Insights into the Fluxional Processes of Monomethylcyclohexenyl Manganese Tricarbonyl

Multiple fluxional processes of 6-monomethylcyclohexenylmanganese tricarbonyl [(6-MeC6H8)Mn(CO)3, complex 1] and 5-monomethylcyclohexenylmanganese tricarbonyl [(5-MeC6H8)Mn(CO)3, complex 2] have been explored using density functional theory (DFT) computations. The contributions of four agostomers—1, 2, 3, and 4—to the (MeC6H8)Mn(CO)3 exchange processes were revealed. The computational results demonstrated that the 1, 2-agostic isomerization only occurred via the η4-diene hydride transition state (TS-1-2, 14.0 kcal/mol), which is consistent with the experimentally proposed high-energy exchange process (16.0 kcal/mol). Excellent agreement is observed (R2 = 0.9862) when comparing the computed and experimentally observed variable temperature 1H NMR chemical shifts. With these results, important insights into the role of agostic interaction in the homogeneous catalysis process could be made, especially with regard to transition metal catalyzed C-H activation.

Several 1 H NMR resonances of complex 1 and 2, such as 6Hexo of complex 1 and 2 and 3H of complex 2, could not be properly assigned experimentally due to the spectral complexities [4]. The experimental 1 H NMR resonances indicated that the 5Hexo (0.4 ppm) of complex 2 was quite different from the 5Hexo (2.2 ppm) and 6Hexo (1.2 ppm) of 5, 6-dimethyl analogue [5, 6-dimethyl cyclohexenyl manganese tricarbonyl, (5, 6-Me2C6H7)Mn(CO)3]. The proton chemical shift of the 6-methyl group (0.1 ppm) of complex 1 was also inconsistent with that of the 5-methyl group (0.6 ppm) of complex 2, 5-methyl (0.8 ppm), and 6-methyl (0.7 ppm) of the 5, 6-dimethyl analogue [1,4]. These inconsistencies raised the question of how the accurate 1 H NMR spectra of these complexes with multiple exchange processes could be found. Previous results demonstrated the important role of the chair agostomer with weak agostic interaction (complex 3, Scheme 2) in the fluxionality of the unsubstituted analogue [(C6H9)Mn(CO)3] [5]. Two possible chair agostomers (complexes 3 and 4, Scheme 2) could also exist during the conversion between 6-monomethyl (complex 1) and 5-monomethyl systems (complex 2). However, some difficulty was encountered in experiments to clarify the nature of the M-H-C bond (agostic or anagostic interaction) of the second chair conformation (complex 4), which is caused by the effect of the substituted methyl group. The purposes of this study are to understand the fluxionalities of the monomethyl cyclohexenyl manganese tricarbonyl [(MeC6H8)Mn(CO)3, complex 1 and 2], to accurately characterize the Mn-H-C agostic interaction for the isomers, to correctly investigate these multiple exchange processes of (MeC6H8)Mn(CO)3, and to computationally simulate the accurate 1 H NMR spectra of these exchange processes. The results could potentially establish insights into the role of Mn-H-C agostic interaction in the homogeneous catalysis [6][7][8].

