Chapter 3: Density Functional Theory Modeling of 1Tʹ-MoS 2 Methylation
3.3 Results and Discussion
3.3.3 Thermodynamics of progressive methyl functionalization of 1Tʹ-MoS 2 as a
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
Figure 3.10. (a) Free energies of 2-methyl functionalization patterns that include one methyl on S7, minimized with a negative charge of 2. (b) MoS2 surface prior to the addition of the 2nd methyl.
Figure 3.11. (a) Free energies of 3-methyl functionalization patterns that include methyls on S7 and S14, minimized with a negative charge of 2, (b) the MoS2 surface prior to the addition of the 3rd methyl. (c) Free energies of 4-methyl functionalization patterns that include methyls on S5, S7, and S14, minimized with a negative charge of 2, (d) MoS2 surface prior to the addition of the 4th methyl.
we see that the methylation pattern 7-5 (i.e. positions S7 and S5 are methylated) and 7-14 are the patterns with the lowest free energy. Thus, we chose to functionalize S14 for the 2nd methyl and the reaction can be represented as 0N-7-(14) using our notation.
For the 3rd methyl, we repeated the same procedure and observed that methylation at positions 5 (low-S), 11 (high-S), and 16 (low-S) resulted in the structures with the lowest free energy (Figure 3.11a, b). Since we know that low-S are preferrable for functionalization compared to high-S and noting that the potential of the final structure with S11 methylated is ~0.15 V positive relative to all other structures, we chose S5 for the third methylation
Figure 3.12. (a) Free energies of 5-methyl functionalization patterns that include methyls on S5, S7, S14, and S16, minimized with a negative charge of 4.2, (b) the MoS2 surface prior to the addition of the 5th methyl. (c) Free energies of 6-methyl functionalization patterns that include methyls on S5, S7, S13, S14, and S16, minimized with a negative charge of 4.2, (d) MoS2 surface prior to the addition of the 6th methyl.
reaction, 0N-(5)-7-14. For the 4th methylation, the same procedure was repeated, and resulted in a clear favored methylation position at S16, the 0N-5-7-14-(16) reaction (Figure 3.11c, d).
For the 5th methylation, we observed the free energies to be similar for positions 1, 2, 3, 6, 8, 13, and 15 (Figure 3.12a, b). Positions 1, 2, and 3 are high-S, whereas 6, 8, 13, and 15 are low-S. We encountered a similar situation during the 6th methylation, where S3 and S4 (high- S) and S6, S8, and S15 (low-S) were the lowest in energy (Figure 3.12c, d).
Figure 3.13 shows the ΔG of methylation obtained using grand canonical potential kinetics for the 5th and 6th methylation reactions on either a low-S or a high-S. The ΔG is ~0.3 eV lower for the low-S option relative to the high-S option when the number of neighbors is held constant, as is the case for the two 6-methyl examples (2N-5-7-13-14-(15)-16 and 2N-(h4)- 5-7-13-14-16). On the other hand, the ΔG between methylation of a low-S with 2 neighbors vs a high-S with 1 neighbor is similar, which can be seen for the 5-methyl examples 2N-5- 7-(13)-14-16 and 1N-(h1)-5-7-14-16. The reason for this discrepancy between comparing the free energies of the final structure and the ΔG of reaction may be due to differences in potential at fixed charge depending on where the methyl is located. Thus, it is not immediately obvious from free energies of minimized structures at fixed charge what their relationship will be at fixed potential.
Figure 3.13. The ΔG of the methylation reaction vs potential for the 5th and 6th methylations, indicated in the notation with numbers corresponding to methylated sulfurs, brackets around the most recent methyl position, a prefix indicating the number of neighbors for the bracketed position, and “h” to indicate high-S positions.
We also calculated the free energies of 7-methyl patterns and found that the remaining low- S positions, S6 and S8, were equally favored (Figure 3.15).
In addition to calculating the thermodynamics of functionalizing the “most favorable” position at each step to determine the methylation pattern, we also calculated the thermodynamics for reactions that would yield useful comparisons in terms of steric effects.
For the 4th methylation, although we found that 0N-5-7-14-(16) is the most favorable reaction,
Figure 3.14. The free energy of the methylation reaction, ΔG, vs potential for the 4th and 5th methylations, comparing the effect of neighboring groups on the ΔG value. For the 4th methylation reaction (blue solid and dashed lines), 0N-5-7-14-(16) and 1N-5-7-(13)-14 functionalizes a sulfur adjacent to 0 and 1 methyl group respectively.
For the 5th methylation reaction (orange solid and dashed lines), 1N- 5-7-13-14-(16) and 2N-5-7-(13)-14-16 functionalizes sulfurs adjacent to 1 and 2 methyl groups, respectively. The 5-methyl reactions result in the same pattern of methyls on the surface.
