A Series of Crystallographically Characterized Linear and Branched σ-Alkane Complexes of Rhodium: From Propane to 3-Methylpentane

Using solid-state molecular organometallic (SMOM) techniques, in particular solid/gas single-crystal to single-crystal reactivity, a series of σ-alkane complexes of the general formula [Rh(Cy2PCH2CH2PCy2)(ηn:ηm-alkane)][BArF4] have been prepared (alkane = propane, 2-methylbutane, hexane, 3-methylpentane; ArF = 3,5-(CF3)2C6H3). These new complexes have been characterized using single crystal X-ray diffraction, solid-state NMR spectroscopy and DFT computational techniques and present a variety of Rh(I)···H–C binding motifs at the metal coordination site: 1,2-η2:η2 (2-methylbutane), 1,3-η2:η2 (propane), 2,4-η2:η2 (hexane), and 1,4-η1:η2 (3-methylpentane). For the linear alkanes propane and hexane, some additional Rh(I)···H–C interactions with the geminal C–H bonds are also evident. The stability of these complexes with respect to alkane loss in the solid state varies with the identity of the alkane: from propane that decomposes rapidly at 295 K to 2-methylbutane that is stable and instead undergoes an acceptorless dehydrogenation to form a bound alkene complex. In each case the alkane sits in a binding pocket defined by the {Rh(Cy2PCH2CH2PCy2)}+ fragment and the surrounding array of [BArF4]− anions. For the propane complex, a small alkane binding energy, driven in part by a lack of stabilizing short contacts with the surrounding anions, correlates with the fleeting stability of this species. 2-Methylbutane forms more short contacts within the binding pocket, and as a result the complex is considerably more stable. However, the complex of the larger 3-methylpentane ligand shows lower stability. Empirically, there therefore appears to be an optimal fit between the size and shape of the alkane and overall stability. Such observations are related to guest/host interactions in solution supramolecular chemistry and the holistic role of 1°, 2°, and 3° environments in metalloenzymes.


INTRODUCTION
The coordination of alkanes with metal centers and their subsequent C−H activation are central to chemical transformations that add value to these simple feedstocks, 1 such as dehydrogenation, 2,3 C−H functionalization, 4,5 and isotopic enrichment through H/D exchange. 6 Coordination with a metal center prior to C−H bond cleavage occurs through 3c-2e [M]···H−C interactions, 7 forming so-called σ-complexes. 8 For alkanes, such complexes are challenging to generate and observe under standard laboratory conditions. This is because the strong, nonpolar, and relatively sterically congested C−H bonds make alkanes very poor ligandsbinding to metal centers often with bond enthalpies of 15 kcal/mol or less. 9 In solution such complexes have only been observed using lowtemperature in situ NMR spectroscopy (lifetimes of minutes), 10 or on very short time scales (lifetimes of microseconds to seconds) using time-resolved infrared (TRIR) 11 or XAFS techniques. 12 These analyses are necessarily coupled with the generation of a vacant site on the metal center using ligand photoejection or protonation of a metal−alkyl bond. Using these methodologies, σ-alkane complexes from methane to dodecane have been generated. 13,14 Chart 1 shows examples characterized using NMR spectroscopy where methane, 15 propane, 16 cyclopentane, 17 pentane, 18 2-methylbutane, 19 and 2,2-dimethylbutane 20 act as ligands.
These solution-based techniques provide unequivocal evidence for alkane coordination at a metal center. However, their use for the subsequent isolation of a crystalline material that allows for detailed structural characterization using singlecrystal X-ray diffraction, or onward reactivity studies, has yet to be realized. 21,22 This is because rapid alkane displacement by a solvent or a photogenerated ligand leads to lifetimes unsuitable for solution-based crystallization techniques, a situation compounded by the low temperatures used and less than 100% photoconversations achieved.
