Unveiling the Unusual Mn(CO)3 Migration in a Manganese Cyclohexenyl Complex by DFT Computations

Homogeneous catalysis involving a transition metal agostic interaction (TM…H…C) is an attractive strategy for C–H bond activation, in which the transition metal agostic intermediates serve as the critical component. To investigate the roles of manganese agostic intermediates in the unusual migration of the Mn(CO)3 fragment in the (exo-phenyl)(η3-cyclohexenyl)manganese tricarbonyl [(Ph)(η3-C6H8)Mn(CO)3] (complex 1) under the protonation of tetrafluoroboric acid–diethyl ether (HBF4.Et2O), a comprehensive density functional theory (DFT) theoretical study was performed. The computational results showed that formation of the [(cyclohex-3-enyl)-η6-benzene]manganese tricarbonyl complex [(C6H9)(η6-Ph)Mn(CO)3+][BF4] (complex 2) was achieved via a series of mono-agostic and di-agostic intermediates. The overall rate-limiting step for this unusual migration of the Mn(CO)3 fragment is the formation of the di-agostic (η2-phenyl)manganese complex 8 (4 → 5 → 8) with a Gibbs barrier of 15.4 kcal mol−1. The agostic intermediates with TM…H…C agostic interactions were well-characterized by geometry parameters, Atoms-In-Molecules (AIM) analyses, and the Natural Adaptive Orbitals (NAdOs). The located pathways in the current study successfully explained the experimental observations, and the findings on the TM…H…C agostic interaction provided a new aspect of the catalytic reaction with the manganese complex.

The previous studies on the haptotropic migration of the Cr(CO) aromatic rings (Scheme 3) suggested that the Cr(CO)3 fragment mig tively electron-deficient aromatic ring to the electron-rich aromatic ri mational effects could inhibit the migration [15,16].Experimental and have shown that the degree of ring coplanarity typically affects the migration of Cr(CO)3 fragment, and the possible participation of the has been verified by the comparison between the azaborine chromiu plex [(η 6 -C4BNH5)-(C6H5)Cr(CO)3] and para-aminobiphenyl chromiu plex [(η 6 -C6H5)(C6H4-4-NH2)]Cr(CO)3] [ [15][16][17][18][19].As for (exo-phenyl)(η 3 ganese tricarbonyl [(Ph)(η 3 -C6H8)Mn(CO)3] (complex 1, Scheme 2), it the protonation-induced migration of the Mn(CO)3 group follows the ular inter-ring haptotropic rearrangement as observed in the Cr(CO)3 tion, the conformational effects resulting from the possible agostic in promote the migration of Mn(CO)3 group from the relatively electron enyl group to the electron-rich phenyl group, which also needs to be In this paper, the density functional theory (DFT) computations investigate the migration mechanism of Mn(CO)3 from the cyclohexen group of (exo-phenyl)(η 3 -cyclohexenyl)manganese tricarbonyl [(Ph (complex 1, Scheme 2) under the protonation of HBF4 .Et2O.The poss the above proposed Mn … H … C agostic intermediates during the migra and the relative strength of the Mn … H … C agostic interaction was al Atoms-In-Molecules (AIM) analyses and the Natural Adaptive Orbita

Results and Discussion
To verify the reliability of the above computational method, the gas-phase PBEPBE/BS1-Auto optimized structure of [(cyclohex-3-enyl)-η 6 -benzene]manganese tricarbonyl complex 2, [(C 6 H 9 )(η 6 -Ph)Mn(CO) 3 + ][BF 4 ], was compared with its reported X-ray structure (CSD entry: YUBXOI) [12] (Tables S1 and S2).A reasonable root-mean-square deviation (RMSD) of 0.2105 Å was obtained, with the crystal packing of CO groups causing the largest deviation.The additional comparisons from the gas-phase optimization of PBE-D3(BJ)/BS1-Auto and PBE-D3(BJ)/BS2-Auto were also performed, and slight improvements in RMSDs were observed.To further confirm the accuracy of the gas-phase optimization, the Gibbs free energies computed from gas-phase PBE/BS1-Auto and PBE-D3(BJ)/BS1-Auto were compared.An acceptable mean absolute deviation (MAD) of 1.64 (Table S3) and an excellent linear fitting (R 2 = 0.9908, Figure S1) were presented.To reasonably address the effect of polarization functions of hydrogen atoms on the geometry optimization, the PBE/BS4-Auto optimized structures were matched with the PBE/BS1-Auto optimized ones, and significantly small values of RMSD (in Å) were obtained (Table S4).Additionally, no obvious differences in the electron density of bond critical point ρ (BCP) from PBE/BS1-Auto optimized structures and PBE/BS4-Auto optimized ones could be observed (MSD = 0.004, MAD = 0.004) (Figures S3 and S4).These observations clearly demonstrated the suitability of current method in the geometry optimization, which is also consistent with our previous studies and the other reported work [20][21][22][23].