Structure and Bonding
The PBEPBE/BS1-Auto optimized gas-phase structures of 6-monomethyl isomer (complex 1, Figure 1) and 5-monomethyl isomer (complex 2, Figure 1) showed they were halfchair conforms. The computationally optimized 6-monomethyl isomer (complex 1, Figure   Scheme 1. Structures of 6-monomethyl, 5-monomethyl isomers of (MeC 6 H 8 )Mn(CO) 3 and the proposed transition state. Several 1 H NMR resonances of complex 1 and 2, such as 6H exo of complex 1 and 2 and 3H of complex 2, could not be properly assigned experimentally due to the spectral complexities [4]. The experimental 1 H NMR resonances indicated that the 5H exo (0.4 ppm) of complex 2 was quite different from the 5H exo (2.2 ppm) and 6H exo (1.2 ppm) of 5, 6-dimethyl analogue [5, 6-dimethyl cyclohexenyl manganese tricarbonyl, (5, 6-Me 2 C 6 H 7 )Mn(CO) 3 ]. The proton chemical shift of the 6-methyl group (0.1 ppm) of complex 1 was also inconsistent with that of the 5-methyl group (0.6 ppm) of complex 2, 5-methyl (0.8 ppm), and 6-methyl (0.7 ppm) of the 5, 6-dimethyl analogue [1,4]. These inconsistencies raised the question of how the accurate 1 H NMR spectra of these complexes with multiple exchange processes could be found. Previous results demonstrated the important role of the chair agostomer with weak agostic interaction (complex 3, Scheme 2) in the fluxionality of the unsubstituted analogue [(C 6 H 9 )Mn(CO) 3 ] [5]. Two possible chair agostomers (complexes 3 and 4, Scheme 2) could also exist during the conversion between 6-monomethyl (complex 1) and 5-monomethyl systems (complex 2). However, some difficulty was encountered in experiments to clarify the nature of the M-H-C bond (agostic or anagostic interaction) of the second chair conformation (complex 4), which is caused by the effect of the substituted methyl group.
Molecules 2023, 28, x FOR PEER REVIEW 2 of 12 possible transition states, made it inconvenient to assign resonances in the variable temperature 1 H NMR spectra.
Several 1 H NMR resonances of complex 1 and 2, such as 6Hexo of complex 1 and 2 and 3H of complex 2, could not be properly assigned experimentally due to the spectral complexities [4]. The experimental 1 H NMR resonances indicated that the 5Hexo (0.4 ppm) of complex 2 was quite different from the 5Hexo (2.2 ppm) and 6Hexo (1.2 ppm) of 5, 6-dimethyl analogue [5, 6-dimethyl cyclohexenyl manganese tricarbonyl, (5, 6-Me2C6H7)Mn(CO)3]. The proton chemical shift of the 6-methyl group (0.1 ppm) of complex 1 was also inconsistent with that of the 5-methyl group (0.6 ppm) of complex 2, 5-methyl (0.8 ppm), and 6-methyl (0.7 ppm) of the 5, 6-dimethyl analogue [1,4]. These inconsistencies raised the question of how the accurate 1 H NMR spectra of these complexes with multiple exchange processes could be found. Previous results demonstrated the important role of the chair agostomer with weak agostic interaction (complex 3, Scheme 2) in the fluxionality of the unsubstituted analogue [(C6H9)Mn(CO)3] [5]. Two possible chair agostomers (complexes 3 and 4, Scheme 2) could also exist during the conversion between 6-monomethyl (complex 1) and 5-monomethyl systems (complex 2). However, some difficulty was encountered in experiments to clarify the nature of the M-H-C bond (agostic or anagostic interaction) of the second chair conformation (complex 4), which is caused by the effect of the substituted methyl group. The purposes of this study are to understand the fluxionalities of the monomethyl cyclohexenyl manganese tricarbonyl [(MeC6H8)Mn(CO)3, complex 1 and 2], to accurately characterize the Mn-H-C agostic interaction for the isomers, to correctly investigate these multiple exchange processes of (MeC6H8)Mn(CO)3, and to computationally simulate the accurate 1 H NMR spectra of these exchange processes. The results could potentially establish insights into the role of Mn-H-C agostic interaction in the homogeneous catalysis [6][7][8].

Structure and Bonding
The PBEPBE/BS1-Auto optimized gas-phase structures of 6-monomethyl isomer (complex 1, Figure 1) and 5-monomethyl isomer (complex 2, Figure 1) showed they were halfchair conforms. The computationally optimized 6-monomethyl isomer (complex 1, Figure   Scheme  The purposes of this study are to understand the fluxionalities of the monomethyl cyclohexenyl manganese tricarbonyl [(MeC 6 H 8 )Mn(CO) 3 , complex 1 and 2], to accurately characterize the Mn-H-C agostic interaction for the isomers, to correctly investigate these multiple exchange processes of (MeC 6 H 8 )Mn(CO) 3 , and to computationally simulate the accurate 1 H NMR spectra of these exchange processes. The results could potentially establish insights into the role of Mn-H-C agostic interaction in the homogeneous catalysis [6][7][8].

