Active catalyst models used in the calculations

Explanation of terms and abbreviations

Scheme 1. Active catalyst models used in the calculations

The catalytic cycle involves the following steps: (1) activation of CH4 via heterolytic C-H bond dissociation and (2) transfer of the proton and the methyl group to CO2 via a 6-membered transition state to produce acetic acid and regenerate the catalyst. It is proposed that the active 16- electron complexes are derived from their 18-electron precursors by treatment with base under standard experimental conditions. Scheme 2 summarized the reaction cycle proposed for the model catalysts. Based from previous papers, the heterolytic C-H activation of methane may proceed via alkyl (H3C^δ--H^δ+ transition state) or carbenium (H3C^δ+-H^δ- transition state) pathways. However, the alkyl path was followed in this study as this pathway was found to be more favourable in initial calculations.

21

Scheme 2. Proposed catalytic cycle for the formation of acetic acid from CH4 and CO2 catalyzed by the bifunctional half-sandwich complex Ru(C6H6)(O,O).

To determine the metal effects, catalytic cycles were computed for Ru(C6H6)(O,O), RhCp(O,O) and IrCp(O,O). The overall energy profile calculated for the gas phase at 0 K is presented in Figure 2 [energies corrected for zero-point energies (ZPE)]. All metal complexes were found to proceed via a similar mechanism. When methane was added to active catalyst (G0), one of the hydrogen atoms of CH4 is attracted by trhe 1,2-ethanediolato ligand while the carbon atom approaches the metal center (G1). Activating and cleaving of the C-H bond through 1^st transition state GTS1 produces the methyl complex (G2). Carbon dioxide is then added and interacts with the protonated ligand, followed by the concerted transfer of the methyl group and the proton from the complex to CO2 (GTS2), yielding acetic acid and regenerating the active catalyst (G4).

22

Figure 2. Zero-point energy (ZPE) profiles for the reaction of CH4 with CO2 catalyzed by Ru(C6H6)(O,O), RhCp(O,O) and IrCp(O,O).

23

The C-H bond activation step is uphill for each of the three catalysts. A comparison of the energy profiles reveals that the lowest energy barriers are found for the Ru catalyst, with 26.0 kcal/mol for GTS1 and 25.2 kcal/mol for GTS2 (acetic acid formation step). For RhCp(O,O), the first barrier is calculated to be similar with 26.2 kcal/mol and the second barrier is higher with 29.6 kcal/mol, whereas for IrCp(O,O) both barriers are substantially higher with 32.2 and 32.3 kcal/mol (Figure 1 and Table 4). The structure of the first transition state (TS1) is consistent for all the three complexes and shows concerted movement of the proton toward the ligand oxygen atom and of the carbon atom approaching the metal center. Natural bond orbital (NBO) charges of the interacting atoms, as shown in Table 5, confirm that CH4 activation follow the alkyl pathway rather than carbenium pathway, showing partial positive charges on the hydrogen atom and partial negative charge on the methyl carbon atom. the C–H bond is more activated by Ru(C6H6)(O,O) than by RhCp(O,O) or IrCp(O,O). The C-H bond length is increased from 1.11 Å in CH4 to 1.38 Å in the Ru complex, to 1.37 Å in the Rh complex, and to 1.36 Å in the Ir complex.

Table 4. Activation energies corrected for zero-point energies (ΔE^{0 K}, in kcal/mol) and imaginary frequencies (IF, in cm^–1) of the first and second transition states.

Complexes

TS1 TS2

𝛥𝐸𝑔𝑎𝑠0 𝐾 IF 𝛥𝐸𝑔𝑎𝑠0 𝐾 IF

Ru(C6H6)(O,O) 26.0 -1406.1i 25.2 -447i

RhCp(O,O) 26.2 -1507.4i 29.6 -431i

IrCp(O,O) 32.2 -1490.0i 32.3 -430i

Table 5. NBO charges of interacting atoms in the 1^st and 2^nd transition states of model catalysts.