In response to this challenge, we have developed techniques where competing ligands (solvent or otherwise) and photogeneration of a vacant site are eliminated by using single-crystal to single-crystal (SC-SC 23 ) solid/gas reactivity on molecular organometallic precursors. 24 We term this solid-state molecular organometallic chemistry (SMOM). 25 This approach is exemplified by addition of H 2 to the simple precursor [Rh(Cy 2 PCH 2 CH 2 PCy 2 )(NBD)] [ F 4 ], NBD = norbornadiene, NBA = norbornane, Ar F = 3,5-(CF 3 ) 2 C 6 H 3 ), 26 (Scheme 1A). This σ-alkane complex is remarkably stable, surviving months at 298 K under an Ar atmosphere. The [BAr F 4 ] − anions play a key role in this stability, providing an approximately octahedral microenvironment around the cation, which supports the weak alkane binding with the metal center through multiple noncovalent interactions. This crystalline 27 nanoreactor 28 environment allows for long-range order to be retained, local coordinate flexibility at the reactive site, and hydrophobic pathways through the lattice from the CF 3 groups. 29 The retention of crystallinity also allows for detailed characterization by singlecrystal X-ray diffraction and solid-state NMR spectroscopy (SSNMR). When these structural and spectroscopic data are combined with an analysis of the electronic structures and noncovalent environment using periodic-DFT techniques, 30 a detailed description of the bonding in these complexes is possible. For example, σ-alkane complexes have been characterized in which the alkane (e.g., isobutane) engages in two different η 2 :η 2 -C−H interactions with a Rh(I) center, 31 η 1 :η 1 -NBA at a 3 {Co(I)} center, 32 or η 1 -cyclooctane with Rh(III) (Scheme 1B). 33 The mobility and reactivity of the alkane ligand can also be studied using combined experimental and computational techniques: for example in H/D exchange, 31,34 acceptorless dehydrogenation, 31 and ligand substitution processes. 25 A systematic variation of the ligand and anion 33,35,36 can lead to systems that promote solid/gas SMOM catalysis: e.g., 1-butene isomerization under a continuous flow. 37 Despite these advances, a fundamental question is what are the limits of the SMOM methodology in terms of the smallest and largest alkane fragment that can be incorporated into the solid-state microenvironment provided by the [BAr F 4 ] − anions? Exploring this chemical space would provide structural data for the broadest set of σ-alkane complexes yet and also probe comparative reactivity and stability profiles. In this contribution we report the synthesis, structures, bonding, and reactivity of four new σ-alkane complexes of the [Rh-(Cy 2 PCH 2 CH 2 PCy 2 )] + fragment, ranging from propane to 3methylpentane (Scheme 2). For one, a 2-methylbutane complex, a quantitative SC-SC acceptorless dehydrogenation occurs at room temperaturean endothermic process that normally requires high temperatures. 38  . This technique also allows for the relative stability toward decomposition by loss of alkane, or onward reactivity, of the σ-alkane complexes to be assessed at 298 K, by monitoring the evolution of the system with time.

RESULTS
For complexes that are particularly sensitive to alkane loss and decomposition, synchrotron radiation at the Diamond Light Source (Beamline I19) was combined with a bespoke gas cell that allows for addition of H 2 to a selected single crystal with concurrent cooling (see the Supporting Information). Figure 1 shows the structurally characterized σ-alkane complexes and the precursor alkene complexes used (which are fully described in the Supporting Information). as the starting material, 25 addition of H 2 with concurrent cooling from 298 to 150 K in situ on the I19 Beamline resulted in loss of diffraction. While the ethene is likely hydrogenated to ethane under these conditions (vide inf ra), the subsequent σalkane complex is not sufficiently stable to allow for a structural determination. This suggests a lower size limit for σ-alkane complex formation using this metal/ligand/anion combination. The interaction of ethane with metal centers has been described using in situ solution NMR spectroscopy for Mn(η 5 -C 5 H 5 )(CO) 2 (ethane) (135 K) 19  . This is reflected in the relatively high residual (R(2σ) = 10.5%) observeda consequence of the falloff in high-angle data.
