Chapter 3: Density Functional Theory Modeling of 1Tʹ-MoS 2 Methylation
3.3 Results and Discussion
3.3.2 Thermodynamic and kinetic differences during methylation of the two types of
The first aspect of methylation that we wanted to understand is how the two different types of sulfur, which emerge because of the distortion of the 1T phase to the 1Tʹ phase, differ in their reactivity towards nucleophilic addition with methyl chloride. These two types of sulfur we will refer to as “low-S” and
“high-S” sulfur, as shown in Figure 3.4, following the nomenclature used in previous computational studies of 1Tʹ- MoS2.16
Prior to investigating the thermodynamics and kinetics of the methylation reaction, we ascertained that methylated MoS2 of a particular type of sulfur results in a structure that has little intra-type free energy variation within either low-S or high-S, and a much larger inter-type free energy variation between low- and high- S using two sulfurs of each type: S6 and S7 for low-S, S10 and S11 for high-S. Figure 3.5 graphs the free energy of S6-, S7-, S10-, and S11-functionalized MoS2, showing that the free energy of methylated MoS2 depends largely on whether it is high-S or low-S, with little variation within the low-S and high-S groups. Thus, we selected S7 and S10 as the low-S and high-S sulfurs to study the first methyl group addition reaction to MoS2.
Figure 3.6 shows the relationships between the thermodynamic favorability (ΔG) of methylation on S7 and S10 in terms of the final state free energy minus the initial state free energy, and the kinetic barrier of a reaction (ΔG‡) calculated from the transition state free
Figure 3.4. Top-down and side view of the rectangular unit cell of the minimized 1Tʹ-MoS2
supercell, color-coded to show the two types of sulfur in the unit cell: low-S and high-S, with low-S having a longer average Mo–S distance and high-S having a shorter average Mo–S distance and protruding further out-of-plane compared to the low-S.
energy minus the initial state free energy.
The computations for ΔG and ΔG‡ were computed in intervals of 0.1 V from 0.5 to –0.9 V vs SHE and are based on interpolations using the grand canonical potential free energies to show the potential dependency of the free energy of the system. The process of quadratic fitting and interpolation is described in greater detail in Appendix C.5. The potential interval that is plotted in Figure 3.6 is the narrowest potential window within which all the values used to calculate ΔG and ΔG‡ are interpolated values, as opposed to extrapolated. The reductant potentials that correspond to the reductants used in Chapter 2 are notated on the plot to aid comparison with the experimental data. To determine the potential of ceMoS2 for the no-reductant case, we made drop cast ceMoS2
electrodes and measured the open circuit voltage in acetonitrile with 0.10 M tetrabutylammonium perchlorate and 0.10 M methyl iodide (see Appendix A.4), which was determined to be –0.07 V vs E(Fc+/0), or ~0.3 V vs SHE, and also corresponds to the potential of the ferrocene condition. XPS of drop cast ceMoS2 showed the same peaks in the Mo3d and S2p regions as the ceMoS2 spectra in Chapter 2.
From Figure 3.6, we can see that at the ΔG for methylation of S10, a high-S sulfur, is consistently ~0.5 eV higher than the ΔG for methylation of S7, a low-S sulfur. The barrier height of S10 methylation, ΔG‡, is ~0.2 eV higher than the ΔG‡ of S7 methylation. These results show that low-S functionalization is preferred over high-S functionalization both thermodynamically and kinetically. Figure 3.7 shows the correlation between ΔG and ΔG‡ of S7 and S10 methylation. If we use the Boltzmann distribution to evaluate the significance of the difference of 0.5 eV between the ΔG values, we see that the probability of S10
Figure 3.5. Free energy of (MoS2)16(CH3) with methyl on either S6, S7, S10, or S11, the former two being low-S and the latter two being high-S.