Characterization of Agostic Complexes
The above established pathways on the unusual protonation-induced migration of the Mn(CO) 3 fragment from the cyclohexenyl group to the phenyl group (Figures 1 and 2) presented the following observations: (1) the overall rate-limiting step for this unusual migration is the formation of di-agostic (η 2 -phenyl)manganese complex 8 (4 → TS-4-5 → 5 → TS-5-8 → 8, Figure 1) with a Gibbs barrier of 15.4 kcal mol −1 (24.8 kcal mol −1 for 4 vs. 40.2kcal mol −1 for TS-5-8); (2) the exothermic reaction from complex 3 to complex 2 is overall favorable by 33.9 kcal mol −1 ; and (3) the mono agostic complexes (3, 5, 6, 7, and 10) and di-agostic complexes (4, 8, and 9) served as the main intermediates in the above exothermic migration.To better understand the roles of these agostic complexes in the migration of Mn(CO) 3 , the agostic bonds in these intermediates were further computationally characterized and well analyzed.
Table 1.DFT-computed agostic parameters of the agostic complexes.Bond length of Mn-hydride in complex 3 is 1.546 Å, Wiberg bond index of Mn-hydride is 0.51, and 1 H chemical shift is −8.7 ppm.The asterisks represent the endo agostic Mn . . .H . . .C bond in the di agostic complexes 4, 8 and 9. Non # represents the non-agostic C-H bond.