Structure and Bonding
The PBEPBE/BS1-Auto optimized gas-phase structures of 6-monomethyl isomer (complex 1, Figure 1) and 5-monomethyl isomer (complex 2, Figure 1) showed they were half-chair conforms. The computationally optimized 6-monomethyl isomer (complex 1, Figure 1) matched well with the reported X-ray crystal structure (CSD entry: BEZYEK) [2], and the RMSD (root mean square deviation) for atoms without H was 0.037 Å (Table S1). A negligible effect of dispersion correction on the optimized gas-phase structure was observed, and the RMSD (root mean square deviation) for PBEPBE-D3(BJ)/BS1-Auto was  (Table S1). The agostic bonding characters [9,10], such as the M-H bond length, the C-H bond length, the proton chemical shifts, and the spin coupling constants (J CH ) of the optimized structures of complexes 1, 2, and two other complexes 3, 4 are listed in Table 1.
Molecules 2023, 28, x FOR PEER REVIEW 3 of 12 1) matched well with the reported X-ray crystal structure (CSD entry: BEZYEK) [2], and the RMSD (root mean square deviation) for atoms without H was 0.037 Å (Table S1). A negligible effect of dispersion correction on the optimized gas-phase structure was observed, and the RMSD (root mean square deviation) for PBEPBE-D3(BJ)/BS1-Auto was 0.034 Å (Table  S1). The agostic bonding characters [9,10], such as the M-H bond length, the C-H bond length, the proton chemical shifts, and the spin coupling constants (JCH) of the optimized structures of complexes 1, 2, and two other complexes 3, 4 are listed in Table 1.  The prolonged C-H bond length (Hendo vs. Hexo), and the upfield proton chemical shifts (Hendo vs. Hexo) were all observed for complexes 1, 2, 3, and 4 (Table 1), which clearly demonstrated the existence of the Mn-C-H agostic interaction [9,11]. The Mn-C-H bond angle in complex 1 is 97.6°, which is notable for being slightly smaller than that of complex 2 (97.9°). The Mn-H bond distance in complex 1 is 1.849 Å, which is also slightly longer than that of complex 2 (1.844 Å). The observed Mn-C-H bond angles and Mn-H bond distances in complexes 1 and 2 demonstrated that the strengths of the Mn-C-H agostic interaction in complexes 1 and 2 are equivalent. This is also supported by the AIM (atoms-inmolecules) analysis of the optimized complexes 1 and 2 ( Figure 2). The electron density of the Mn-H bond critical points (ρBCP) in complexes 1 and 2 are 0.0477 and 0.0471, respectively. Negligible differences of the electron density of C-H(endo) bond critical points (ρBCP) in complexes 1 (0.2142, Figure 2) and 2 (0.2144, Figure 2) were also observed. The Mn-C-H bond angle in complexes 3 and 4 are 104.6° and 130.0°, respectively, which are significantly bigger that those in complexes 1 (97.6°, Table 1) and 2 (97.9°, Table 1). The C-H(endo) bond distance in complexes 3 and 4 are 1.136 Å and 1.131 Å, respectively, which are considerably shorter that those in complexes 1 (1.180 Å, Table 1) and 2 (1.179 Å, Table 1). The relatively stronger C-H(endo) bonds in complexes 3 and 4 are also verified by the higher electron density of C-H(endo) bond critical points, and ρ(BCP, C-H) for C-H(endo) bond in complexes 3 and 4 are 0.2404 and 0.2389, respectively. A weak Mn-C-H agostic interaction is characterized by a strong C-H(endo) bond and a weak Mn-C-H bond [6], and complex 3 has a much weaker Mn-C-H agostic interaction than complex 4. The Laplacian of the electron density (∇ 2 ρ) is utilized in classifying the covalent interaction (locally concentrated with ∇ 2 ρ < 0) and the non-covalent interaction (locally depleted with ∇ 2 ρ > 0) [12,13]. With