In the second transition state, CO2 interacts via its oxygen atom with the ligand proton (derived from CH4), while the carbon atom of the CO2 move toward the carbon atom of the methyl group. For the Ru complex, the distance between the carbon atoms of the methyl group and CO2

decreases from 3.15 Å in G3 to 1.98 Å in GTS2, as the methyl group moves away from the metal center by 0.23 Å (cf. Table 1 for imaginary frequencies). As mentioned above, the energy barrier for acetic acid formation increases from Ru(C6H6)(O,O) to RhCp(O,O) to IrCp(O,O). In the same order,

Complexes TS1 TS2

Metal O – ligand H - CH4 C - CH4 Metal O – ligand H - CH4 C - CH4 C - CO2

Ru(C6H6)(O,O) 0.110 -0.721 0.418 -0.922 0.107 -0.692 0.540 -0.894 1.004

RhCp(O,O) 0.319 -0.715 0.413 -0.921 0.312 -0.700 0.538 -0.874 0.974

IrCp(O,O) 0.354 -0.726 0.421 -0.934 0.376 -0.695 0.541 -0.886 0.962

24

the carbon atom of CO2 in GTS2 becomes less electrophilic, as indicated by the NBO charges of +1.004 |e| for Ru(C6H6)(O,O), +0.974 |e| for Rh(Cp)(O,O), and +0.962 |e| for Ir(Cp)(O,O) (Table 2)

Effects of Temperature and Solvents on the Activation Energies

The mechanism was computed for reactions of the three complexes in the gas phase at 298 K and 373 K, as well as in benzene and water at 298 K (Table 6). The reactions follow the same mechanism under all conditions studied. There was observed similar trends between the zero-point energy barriers and free energy barriers for gas phase reactions at 298 K and 373 K: Ru(C6H6)(O,O)  RhCp(O,O) < IrCp(O,O) for the activation of methane and Ru(C6H6)(O,O) < RhCp(O,O) < IrCp(O,O) for the acetic acid formation. In the case of benzene solution, the barriers of the first TS are nearly the same as those of the reactions in the gas phase while the barriers of the second TS are 2 kcal/mol lower relative to the gas phase. In the case of reactions in water, the barriers of the first TS are about 1 kcal/mol higher than those in the gas phase, while the second TS are 2-3 kcal/mol lower as compared with gas phase values. Overall, both benzene and water ease the second step of the mechanism.

Table 6. Transition free energies (ΔG^{298 K}) of 1^st and 2^nd TS of model complexes in gas phase, benzene (C6H6), and water at 298 K, as well as free energies at 373 K (ΔG^{373 K}), in kcal/mol.

Complexes

TS1 TS2

𝛥𝐺_𝑔𝑎𝑠^{298 𝐾} 𝛥𝐺_𝐶6𝐻6^{298 𝐾} 𝛥𝐺_{𝑤𝑎𝑡𝑒𝑟}^{298 𝐾} 𝛥𝐺_𝑔𝑎𝑠^{373 𝐾} 𝛥𝐺_𝑔𝑎𝑠^{298 𝐾}𝛥𝐺_𝐶6𝐻6^{298 𝐾} 𝛥𝐺_{𝑤𝑎𝑡𝑒𝑟}^{298 𝐾} 𝛥𝐺_𝑔𝑎𝑠^{373 𝐾} Ru(C6H6)(O,O)

27.6 27.6 28.7 27.9 26.7 24.5 24.5 26.1

RhCp(O,O) 27.5 27.8 28.5 27.6 31.0 28.7 27.9 30.6

IrCp(O,O) 33.6 33.4 34.4 32.9 33.6 32.0 31.0 32.8

Notably, the calculated barriers reveal differences in the nature of the rate determining step for the three catalysts. The Ru complex has the heterolytic cleavage of methane as its rate-determining step for all conditions studied. In Rh complex, the formation of acetic acid is rate-determining in the gas phase and benzene solution but not in water. Both reaction steps require same activation free energies in the gas phase for Ir complex, while methane activation is rate-determining in benzene and water.