Geometry optimizations and free energy calculations were performed on solvated structures that were negatively charged with 2 electrons, resulting in structures with potentials –0.15, –0.16, –0.11, and –0.11 V vs SHE, respectively.
methylation is 9 orders of magnitude lower than that of S7 methylation. Using the Eyring equation to evaluate the difference in rate constants, the details in Appendix C.6, we see that the rate constant k for S7 methylation is 2 s-1, but only 0.002 s-1 for S10 methylation at 0.3 V vs SHE, a difference of 3 orders of magnitude in the rate constant. The Boltzmann distribution and Eyring equation are given by eq. 1 and 2:
pi/pj = exp(–(Ei – Ej)/kBT) (1)
Figure 3.6. (a) Thermodynamic favorability, ΔG, and (b) kinetic barrier, ΔG‡, of methylation on S7 and S10 of 1Tʹ-MoS2 as a function of potential based on interpolations of the initial, transition, and final state free energies (see Appendix C.5). (c) Side-view of the initial state, transition state, and final states for S7 and S10 methylation with negative charge of 2.
k = (kBT/h)exp(–ΔG‡/RT) (2) where pi is the probability of the system being in state i, Ei is the energy of state i, kB is the Boltzmann constant, T is the temperature, k is the reaction rate constant, h is Planck’s constant, and R is the gas constant.
Thus, there is a significant thermodynamic and kinetic preference for the functionalization of low-S sulfurs. The reason for this is likely due to the differences in Mo–S bond lengths between low-S and high-S. As the Mo–S bond length increases, the covalent bond is weaker, there is greater electron density localized on the sulfur atom and less stabilization with the Mo atom, making the sulfur more nucleophilic. Conversely, as the Mo–S bond shortens, more electron density from the sulfur participates in the Mo–S bond and becomes unavailable to participate in nucleophilic addition. For high-S sulfurs, the Mo–S bond distances are 2.34, 2.39, and 2.46 Å, whereas the Mo–S bond distances for low-S sulfurs are 2.35, 2.51, and 2.54 Å. Given that two of the Mo–S bonds for low-S are longer by 0.08–0.11 Å each, it is reasonable to expect that low-S sulfurs preferentially engage in nucleophilic attack compared to the high-S sulfurs. Similar conclusions have been made in computational studies of hydrogen adsorption on low-S and high-S sulfurs, with the conclusion that the ~0.7 eV difference in the free energy of H adsorption (0.06 eV on low-S, 0.73 eV on high-S) is due to the more negatively charged low-S with a charge –0.54, compared to high-S with a charge of –0.47.16 These values were obtained using Bader’s charge population analysis.99 The same study also found that H atoms adsorbed onto high-S moved to the nearest low-S with a barrier height of 0.15 eV that can be easily
Figure 3.7. The correlation between the barrier height and the free energy of reaction for S7 and S10 methylation, plotted using the same points as shown in Figure 3.6. The reaction potential varies along each curve and can be determined using Figure 3.6.
overcome at room temperature.16 A similar reaction was not performed in this work, which we believe would be interesting to note in future work.
Consistent with the decrease in barrier height and increased thermodynamic favorability of S7 methylation as the potential becomes more negative, we found that the S–C bond distance in the transition state increases as the potential decreases, as illustrated in Figure 3.8. An increase in the S–C bond distance implies that the transition state occurs earlier along the reaction coordinate, closer to the reactants. According to Hammond’s postulate, the closer the energy between the transition state and another state, the more their geometries resemble each other and vice versa. In exothermic reactions, the transition state is closer in energy to the reactants than to the products, which is what we observed in Figure 3.6 as the potential becomes more negative. To summarize, as the potential becomes more negative, the reaction becomes more exothermic, and the transition state moves closer to the initial state along the reaction coordinate.
In addition to methylation of the 1Tʹ phase, we also performed a minimization of a methyl- functionalized 1T phase. Notably, the methylated 1T-MoS2 distorted to a 1Tʹ-like structure, although its minimized free energy was higher than the structures shown above. Since we were able to minimize the 1T phase by itself without observing distortion, this suggests that there is a local minimum for the 1T phase with a barrier for distortion that is overcome upon the addition of a methyl group. Thus, functionalization necessitates that the 1T phase
Figure 3.8. Transition state S–C bond distance as a function of potential in V vs SHE. Each point is based on a single nudged elastic band calculation. As the potential becomes more negative, the S–C bond length increases, indicating that the transition state resembles the initial state more than the final state, consistent with the data in Figure 3.6 indicating a more exothermic reaction as the potential decreases.
becomes distorted.
The structures before and after the geometry optimization of the 1T phase without and with methylation are shown in Figure 3.9.
3.3.3 Thermodynamics of progressive methyl functionalization of 1Tʹ-MoS2 as a