Inverse Isotope Effects in Single-Crystal to Single-Crystal Reactivity and the Isolation of a Rhodium Cyclooctane σ-Alkane Complex

The sequential solid/gas single-crystal to single-crystal reaction of [Rh(Cy2P(CH2)3PCy2)(COD)][BArF4] (COD = cyclooctadiene) with H2 or D2 was followed in situ by solid-state 31P{1H} NMR spectroscopy (SSNMR) and ex situ by solution quenching and GC-MS. This was quantified using a two-step Johnson–Mehl–Avrami–Kologoromov (JMAK) model that revealed an inverse isotope effect for the second addition of H2, that forms a σ-alkane complex [Rh(Cy2P(CH2)3PCy2)(COA)][BArF4]. Using D2, a temporal window is determined in which a structural solution for this σ-alkane complex is possible, which reveals an η2,η2-binding mode to the Rh(I) center, as supported by periodic density functional theory (DFT) calculations. Extensive H/D exchange occurs during the addition of D2, as promoted by the solid-state microenvironment.


■ INTRODUCTION
The isotopic substitution of hydrogen for deuterium is an invaluable tool for the study of the mechanism in synthesis and catalysis. 1−3 Zero-point energy differences of E−H/D bonds (e.g., C−H/D) lead to changes in the temporal evolution of a reaction manifold if E−H bond activation, or formation, occurs at or before the rate-controlling step. This can be associated with a single transition state (a kinetic isotope effect, KIE) or preceding equilibria that result in a composite KIE (equilibrium isotope effect, EIE). While KIE or EIE normally act to slow the overall progress of a reaction when using the heavier isotopologue, an acceleration reflects an inverse isotope effect. 4 While not always straightforward, 5,6 this can be a result of EIE that favor productive intermediates in which D resides in a higher vibrational oscillator (i.e., C−D over M−D). The study of alkane C−H activation [3][4][5]7 and the evidence for key, but fleeting in solution, σ-alkane intermediates 8,9 have relied heavily on KIE or EIE effects.
We have previously reported on the use of in crystallo, 10 solid-state molecular organometallic (SMOM) chemistry to isolate and characterize cationic σ-alkane complexes of Rh and Co by single-crystal to single-crystal (SC−SC) solid/gas hydrogenation of an alkene precursor. 11−13 The secondary microenvironment provided by supporting [BAr F 4 ] − anions [Ar F = 3,5-(CF 3 ) 2 C 6 H 3 ] is crucial in stabilizing weak 3-center 2-electron M···H−C bonds, meaning these complexes can be isolated and structurally characterized. However, for one precursor, [Rh(Cy 2 P(CH 2 ) 3 PCy 2 )(COD)][BAr F 4 ], [1-COD]-[BAr F 4 ] (COD = cyclooctadiene), the formed alkane, cyclooctane (COA), does not remain bound to the metal when analyzed by X-ray crystallography after 3 h of hydrogenation. 14 Instead, a Rh(I) cation with agostic 15 interactions from the cyclohexyl groups is formed, with the liberated COA encapsulated in an octahedral array of [BAr F 4 ] − anions: [1][COA⊂BAr F 4 ], Scheme 1A. This multistep reaction involves sequential alkene hydrogenation and the loss of COA, presumably via an intermediate σ-cyclooctane complex. We now report that, by following the progress of this solid/gas reaction with H 2 or D 2 , using a variety of methods, an inverse isotope effect is revealed, the leverage of which using D 2 allows for the optimal temporal window to be determined for structural characterization of the intermediate σ-cyclooctane complex. Extensive H/D exchange at the alkane has also occurred, exchange that is promoted by the solid-state microenvironment. These observations add to the isotope effects previously reported in solid-state organometallic reactivity, 11 103 Rh not resolved, masked in the line width of the signals (fwhm = ∼335 Hz). In our initial report of the characterization of [1][COA⊂BAr F 4 ] using SC−SC techniques, we correlated the structural solution (from weakly diffracting crystals selected from the reaction ensemble after 3 h of reaction) with these two signals in the 31 P{ 1 H} SSNMR spectrum. 14 We now suggest this assignment was wrong and that these signals are instead due to a complex that has undergone further addition of H 2 to form a Rh(III) complex of the general formula [Rh(Cy 2 P(CH 2 ) 3 24 and free COA (eq 1). (ii) The reduced magnitude of J(RhP) is indicative of a Rh(III) center. (iii) The formation of the hydride species in related systems by solid/gas reactivity has been reported previously. 19,[25][26][27]29 The rapid loss of H 2 means we cannot comment on the precise number of hydrogen ligands, i.e., Rh(H) 2 or Rh(H 2 )(H) 2 , or whether the Rh complex is still monomeric or has dimerized through bridging hydrides with the resulting loss of crystallinity. 