Generally, Ru(C6H6)(O,O) exhibits the lowest barriers for the rate-determining step both in the gas phase and in benzene (27.6 kcal/mol each), with the barriers increasing in the order of Ru(C6H6)(O,O)

< RhCp(O,O) < IrCp(O,O). In water, the Ru and Rh complexes have competing barriers (28.7 and 28.5 kcal/mol, respectively), showing a trend of Ru(C6H6)(O,O)  RhCp(O,O) < IrCp(O,O).

25

Metal effects on methane activation and acetic acid formation

In this section, the interaction of the catalysts with the substrates in the transition states were investigates to gain insights into different activities. In a related study, Hou⁸⁴ and co-workers investigated the hydrogenation of CO2 with H2 catalyzed by bifunctional half-sandwich complexes of Co, Rh and Ir. In that work, H2 was heterolytically cleaved by the catalyst's metal center with assistance from the ligand, followed by transfer of a hydride and a proton to CO2. A key factor for H2

activation by those complexes is M-to-H2 π back-donation, and the different catalytic activities of the complexes were explained by varying extent of π back-donation. In our study, we analyzed the orbital interactions that cause heterolytic C–H bond cleavage of methane.

Table 7. Second order stabilization energies (in kcal/mol) for interactions between natural bond orbitals of the model complexes in the first transition state (in parenthesis is the 𝑬^(𝟐) 𝝈_𝑪−𝑯 → 𝒅_𝑴^∗ from abstracted H only).

Complexes 𝑬^(𝟐) 𝝈_𝑪−𝑯 → 𝒅_𝑴^∗ 𝑬^(𝟐) 𝑳𝑷 _𝑶 → 𝝈_𝑪−𝑯^∗ ∑ 𝑬^(𝟐)

Ru(C6H6)(O,O) 118.44 (105.53) 70.46 188.9

RhCp(O,O) 83.71 (71.30) 125.00 208.71

IrCp(O,O) 16.09 (11.69) 192.49 208.58

NBO second order perturbation delocalization analysis was performed to determine donor–

acceptor orbital stabilization energies, E⁽²⁾, in the first transition state. Two significant stabilization energies were observed in the analysis: (1) interaction between bonding orbitals of methane and a vacant metal d orbital, E⁽²⁾ σ C-H → d^* M, and (2) interaction between lone pairs of oxygen atom and an antibonding orbital of methane, E⁽²⁾ LP O → σ ^* C-H. The values of E⁽²⁾ σ C-H → d^* M are 118.41, 83.71, and 16.09 kcal/mol for the Ru, Rh, and Ir complexes, respectively, indicating substantial donation from methane to the metal center in case of the Ru and Rh complexes but not in case of the Ir complex. The values of E⁽²⁾ LP O → σ ^* C-H are 70.46, 125, and 192.49 kcal/mol for the Ru, Rh, and Ir catalysts, respectively. The magnitude of these stabilization energies suggests that lone-pair donation to methane (attraction of the proton by one of the catalysts’ ligand oxygen atoms) makes an important contribution in activation of C-H bond in 1^st transition state. On the other hand, stabilization energies for the interaction between a filled metal d orbital and an antibonding orbital of methane, E⁽²⁾ dM → σ*C-H, are negligibly small (< 1 kcal/mol). Therefore, M-to-CH4 back-donation does not appear to contribute to the activation and cleavage of methane by these complexes.

The NBO analysis also shows that the relative contribution of the two components of the interaction changes from Ru(C6H6)(O,O) to RhCp(O,O) to IrCp(O,O), with the Ru complex relying predominantly on CH4-to-M donation and the Ir complex almost entirely on lone-pair donation back to CH4. Overall, these results present a quite different picture of the mode of small-molecule activation than that reported by Hou et al. for H2 activation, which consists of the traditional H2-to-M

26 donation and M-to-H2 back-donation components.

