Solution, Solid‐State, and Computational Analysis of Agostic Interactions in a Coherent Set of Low‐Coordinate Rhodium(III) and Iridium(III) Complexes

Abstract A homologous family of low‐coordinate complexes of the formulation trans‐[M(2,2′‐biphenyl)(PR3)2][BArF 4] (M=Rh, Ir; R=Ph, Cy, iPr, iBu) has been prepared and extensively structurally characterised. Enabled through a comprehensive set of solution phase (VT 1H and 31P NMR spectroscopy) and solid‐state (single crystal X‐ray diffraction) data, and analysis in silico (DFT‐based NBO and QTAIM analysis), the structural features of the constituent agostic interactions have been systematically interrogated. The combined data substantiates the adoption of stronger agostic interactions for the IrIII compared to RhIII complexes and, with respect to the phosphine ligands, in the order PiBu3>PCy3>PiPr3>PPh3. In addition to these structure–property relationships, the effect of crystal packing on the agostic interactions was investigated in the tricyclohexylphosphine complexes. Compression of the associated cations, through inclusion of a more bulky solvent molecule (1,2‐difluorobenzene vs. CH2Cl2) in the lattice or collection of data at very low temperature (25 vs. 150 K), lead to small but statistically significant shortening of the M−H−C distances.


Introduction
The coordination chemistry of CÀHb onds is an important facet of contemporary organometallic chemistry. [1][2][3] Adoption of 3-centre-2-electronM ÀHÀCb onds can help stabilise otherwise reactivel ow-coordinate metal complexes that are implicated in many catalytic reactions, and from af undamental perspectiver epresent an opportunity to gain insighti nto transition-metal-mediated CÀHb ond activation reactions. [4] As a consequence of the weakly interacting nature of CÀHb onds, well-defined examples are almost exclusively limited to intramolecular systemst hat are promoted through the chelate effect. As first articulated by Brookhart and Green, the consistent interactions are termed" agostic" and typified by MÀHÀC contacts of < 3 . [1,5] The characterisation of alkane complexes is significantly more experimentally demanding, but has been achievedi ns olutionu sing time-resolveds pectroscopicm eth-ods under low temperature regimes, [3,6] and recently in the solid-state by X-ray crystallography through application of single-crystal to single-crystalt ransformations. [7] Given that the development of CÀHb ond activation chemistry has been closely connected with the organometallic chemistry of rhodiuma nd iridium, [8] it is perhaps unsurprising that al arge number of well-definedc omplexes of these group 9m etals featuring agostici nteractions have been reported. [9][10][11][12][13][14][15] Indeed amongstk nown examples an umber of families can be identified,w ith M III complexes of the formulation trans,cis-[ML 2 H 2 ] + (A:M= Rh, Ir;L= phosphine or NHC), [9] [M(Binor-S)L] + (B:B inor-S = 1,2,4,5,6,8-dimetheno-S-indacene; L = phosphine), [10] and bearingc yclometalated ItBu (C, D)t he most outstanding ( Figure 1). [11] Structurally relatedc lusters of this nature are of interest to gauge an understanding of the effect of the metal alongside subtle variations of the ligand composition on the constituent agostici nteractions. Unfortunately,a st hey currently stand, neither the size nor specific membership of these three families is wellsuited to an analysis of this nature.
Whilst it is conceivably possible to extend the membership of the aforementioneds ets, the synthetic chemistry underlying the isolation of these highly reactive organometallics presents an umber of practical challenges. Recognising ad egree of commonality amongst A-C and others, [12] namely sawhorse metal geometriesw ith high trans influence ligands in the cisequatorial positions, and building upon the previous report of low-coordinate Rh III complex trans-[Rh (2,2'-biphenyl)

(PiPr 3 ) 2 ]
[BAr F 4 ]( 1c;A r F = 3,5-(CF 3 ) 2 C 6 H 3 ), [13] we reasoned that utilising 2,2'-biphenyl as an ancillary ligand would be as traightforward means to gatheras et of solutionand solid-state data for agostic interactions between phosphine ligand substituents and Rh III and Ir III centres. To this end, and with av iew to elucidating structure-property relationships within such data, we report the synthesis and extensive characterisation of low-coordinate complexes of the formulation trans-[M (2,2'-biphenyl) [BAr F 4 ]( M= Rh, 1;I r, 2;R= Ph, a;C y, b; iPr, c; iBu, d;F igure 2). This series of complexes encompasses both aryl and alkyl phosphine ligands (i.e. Ph vs. Cy), cyclic and acyclic alkyl phosphine substituents (i.e. Cy vs. iPr) and the possibility to adopt both g-a nd d-agostic interactions (i.e. iPr vs. iBu). DFT calculations have also been carriedo ut to aid structurali nterrogation.