25,26 However, what is now clear is that this final species is not [1]-[COA⊂BAr F 4 ] as initially proposed. This highlights the potential problems associated with the analysis of a solitary single crystal by diffraction techniques and correlation with bulk analytical methods (e.g., NMR spectroscopy). As the final product, [1-H x ][BAr F 4 ] has lost long-range order (i.e., no discrete Bragg peaks); we suggest that, even though it is the only species observed by 31  Reaction with D 2 and the Crystallographic Characterization of a σ-Cycloalkane Complex. The solid/gas reaction of finely crushed and sieved [1-COD][BAr F 4 ] with D 2 was followed in situ using the same protocol as for H 2 . While this showed the equivalent set of sequential events occurring to ultimately form [1-D x ][BAr F 4 ], Figure 1, a qualitative comparison of the evolution of the system provides insight into any isotope effects that are operating. First, [1-COD][BAr F 4 ] is completely consumed in the same time scale as for H 2 (40 min), suggesting that no (or small at best) isotope effect is operating for the first hydrogenation of COD.  F 4 ] remains. This suggests a normal isotope effect is operating for the formation of this hydride species. These isotope effects will be discussed in more detail later.
This reaction was repeated with D 2 on larger single crystalline material. By optimization of the time of D 2 addition a structural solution for d x -[1-COA][BAr F 4 ] could be obtained after 40 min using single-crystal X-ray diffraction. 28 While the   Figure 2C, and there are a number of relatively close C−H···F contacts that act to further stabilize the complex, as described before for other alkane complexes of this type. 13,29,30 QTAIM, noncovalent interaction plots, and NBO analyses support the assigned hapticity and microenvironment effects (Supporting Information).
Cyclooctane complexes have been identified as early intermediates in C−H activation, using fast time-resolved infrared techniques, having lifetimes on the ns−μs time scale, e.g., Rh(η 5 -C 5 Me 5 )(CO)(cyclooctane) 31 and Tp*Rh(CNR)-(cyclooctane). 32 σ-Alkane complexes of cyclooctane have also been identified as intermediates in alkane dehydrogenation reactions using computational methods. 33  Exposure of single crystals of [1-COD][BAr F 4 ] to D 2 for a total of 60 min and analysis of selected crystals by single crystal X-ray diffraction resulted in a structural refinement that confirmed the formation of d x -[1][COA⊂BAr F 4 ] (Supporting Information), but due to a drop off in data quality, alongside significant superpositional disorder, this only provided atom connectivity. Nevertheless, this confirms the previous report of the formation of this complex in a SC−SC reaction. 14 Quantification of the Isotope Effects in the Solid/Gas Reaction Using Johnson−Mehl−Avrami−Kologoromov (JMAK) Analysis. The time course of these solid/gas reactions was followed using solution quenching experiments that determine the relative ratios of COD, COE, and COA. Starting from [1-COD][BAr F 4 ], the same method described for the 31 P{ 1 H} SSNMR experiments was used for individual samples that were exposed, over incrementally longer reactions times, to either H 2 or D 2 in NMR tubes ( Figure 3A, 7.6 mg each sample, 1.5 bar, 293 K). Each of these was quenched by evacuation of the tube, refilling with Ar, and then addition of a suitable coordinating solvent. Using acetone-d 6 , a mixture of [Rh(Cy 2 P(CH 2 ) 3 PCy 2 )(acetone-d 6 23 and the resulting COA/COE/COD ensemble was analyzed using GC-MS for H 2 and D 2 additions. Both methods give very similar temporal profiles for H 2 addition, but GC-MS-derived data allow for quantification of both H 2 and D 2 addition without interference from additional H/D exchange processes (vide infra) that affect analysis by 1 H NMR spectroscopy. 36 These data were then used as a proxy for the organometallic solidstate reactivity that is occurring. As this methodology determines [COA] TOTAL , and does not discriminate between bound and free alkane, it reports on the ensemble of [  F 4 ], as this is the first formed species in this set. Figure 3B presents the resulting reaction course plots for H 2 and D 2 addition over a 5 h sampling period. Qualitatively, both show the same rate of consumption of [1-COD][BAr F 4 ] that is complete after 40 min. COE is observed to be formed as an intermediate, but its relative maximum is lower; COA is formed faster for D 2 addition. This signals faster progress of COE to COA using D 2 , i.e., an inverse isotope effect as suggested from the complementary 31 P{ 1 H} SSNMR experiments described earlier.