Fragment analysis of the interactions between the metal centers of the catalysts and methane was done to scrutinize the orbital interactions further (Figure 3). Table 8 shows the percent contributions of the atomic orbitals to the frontier molecular orbitals of the two fragments. The HOMO of the CH4 fragment has high contributions from the C px orbital in all of the three metal complexes (35-43 %) while the LUMO of the catalyst fragment is composed of 44% dx²-y² for Ru(C6H6)(O,O), 33% dx²-y² for RhCp(O,O), and 23% dxy and 14% dx²-y² for IrCp(O,O). These data imply that Ru(C6H6)(O,O) activates C-H bond more strongly by engaging it in strong σ interaction with the C px orbital to the Ru dx2-y2 orbital because of their complementary geometry for σ interaction. This interaction is much weaker for RhCp(O,O) and IrCp(O,O). (The dxy orbital has not the appropriate geometry for constructive interaction with the C px orbital.) Thus, the trend of the NBO stabilization energies for CH4-to-M donation can be explained in terms of atomic orbital contributions to the donor and acceptor orbitals of the participating species. No interaction was observed between the HOMO of the catalyst fragment and the LUMO of the CH4 fragment for any of the three cases.

Table 8. Orbital contributions of the frontier molecular orbitals of the two fragments at GTS1 state for different metals.

Ru(C6H6)(O,O)-CH4

Ru(C6H6)(O,O) CH4

HOMO LUMO HOMO LUMO

31.87 % O px 43.82 % Ru dx²-y² 42.48 % C px 50.66 % H 1s

18.34 % O pz 5.23 % Ru dxy 28.25 % H 1s 21.56 % H 2s

9.91 % Ru dz²

RhCp(O,O)-CH4

RhCp(O,O) CH4

HOMO LUMO HOMO LUMO

27.42 % O py 33.11 % Rh dx²-y² 39.98 % C px 49.13 % H 1s

19.22 % O pz 4.61 % Rh dxz 28.71 % H 1s 21.75 % H 2s

14.11 % Rh dz² 2.87 % Rh dxy

IrCp(O,O)-CH4

IrCp(O,O) CH4

HOMO LUMO HOMO LUMO

23.14 % O px 22.92 % Ir dxy 35.15 % C px 48.90 % H 1s

22.01 % O pz 13.78 % Ir dx²-y² 28.54 % H 1s 22.02 % H 2s 10.64 % Ir dz² 11.22 % O py

27

Figure 3. Orbital interactions between half-sandwich complexes (44: Ru of Ru(C6H6)(O,O); 45: Rh of RhCp(O,O); 77: Ir of IrCp(O,O)) and methane at 1^st transition state (GTS1 complex). [A: LUMO of catalyst, B: HOMO of catalyst, C: LUMO of CH4, and D: HOMO of CH4]

28

The second transition state paves the way to acetic acid formation by weakening the M-CH3

bond while a bond between the carbon atoms of the methyl group and CO2 is formed. The results of NBO analysis showed great differences between the three complexes. The most significant stabilization in the Ru complex results from the donation from the methyl group to an antibonding orbital of CO2, E⁽²⁾ LPCH3 → π*C-O = 154.9 kcal/mol; this already necessitates the strong possibility of fast acetic acid formation. Table 6 shows the additional weaker interactions between the methyl group and the Ru center as well as between CO2 and the Ru center that contribute to the stabilization of the transition state. However, it is also observed that no such interactions were found for the Rh and Ir complexes. For these complexes, it appears that a rather late transition state was computed, which resembles the products more closely than does the transition state for Ru(C6H6)(O,O). This is indicated by the presence of a C-C σ-bonding orbital involving the carbon atoms of the methylgroup and CO2. Interaction of this orbital with a vacant metal d orbital gives rise to a considerable stabilization energy (E⁽²⁾ σ CO2-CH3 → d*M) of 88.0 kcal/mol for RhCp(O,O) and a very high energy of 456.4 kcal/mol for IrCp(O,O). Due to the perceived bond formation between the methyl group and CO2 in these two cases and the different interactions between the fragments, the stabilization energies are difficult to compare with those of Ru(C6H6)(O,O).