Solid-state structures of 1and 2
Single crystalline samples of 1 and 2,g rown as described above,w ere analysed in the solid-stateu sing X-ray diffraction under typical experimental conditions (i.e. MoKa radiation, T = 150 K). [18] Agostic interactions are evident in the complexes bearing trialkylphosphines, while the triphenylphosphine derivatives are conspicuously obtained as adducts of solvent in the solid-state, namely 1a·CH 2 Cl 2 and 2a·CH 2 Cl 2 . [19] For ag iven phosphine, 1 and 2 are in general isomorphous; [20] those of 1 are depicted in Figure 3, with selected metrics for 1 and 2 compiled in Table 1. The salient features ande xperimental attempts to perturb crystal packing in 1b and 2b,a re discussed below in turn.
In the case of the triisobutylphosphined erivatives 1d and 2d,m eaningful analysis in the solid-state was impeded by extensived isorder of the phosphine ligands (see the Supporting Information for full details), necessitating alternative analysiso f samples bearingi nsteadt he [Al{OC(CF 3 ) 3 } 4 ] À counter anion; 1d* and 2d*.A lthough even in this case there are some subtle crystallographic differences between the rhodium and iridium congeners,t hese samples enable interrogation of nondisordered isostructural triisobutylphosphine complexes (1d* shown in Figure 3, see the Supporting Information for full details). Contrasting the other trialkylphosphine variants, which feature g-agostic interactions, thesec omplexes each show two d-agostic interactions, with M1ÀC21/C31 distances of 2.863(5)/ 2.979(4) and 2.781 (7)/2.956(6) for the rhodium and iridium congeners, respectively.Ad ifference easily reconciled when recognising the more flexible nature of the isobutyl substituent, which enables such interactions to be formed with significantly reduced distortion of the ligand. For instance, the triisobutylphosphine ligands in 1d* and 2d* are associated with distinctly more perpendicular C4-M1-P2/C15-M1-P3 and open M1-P2-C20/M1-P3-C30 angles than the other trialkylphosphine derivatives ( Table 1).
Characterisation of 1a nd 2u sing NMR spectroscopy The NMR spectra of 1b-d and 2b-d measured in CD 2 Cl 2 solution at 298 K( 500 MHz) are notable for the absence of low frequency 1 Hr esonances [1] and time averaged C 2v symmetry,i ndicating that persistent agostic interactions are not adopted under ambient conditions. This is perhaps not surprising given the inherently weak nature of 3-centre-2-electron MÀ-HÀC bonds, associated distortion of the phosphine ligand from ideal coordination geometry,a nd capacity forf ast exchange between substituents on the NMR time scale. In attempt to probe the latter,l ow temperature 1 H( 500 MHz) and 31 P (202 MHz) NMR data were acquired in CD 2 Cl 2 ,d own to 185 K: the practical working limit for the solvent. Whilst in each case the onset of signal decoalescence was observed in the 1 H spectra on cooling, in no instance was the slow exchange regime reached (see the Supporting Information). Consequently,c onclusive interpretation and quantitative comparison of the variable temperature dataw as not possible. Nevertheless some general trends can be elucidated from qualitative inspection of the NMR data. For instance, as gauged though relative changes in the line broadening of the 1 Hs ignals, the onset of decoalescence occurs at noticeably highert emperatures for the iridium trialkylphosphine complexes 2b-d comparedt o the rhodium variants 1b-d.F or the triisobutylphosphine derivatives, for example, appreciable line broadening is apparent in the 1 HNMR spectrum of 2d on cooling from 298 to 225 K, whereas additional cooling to 200 Ki sr equired for similar changes in the spectrum of 1d ( Figure 5). Reinforcing interpretation of the solid-state data, this observation is consistent with stronger agostici nteractions in the heavier group 9c ongeners. In as imilar manner analysisoft he 1 HNMR spectra indicates that more persistentM ÀHÀCb onding is adopted in 1d and 2d than the other trialkylphosphine complexesa nd moreover in the relative order PiBu 3 > PCy 3 > PiPr.A lthough such a trend is not borne out in the observed M1ÀC21/C31 distances, negative correlationsc an be drawn out through the extent of phosphine distortion associated with forming as ignificant agostici nteraction, that is, the P2 < npln and C4-M1-P2 angles ( Table 1).