The generation of a σ-alkane complex in the singlecrystalline sample is signaled by a change in the binding mode of the hydrocarbon: from propene (π-face/C−H agostic interaction) to one where the ligand now lies in the square plane of the Rh(I) center, ligated to the metal through two Rh···H−C σ-interactions. The C−C distances in the hydrocarbon are consistent with single bonds, and the Rh···C distances are ∼0.2 Å longer than in the starting propene complex (Table 1). 39 The propane binds in a 1,3-motif: Rh···C 2.46(2), 2.45(2) Å (calculated 2.50 and 2.51 Å, section 2.3), and the central carbon (C2) is considerably farther away, being nonbonding (Rh···C2 2.99(3) Å), further signaling a change from the π-bound propene complex. Given the quality of the data, we cannot rule out that the propane binds slightly asymmetrically, as suggested by the DFT-calculated distances. With this caveat, the Rh···C1 and Rh···C3 distances sit in the range of those measured for other σ-alkane complexes ( , which have 1,2-and 1,3-alkane binding motifs, respectively. They are considerably shorter than for d 6 -propane weakly bound to an open Fe site in the MOF Fe 2 (dobdc) (∼3 Å), as analyzed by powder neutron diffraction at 4 K. 41 The 1,3-motif is similar to that proposed for propane coordination to a PdO(101) surface, albeit spanning two Pd sites. 45 The propane σ-complex Mn(η 5 -C 5 H 5 )(CO) 2 (propane) has been characterized in solution using in situ NMR spectroscopy at low temperature (133 K). 16 Given the quality of the refinement, hydrogen atoms were not located, and so the hapticity of the Rh···H−C interaction in [1-propane] Figure 1B). While this complex is stable toward decomposition at 298 K in the solid state, it slowly loses H 2 (6 h) in an SC-SC acceptorless dehydrogenation under an Arflow, similar to the closely related The molecular structure of [1-(2-methylbutane)][BAr F 4 ] demonstrates that the branched C5-alkane binds to the metal center in a 1,2-motif, via methyl (C1) and methine (C2) Rh··· H−C interactions. All of the C−C bonds in the hydrocarbon fragment are in the range associated with C−C single bonds (Table 1 and Figure S51). The two Rh···C distances, 2.348(9) and 2.39 (1) (14) and 2.442(7) Å) ( Table S2). The C−C angles around C2 sum to 328.6°, supporting the formation of an alkane ligand (sp 3 hybridization) on hydrogenation. While the residual of R(2σ) = 9.6% may reflect a small amount of superpositionally disordered alkene in the unit cell, we were unable to sensibly model a secondary alkene fragment being present ( Figure 5 shows the corresponding alkene structure that arises from acceptorless dehydrogenation of [1-(2-methylbutane)][BAr F 4 ]). Solution trapping experiments (CD 2 Cl 2 ) on the bulk sample immediately after hydrogenation recover 2-methylbutane with no evidence for residual alkene. However, we cannot discount the presence of a small amount of alkene complex in the unit cell of the analyzed sample that may contribute to these apparently shorter Rh···C distances. 46 The hydrogen atoms were placed at calculated positions, and a full discussion of the bonding with the metal center is provided in section 2.3.
The 2-methylbutane ligand is not disordered, which is in contrast with the precursor diene complex [1-isoprene]-[BAr F 4 ], which exists in the solid state as a 50:50 mixture of superpositionality-imposed orientations of the diene that are related by a noncrystallographically imposed C 2 rotation (Scheme 3 and Figure S52). 31 also confirms that a single isomer is formed in the bulk sample (section 2.2). As hydrogenation might be expected to initially form two different orientations of the bound 2-methylbutane ligand, we suggest that a relatively low energy reorganization of the alkane ligand is accessible to give the thermodynamically preferred orientation, which is both observed and computed in the solid state. This is likely a simple rotation. Low-energy fluxional processes for related σ-alkane complexes in the solid state have reported for NBA, 34 pentane, 47 and cyclohexane ligands. 31 We cannot discount alternative mechanisms in which the stepwise hydrogenation accesses intermediates that result in a single isomer being favored.