Table 9. Second order stabilization energies (in kcal/mol) between natural orbitals of model complexes in 2^nd transition state.

𝑬^(𝟐)𝑳𝑷_𝐂𝐇𝟑

→ 𝛑_𝐂−𝐎^∗

𝑬^(𝟐) 𝝈 _𝑪−𝑯

→ 𝒅_𝑴^∗

𝑬^(𝟐) 𝝅 _𝑪−𝑶

→ 𝒅_𝑴^∗

𝑬^(𝟐) 𝒅_𝑴

→ 𝝈_𝐂𝐎𝟐^∗

𝑬^(𝟐)𝝈_{𝐂𝐎𝟐− 𝐂𝐇𝟑}

→ 𝐝_𝐌^∗

Ru(C6H6)(O,O) 154.9 37.5 7.66 0.44 N.A.

RhCp(O,O) N.A. N.A. N.A. N.A. 88.0

IrCp(O,O) N.A. N.A. N.A. N.A. 456.4

With this in regard, quantum theory of atoms in molecules (QTAIM) calculations were performed and rather interesting images were observed (Figure 4). For Ru(C6H6)(O,O), a possible bond path between the Ru center and CO2 as well as a probable hydrogen bond between an H atom of the benzene ligand and an oxygen atom of CO2 are indicated. The Ru–CO2 bond path may be attributed to the stabilization energies E⁽²⁾ πC-O → d*M = 7.66 kcal/mol and E⁽²⁾ d M → σ*CO2 = 0.44 kcal/mol obtained from the NBO analysis for Ru(C6H6)(O,O). These bond paths suggest the anchoring stabilization of both Ru and benzene for CO2, which could explain the comparably low activation energy for the Ru complex. In the case of Rh complex, hydrogen bonding between H atom of cyclopentadienyl ligand and O of CO2 is observed while there is lack of a Rh-CO2 interaction that makes Rh complex a less effective catalyst than Ru complex. The Ir complex showed neither a hydrogen bond now an Ir-CO2 interaction; hence, cannot anchor the CO2 molecule as opposed to Ru

29

and Rh catalysts. Thus, Ru(C6H6)(O,O) is the most effective catalyst for the second step of this reaction. In addition, a fragment analysis shows an interaction between the HOMO of the methyl group and the LUMO of CO2 for each of the three complexes.

Figure 4. Visualization of QTAIM calculation including the critical points and the respective bond paths for model catalysts with different metallic centers for 2^nd transition state (Visualization made by AIM 2000 package).

Ligand Effects on methane activation and acetic acid formation

As Ru-based catalyst was deemed the best for the two transition states, different ligands were used to determine which would provide best catalytic activity (Scheme 1). As shown in Figure 5, the energy profile of different ligands of Ru complex shows similar mechanism for all ligands. Table 10 presents the 1^st and 2^nd activation energies of Ru-based complex with varied ligands. Comparing the 1^st transition free energies of the ligands, (O,O), (P,P) and (N,NTs) have the three lowest values of 27.6, 25.9, and 32.3 kcal/mol, respectively. The rest of the ligands have > 2 kcal/mol difference from (N,NTs) in their 1^st TS. For the 2^nd TS, (O,O), (S,S), and (N,NTs) gave the lowest values of 26.7, 34.8, and 32.7 kcal/mol, respectively, while the other ligands have > 4 kcal/mol difference from (S,S).

30

Figure 5. Zero-point energy profile of catalysts with varying ligands attached to Ru metal center.

31

Table 10. Activation energies corrected for zero-point energies (ΔE^{0 K}), transition free energies (both in kcal/mol) and imaginary frequencies (IF, in cm^–1) of 1^st and 2^nd TS of model complexes in gas phase at 298 K.

