Communication pubs.acs.org/Organometallics
Degenerate Pathways for Metallacycle Ring Inversions: A Common Phenomenon Consistent with the Principle of Microscopic Reversibility Roger G. Letterman,† Charles B. Duke, III,† Tung T. To,† Theodore J. Burkey,*,† and Charles Edwin Webster*,†,‡ †
Department of Chemistry, The University of Memphis, Memphis, Tennessee 38152, United States Department of Chemistry, Mississippi State University, Mississippi State, Mississippi 39762, United States
‡
S Supporting Information *
ABSTRACT: Competing degenerate pathways for ring inversion in organometallic complexes are proposed to be ubiquitous examples that adhere to the principle of microscopic reversibility. The NMR spectra for ring inversion of two chromium arene dicarbonyl pyridyl chelates ([Cr{η6-C6H5(CH2)n(2-Py-κN)}(CO)2]; 2-Py = 2-pyridyl, n = 2 (1), and 3 (2)) and a manganese cyclopentadienyl dicarbonyl methyl sulfide chelate ([Mn{η5-C5H4COC(SCH3)2(SCH3-κS)}(CO)2] (3)) were characterized via variable-temperature NMR spectroscopy and DFT theoretical calculations.
A
of activation are compared with those from our computationally proposed ring inversion mechanisms (reaction coordinates). While exploring the reaction coordinates, we discovered that 2 and 3 each have a pair of mechanisms for ring inversions with identical but asymmetric mirror image reaction coordinates. The existence of multiple symmetry-related pathways is discussed with respect to the principle of microscopic reversibility. The principle of microscopic reversibility applies to thermal processes and follows from the fact that the lowest-energy path for a reversible reaction in the forward direction is also available in the reverse direction and, therefore, occurs with the same rate at equilibrium.2 Thus, the same path is also favored in the reverse direction, since it is faster than any other. The current study is the first report of two different paths for a ring inversion: that is, the atomic reaction coordinates of each path are not superimposable.3 The ring inversion connects two mirror image conformers of P and M helical chirality, and because the conformers are enantiomeric, their energies are identical.4,5 It might be expected that a single path between the conformers would necessarily be symmetric, where each step in one direction has an identical counterpart in the reverse direction. This is the situation, except when the counterpart is a mirror image on another path, and therefore the two paths are asymmetric and mirror images of each other. The existence of multipath reactions (with identical activation free energies) were first postulated by Burwell and Pearson for homogeneous isotopic exchange reactions and homogeneous substitution reactions, where the mechanism could be asymmetric in each direction.6
major focus of our research is the design of organometallic photochromes based on a linkage isomerization of bifunctional chelates. The isomerization may pass through a number of chelate ring conformations; therefore, it is important to identify and understand the participation of those ring conformations. Rings can have helical chirality, and ring inversion of enantiomeric conformers leads to the exchange of symmetry-related protons (enantiomerization).1 The chelates Cr{η 6 -C 6 H 5 (CH 2 ) 2 (2-C 5 H 4 N)-κN}(CO) 2 (1), Cr{η 6 C6H5(CH2)3(3-C5H4N)-κN}(CO)2 (2), and Mn{η5-C5H4C(O)C(SCH3)2(2-SCH3)-κS}(CO)2 (3) (Figure 1) occur in enantiomeric pairs, and utilizing variable-temperature proton NMR spectra we report the free energy of activation for the ring inversion connecting each pair. These experimental free energies
Figure 1. Structural representations of 1M (left), 2M (center), and 3M (right). The subscript M indicates chirality. See Designations of Helical Chirality in the Supporting Information. © 2014 American Chemical Society
Received: July 14, 2014 Published: October 8, 2014 5928
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The syntheses of 1−3 have been reported previously.7,8 Variable-temperature 1H nuclear magnetic resonance (VTNMR) experiments and DFT theoretical calculations are described in the Supporting Information. For 1 and 2, residual THF proton peaks account for the largest peaks at 1.72 and 3.58 ppm, which were used as an internal reference. Complete spectral assignments (Spectral Assignments for 1−3) are presented in the Supporting Information and are consistent with calculated chemical shift peaks at low- and high-temperature limits (Supporting Information, Simulated NMR Spectra for 1− 3). The coalescences of peaks in variable-temperature NMR spectra for 1−3 are consistent with chelate ring inversions that exchange symmetry-related nuclei (Figure 2 and Supporting
chirality (for example, 1M and 1P, respectively). The experimental free energies of activation provide benchmarks to calculate energies of possible transition states and, by association, the ring inversion pathways between the M and P enantiomers. Potential mechanisms for ring inversion could be dissociative (tethered functional group dissociates from the metal) or nondissociative (tethered functional group remains coordinated). The PBEPBEDFT computed dissociative free energies of activation for 1−3 (25.1, 19.9, and 18.4 kcal mol−1, respectively) are significantly greater than the experimental free energies of activation. These differences were found even if a solvent molecule was explicitly added to the coordinatively unsaturated metal center during the inversion (Supporting Information, Energetics of Dissociative Pathways). For the proposed mechanism illustrated in Figure 3, the pyridyl group rotates without dissociation about the Cr to N axis
Figure 2. Selected 1H VT-NMR spectra of 1 from 177 to 282 K in THFd8. All spectra are reported in the Supporting Information, Figure S3. The water peak moves from 3.1 ppm at 177 K to 2.5 ppm at 282 K.