Figure 3.15. (a) Free energies of 7-methyl functionalization patterns that include methyls on S5, S7, S13, S14, S15, and S16, minimized with a negative charge of 1, (b) MoS2 surface prior to the addition of the 7th methyl.
we also calculated the thermodynamics for the 1N-5-7-(13)-14 reaction to understand the effects of functionalizing a low-S (S13) adjacent to an existing methyl group (S14) (Figure 3.14). Similarly, although the only low-S sites available were between two methyl groups for the 5th methylation, 2N-5-7-(13)-14-16, we also calculated the thermodynamics for the 1N-5-7-13-14-(16) reaction which has the same methylation pattern in the product, but the reaction was adjacent to only one methyl group rather than two (Figure 3.14). Note that positions S13 and S16 are adjacent since the unit cell repeats in all directions.
Notably, in the example shown in Figure 3.14, the ΔG of the two-neighbor (2N) reaction is substantially higher than the 1N reaction that results in the same pattern of 5 methyls (5-7- 13-14-16) in the product. In the 4-methyl cases, the ΔG of the 1N reaction is higher than the 0N reaction, but they result in different methylation patterns. Also, the 1N 4-methyl reaction appears to be as thermodynamically unfavorable as the 2N 5-methyl reaction. This may be because the 5-6-13-14 pattern, with its adjacent methyls on S13 and S14, is more strained than the 5-7-14-16 pattern, where no methyls are adjacent to each other. Since their initial states are equally unstrained, this results in a more positive ΔG for the reaction that produces more steric hinderance in the product.
From this perspective, the similarity in free energy change in the overall system, ΔG, for the 1N-5-7-(13)-14 and 2N-4-7-(13)-14-16 reactions suggests that the addition of the S13 methyl adds a similar amount of strain to both systems.
In the process of calculating the thermodynamics of the reactions described above, we also found, perhaps unsurprisingly, that the potential of the reaction products becomes more negative as more
Figure 3.16. Potential in V vs SHE of the final state products (MoS2)16(CH3)x + Cl, with a fixed negative charge of 2 in the unit cell, depending on the number of methyls added to the surface (x = 1, 2, 3, 4, 5 or 6).
The potential of the final products becomes more negative as the number of methyls increases due to additional electrons in the system.
methyls are added to the surface. Figure 3.16 plots the potential of the MoS2 slab after each methylation (a chlorine atom is present above the most recently added methyl) at a fixed negative charge of 2. As additional methyls are added to the system, additional electrons are added to the functionalized MoS2, in the form of the S–C bond and the methyl groups, resulting in a more negative potential.
For all the methylation reactions described above, we calculated the ΔG as a function potential and plotted the results altogether in Figure 3.17, interpolated using the same methods as in 3.3.2 (see Appendix C.5). Methyl additions involving 0, 1, or 2 neighboring methyls during the reaction are grouped using solid, dashed, and dotted lines. The potentials corresponding to the reductants used in Chapter 2 are indicated with vertical lines.
From the data in Figure 3.17, we can make several observations. First, methylations that occur surrounded by empty sites (i.e. those labeled 0N) have similar thermodynamic favorability. The ΔG of methylation actually decreases after the first methylation. This is reminiscent of the effects observed for 2H-MoS2 vacancy-induced radical functionalization,
Figure 3.17. The free energy of the methylation reaction, ΔG, vs potential for all methylation reactions, where XN stands for X neighbors for the methyl being added, the numbers representing the sulfur positions that are methylated, and brackets surround the position undergoing the methylation reaction. Potentials corresponding to experimental conditions in Chapter 2 are marked with vertical lines.
whereby the initial functionalization reaction can only occur next to a vacancy, but functionalization induces higher reactivity in nearby sulfurs, resulting in a nucleation- propagation pattern of functionalization across the surface.72 A similar mechanism may be present in this system that promotes functionalization of non-sterically hindered nearby sites.
Second, high-S functionalizations in the 0N and 2N cases (0N-(h10) and 2N-(h4)-5-7-13-14- 16) have the highest ΔG values out of all the reactions in this potential range and are thus less likely to be functionalized than low-S, except in the case of 1N-(h1)-5-7-14-16 which is comparable to 2N low-S functionalization.
Third, the ΔG of 2N methylations are substantially higher than the 0N and a subset of 1N methylations. The ΔG values of 1N methylations are split between being those of 0N or 2N, depending on the methylation pattern on the surface. If we compare the ΔG reactions that result in methyl functionalization at the same positions, as in 1N-5-7-13-14-(16) and 2N-5- 7-(13)-14-16, and assume that the thermodynamics of a reaction are correlated with the kinetics of the reaction which is true in the case of the first methylation reaction (Figure 3.7), the ~0.5 eV increase in ΔG of the latter suggests that from both the thermodynamics and kinetics perspectives, methylation of sites with two neighboring methyl groups is substantially disfavored relative to methylation of sites with either zero or one neighbors.
This difference for 2N reactions may be a key factor in limiting the achievable coverage in the experimental system. Based on Figure 3.17, for a 2N reaction to have a ΔG close to that of a 0N reaction in the no-reductant case (0.3 V vs SHE), at least –0.7 V of additional potential needs to be applied (~ –0.4 V vs SHE).
We will use these insights later in Section 3.3.5 to simulate and obtain the expected coverage distributions of random surface functionalization according to different functionalization models and suggest the models that are most likely to represent this system.