Complexes TS1 TS2

𝛥𝐸_𝑔𝑎𝑠^{0 𝐾} 𝛥𝐺_𝑔𝑎𝑠^{298 𝐾} IF 𝛥𝐸_𝑔𝑎𝑠^{0 𝐾} 𝛥𝐺_𝑔𝑎𝑠^{298 𝐾} IF Ru(C6H6)(O,O) 26.0 27.6 -1406.1i 25.2 26.7 -447.0i Ru(C6H6)(N,N) 32.6 34.2 -1445.3i 41.3 41.6 -345.5i Ru(C6H6)(N,NTs) 30.9 32.3 -1458.4i 31.5 32.7 -431.2i Ru(C6H6)(N,O) 32.7 34.1 -1318.3i 44.6 44.9 -394.7i Ru(C6H6)(S,S) 34.9 36.5 -879.7i 33.6 34.8 -383.9i Ru(C6H6)(P,P) 24.5 25.9 -561.1i 37.4 38.7 -698.6i

Electronically, (N,NTs) has the tosyl group which is a known electron withdrawing group, withdrawing electrons both from nitrogen attached to it and the Ru metal center. This scenario would make the Ru more electrophilic, while the other N would still have its Lewis basicity. This makes (O,O) and (N,NTs) might have competing 1^st activation energies due to the similarity of their mechanism. The presence of d orbitals in phosphorus and sulfur atom may have significant effects on the complexes.

In the NBO analysis, (P,P) gave results that are different from the (O,O) and (N,NTs). It has a supposed bond formation between the Ru and C of methane, while the H to be abstracted was treated as a separate fragment. Furthermore, s* of H has interactions with Ru-CH3 (E⁽²⁾ σ Ru-CH3 → s*H = 360.15 kcal/mol), LP of P (E⁽²⁾ LP P → s*H =189.17 kcal/mol), and a d orbital of Ru (E⁽²⁾ d*M → s*H

= 109.68 kcal/mol). This could mean that H was abstracted easily from methane due to the strong interaction with all these three fragments; thus, it has a different approach on the stabilization of TS.

(N,NTs) showed the same NBO interactions with (O,O) with E⁽²⁾ σ C-H → d^* M = 198.56 kcal/mol and E⁽²⁾ LP N → σ ^* C-H = 70.99 kcal/mol. Based from these stabilization energies, (N,NTs) should have a lower activation energy than (O,O), but that was not observed. The d*M for both (O,O) and (N,NTs) comes from different possible d*M in the LUMO of model catalysts; however, not all d*M complement the interaction with σ C-H. (N,NTs) showed major contributions of 71.07 kcal/mol and 69.15 kcal/mol for 2 different d*M (not specified in NBO analysis) while (O,O) has only one major contributor of 118.85 kcal/mol. These results were confirmed by fragment analysis (Table 11 and Figure 6) of (N,NTs) that exhibited 25 % of dxy and 20 % dx2-y2 contributions for its LUMO as compared with 44 % dx2-y2 LUMO of (O,O). Hence, NBO and fragment analyses showed there is weaker Ru-CH3

interaction for (N,NTs) due to less dx2-y2 which would provide weaker σ interaction with methane’s px

32

orbital as compared with Ru(C6H6)(O,O) complex. In the case of (P,P), fragment analyses showed a 48 % dx2-y2 contribution to LUMO of Ru(C6H6)(O,O) and 40 % H 1s and 39 % C px contribution to HOMO of CH4 but this could not explain well yet about the NBO interactions.

Table 11. Orbital contributions of the frontier molecular orbitals of the two fragments at GTS1 state for different ligands.

Ru(C6H6)(O,O)-CH4

Ru(C6H6)(O,O) CH4

HOMO LUMO HOMO LUMO

31.87 % O px 43.82 % Ru dx²-y² 42.48 % C px 50.66 % H 1s

18.34 % O pz 5.23 % Ru dxy 28.25 % H 1s 21.56 % H 2s

9.91 % Ru dz²

Ru(C6H6)(N,NTs)-CH4

Ru(C6H6)(N,NTs) CH4

HOMO LUMO HOMO LUMO

27.10 % N px 24.93 % Ru dxy 36.24 % C px 45.57 % H 2s

12.27 % N px (other side)