As for the trialkylphosphine complexes, 1a and 2a display time averaged C 2v symmetry in CD 2 Cl 2 solution at 298 K (500 MHz). For these complexes,h owever,p artial decoalescence of the 1 Hs ignals of the phosphine substituents occurred on cooling to 185 Kt hat we attributet oP ÀPh restricted rotation of the phosphine ligands. The slow exchange regime is most advanced for 1a compared to 2a and at this temperature the phosphine 31 Pa nd the four 2,2'-biphenyl 1 Hr esonances remained sharp. The 1 HNMR spectrum of 1a recorded at 185 Ks hows as ignificantly upfields hifted ortho-phenyl 3H signal at d 6.02 (fwhm = 74 Hz) that exhibitsas trong NOE interaction with the 6,6'-biphenyl resonances indicating that they are pointing downwards towards the metal.B ased on this data we suggest that coordination of the solvent is not significant under the range of temperatures we have studied, and instead there is av ery weak bondingi nteraction between the phenylr ing of one of the phosphine ligands and the metal (time averaged across all the substituents). Such an interaction would explain why PÀPh restricted rotationi so bserved at low temperature by 1 HNMR spectroscopy (large Dd 1H ), but not by 31 PNMR spectroscopy (small Dd 31P ).
An alternative approacht og auge the degree of metal ligation in these homologous series could involve ac hemical shift based-scale employing the 13 Cr esonances of the coordinated carbonso ft he 2,2'-biphenyl ancillary ligand (d C ,T able 3) that are trans to the "free" coordinations ites. Similar approaches employing the 13 Cr esonances of trans-disposed NHC ligands [29] or metal-carbides [30] as ligand electronicp arameters have been used to excellent effect. For 1 and 2,a bsolute values of d C cannotb eu sed due to non-negligible contributionsf rom the different cis phosphine ligands. [31] We have attempted to deconvolute such contributions by using the chemical shift difference between 1 and 2 and their respective precursors 3 and 4, however,i ti sn ot possible to draw ac onclusive trend for all the phosphinel igandss tudied ( Table 3). The smallest differences, however,a re observed for the triisobutylphosphine derivatives, consistent with the adoption of the strongest agostici nteractions.

Computational insights
Supplementing the experimental findings, the structures of low-coordinate complexes 1 and 2 have been examined in silico using DFT-based calculations at the pbe0/def2-tzvp level of theory. [32] In accord with the preceding analysis, structures of the associated cations were optimised startingf rom geometries of only the well-ordered/major disordered componentso f cations observed in the solid-state; 1' and 2'.I nt he case of the triphenylphosphine adducts, structures of both low-coordinate 1a' and 2a' (1a' depicted in Figure 6) and dichloromethane complexes 1a'·CH 2 Cl 2 and 2a'·CH 2 Cl 2 were interrogated.T he binding of dichloromethanet ol ow-coordinate 1a' and 2a' is calculated to be weak( DH = À5.18/À5.96 kcal mol À1 )a nd ultimately formation of 1a'·CH 2 Cl 2 and 2a'·CH 2 Cl 2 are predicted to be significantly endoergic at 298 K( DG 298K =+9.20/ + 9.34 kcal mol À1 ). These data therefore imply retention of the halocarbon would be entropically disfavoured in solution, [33] reconciling the experimental evidence.
The presence of agostic interactions in the trialkylphosphine complexes was fully corroborated by analysis of 1b-d' and 2b-d' using both the Natural Bond Orbital (NBO) and Quantum Theoryo fA toms in Molecules (QTAIM) approaches ( Figure 7, Table 4). [34] Using the former,a doption of 3-centre-2electron MÀHÀCb onds is evidenced through significant perturbation energies associated with s CH !ML* andM L!s* CH interactions (21.81-63.64 kcal mol À1 ), while examination of the electron density using the latter reveals characteristic curved bond paths between the metal centre and hydrogen atom and associated critical point properties (1 MH = 0.017-0.051; r 2 1 MH = + 0.049-+ 0.167). [35] Moreover,u sing the more intuitive bond delocalisation parameter,s ignificant MÀHa nd correspondingly reduced CÀH" bond orders" are apparent from the QTAIM analysis.