Figure 3. Free energy (kcal mol−1) profile along a reaction coordinate illustrating the mechanism for interconversion of the enantiomers 1M and 1P.
Information, Figures S3−S5). The results for 1 in Figure 2 are illustrative. Two peaks (5.98 and 4.65 ppm) at 177 K, assigned to the ortho phenyl protons, coalesce near 222 K and narrow to a single peak at 282 K (5.14 ppm). Coalescence is also observed for meta phenyl peaks (5.61 and 3.92 ppm at 177 K to 4.67 ppm at 282 K) and methylene (CH2) peaks (2.75 and 1.84 ppm at 177 K to 2.27 ppm at 282 K). Coalescence appears to have already occurred at 177 K for the other CH2 peak (3.1 ppm), which narrows as early as 197 K (see Figure S3, Supporting Information). The para phenyl peak (3.69 ppm at 177 K) shows a temperature-dependent chemical shift upfield under the solvent peak (3.58 ppm at 282 K). Indeed, all peaks but that at 3.1 ppm display a chemical shift dependence on temperature. Analogous temperature dependencies of aromatic and aliphatic peaks were observed for 2 and 3 (Supporting Information, Figures S4 and S5, respectively). The experimentally derived free energies of activation (ΔG⧧exp) for ring inversion were calculated from Δυ (the frequency difference between exchanging nuclei) and Tc (coalescence temperature) with eq 1.9 Inspection of spectra obtained from 212 ⎛ ⎛ T ⎞⎞ ⧧ ΔGexp = 0.00458 (kcal/(mol/K)) × Tc ⎜9.97 + log⎜ c ⎟⎟ ⎝ Δυ ⎠⎠ ⎝
as the arene ring rotates about the Cr−arenecentroid axis. The transition state is a Cs-symmetric chelate with a ΔG⧧comp value of 11.7 kcal mol−1, which is close to the experimentally observed ΔG⧧exp value of 10.0 kcal mol−1. The reaction coordinate is symmetric; therefore, both pathways from 1M and 1P to TS-1M1P are geometrically and energetically identical. In the case of 2 and 3, the nondissociative ring inversion, where the tethered functional group remains coordinated to the metal, was examined for pathways that occur via a Cs-symmetric transition state and via a series of asymmetric steps. In contrast to 1, the ring inversion of 2 between 2P to 2M is considerably more complicated (Figure 4). A higher-energy pathway with a Cs-
(1)
to 227 K for 1 (Supporting Information, Figure S3) indicates that the coalescence temperature is within this range and is estimated to be 222 K for Δυ = 354 Hz (Supporting Information, Table ⧧ S2), yielding 10.0 kcal mol−1 for ΔGexp . From similar experiments, the ΔG⧧exp values for 2 and 3 are 10.6 and 14.2 kcal mol−1, respectively. Over a range up to 20 K, the value determined for ΔG⧧exp varies by 1.0 kcal mol−1 or less (see Supporting Information, Tables S2 and S4 and Spectral Assignments for 3). Like cyclohexane, each chelate ring for 1−3 has a pair of degenerate, lowest energy conformers. However, the chelate conformers for 1−3 are enantiomeric with M and P helical
Figure 4. Free energy (kcal mol−1) profile along a reaction coordinate illustrating the mechanism for interconversion of the enantiomers 2P and 2M.