Structures
Mn-H (Å) The prolonged C-H bond length (H endo vs. H exo ), and the upfield proton chemical shifts (H endo vs. H exo ) were all observed for complexes 1, 2, 3, and 4 (Table 1), which clearly demonstrated the existence of the Mn-C-H agostic interaction [9,11]. The Mn-C-H bond angle in complex 1 is 97.6 • , which is notable for being slightly smaller than that of complex 2 (97.9 • ). The Mn-H bond distance in complex 1 is 1.849 Å, which is also slightly longer than that of complex 2 (1.844 Å). The observed Mn-C-H bond angles and Mn-H bond distances in complexes 1 and 2 demonstrated that the strengths of the Mn-C-H agostic interaction in complexes 1 and 2 are equivalent. This is also supported by the AIM (atoms-in-molecules) analysis of the optimized complexes 1 and 2 ( Figure 2). The electron density of the Mn-H bond critical points (ρ BCP ) in complexes 1 and 2 are 0.0477 and 0.0471, respectively. Negligible differences of the electron density of C-H (endo) bond critical points (ρ BCP ) in complexes 1 (0.2142, Figure 2) and 2 (0.2144, Figure 2) were also observed. The Mn-C-H bond angle in complexes 3 and 4 are 104.6 • and 130.0 • , respectively, which are significantly bigger that those in complexes 1 (97.6 • , Table 1) and 2 (97.9 • , Table 1). The C-H (endo) bond distance in complexes 3 and 4 are 1.136 Å and 1.131 Å, respectively, which are considerably shorter that those in complexes 1 (1.180 Å, Table 1) and 2 (1.179 Å, Table 1). The relatively stronger C-H (endo) bonds in complexes 3 and 4 are also verified by the higher electron density of C-H (endo) bond critical points, and ρ (BCP, C-H) for C-H (endo) bond in complexes 3 and 4 are 0.2404 and 0.2389, respectively. A weak Mn-C-H agostic interaction is characterized by a strong C-H (endo) bond and a weak Mn-C-H bond [6], and complex 3 has a much weaker Mn-C-H agostic interaction than complex 4. The Laplacian of the electron density (∇ 2 ρ) is utilized in classifying the covalent interaction (locally concentrated with ∇ 2 ρ < 0) and the non-covalent interaction (locally depleted with ∇ 2 ρ > 0) [12,13]. With regard to the C-H BCPs, the ∇ 2 ρ is evidently negative, which strongly demonstrates the covalent nature of the C-H bonds ( Figure 2). The ionic Mn-H interaction is demonstrated by the positive ∇ 2 ρ the Mn-H BCPs. The absolute values of ∇ 2 ρ correspond to the strengths of the covalent and non-covalent interaction, and the order of C-H is 3 > 4 > 2~1. The observed values of the Laplacian of the electron density (∇ 2 ρ) of the Mn-H and C-H BCPs are consistent with the relative strengths of Mn-C-H agostic interaction in complexes 1, 2, 3, and 4. Based on the above discussions, complexes 1 and 2 could be assigned as the classical agostomers with a stronger Mn-C-H agostic interaction, but only a weak Mn-C-H agostic interaction could be presented in complexes 3 and 4. Therefore, the order of the relative strengths of the Mn-C-H agostic interaction in complexes 1, 2, 3 and 4 is 1~2 > 4 > 3.