C-H (Å)
Mn-H-C (  1 that all these complexes (3, 4, 5, 6, 7, 8, 9 and 10) fit the above well-known geometrical parameters of an agostic complex with the shortened Mn-H distance (1.813-2.085Å), the prolonged C-H (agostic) bond length (1.133-1.189Å), and the small Mn . . .H . . .C bond angle (93.7-119.8• ).The J CH coupling constants in the Mn . . .H . . .C unit of these mono-agostic complexes (3, 5, 6, 7 and 10) and di-agostic complexes (4, 8 and 9) were about 53 Hz (averaged) lower than those J CH couplings of the non-agostic ones.The high field agostic hydrogen atoms in the Mn . . .H . . .C agostic unit compared to the non-agostic hydrogen were also confirmed by the proton chemical shifts (by 6.9 ppm, averaged).The AIM (Atoms-In-Molecules) analyses of the Mn . . .H . . .C unit in the monoagostic complexes (3, 5, 6, 7 and 10) and di-agostic complexes (4, 8 and 9) were presented in Figure 3.The relative strength of a Mn-H bond and a H-C bond in the Mn . . .H . . .C agostic unit could be measured by the calculated electron densities of bond critical points [ρ (BCP) ] and the absolute value of the Laplacian of electron density (∇ 2 ρ) (Figure 3), and a stronger chemical bond is characterized as a shorter bond distance and bigger Wiberg bond index, which could be demonstrated by the comparison of agostic complexes 3 and 5.The Mn-H distance in agostic complexes 3 and 5 are 1.823 and 1.977 Å (Table 1), respectively, showing a stronger Mn-H bond in agostic complex 3 compared with complex 5.It was also confirmed by the computed Wiberg bond index of complexes 3 and 5 (0.16 vs. 0.11, Table 1).The calculated electron densities of Mn-H bond critical points [ρ (BCP) ] for agostic complexes 3 and 5 are 0.0534 and 0.0461 a.u.(Figure 3), and the related absolute value of the Laplacian of electron density (∇ 2 ρ) are 0.234 and 0.223 a.u., respectively (Figure 3).It is worth noting that the endo Mn . . .H . . .C agostic unit in the di-agostic complex 9 (the 9*) had the longest Mn-H distance of 2.085 Å among all the agostic Mn-H bonds and had the shortest C-H bond of 1.133 Å (Table 1) among all the agostic C-H bonds.Consequently, the smallest value of electron density of Mn-H bond critical points [ρ (BCP) ] (0.0268 a.u., Figure 3) and the smallest value of Laplacian of electron density (∇ 2 ρ) (0.113 a.u., Figure 3) were observed in endo-agostic Mn-H-C unit of the di-agostic complex 9 (the 9*).In contrast to the weak agostic Mn-H bond, the strongest agostic C-H bond of 1.133 Å in the di-agostic complex 9 (the 9*) was verified by the biggest value of electron density of agostic C-H bond critical points [ρ (BCP) ] (0.241 a.u., Figure 3) and the biggest absolute value of Laplacian of electron density (∇ 2 ρ) (0.657 a.u., Figure 3).The AIM analyses of other agostic intermediates were also obtained and presented in Figure 3, confirming the existence of the Mn . . .H . . .C agostic interaction, which was consistent with previous reports [20,21].To visually evaluate the agostic interactions in mono-agostic complexes (3, 5, 6, 7 and 10) and di-agostic complexes (4, 8 and 9), the NAdOs (natural adaptive orbitals) of the Mn … H … C agostic interaction were introduced (Figure 4).Analyses of the NAdOs provided the following facts: (1) the eigenvalues of NAdOs of the Mn … H … C agostic unit in the complexes 3, 4 and 4* are significantly bigger than others (0.281,0.277 and 0.285, respectively, Figure 4); (2) the smallest eigenvalue of 0.177 for agostic complex 9* is observed with the least contribution of 3d(Mn) orbital into the NAdO of the Mn … H … C agostic unit (9.1%); (3) the highest contribution of 3d(Mn) to the NAdO of the Mn … H … C agostic unit (20.9%) is observed in the mono agostic complex 3; and (4) the contribution of 2p(C) orbital to the NAdO of the Mn … H … C agostic unit in agostic complex 9* is remarkably higher than that of agostic complex 3 (35.2% vs. 27.0%, Figure 4).The higher contribution of the 3d(Mn) orbital to the NAdOs of the Mn … H … C agostic unit in agostic complex 3 compared to complex 9* agrees with the relative stronger Mn-H bond in complex 3 than that of complex 9* (Table 1, Figure 3) [20].Meanwhile, the higher contribution of 2p(C) orbital to the NAdOs of the Mn … H … C agostic unit in agostic complex 9* compared to complex 3 is entirely consistent with the stronger agostic C-H bond in complex 9* than that of complex 3 (Table 1, Figure 3).Additionally, to investigate the role of Mn … H … C agostic interactions in the stabilization of Mn agostic intermediates, the second order perturbative energy, E (2) , was obtained from the NBO computation.NBO analyses showed that the interaction of the σ(C-H) To visually evaluate the agostic interactions in mono-agostic complexes (3, 5, 6, 7 and 10) and di-agostic complexes (4, 8 and 9), the NAdOs (natural adaptive orbitals) of the Mn . . .H . . .C agostic interaction were introduced (Figure 4).Analyses of the NAdOs provided the following facts: (1) the eigenvalues of NAdOs of the Mn . . .H . . .C agostic unit in the complexes 3, 4 and 4* are significantly bigger than others (0.281,0.277 and 0.285, respectively, Figure 4); (2) the smallest eigenvalue of 0.177 for agostic complex 9* is observed with the least contribution of 3d (Mn) orbital into the NAdO of the Mn . . .H . . .C agostic unit (9.1%); (3) the highest contribution of 3d (Mn) to the NAdO of the Mn . . .H . . .C agostic unit (20.9%) is observed in the mono agostic complex 3; and (4) the contribution of 2p (C) orbital to the NAdO of the Mn . . .H . . .C agostic unit in agostic complex 9* is remarkably higher than that of agostic complex 3 (35.2% vs. 27.0%, Figure 4).The higher contribution of the 3d (Mn) orbital to the NAdOs of the Mn . . .H . . .C agostic unit in agostic complex 3 compared to complex 9* agrees with the relative stronger Mn-H bond in complex 3 than that of complex 9* (Table 1, Figure 3) [20].Meanwhile, the higher contribution of 2p (C) orbital to the NAdOs of the Mn . . .H . . .C agostic unit in agostic complex 9* compared to complex 3 is entirely consistent with the stronger agostic C-H bond in complex 9* than that of complex 3 (Table 1, Figure 3).Additionally, to investigate the role of Mn . . .H . . .C agostic interactions in the stabilization of Mn agostic intermediates, the second order perturbative energy, E (2) , was obtained from the NBO computation.NBO analyses showed that the interaction of the σ (C-H) donor with the 3d* (Mn) empty acceptor (σ (C-H) → 3d* (Mn) ) was the major contribution in Mn . . .H . . .C agostic interaction, and relative weak contribution from the back-donation of 3d (Mn) donor to the σ* (C-H) acceptor was also located (Table S5).Not surprisingly, the lowest estimated stabilization energy of the Mn . . .H . . .C agostic interaction via the computed E (2) from the dominant σ (C-H) → 3d* (Mn) interaction in agostic complex 9* was observed (28.95 kcal mol −1 , Table S5), which was notably lower than that of agostic complex 3 (63.63kcal mol −1 , Table S5).