symmetric transition state (Supporting Information, HigherEnergy Cs-Symmetric Ring Inversion for 2 and 3) is avoided when the pyridyl group remains coordinated during a series of concerted arene and pyridyl group rotations about the Cr− arenecentroid and Cr−N axes, respectively. This transformation proceeds via four steps with concomitant rotations about the C− C bonds of the propylene tether: (1) for 2P to 4P, the arene ring 5929
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Figure 5. Free energy profile along a reaction coordinate illustrating the mechanism for interconversion of conformers 2P to 2M and return to 2P by the mirror image pathway. The inset is an overlay of the two pathways, which appear to intersect at the center because the energies (vertical axis) are the same. However, the two paths do not intersect because the spatial coordinates are different for 5P and 5M.
rotates 43° counterclockwise about the arenecentroid−Cr axis while the pyridyl ring rotates 12° counterclockwise about the N− Cr axis (clockwise and counterclockwise are based on observations of the vector originating at the centroid of the arene and terminating at the metal center and likewise N to Cr for the N−Cr axis); (2) for 4P to 5P, the arene ring rotates 36° clockwise as the pyridyl ring rotates 45° counterclockwise; (3) for 5P to 6M, the phenyl ring rotates 54° clockwise and the pyridyl ring rotates 69° counterclockwise; (4) for 6M to 2M, the arene ring rotates 32° clockwise and the pyridyl ring rotates 4° clockwise. The ΔG⧧comp value for ring inversion of 2P to 2M via this mechanism is 9.1 kcal mol−1 (2P to 2M through TS-4P-5P), in good agreement with the experimentally observed ΔG⧧exp value of 10.6 kcal mol−1.10 There are two asymmetric, mirror image pathways from 2M to 2P (solid line and dashed lines in Figure 5): the first step in the ring inversion from 2M to 2P may occur along the solid line (via TS-2M-6M) or along the dashed line (via TS-2M-4M). The absolute atomic positions of each species along the two independent pathways are different, although the reaction coordinates of each pathway are related by symmetry. Furthermore, the sequences of steps from 2M to 2P are different for the two paths. This asymmetric reaction coordinate seems to violate the principle of microscopic reversibility, since 2M can “return” to 2P by a different reaction coordinate. Like a road circumscribing a centrosymmetric mountain, together the two pathways form a symmetric “cyclic” reaction coordinate (inset, Figure 5). It is important to emphasize that the solid and dashed reaction coordinates do not spatially intersect at any point in the forward or reverse directions: i.e., each series of structures are the enantiomers of the other series and, therefore, inhabit different regions of the coordinate space.11,12 The apparent spatial intersection at the middle of the inset of Figure 5 is an artifact of the two-dimensional representation in the figure and the choice of beginning and end points.13 Similar to the case for 1 and 2, dissociative pathways for 3 are higher in energy (Supporting Information, Dissociative Ring Inversion of 1, 2, and 3). For nondissociative pathways, an “umbrella inversion” of the coordinated sulfur can occur. In general, multiple conformations of the methyl groups complicate the ring inversion of 3 (3P to 3M). If the first step from 3P is an umbrella inversion of the metal-bound S group (S−Me(3)) followed by rotations of S−Me(1) and S−Me(2), then the pathway has a ΔG⧧comp value of 17.7 kcal mol−1, which is inconsistent with the experimental results (the close contact of the two methyl groups of S−Me(3) and S−Me(1) in the transition state leads to a higher relative energy; Supporting
Information, Figure S13). Alternately, several S−Me rotations followed by an umbrella inversion lead to an eight-step pathway with the lowest free energy of activation (Figure 6 and Supporting Information, Non-Dissociative Ring Inversion of 3).
Figure 6. Free energy profile along one reaction coordinate illustrating the mechanism for interconversion of enantiomers (3P to 3M). The mirror image reaction coordinate is not shown (see the Supporting Information, Figure S12).