C-H (Å) H (ppm) J CH (Hz
regard to the C-H BCPs, the ∇ 2 ρ is evidently negative, which strongly demonstrates the covalent nature of the C-H bonds ( Figure 2). The ionic Mn-H interaction is demonstrated by the positive ∇ 2 ρ the Mn-H BCPs. The absolute values of ∇ 2 ρ correspond to the strengths of the covalent and non-covalent interaction, and the order of C-H is 3 > 4 > 2 ~ 1. The observed values of the Laplacian of the electron density (∇ 2 ρ) of the Mn-H and C-H BCPs are consistent with the relative strengths of Mn-C-H agostic interaction in complexes 1, 2, 3, and 4. Based on the above discussions, complexes 1 and 2 could be assigned as the classical agostomers with a stronger Mn-C-H agostic interaction, but only a weak Mn-C-H agostic interaction could be presented in complexes 3 and 4. Therefore, the order of the relative strengths of the Mn-C-H agostic interaction in complexes 1, 2, 3 and 4 is 1 ~ 2 > 4 > 3. The computed proton shifts showed that Hs in the Mn-H-C agostic unit of agostomers 1 (−9.8 ppm) and 2 (−9.9 ppm) were more shielded to those in the agostomers 3 (−5.5 ppm) and 4 (−8.7 ppm) ( Table 1). Upon the introduction of extra magnetic fields, the agostomers 1 and 2 with the η 4 -(MeC6H8) fragment could form the pseudo ring current, generating outside-the-ring deshielded protons (non-agostic protons) and inside-the-ring shielded protons (agostic protons) ( Figure S3). A similar effect could also be proposed for agostomers 3 and 4; however, the presence of the η 3 -(MeC6H8) fragment in agostomers 3 and 4 instead of the η 4 -(MeC6H8) fragment in the agostomers 1 and 2 made the inside-thering protons (agostic protons) less shielded. It is also notable that the Mn-H distances in agostomers 1 and 2 are 1.849 Å and 1.844 Å (Table 1), respectively, which suggests that the agostic H in the Mn-H-C agostic unit could be treated as a classical hydride. The shielding from the d orbitals of Mn to the agostic hydride is critical and nonnegligible, and the shielded agostic hydride at very upfield conditions is expected. However, the Mn-H distances in agostomers 3 and 4 are 2.051 Å and 1.958 Å, respectively, which is significantly longer that those in agostomers 1 and 2. The relatively weak Mn-H interactions in agostomers 3 and 4 suggest that it should be an agostic proton in the Mn-H-C agostic unit instead of the hydride. Therefore, the more shielded agostic H in the Mn-H-C agostic unit in agostomers 1 and 2 was observed. The computed proton shifts showed that Hs in the Mn-H-C agostic unit of agostomers 1 (−9.8 ppm) and 2 (−9.9 ppm) were more shielded to those in the agostomers 3 (−5.5 ppm) and 4 (−8.7 ppm) ( Table 1). Upon the introduction of extra magnetic fields, the agostomers 1 and 2 with the η 4 -(MeC 6 H 8 ) fragment could form the pseudo ring current, generating outside-the-ring deshielded protons (non-agostic protons) and inside-the-ring shielded protons (agostic protons) ( Figure S3). A similar effect could also be proposed for agostomers 3 and 4; however, the presence of the η 3 -(MeC 6 H 8 ) fragment in agostomers 3 and 4 instead of the η 4 -(MeC 6 H 8 ) fragment in the agostomers 1 and 2 made the inside-the-ring protons (agostic protons) less shielded. It is also notable that the Mn-H distances in agostomers 1 and 2 are 1.849 Å and 1.844 Å (Table 1), respectively, which suggests that the agostic H in the Mn-H-C agostic unit could be treated as a classical hydride. The shielding from the d orbitals of Mn to the agostic hydride is critical and nonnegligible, and the shielded agostic hydride at very upfield conditions is expected. However, the Mn-H distances in agostomers 3 and 4 are 2.051 Å and 1.958 Å, respectively, which is significantly longer that those in agostomers 1 and 2. The relatively weak Mn-H interactions in agostomers 3 and 4 suggest that it should be an agostic proton in the Mn-H-C agostic unit instead of the hydride. Therefore, the more shielded agostic H in the Mn-H-C agostic unit in agostomers 1 and 2 was observed.