2.1.6. Hexane. The precursor to a σ-complex of hexane is the 2,4-hexadiene complex [Rh(Cy 2 PCH 2 CH 2 PCy 2 )(η 2 η 2 - Figure 1C and Figure S53). This complex is isolated in single-crystal form as the symmetric 2,4-isomer but in solution coexists in slow equilibrium with the 1,3-isomer (see the Supporting Information). This likely occurs through successive 1,3-hydride shifts 48 Figure 1C shows the resulting structure determined from a single-crystal X-ray diffraction study. The hexane ligand binds in a 2,4-motif (i.e., the Rh···H−C interactions are separated by a methylene group as in [1-propane][BAr  Table S2). They are similar to those reported for [1-pentane][BAr F 4 ], 2.514(4) and 2.522(5) Å, which also binds in a 2,4-motif. 47 The quality of the data was sufficient to locate and refine the hydrogen atoms associated with the Rh···H−C interactions (R(2σ)= 4.1%). These data suggest that both methylene C−H groups on each carbon are interacting with the metal center, although to differing degrees: i.e., Rh−H4B = 2.14(4) Å versus Rh− H4A = 2.46(A) Å. These interactions are analyzed in the computational section (section 2.3).
In the solid state the [BAr   While a hexane σ-complex has not been directly characterized in solution using NMR techniques, a related heptane complex, W(CO) 5 (heptane), has been observed using time-resolved XAFS. 12 This allowed for the W···C distance to be modeled at 3.07(6) Å for the σ-interaction. This is considerably longer than in [1-hexane][BAr F 4 ], even given the difference in covalent radii between W and Rh (0.2 Å). 49 2  Figure 1E). The resulting structural refinement was of good quality (R(2σ) = 4.8%) and shows the alkane to be interacting with the Rh center through methyl (Rh···C1 2.430(4) Å) and methylene (Rh···C4 2.788(6) Å) groups, in a 1,4-motif (calculated 2.46 and 2.89 Å, section 2.3). On the basis of these distances, the former is likely a η 2 interaction, while the latter is considerably longer, suggesting η 1 bonding. 33 In addition to characterization of the new σ-alkane complexes using singlecrystal X-ray diffraction, 31 P{ 1 H} and 13 C{ 1 H} SSNMR spectroscopy was used to characterize the reaction in the bulk and assess their relative stabilities (Scheme 4). For all of the systems reported here a diagnostic downfield shift is observed in the 31 P{ 1 H} SSNMR spectrum on formation of the σ-alkane complex (δ 102−110) from the alkene precursor (δ 74−90). There is an increase in the J(RhP) coupling constant on forming the σ-alkane complex, consistent with a more weakly bound trans alkane ligand, i.e. 152−182 to 188−236 Hz, respectively. In the 13 C{ 1 H} SSNMR spectrum signals due to the coordinated alkene in the precursor (100−50 ppm) disappear on hydrogenation. The decomposition product  ] is observed as a very broad signal, indicating loss of crystallinity, at δ ∼88.
The propane σ-complex is so unstable at room temperature that on hydrogenation of the bulk precursor in situ only ∼30% of the target alkane complexes is initially observed at 294 K. In addition to [1-propane] F 4 ] is also observed in the first NMR spectrum that is taken after 10 min post H 2 addition. In contrast, [1-(3-methylpentane)]-[BAr F 4 ] is not as stable in the solid state at 298 K. Although a σ-alkane complex is initially formed on hydrogenation ( Figure  1D and Figure S38 and S39), this changes over 16 h ( Figure  S40) to form a mixture of dehydrogenated methylpentene  is considerably more stablelikely a consequence of the branched alkane structure that modifies interactions with the anion microenvironment, and the different motifs of anions ( Figure 2).