Like the ring inversion of 2, the reaction coordinate for the ring inversion of 3 is asymmetric. The ring inversion of 3 occurs in a series of rotations, similar to the mechanism described for 2, thereby avoiding a high-energy Cs-symmetric structure. The pathway illustrated in Figure 6 has a ΔG⧧comp value of 13.7 kcal mol−1, consistent with the ΔG⧧exp value of 14.2 kcal mol−1. For 3, the mechanism for inversion has more steps than the mechanism for 2 because of additional conformers from S−methyl rotations. As for 2, the occurrence of an asymmetric path from 3P to 3M requires that there must be a mirror image pathway from 3M to 3P (the dashed line shown in the Supporting Information, Figure S12). Similar to the ring inversions of 2, the solid and dashed pathways for 3 (Supporting Information, Figure S12) are independent and do not intersect. The chelates in this study are structurally related to photochrome chelates developed in our laboratories.14−16 Understanding and predicting photochrome fluxional behavior are important in the development of functional photochromes based on organometallic chelates. The lowest-energy ring inversion of 1 proceeds via a single step. The ring inversion occurs via a Cs-symmetric transition state; therefore, a single symmetric pathway exists between 1P and 1M conformers (Figure 3). The ring inversions of 2 (Figures 4 and 5) and 3 (Figure 6) each occur via a pair of asymmetric but energetically degenerate pathways and, therefore, do not violate the principle of microscopic reversibility. The pathways for 2 and 3 avoid 5930
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(4) Schleyer and Mauksch examined a simple four-atom S2F2 system which can enantiomerize via a chiral pathway. Schleyer, P. v. R.; Mauksch, M. Angew. Chem., Int. Ed. 2000, 39, 2756−2758. (5) Wolfe et al. previously analyzed hypothetical asymmetric reaction coordinates of enantiomerization: Wolfe, S.; Schlegel, H. B.; Csizmadia, I. G.; Bernardi, F. J. Am. Chem. Soc. 1975, 97, 2020−2024. (6) Burwell, R. L.; Pearson, R. G. J. Phys. Chem. 1966, 70, 300−302. (7) To, T. T.; Heilweil, E. J.; Burkey, T. J. J. Phys. Chem. A 2006, 110, 10669−10673. (8) Duke, C. B.; Letterman, R. G.; Johnson, J. O.; Barr, J. W.; Hu, S.; Ross, C. R.; Webster, C. E.; Burkey, T. J. Organometallics 2014, 33, 485− 497. (9) Sandström, J. Dynamic NMR Spectroscopy; Academic Press: London, 1982. (10) From the X-ray crystal structure of 2, which is monoclinic P21/c, one observes that there are enantiomeric pairs in the unit cell. This observation is consistent with rapid interconversion of the chiral helical conformers in solution at room temperature on the NMR time scale, and the enantiomers must exist in a 1:1 ratio. However, from the computational results for 2 (2 to 6), one can see that there is still fluxionality that is faster than the NMR time scale. (11) In ref 6, Burwell and Pearson state (1) “This principle [PMR] states that any molecular process and its reverse occur with equal rates at equilibrium.” and (2) “The p.m.r. does not permit a one-path mechanism which is not symmetric about the midpoint of the free energy profile. However, it does permit such a process as a two-path mechanism in which the second path is that obtained by reflecting the first in a plane at the midpoint.” In the current contribution, the two paths are mirror images just as described by Burwell and Pearson. (12) Experiments with chiral auxiliaries or NMR resolving agents could be used. At best these experiments would indicate that there are two enantionmers present, but this fact is already established by the dynamic NMR spectra. For example, for 2, the low-temperature NMR spectra clearly establish that there are at least two enantiomeric conformers. Five aromatic proton signals establish that two ortho CH groups are in different chemical environments (likewise for the two meta CH groups). This case can only occur if the compound lacks a mirror plane, which requires that the chelate ring is not planar (barring an unusual arene distortion). Thus, one or more chelate ring members must be out of plane with respect to the Cs-symmetric structure to create a chiral structure. Such a structure must have a mirror image, since there is an equivalent out-of-plane displacement in the opposite direction relative to the Cs-symmetric structure. This point and the fact that the two ortho CH groups (and other symmetry-related nuclei) readily exchange chemically equivalent positions at high temperature indicate that there must be one or more pairs of enantiomeric conformers. The actual structures of the enantiomeric conformers are not revealed by the NMR spectra, and little more would be learned from chiral auxiliaries or NMR resolving agents. Finally, computational results identify the various minimum energy structures and in no way suggest that the structures are rigid. (13) For a given enantiomer, 2 would convert to 6 preferentially compared to 4 because the Boltzmann distribution at equilibrium will have a greater population of 6 than 4. However, comparing the first steps for pathways through 6 or 4 is irrelevant. The experimentally observed 1 H NMR coalescence behavior cannot distinguish between the “forward” and “reverse” pathways. On the basis of the Curtin−Hammett postulate, both pathways are equally probable, since the free energies of activation of the transition states determine the relative rates, and those free energies of activation are necessarily the same. (14) Heilweil, E. J.; Johnson, J. O.; Mosley, K. L.; Lubet, P. P.; Webster, C. E.; Burkey, T. J. Organometallics 2011, 30, 5611−5619. (15) Heilweil, E. J.; To, T. T.; Duke, C. B.; Ruddick, K. R.; Webster, C. E.; Burkey, T. J. J. Phys. Chem. A 2009, 113, 2666−2676. (16) To, T. T.; Duke, C. B.; Junker, C. S.; O’Brien, C. M.; Ross, C. R.; Barnes, C. E.; Webster, C. E.; Burkey, T. J. Organometallics 2008, 27, 289−296.