Exchange Processes
Previous studies suggested that complexes 1 and 2 also were fluxional molecules [1]. However, possible multiple exchange processes made it difficult to distinguish each resonance in the variable temperature 1 H NMR spectra. Only two exchange processes of the monomethyl cyclohexenyl manganese tricarbonyl (MeC 6 H 8 )Mn(CO) 3 ) could be found in the experimentally obtained 1 H NMR spectra: (1) a low-energy process estimated as 8.3 kcal/mol proceeding through the fast endo C-H exchange and (2) a high-energy exchange process estimated as 16.0 kcal/mol proceeding through the diene hydride species [1].
These values are quite similar to the parent system cyclohexenyl manganese tricarbonyl (C 6 H 9 )Mn(CO) 3 (8.3 kcal/mol and 15.4 kcal/mol) [2]. In order to comprehensively interpret the 1 H NMR spectra, explorations of the mechanisms in the exchange processes of complexes 1 and 2 were carried out. The following possible exchange processes were examined: agostomers conformational isomerization, conversion between agostomers and hydride species, and hydride species conversions.

Interpretations of the Fluxionality
Based on the computational results, several important facts about the fluxionalities of the monomethyl cyclohexenylmanganese tricarbonyl [(MeC6H8)Mn(CO)3, complex 1 and 2] were discovered. First, the methyl rotational energy barriers in complexes 1, 2, 3, and 4 showed different patterns. Compared to complexes 1 (3.2 kcal/mol, energy relative to complex 1), 2 (3.6 kcal/mol, relative to complex 2), and 3 (2.8 kcal/mol, relative to complex 3), complex 4 had much higher methyl rotational activation energy (5.3 kcal/mol, relative to complex 4). This fact supported the conclusion on the weak M-H-C agostic interaction in complex 4. Unlike the free methyl group in complexes 1, 2, and 3, the weak Mn-

Interpretations of the Fluxionality
Based on the computational results, several important facts about the fluxionalities of the monomethyl cyclohexenylmanganese tricarbonyl [(MeC 6 H 8 )Mn(CO) 3 , complex 1 and 2] were discovered. First, the methyl rotational energy barriers in complexes 1, 2, 3, and 4 showed different patterns. Compared to complexes 1 (3.2 kcal/mol, energy relative to complex 1), 2 (3.6 kcal/mol, relative to complex 2), and 3 (2.8 kcal/mol, relative to complex 3), complex 4 had much higher methyl rotational activation energy (5.3 kcal/mol, relative to complex 4). This fact supported the conclusion on the weak M-H-C agostic interaction in complex 4. Unlike the free methyl group in complexes 1, 2, and 3, the weak Mn-H-C agostic interaction in complex 4 made two sets of inequivalent H toms (1 endo H and 2 exo H's). The next fluxional process was the rotation of Mn(CO) 3 fragment. The higher reaction free energies of the weak Mn-H-C agostomer 4 compared to agostomer 1, 2, and 3 made it exclude from this CO's ligand equivalence process. Although the 5-monomethyl agostomer (complex 2) could not adopt the similar η 3 -allyl transition state (TS-3) of 6monomethyl agostomer to perform the fast exchange of the two endo Hs adjacent to the terminal positions of the allylic unit, the neighboring endo H exchange (1H endo and 6H endo ) of complex 2 was achieved by a higher energy C 1 symmetrical η 3 -allyl transition state (TS-2-3, 12.9 kcal/mol). Another endo H exchange in complex 1 was the exchange between 5H endo and methyl endo , TS-1-4. The conversion between complex 1 and complex 2 could be accomplished by a single H transfer process (TS-1-2, 14.0 kcal/mol) or by a series of three η 4diene hydride minima. However, the relative high activation energy of the second pathway suggested the high temperature conversion between complex 1 and complex 2 could only occur through η 4 -diene hydride transition state, TS-1-2. Notably, the conversion between complexes 1, 2 and the η 4 -diene hydride minima, complexes 7 and 9 (Scheme 3) could