The stability of any particular alkane σ-complex toward decomposition is likely to be strongly influenced by a combination of the primary coordination sphere interactions (i.e., the strength of the Rh···H−C bonds), stabilizing or destabilizing interactions from the secondary microenvironment, and differences in the tertiary, periodic, crystal structure. To probe both the intimate interactions of the alkane with the Rh(I) centers and the influence of the wider secondary microenvironment, we turned to a computational analysis of these new systems, as well as a comparison with those previously reported. We initially discuss the primary coordination sphere around the metal centers, which provides a baseline for the subsequent analysis of the influence of the wider environment.
2.3. Computational Studies on the Primary and Secondary Coordination Spheres. Further insights into the structure and stability of the Rh σ-alkane complexes were provided by periodic DFT calculations and electronic structure analyses. The latter were based on the fully optimized solidstate structures rather than the crystallographic data, and this choice was prompted by the experimental uncertainties in some of the alkane atom positions, notably in [1-propane]- [BAr F 4 ]. For the other complexes the observed and fully optimized structures provided very similar data, and both sets of results are compared in the Supporting Information. In the following discussion we first assess the intramolecular Rh···H− C σ-interactions, before probing the effect of the extended solid-state environment on the stability of both the Rh σalkane complexes reported here and related complexes from previous studies.  Figure 3A along with the results of the quantum theory of atoms in molecules (QTAIM), noncovalent interaction (NCI) and natural bond orbital (NBO) analyses in Figure 3B−D, respectively.
The computed structure of [1-propane] + shows two short Rh···H contacts (Rh···H 11 2.03 Å; Rh···H 31 2.00 Å) and slightly elongated C 1 −H 11 and C 3 −H 31 bonds (1.13/1.14 Å) that are indicative of two Rh→H−C σ-interactions. These are confirmed by the presence of Rh···H 11 and Rh···H 31 bond paths in the QTAIM analysis that feature bond critical point (BCP) electron densities, ρ(r), of 0.046 and 0.048 au, respectively. The C 1 −H 11 /C 3 −H 31 BCPs also exhibit reduced ρ(r) values of ca. 0.246 au, consistent with σ-donation to Rh (cf. the spectator C 1 −H 13 /C 3 −H 33 bonds 1.10 Å; ρ(r) = 0.272 au). We have previously found NCI plots to be a good indicator of C−H bond hapticity. 33 In this case the stabilizing blue features between the Rh center and the alkane that span both the C 1 −H 11 and C 3 −H 31 bonds suggest an η 2 C−H binding mode. This is confirmed by NBO calculations that quantify σdonation from the C 1 −H 11 and C 3 −H 31 bonds at 14.1 and 13.0 kcal/mol, respectively. This σ-donation is supported by total back-donations of 8.7 and 7.6 kcal/mol, respectively. An inspection of the Rh LP →σ* C−H back-donation confirms that this is dominated by π-character ( Figures S64 and S66). An η 2 C−H binding mode is also consistent with Rh−H−C angles of ca. 102°: 33,50 i.e., a "closed" M···H−C interaction. 51 In addition to these η 2 C−H interactions, some contribution from the geminal C 1 −H 12 and C 3 −H 32 bonds is also evident. Rh···H 12  analysis suggests comparable σ-donation (13.8 kcal/mol), but unusually the degree of back-donation (9.1 kcal/mol) now approaches that of the σ-donation. The major Rh LP →σ* C−H components exhibit π-character (Table S20), and this relatively strong back-donation may be a feature of the wide bite angle of the 1,4-alkane binding mode that is observed here for the first time as the thermodynamically preferred structure. 47 σ-Donation from the geminal C 1 −H 12 bonds is also somewhat larger in [1-(3-methylpentane)] + (4.8 kcal/mol) than in [1-propane] + (ca. 3.5 kcal/mol). In contrast, the C 4 −H 41 →Rh interaction in [1-(3-methylpentane)] + is markedly different and exhibits an η 1 C−H binding mode. This is most evident in the NCI plot, which shows a localized blue disk along the Rh··· H 41 vector. The degree of σ-donation is close to that of the η 2 C1−H11 interaction (12.6 kcal/mol), and a similar degree of back-donation is also found (12.0 kcal/mol). However, in this case back-donation is dominated by σ-donation from the occupied σ Rh−P orbitals into σ* C−H and this reflects a more end-on approach of the C 4 −H 41 31 T h ea l k a n el i g a n d si nt h e[1isobutane] + and [1-NBA] + cations both exhibit a 1,2-binding mode that closely resembles that of the 2-methylbutane ligand in [1-(2-methylbutane)] + . Moreover the 2,4-binding mode of pentane in [1-pentane] + has features similar to those of the alkane ligands in [1-propane] + and [1-hexane] + . These last three linear alkanes all lie parallel to the {RhP 2 } coordination plane. In contrast, the cyclohexane ligand in [1-cyclohexane] + sits perpendicular to this plane and this results in a binding mode that is best described as intermediate between η 2 C−H and η 1 C−H . The different orientation of the cyclohexane also rules out any stabilization from the geminal C−H bonds that was a feature of the linear alkanes (see Figure S97).