The same batch of sieved crystalline material was used for each of the individual H 2 and D 2 experiments shown in Figure  3B. The repetition of selected data points using a different batch of crystalline materials (Supporting Information) showed a small amount of variability between batches, but the data are still fully consistent with the overall temporal profiles recorded for the main experiments. This may be due to surface area effects for different crystalline batches or other experimental variables (e.g., small changes in the pressure of H 2 or D 2 ).
These data have been analyzed using a sequential Johnson− Mehl−Avrami−Kologoromov (JMAK) 37,38 solid-state kinetic model for an A → B → C reaction sequence (see the Supporting Information for full derivation and implementation). Figure 3B shows the resulting fits (solid lines). JMAK analysis describes the progress of a solid-state reaction, i.e., A → B, by a nucleation and growth model, where k is the growth rate constant and n is the Avrami exponent, eq 2. Exponents close to n = 2, 3, and 4 have been suggested to be due to 1-D, 2-D, and 3-D reaction growth dimensionality, respectively, while n = 1 suggests a noncooperative process and can be related to classical first order processes in homogeneous systems. 39 14 which also argues against rate limiting diffusion of H 2 . Instead, we propose a rate-limiting, possibly correlated, intramolecular dissociation of one of the alkene groups in COD. Pertinently, in solution, [Rh(chelating phosphine)(COD)] + complexes also undergo hydrogenation a lot slower than their NBD analogues although the reasons behind this are not clear. 44 This model is complicated by a subtle point of discontinuity at t = 16.5 min for both H 2 and D 2 addition, which when included provides a better fit to the data. This results in a reduced value of k for both H 2 (0.0032(8) min −2 ) and D 2 (0.0038(8) min −2 ) addition to [1-COD][BAr F 4 ] after 16.5 min that are the same within error, with no change in n, and thus no measurable isotope effect. As this change occurs at the same point in time for both H 2 and D 2 addition, we suggest this is not an experimental artifact and is triggered at a certain conversion of [1-COD][BAr F 4 ]. As the microcracking of single crystals 45 would be expected to increase the rate of conversion through surface area arguments, we speculate that this change has to do with a correlated, 46 but subtle, change in the spatially averaged periodic structure that occurs in the hydrogenation of [1-COD][BAr F 4 ]. The repetition of these experiments on larger single crystals and the measurement of the unit cell parameters with time showed no significant step change in axes lengths that would signal a phase change.
In contrast to the consumption of [1-COD][BAr F 4 ], the subsequent hydrogenation of [1-COE][BAr F 4 ] is significantly faster for D 2 addition than that of H 2 (k = 0.45(8) vs 0.11(1) min −1 , respectively) at the initial stages of the reaction, and the Avrami exponent is now unity for both. There is thus an inverse isotope effect observed: k(H)/k(D) = 0.24(5). After 16.5 min, k again decreases significantly, but n is now 2, there is also a significant inverse isotope effect, k(H)/k(D) = 0.06(3) (k = 0.0023(6) vs 0.04(2) min −2 ). The change in "dimensionality", n, makes a direct comparison difficult between the two regimes. Interestingly, in line with Finke's suggestion that k and n are convoluted and cannot be easily separated, 38 for this n = 2 regime, [k(H)] 1/2 /[k(D)] 1/2 = 0.24 (5), which is the same as for the pre-16.5 min value (n = 1). The consequence of these combined inverse isotope effects for [1-COE][BAr F 4 ] hydrogenation is that after 40 min the conversion of COD to COA is essentially complete using D 2 , but considerable (∼20%) COE still remains when using H 2 .