complicate the 1 H NMR spectrum of (MeC 6 H 8 )Mn(CO) 3  Based on the discussion above, the gas phase variable temperature 1 H NMR spectra of (6-MeC6H8)Mn(CO)3 and (5-MeC6H8)Mn(CO)3 were simulated ( Figure 5). An excellent linear relationship (R 2 = 0.9862) between the computed proton chemical shifts and the experimental 1 H NMR chemical shifts ( Figure 6) was reached. The simulated low temperature exchange (methyl rotation TS-1-1-a) and medium temperature exchange (fast exchange of the endo H's adjacent to the terminal positions of the allylic unit, TS-1-1-c) showed that the resonance of the methyl group was 0.77 ppm, which was close to the experimental reported methyl group (0.6 ppm) of complex 2, 5-methyl (0.8 ppm) and 6methyl (0.7 ppm) of the 5, 6-dimethyl analogue. In medium temperature, the Cs symmetrical TS-3 made 2H and 3H equivalent, 1Hendo and 4Hendo equivalent, and 1Hexo and 4Hexo equivalent, which gave six peaks in the 1 H NMR spectrum. In the next high temperature regime, slow endo H exchange between the H5endo and methylendo (TS-1-4) process averaged the 1Hendo, 5Hendo and methylendo. Unlike the two resonances in the super-high temperature 1   Based on the discussion above, the gas phase variable temperature 1 H NMR spectra of (6-MeC 6 H 8 )Mn(CO) 3 and (5-MeC 6 H 8 )Mn(CO) 3 were simulated ( Figure 5). An excellent linear relationship (R 2 = 0.9862) between the computed proton chemical shifts and the experimental 1 H NMR chemical shifts ( Figure 6) was reached. The simulated low temperature exchange (methyl rotation TS-1-1-a) and medium temperature exchange (fast exchange of the endo H's adjacent to the terminal positions of the allylic unit, TS-1-1-c) showed that the resonance of the methyl group was 0.77 ppm, which was close to the experimental reported methyl group (0.6 ppm) of complex 2, 5-methyl (0.8 ppm) and 6-methyl (0.7 ppm) of the 5, 6-dimethyl analogue. In medium temperature, the C s symmetrical TS-3 made 2H and 3H equivalent, 1H endo and 4H endo equivalent, and 1H exo and 4H exo equivalent, which gave six peaks in the 1 H NMR spectrum. In the next high temperature regime, slow endo H exchange between the H5 endo and methyl endo (TS-1-4) process averaged the 1H endo , 5H endo and methyl endo . Unlike the two resonances in the super-high temperature 1 H NMR of the unsubstituted analogue [(C 6 H 9 )Mn(CO) 3 ] [5], the asymmetric 1, 2-agostic isomerization (TS-1-2) process finally gave three peaks for the highest temperature in the 1 H NMR spectrum.
linear relationship (R = 0.9862) between the computed proton chemical shifts and the experimental 1 H NMR chemical shifts ( Figure 6) was reached. The simulated low temperature exchange (methyl rotation TS-1-1-a) and medium temperature exchange (fast exchange of the endo H's adjacent to the terminal positions of the allylic unit, TS-1-1-c) showed that the resonance of the methyl group was 0.77 ppm, which was close to the experimental reported methyl group (0.6 ppm) of complex 2, 5-methyl (0.8 ppm) and 6methyl (0.7 ppm) of the 5, 6-dimethyl analogue. In medium temperature, the Cs symmetrical TS-3 made 2H and 3H equivalent, 1Hendo and 4Hendo equivalent, and 1Hexo and 4Hexo equivalent, which gave six peaks in the 1 H NMR spectrum. In the next high temperature regime, slow endo H exchange between the H5endo and methylendo (TS-1-4) process averaged the 1Hendo, 5Hendo and methylendo. Unlike the two resonances in the super-high temperature 1 H NMR of the unsubstituted analogue [(C6H9)Mn(CO)3] [5], the asymmetric 1, 2-agostic isomerization (TS-1-2) process finally gave three peaks for the highest temperature in the 1 H NMR spectrum. Figure 5. Simulated gas phase 1 H NMR spectra of (MeC6H8)Mn(CO)3 at low temperature limit (black), low temperature exchange (blue), medium temperature exchange (orange), high temperature fast exchange (purple), and highest temperature fast exchange (red).