Stability of the σ-Alkane
Complexes. Scheme 4 summarizes the room-temperature stabilities of the σ-alkane complexes reported here. In this context "stability" refers to the lifetime of the σ-alkane complex before either (i) loss of the alkane to give the [1-BAr F 4 ] zwitterion and/or (ii) dehydrogenation to an alkene complex. . To probe these differing, empirically determined behaviors, we have computed ΔE 1 , the normalized lattice energy (i.e., taking into account the number of formula units per unit cell), and ΔE 2 , the energy required to remove one alkane from the unit cell. These provide a direct measure of the stability of the crystal lattice and of the strength of alkane binding within that lattice, respectively. ΔE 3 quantifies the interaction energy between the alkane ligand and [Rh(Cy 2 PCH 2 CH 2 PCy 2 )] + in the isolated cation. Scheme 5 illustrates these terms for [1propane][BAr F 4 ].
For each energy term all geometries were fixed at those found in the fully optimized structures. In addition to the four σ-complexes characterized here, [1-cyclohexane] F 4 ] have been added to the analysis. Like its hexane congener, the pentane complex loses the alkane to form the zwitterion, whereas the cyclohexane and isobutane complexes undergo room-temperature dehydrogenation. In contrast to all the other σ-alkane complexes [1-NBA][BAr F 4 ] is essentially indefinitely stable when it is maintained under an inert atmosphere. Thus, taken collectively, these σ-alkane complexes provide a good basis to compare the underlying factors that might influence stability in the solid state.
Computed data are presented in Table 2 and are organized by alkane binding mode and anion environment to bring together the most directly comparable structures with the same tertiary, periodic structure of anions. Some evidence for increased stability with a larger alkane can be seen in the higher values of ΔE 1 and ΔE 2 computed for [1-cyclohexane][BAr F 4 ] vs [1-propane][BAr F 4 ] (both 1,3-binding motifs). These differences arise from a greater interaction not only within the cation (ΔE 3 ) but also, more significantly, with the surrounding microenvironment, the latter being quantified by ΔE 4 (=ΔE 2 − ΔE 3 ). Although, as discussed, there are some subtle variations in the C−H→Rh σ-interactions, an additional factor is likely to be the presence of stabilizing dispersive interactions between the alkane ligand and both the cyclohexyl substituents of the chelating phosphine and the surrounding anionic framework. Intramolecular dispersive effects have been highlighted as playing a key role in σ-complex stability; 54 however, our study clearly highlights the role of the solid-state environment in providing additional stabilization and the fact that this factor can be substantial. For example the molecular binding energy of propane (ΔE 3 = 25.7 kcal/mol) is enhanced by almost 33% through intermolecular stabilization (ΔE 4 = 8.3 kcal/mol). Incorporating such environmental effects (be these due to the solid state or solvent) is therefore essential in order to provide a full picture of the factors affecting σ-complex stability.
Similar trends are seen on comparison of [  F 4 ] despite the much greater stability of the latter. This lack of correlation reflects the difficulties in comparing structures with different anion arrangements in the lattice. However, it may also point to the possibility that differential σalkane complex stabilities are kinetic in origin rather than thermodynamic.
