*ln(g), where g is the degeneracy, R the gas constant, and T the absolute temperature.
Energetic values in the presence of water molecules were calculated as follows. The geometry of the stationary points were reoptimized with explicit water molecules added in contact to the main atoms involved in the chemical reaction. The whole system ("real system" 2 ) was optimized at the MP2 level of theory, and the "model system" 2 including all atoms except those belonging to water molecules was treated at the CCSD(T) level of theory. The ONIOM energy 2,3 was calculated according to: (2) The three energy terms in eq. 2 were calculated in the presence of the bulk solvent (CPCM) and for the geometry optimized on the real system. Finally, the Gibbs free energy of the system was calculated from: with ΔGcorr(real) obtained by a frequency calculation performed at the MP2 level of theory on the optimized real system (i.e., in the presence of the bulk solvent). The choice of the pure continuum solvation model has only a limited impact on the calculated Gibbs free energy. For instance, we previously obtained 4 G(FP) = -3.9 kcal mol -1 for reaction (1) (main text) using the pure PCM model, compared to -6.4 kcal mol -1 with the pure CPCM model in the present study (Fig. 1).
The convergence criteria used in the geometry optimizations were the default settings in the Gaussian 09 program : Maximum Force 0.000450 RMS Force 0.000300 Maximum Displacement 0.001800 RMS Displacement 0.001200

Energy profile for the IP to PC structural rearrangement
The energy profile was obtained by constraining the Hga-Sd distance to fixed values. The solvation model used here is the pure CPCM model (i.e., no explicit water molecules). Figure S1. Energy profile for the rearrangement of the reaction product.

Effect of explicit water molecules on the dealkylation energy barrier
The transfer of the CH3 + group is associated with a significant reorganization of the electronic density around Sd, Sa, and the C atom of the transferred methyl group. This process is expected to be sensitive to the presence of solute-solvent hydrogen bonds because of their weak but definite covalent character 5 . Therefore, a more accurate evaluation of the reaction energy barrier is obtained when explicit water molecules are placed nearby the main atoms involved in the reaction 6 . This type of calculation was performed for 2, 4 and 7 explicit solvent molecules. Obviously, in all cases, the atoms from the solute around which the explicit water molecules were placed were the same in the free reactant (FR) and transition state (TS) structures (Table S1). In a first approach (2H2O model in Fig. 1), two water molecules were placed in contact with the Sd atom of the two free reactants and of the TS complex. The length of the two Sd…H hydrogen bonds in the optimized structures decreased from 2.37 Å in the free reactants to 2.24 Å in the TS complex, thus proving the importance of solute-solvent covalent interactions. In a second approach (4H2O model in Fig. 1), two additional solvent molecules were placed in contact with the transferred CH3 group because it is expected to become more electrophilic in the TS configuration. In a third approach (7H2O model in Fig. 1), the water molecules were placed as follows: three near Sd, two near Sa and two near the CH3 group. This arrangement approximately corresponds to the first solvation shell of the directly reacting atoms. In all model systems, the free reactant state is represented by two free supermolecules, each formed of a Hg(II)-methanethiolate complex (CH3S-Hg-SCH3) carrying several water molecules (0 and 2, 0 and 4, 2 and 5, respectively). The structure of the TS complex including the seven water molecules is shown in Fig. S2. Details of the reaction energetics are given in Tables S1-S3. E is the total electronic energy, H the enthalpy, Stot the total entropy, and Str the translation-rotation entropy.  Figure S2. Structure of the TS configuration optimized with seven explicit water molecules

Correction of the contribution of translation-rotation solvation entropy to the energy barrier
A general source of error attributed to the continuum solvent models is the improper evaluation of the solvation entropy 7-10 . When the translation-rotation entropy of the molecule in solution is calculated using the same method as in the gas phase, this entropy is largely overestimated. The result is a systematic error in the evaluation of the Gibbs free energy difference between molecular states involving a different number of molecules. For instance, this error occurs systematically in the calculation of the Gibbs free energy of molecular association and dissociation. In the case of an association, the reactants have six translational and six rotational degrees of freedom in total, which transform in the product to three translational and three rotational degrees of freedom plus six new vibrational degrees of freedom. To avoid this error, Wertz 7 proposed an alternative semi-empirical mode of calculation of the translation-rotation entropy for a molecule in solution which consists of attributing to the dissolved molecule an energy equivalent to one-half the gas phase value (see also ref. 10 ). In the present study, the contribution of the translation-rotation entropy to the reaction energy barrier is about 20 kcal mol -1 . According to Wertz's approach, it should be about half this value. In another approach, based on the analysis of data from the association of two weakly interacting molecules in aqueous solution, Yu et al. 9 concluded that the contribution of the translation-rotation entropy to the Gibbs free energy of association is less or equal to 9RT. From this approach, our calculated reaction energy barrier should be corrected by at least -14.6 kcal mol -1 . By corroborating the two approaches, we conclude that a minimum correction of -10 kcal mol -1 should be applied to the calculated energy barrier. The resulting predictive value for this barrier is 22 kcal mol -1 .

Cleavage of the S-C bond by direct insertion of a Hg atom
The alkyl group transfer between two thiolates could also occur indirectly through the formation of an intermediate product, in which mercury is inserted between the two atoms of the S-C bond. A first possibility is an insertion that occurs by an intramolecular rearrangement in a RS-Hg*-S*R* complex: Hg* is inserted between S* and R*, the R* group is transferred to SR, and the resulting R*SR group is eliminated. However, the scan of the potential energy surface of this system with respect to the Hg*-C* (from R*) distance (results not shown) invalidates this reaction pathway because it yields a significant increase of energy. Besides, a direct consequence of an insertion reaction should be the formation of an intermediate product in which the C* and S* atoms are both bonded to Hg*. No energy minimum could be found for this molecular conformation.
A second possibility is an insertion reaction involving two RS-Hg-SR complexes. In this case, the Hg atom from one complex interacts with a thiolate group from the other complex. The corresponding insertion product was identified and its optimized structure shown in Figure S3. In a second reaction step, the CH3 group bonded to Hg could be transferred to an adjacent S atom. The CH3-S-CH3 group thus formed could dissociate as in the case of the direct alkyl group transfer channel shown in Figure 1. The global reaction also is described by reaction (1) (main text). The difficulty with this model is that the Gibbs free energy of the insertion product is too high relative to that of the free reactants. A calculation performed at the ONIOM (CCSD(T)/MP2) level of theory using four explicit water molecules gives a positive difference of 49.0 kcal mol -1 . This is about 15 kcal mol -1 higher than the energy barrier for the direct alkyl group transfer calculated under the same conditions (34.7 kcal mol -1 ). Obviously, the transition state leading to the formation of this insertion product should be even higher in energy. We conclude that this pathway should be disregarded.