19.57 % Ru dx²-y² 27.05 % H 1s 24.08 % H 1s

11.58 % Ru dxz 9.02 % N px

Ru(C6H6)(P,P)-CH4

Ru(C6H6)(P,P) CH4

HOMO LUMO HOMO LUMO

32.79 % Ru dxz 47.78 % Ru dx²-y² 39.62 % H 1s 59.19 % H 1s

17.33 % P pz 39.41 % C px 26.82 % C px

11.50 % P px

33

Figure 6. Orbital interactions between half-sandwich complexes (8: O of Ru(C6H6)(O,O); 7: N of Ru(C6H6)(N,NTs); 15: P of Ru(C6H6)(P,P)) and methane at 1^st transition state (GTS1 complex). [A: LUMO of catalyst, B: HOMO of catalyst, C: LUMO of CH4, and D: HOMO of CH4]

34

QTAIM analysis (see Appendix 1b) showed similar bond paths for (O,O) and (N,NTs) while (P,P) showed no bond paths between abstracted H and CH3, and abstracted H and P for its 1^st TS, but there is still bond path between Ru and abstracted H. The imaginary frequency of (P,P) is quite different from the other catalysts (besides (S,S)) due to the presence of d orbitals. Based on the direction of vibration, the proton of methane is nearer to the metal due to the electron-rich character of the latter, suggesting the attraction between the two species which were confirmed by QTAIM bond critical point that is present only for Ru-H and Ru-CH3 and NBO charges of -1.020 au for Ru in (P,P) (as opposed with the cases of (O,O): 0.110 and (N,NTs): -0.046) and +0.304 for abstracted H in (P,P) (as opposed with the cases of (O,O): 0.418 and (N,NTs): 0.394). NBO charges of interacting atoms of ligands are shown in Table 12.

Table 12. NBO charges of interacting atoms in the 1^st and 2^nd transition states of model catalysts with varying ligands.

Complexes

TS1 TS2

Metal Ligand H – CH4

C in CH4

Metal Ligand H – CH4

C – CH4

C – CO2

Ru(C6H6)(O,O) 0.110 -0.721 0.418 -0.922 0.107 -0.692 0.540 -0.894 1.004 Ru(C6H6)(N,N) -0.057 -0.868 0.392 -0.901 -0.025 0.772 0.444 -0.866 0.982 Ru(C6H6)(N,NTs) -0.046 -0.852 0.394 -0.902 -0.021 -0.779 0.446 -0.917 1.009 Ru(C6H6)(N,O) -0.024 -0.711 0.409 -0.865 0.026 -0.686 0.540 -0.887 1.005 Ru(C6H6)(S,S) -0.597 0.132 0.259 -0.798 -0.482 0.314 0.210 -0.860 0.980 Ru(C6H6)(P,P) -1.020 0.412 0.304 -0.675 -0.739 0.809 0.043 -0.850 0.953

Table 13. Reactivity indices, in a.u., of the three model catalysts with the least first activation energy:

µ represents chemical potential, ƞ is chemical hardness and ω is global electrophilicity index.

Complexes HOMO LUMO µ ƞ ω

Ru(C6H6)(O,O) -0.20547 -0.06833 -0.1369 0.13714 0.06833

Ru(C6H6)(N,NTs) -0.20373 -0.06451 -0.13412 0.13922 0.064603

Ru(C6H6)(P,P) -0.18912 -0.06376 -0.12644 0.12536 0.063765

Reactivity indices (Table 13) of the three model catalysts were calculated to verify which has higher global electrophilicity index to complement the NBO charges, and as it turned out Ru(C6H6)(O,O) (ω = 0.0683) is more electrophilic than Ru(C6H6)(N,NTs) (ω = 0.0646) while Ru(C6H6)(P,P) proved to be least electrophilic (ω = 0.0638). This makes (O,O) a better suited ligand for Ru metallic center than (N,NTs), making it more viable to attract the nucleophilic CH3-; while (P,P) made the complex more nucleophilic, attracting the electrophilic H⁺. Hence, (P,P) ligand has similar