2.3.4. Anion Microenvironment Effects. We have previously commented on the role of nonclassical C−H δ+ ···F δ− −C H-bonds in stabilizing σ-alkane complexes in the solid state. 26,36 Figure 4 highlights short contacts (at or below the sum of the van der Waals radii 55 ) of this type, as well as C− H···C contacts between the alkane H atoms and the surrounding anions in the computed structures. For [1propane][BAr F 4 ] only two C−H···C contacts are present. In [1-(2-methylbutane)][BAr F 4 ] four C−H···C and three C− H···F contacts are seen and these increase in number to five and six, respectively, in [1-(3-methylpentane)][BAr F 4 ]. The C−H···F contacts are also apparent in NCI plots of the proximal ion pairs (Supporting Information). Although it is difficult to quantitively compare these noncovalent interactions, the paucity of such contacts in [1-propane][BAr F 4 ] does correlate with the instability of this system. However, the presence of several C−H δ+ ···F δ− −C contacts is not a sufficient  Overall, several factors appear to be at play in controlling σalkane complex stability in the solid state: the strength of the intramolecular Rh···H−C interactions, the extent of intermolecular interactions in the microenvironment, and the fito f the alkane to the binding pocket. In addition, the kinetics of alkane displacement by the incoming [BAr F 4 ] − anion may also be a factor and this will itself also be related to the microenvironment and the periodic, tertiary structure of the anion framework. Addition of CO at 298 K to the resulting single crystals liberates the bound alkenes from the metal center, and an analysis by 1 H NMR spectroscopy shows that 2-methylbut-1-ene and 2-methylbut-2-ene are formed in a 1.4:1 ratio under these conditions.
Following the overall process from the initial formation of [1-(2-methylbutane)][BAr F 4 ] to the products of dehydrogenation using 31 P{ 1 H} SSNMR spectroscopy shows that the reaction is remarkably clean (Figure 5A). At room temperature the 13 C{ 1 H} SSNMR spectrum of the dehydrogenation products is featureless in the alkene region (100−50 ppm). However, cooling to 158 K reveals three (1 + 1 + 2) alkene environments. This suggests that in the solid state there is a low-energy isomerization process occurring, as described for [1-propene][BAr F 4 ], likely operating via an allyl/hydride intermediate. 25,36 This dehydrogenation is an SC-SC process, and the resulting structural refinement of the alkene products (R(2σ) = 8.6%) is of sufficient quality to unambiguously determine the formation of a 50:50 mixture of superpositional isomers of [1-(2methylbut-1-ene)][BAr F 4 ] and [1-(methylbut-2-ene)]-[BAr F 4 ] ( Figure 5B) at 150 K. The formation of an alkene ligand is signposted by coordination of a π-face of the ligand, sp 2 geometries of the salient carbon atoms, and a corresponding short C−C distance in each isomer. Each monoene ligand also engages in a supporting Rh···H−C  agostic interaction (Rh···C3, 2.36(2) Å; Rh···C1A, 2.41(3) Å). These are revealed in the 183 K 1 H NMR spectrum in CD 2 Cl 2 solution by the observation of resonances in the alkene region and signals diagnostic of agostic interactions at δ −0.25 and −1.23 (two overlapping signals); the latter are assigned to the diastereotopic agostic interactions from methylene C3 that results in two different agostomers. 56 The 31 P{ 1 H} NMR spectrum shows resonances due to three Rh(I) complexes, each with inequivalent phosphines. At 298 K this becomes a single environment with coupling to 103 Rh, and alkene/agostic signals in the 1 H NMR spectrum are lost, indicating a fluxional process at this temperature, likely a rapid alkene isomerization, as proposed in the solid state.