H/D Exchange in COE and COA and the Inverse Isotope Effect. The evolution of the reaction between [1-COD][BAr F 4 ] and D 2 was monitored using GC-MS on the same finely powdered samples as that used for the quenching experiments. This showed that significant, almost complete, H/D exchange was occurring into both COE and COA in this SC−SC solid/gas reaction. No H/D exchange was observed into COD. Figure 4 shows the resulting time course versus %D incorporation for COE and COA TOTAL using D 2 . After 40 min, the remaining COE reaches ∼95% D incorporation with a weighted average of ∼d 13 O 40 ]. 19 Both processes would result in double bond isomerization. Repetition exchanges all the C− H bonds for C−D, if combined with a process that allows for all C−H bonds to interact with the Rh center (see below). Consistent with H/D exchange at a Rh−H intermediate that introduces a single D atom, there is no enhancement of odd or even numbers of d x (Supporting Information). These reversible processes must be thermodynamically balanced and be connected by low barriers for such rapid H/D exchange to occur. Periodic DFT calculations on hydride insertion/βelimination show this to be the case for closely related [Rh(Cy 2 PCH 2 CH 2 PCy 2 )(cyclohexene)][BAr F 4 ] in the solid state with barriers being less than 13.9 kcal mol −1 . 11 A low barrier to a 1,3-hydride shift in the isomerization of propene in [Rh(Cy 2 PCH 2 CH 2 PCy 2 )(propene)][BAr F 4 ] that operates via an allyl hydride intermediate has also been reported (10.9 kcal mol −1 ). 22 H/D exchange at Rh(III)-H with D 2 would likely operate via a σ-CAM mechanism. 47,48 In order to achieve such high levels of deuteration in both COE and COA, all the C−H bonds in the cyclic hydrocarbon need to interact with the metal center, and the pathways shown in Scheme 2 would result in only one face of COA being deuterated. Scheme 3 suggests routes that allow for both faces to be deuterated: a face flip of COE or a nondegenerate βelimination of an antiorientated C−H bond from intermediate A′ that may be promoted by ring strain in the cyclooctyl ligand. 49 (Figure 4). This analysis is further complicated by a number of factors that are unique to the solid-state reactivity described here. The cumulative effects of thermodynamically favorable perdeuteriation, 50 feasible because of the encapsulation, will induce a net secondary isotope effect on the reductive bond formation from A. Isotopologue induced changes in noncovalent interactions between the alkane and anion microenvironment will also affect both the equilibrium thermodynamics and transition state energetics and, thus, may also contribute to the observed isotope effects. Related binding isotope effects (BIEs) have been observed with enzymes and molecular capsules on binding different isotopologues of the same guest substrate. 2 So, while the observation of an inverse isotope effect in a SC− SC molecular organometallic solid/gas reaction is clear-cut here, the additional complexity introduced by reactivity in the single crystal makes the detailed analysis of the underlying reasons for this more challenging.
An inverse isotope effect has been reported for the solutionbased deuteration of NBD using [Ir(PPh 3 ) 2 H 2 (acetone) 2 ]-[PF 6 ] and is explained by a mechanism that favors norborenylhydride intermediates closely related to intermediates described here such as A. 51 Inverse EIEs have previously been used to identify the intermediacy of σ-alkane complexes in overall reductive elimination of alkanes from alkyl-hydrides in solution where the loss of the alkane from the metal center is rate determining. 4

■ CONCLUSIONS
The study of isotope effects has been central to the understanding of mechanisms in organometallic synthesis and catalysis in the solution phase. The inverse isotope effect described here for the sequential SC−SC hydrogenation of [1-COD][BAr F 4 ] adds to the small number of reports where (albeit normal) isotope effects have been noted in molecular organometallic chemistry in the crystalline phase. 11,16−20 The leverage of the isotopologue-induced changes in relative rates results in the structural characterization of a σ-alkane complex of cyclooctane. While reactivity in the single-crystalline environment presents challenges in both data collection and analysis of isotope effects, the installed secondary microenvironment around the reactive metal center promotes temporal control over composition, stability (σ-alkane complex formation), and reactivity (extensive H/D exchange). This highlights that the advantages of isotopic substitution in the study of mechanism and synthesis are not unique to homogeneous systems, and it should also be considered as a useful tool in SC−SC transformations of molecular organometallics.
Full details of synthesis, characterization (including single crystal X-ray determinations), kinetic measurement protocols, sequential JMAK analysis, and connectivity-only structure for the redetermination of