higher-energy Cs-symmetric structures via a sequence of bond rotations of the chelate rings and functional groups. This experimental and computational study of the fluxional behavior of complexes 1−3 provides further insights for rational design. It is likely that multiple degenerate pathways are common for ring inversion. An example is the well-known cyclohexane ring inversion that can pass through six symmetry-related, asymmetric, twist boat intermediates.3
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ASSOCIATED CONTENT
* Supporting Information S
Text, figures, tables, and xyz files giving full computational and model details, comparison of results from various methodologies (PBEPBE and PBEPBE-D), and coordinates for optimized geometries. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Authors
*E-mail for T.J.B.:
[email protected]. *E-mail for C.E.W.:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This work was partially supported by the National Science Foundation under Grant Nos. CHE0227475 and CHE0911528. Computational work was performed on resources at the University of Memphis High-Performance Computing Facility and Computational Research on Materials Institute.
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REFERENCES
(1) Enantiomerization and enantiotopomerization. Binsch, G.; Eliel, E. L.; Kessler, H. Angew. Chem. Int. Ed. 1971, 10, 570−572. Eliel, E. L.; Wilen, S. H.; Mander, L. N. Stereochemistry of Organic Compounds; John Wiley & Sons: New York, 1994. Nasipuri, D. Stereochemistry of Organic Compounds: Principles and Applications, 3rd edition; New Academic Science: New Dehli, 2011. (2) The basis for PMR has been presented in various ways and was first articulated by Tolman: Tolman, R. C. Proc. Natl. Acad. Sci. U.S.A. 1925, 11, 436−439. Further references may be found in the Supporting Information. (3) Six identical twist boat conformations were proposed for cyclohexane, but independent reaction coordinates were not noted: Cremer, D.; Pople, J. A. J. Am. Chem. Soc. 1975, 97, 1354−1358. Chirality in fluxional ring systems has been previously reported. Bushweller, C. H.; Golini, J.; Rao, G. U.; O’Neil, J. W. J. Am. Chem. Soc. 1970, 92, 3055−3058. Snow, M. R. J. Am. Chem. Soc. 1970, 92, 3610− 3617. Jurnak, F. A.; Raymond, K. N. Inorg. Chem. 1972, 11, 3149−3152. Bosnich, B.; Harrowfield, J. M. Inorg. Chem. 1975, 14, 853−860. Anet, F. A. L.; Ragini, R. Conformational Processes in Rings. In Dynamic Nuclear Magnetic Resonance Spectroscopy; Jackman, L. M., Cotton, F. A., Eds.; Academic Press: New York, 1975; pp 543−619. Abel, E. W.; Booth, M.; Orrell, K. G. J. Organomet. Chem. 1976, 160, 75−79. Shaver, A.; McCall, J. M. Organometallics 1984, 3, 1823−1829. Bernal, I.; Reisner, G. M.; Bartsch, R. A.; Holwerda, R. A.; Czech, B. P. Organometallics 1988, 7, 253−258. Doman, T. N.; Hollis, T. K.; Bosnich, B. J. J. Am. Chem. Soc. 1995, 117, 1352−1368. Bernal, I.; Vogt, H. J. Organomet. Chem. 1995, 502, 103−108. Espinet, P.; Casares, J. A. Fluxional Organometallic and Coordination Compounds; Gielen, M., Willem, R., Wrackmeyer, B., Eds.; John Wiley & Sons, Ltd.: 2004; pp 131−161. Stereochemically nonrigid structures: Cotton, F. A. Inorg. Chem. 2002, 41, 643−658 (see the Supporting Information for further references). 5931
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