Kinetic data for this dehydrogenation process were collected by running individual reactions using batches of finely ground   (Figure 6). 57 These data were modeled using modified Johnson−Mehl−Avrami−Kologoromov (JMAK) kinetics. This approach describes reaction progress in the solid state in terms of a nucleation and growth model, where k is the growth rate constant and n is the Avrami exponent. 58 JMAK analysis has been used to describe SC-SC photoreactions in the solid state. 58−61 For the process here k = 9.5 × 10 −4 (±6 × 10 −5 )s −1 and n = 0.50 ± 0.02. Avrami exponents close to n = 4, 3, and 2 are suggestive of 3-D, 2-D, and 1-D growth, respectively, while n = 1 is indicative of a noncooperative transformation that occurs throughout the crystal. It has been suggestedt h a tn o n i n t e g e rA v r a m i constants, such as those observed here, point to the kinetics being diffusion controlled. 62 This could be related to a reaction front (i.e., H 2 loss) that moves through the crystal from outside to inside. A JMAK analysis of the dehydrogenation of [1isobutane][BAr F 4 ] also has n ≈ 0.5, 31 suggesting that this may be a more general observation for this type of reactivity in the single crystal. Avrami exponents of n ≈ 0.5 have been measured for other SC-SC processes. 59 A similar dehydrogenation process occurs for [1-(3methylpentane)][BAr F 4 ] in the single crystal over the course of 16 h under a dynamic vacuum (10 −2 mbar) to form a mixture of methylpentene isomers bound to Rh(I): [1-(methylpentenes)][BAr F 4 ]. However, this is not an SC-SC process; the crystallinity is lost, and signals due to the decomposition product  ] grow in considerably (∼35%). For this reason a reaction progress analysis using the JMAK approach was not appropriate. The presence of  ] and other decomposition products also meant that the solution characterization was not unambiguous. Dissolution of the solid in C 6 D 6 /d 6 -acetone liberated the bound alkenes from the metal center by forming the corresponding benzene adduct of Rh(I). 31 1 H NMR spectroscopy and ESI-MS data show that these alkenes are a mixture of isomers of methylpentene (Scheme 7)confirming that an acceptorless dehydrogenation in [1-(3-methylpentane)][BAr F 4 ] has occurred.
The acceptorless dehydrogenation of alkanes to alkenes is an important industrial process that requires high temperatures and a heterogeneous catalyst, as it is an endothermic process. 63 Using molecular organometallic systems it can be driven catalytically by removing H 2 64 or working in the solid phase under continuous-flow conditions. 38,65 We have recently demonstrated that spontaneous, albeit stoichiometric, dehydrogenation and H 2 loss occur in the well-defined σ-alkane complexes [1-isobutane][BAr F 4 ] and [1-cyclohexane]-[BAr F 4 ] to form isobutene and cyclohexadiene complexes, respectively. 31 This demonstrates that, if pre-equilibria for alkane binding at a metal center is biased to the σ-alkane complex, dehydrogenation is kinetically a rather straightforward process. While the coordination of the alkene product makes these processes more thermodynamically favorable than for the free alkane/alkene, calculations show that they are still slightly endergonic. 31 The same concept operates here but is now extended to methylbutane and methylpentane alkane ligands. The mechanism for dehydrogenation (which is also the microscopic reverse of hydrogenation), as described in detail for [1-cyclohexane][BAr F 4 ], 31 likely proceeds via initial C−H oxidative cleavage followed by β-H elimination and loss of H 2 , closely related to solution-based dehydrogenation systems. 2 ■ CONCLUSIONS By using the {Rh(Cy 2 PCH 2 CH 2 PCy 2 )} + metal fragment 1 with a supporting anionic framework of [BAr F 4 ] − anions, we have prepared a series of C 3 −C 6 linear and branched σ-alkane complexes using single-crystal to single-crystal solid/gas transformations from the corresponding alkene precursors. In combination with our previous studies using the same metal/ ligand/anion combination, this provides structurally characterized σ-alkane complexes of propane, isobutane, 31 pentane, 47 2-methylbutane, hexane, cyclohexane, 31 3-methylpentane, and norbornane. 26,34 These complexes display a wide variety of