Computational Methods
Gas-phase geometry optimizations were performed using the Gaussian 16 (Revision C 01) [26] package with PBE functional [27] (as PBEPBE in the Gaussian 16 package) and basis sets 1 (BS1).In BS1, the modified-LANL2DZ with the f polarization (modified-LANL2DZ(f )) [28][29][30] and the effective core potential (ECP, LANL2DZ) were utilized for the Mn atom, the 6-31G (d') [31][32][33] basis sets were employed for the C, O, and H atoms, and the LANL2DZ(d, p) [34,35] with the related ECP (LANL2DZ) were used for the Si atom in the reference system TMS.Vibrational frequency computations were used to verify the natures of all stationary points, all located minima were confirmed with no imaginary frequency, and all located transition states were obtained with only one imaginary frequency.The IRC (intrinsic reaction coordinate) computations following the transition state were performed.Natural bond orbital (NBO) [36][37][38][39] analysis and Wiberg bond index [40,41] were performed with the Gaussian 16 integrated NBO program (NBO version 3).To address the solvation effect in dichloromethane (DCM), the PBEPBE/BS2 self-consistent reaction field (SCRF) single-point computations were performed with the solvation model based on density (SMD) [42].The reported value solvation free energy of the proton (∆G H + ,solv = −207.79kcal mol −1 ) [43,44] and the experimental value of the gas-phase Gibbs free energy of a proton (∆G H+,gas = −6.28kcal mol −1 ) [45] were used.In BS2, the Ahlrichs redefined Def2-TZVP [46,47] basis sets were utilized for H, C, O and Mn atoms.The counterion BF 4 − was excluded from the computations.All computations were performed at 1 atm and 298.15 K, and the automatic density fitting approximation (via Auto keyword) [48,49] with pure spherical harmonic 5d and 7f functions were utilized.For comparison, the gas-phase optimizations using Grimme's D3 [50] dispersion with Becke-Johnson damping [D3(BJ)] [51] (PBE-D3(BJ)/BS1-Auto and PBE-D3(BJ)/BS2-Auto) were also performed (see Supporting Information for the detailed comparisons).The Gibbs free energies from SMD(DCM)-PBE/BS2-Auto//PBE/BS1-Auto computations are presented in the main text, and the results from the PBE-D3(BJ)/BS1-Auto and PBE-D3(BJ)/BS2-Auto computations are presented in the Supporting Information.To reasonably evaluate the effect of polarization functions on hydrogen atoms, additional geometrical optimizations with BS4 (PBE/BS4-Auto) were performed.In BS4, the modified-LANL2DZ with the f polarization (modified-LANL2DZ(f )) [28][29][30] and the effective core potential (ECP, LANL2DZ) were utilized for the Mn atom, while the 6-31G (d, p) basis sets [31,32] were employed for the C, O, and H atoms.

Scheme 2 .
Scheme 2. Migration of Mn(CO)3 from cyclohexenyl to benzene and the proposed interm

Scheme 2 .
Scheme 2. Migration of Mn(CO) 3 from cyclohexenyl to benzene and the proposed intermediates.

Figure 3 .
Figure 3.The AIM (Atoms-In-Molecules) analysis of the agostic complexes.The orange balls represent the BCP (bond critical point), the yellow balls represent RCP (ring critical point), the green balls represent CCP (cage critical point), and the bond paths are shown in orange.Atom color codes: C, gray; H, white; O, red; Mn, ochre.The electron densities of bond critical points [ρ(BCP)] and Laplacian of electron density (∇ 2 ρ) are given in a.u.The asterisks represent the endo-agostic Mn … H … C unit in the di agostic complexes 4, 8 and 9.The counterion BF4 -is omitted for clarity.The asterisks represent the endo agostic Mn … H … C bond in the di agostic complexes 4, 8 and 9.

Figure 3 .
Figure 3.The AIM (Atoms-In-Molecules) analysis of the agostic complexes.The orange balls represent the BCP (bond critical point), the yellow balls represent RCP (ring critical point), the green balls represent CCP (cage critical point), and the bond paths are shown in orange.Atom color codes: C, gray; H, white; O, red; Mn, ochre.The electron densities of bond critical points [ρ (BCP) ] and Laplacian of electron density (∇ 2 ρ) are given in a.u.The asterisks represent the endo-agostic Mn . . .H . . .C unit in the di agostic complexes 4, 8 and 9.The counterion BF 4 − is omitted for clarity.The asterisks represent the endo agostic Mn . . .H . . .C bond in the di agostic complexes 4, 8 and 9.