The associated metricsh elp quantify previoust rends elucidated from the experimental work:s ignificantly stronger agos- Table 3. SelectedNMR data for 1 and 2 (CD 2 Cl 2 ,298 K). [a] Change in parameter relative to that measured in 3 (M = Rh) or 4 (M = Ir). tic interactions are adopted in the iridium congeners, with around4 0% larger NBO donor-acceptor energies and QTAIM MÀHd elocalisation indices, and the degree of agostic bonding decreases in the order,P iBu 3 @ PCy 3 > PiPr 3 (notably for 1c' only one agostic interaction is detectedi nt he QTAIM analysis).
Although the optimised structures of 1a' and 2a' show significantd istortion of the phosphine substituents towards the metal, only very weak agostic interactions are inferred from the NBO analysisw itht he perturbatione nergiesa ssociated with s CH !ML* and ML!s* CH interactions < 6kcal mol À1 (cf. > 15 kcal mol À1 fort he alkyl phosphine complexes). Moreover, inspection of the donor-acceptor NBO interactions associated with the phosphine substituents proximate to the metal centre show no significant p-interactions. No bond paths between the metal centre and associated hydrogen atoms were detected in the QTAIM analysis. The data are therefore consistent with very low-coordinate complexes. Indeed, the metal centres in these complexes have the lowest sum of delocalisation indices for each respective metal series (3.664, 1a';3.997, 2a').

Conclusion
Ah omologous family of low-coordinate complexes of the formulation trans-[M(2,2'-biphenyl)(PR 3 ) 2 ][BAr F 4 ]( M = Rh, 1;I r, 2; R = Ph, a;Cy, b; iPr, c; iBu, d)h as been prepared and extensively structurally characterised. The formation of these sawhorse complexes is promoted throughi ncorporation of the high trans influence 2,2'-biphenyl ancillary ligand and stabilised through the adoption of weak agostic interactions, at the opposing open coordination sites, between the phosphine ligand substituents and the metal centres.
Enabled through ac omprehensive set of solution phase (VT 1 Ha nd 31 PNMR spectroscopy) and solid-state (single crystal Xray diffraction) experimental data, and analysisi ns ilico (DFTbased NBO andQ TAIM analysis), the structural features of the constituent agostic interactions have been systematically interrogated. The combined data substantiates the adoption of stronger agostic interactions for the Ir III compared to Rh III complexes and, with respectt ot he phosphine ligands, in the order PiBu 3 > PCy 3 > PiPr 3 > PPh 3 . In contrast to the trialkylphosphine complexes which feature notable MÀHÀCb onds, the triphenylphosphinev ariants are instead only obtained in the solid-state as adducts of the weakly coordinating solvent dichloromethane employed; 1a·CH 2 Cl 2 and 2a·CH 2 Cl 2 .T he entropically unstable nature of thesea dducts was, however,e videnced in solution by 1 Ha nd 31 PNMR spectroscopy and is supported by DFT calculations. Moreover, NBO and QTAIM analysis of optimised structures of 1a and 2a highlight the insubstantialn ature of MÀHÀCb onds in these low-coordinate complexes.T he formation of the strongest agostic interactions observedi nt riisobutylphosphine derivatives is attributed to the flexible nature of the isobutyl substituents, anda ssociated with RhÀCa nd IrÀCd istances of 2.863(5)/2.979(4) and 2.781(7)/2.956 (6) ,r espectively,i nt he solid-state and reduceds tructural dynamics in solution. For these complexes, extensive s CH !ML* and ML!s* CH interactions are apparent in the NBO perturbation analysis( 1d', 43.13; 2d',6 3.64 kcal mol À1 )a nd significant QTAIM MÀHb ond delocalication indicesa re calculated (1d',0 .181/0.160; 2d', 0.234/0.207).
In addition to the above structure-property relationships, the effect of crystal packing on agosticinteractions was investigated in 1b and 2b.C ompression of the associated cations, throughi nclusion of am ore bulky solventm olecule (1,2-difluorobenzene vs. CH 2 Cl 2 )i nt he lattice or collection of data at very low temperature (25 Kv s. 150 K), lead to small but statistically significant shortening of the MÀHÀCd istances.