Computational Methods
Molecular structures were optimized in the gas phase using the Perdew, Burke, and Ernzerhof exchange functional and gradient-corrected correlation functional (PBEPBE) [15] with basis set 1 and the density fitting approximation [16,17] (BS1, the modified-LANL2DZ with the f polarization [(modified-LANL2DZ(f)] [18][19][20] and related effective core potential (ECP, LANL2DZ) for Mn atom, LANL2DZ(d, p) [21,22] with the related LANL2DZ ECP for Si atom of the reference TMS, and the 6-31G (d ) [23][24][25] for all other atoms (C, O, and H)). All computations (PBEPBE/BS1-Auto) were carried out with Gaussian 09 software (Revision C01) [26]. Pruned fine integration grids with 75 radial shells and 302 angular points per shell were used for all computations. Free energy corrections were computed at 1 atm and 298.15 K. Optimization using Grimme's D3 [27] dispersion with Becke-Johnson damping (D3(BJ)) [28] was also compared (PBEPBE-D3(BJ)/BS1-Auto). For comparisons, the single-point energy calculations using Def2-TZVPP basis sets (BS3, Def2-TZVPP for Mn, C, O, and H) for serval salient transition states were also performed (see Supplementary Materials, Figures S1 and S2). All located minima were verified by vibrational frequency computations with no imaginary frequency, and all located transition states were obtained with only one imaginary frequency. The intrinsic reaction coordinate computations from the located transition states were performed, and both directions of the reaction path following the transition state were computed [29]. The electron density of the bond critical point [ρ (BCP) ] based on Bader's theory of atoms-in-molecules (AIM) [12,30,31] was calculated with the Multiwfn package (version 3.8) [32,33], and were visualized with the VMD package (version 1.9.3) [34,35]. Notably, the reliability of quantum mechanics (QM) computation instead of molecular dynamics (MD) simulation in the study of the fluxional processes of organometallics has been established [5,36].

Conclusions
Compared to the unsubstituted analogue [(C 6 H 9 )Mn(CO) 3 ], multiple exchange processes in the fluxionalities of the monomethyl cyclohexenyl manganese tricarbonyl [(MeC 6 H 8 )Mn(CO) 3 ] were revealed. First, two different conversion pathways between agostomer 1 (6-monomethyl) and agostomer 2 (6-monomethyl) were located: (1) via the η 4 -diene hydride transition state; and (2) via three η 4 -diene hydride minima. The computational results demonstrated that the 1, 2-agostic isomerization only occurred via the η 4 -diene hydride transition state (TS-1-2, 14.0 kcal/mol). The previously proposed two exchange processes, including a low-energy fast endo C-H exchange and a high-energy exchange process proceeding through the diene hydride species, were verified. The computed Gibbs barriers are 6.0 kcal/mol and 14.0 kcal/mol, respectively, for these exchange processes, which are consistent with the experimentally estimated barriers (8.3 kcal/mol and 16.0 kcal/mol). Other exchange processes, such as methyl group rotation, CO ligand equivalence, fast exchange of the endo H's in agostomer 1, low exchange of the neighboring endo H in agostomer 2, low endo H exchange between 5H (endo) and methyl (endo) in complex 1, and the possible high temperature H atom migration of the agostic Mn-H-C unit were also studied. Moreover, the bonding characters and the AIM (atoms-in-molecules) analyses of complexes 3 and 4 demonstrated 3 and 4 also were agostomers with weak Mn-H-C agostic interaction compared to agostomers 1 and 2. Finally, the gas-phase variable temperature 1 H NMR spectra of (MeC 6 H 8 )Mn(CO) 3 based on the exchange processes provided were simulated, and the detailed resonances were revealed. These results could potentially establish fundamental insights into the role of agostic interaction in the homogeneous catalysis, especially with regard to transition metal catalyzed C-H activation.