Sizing the role of London dispersion in the dissociation of all-meta tert-butyl hexaphenylethane† †Electronic supplementary information (ESI) available: Experimental procedures, spectra and computational details. See DOI: 10.1039/c6sc02727j Click here for additional data file.

The structure and dynamics of enigmatic hexa(3,5-di-tert-butylphenyl)ethane was characterized via NMR spectroscopy for the first time.

Hexaphenylethane (HPE; H-1 2 ) was long assumed to have been synthesized by  in the context of preparing the rst organic free radical, the triphenylmethyl radical (H-1$) (Scheme 1). 1,2 However, it was shown in 1968 that H-1 2 rather corresponded to quinoid H-2. 3 While steric repulsion between the phenyl moieties was readily made responsible for instability of H-1 2 , the introduction of bulky tert-butyl groups in all meta positions, which should lead to signicantly higher steric crowding, resulted in isolable hexa(3,5-di-tert-butylphenyl) ethane ( t Bu-1 2 ) that could even be characterized through X-ray crystal diffraction. [4][5][6] Clearly, this questions our (conceptual) understanding of the balance of steric repulsion vs. noncovalent attraction, and a dispersion energy donor (DED) concept employing large alkyl groups may be invoked to rationalize such surprising bonding situations. 7 The classic HPE system therefore seems well suited to probe this concept. Here we report on the challenging re-synthesis and the rst NMR-spectroscopic characterization of t Bu-1 2 as well on density functional theory (DFT) computations to gauge the ne balance between Pauli repulsion and London dispersion (LD) attraction.
It is quite remarkable that the structural proposal for H-1 2 prevailed for almost 70 years because Gomberg himself noted that "Der Körper zeigt in höchstem Maasse die Eigenschaen einer ungesättigten Verbindung" (the substance shows pronounced properties of unsaturation) and readily adds oxygen and halogens. 1 He concluded: "Die oben mitgetheilten experimentellen Ergebnisse zwingen mich zu der Annahme, dass in dem 'ungesättigten Kohlenwasserstoff' das Radical Triphenylmethyl vorliegt" (the disclosed experimental ndings force me to assume that the "unsaturated hydrocarbon" presents the radical triphenylmethyl). 1 In addition, the neat colourless hydrocarbon was found to be in equilibrium with a coloured form in solution. 8 This triggered an intense discussion regarding the proper structure of triphenylmethyl where, apart from the highly symmetric HPE structure, 9 quinoid structures H-2 10 and H-3 11 were suggested (Scheme 1). In an early review Gomberg described an equilibrium between an associated and a free radical, the monoquinoidal structure, and HPE. 12 In the following years an equilibrium between H-1$ and H-1 2 suggested rst by Flürscheim 13,14 was gradually accepted and the quinoid structures vanished from the discussion, despite Gomberg mentioning later that a quinoid tautomer of H-1$ causes the yellow colour of the solution. 15 Notwithstanding the fact that some had misgivings regarding the correct structure of HPE, 16 dimer H-1 2 was generally accepted until Nauta et al. reinvestigated it utilizing 1 H-NMR and IR spectroscopies. These studies demonstrated that HPE adopted Jacobsen's monoquinoidal dimer H-2. 3 The rst computational investigation of H-1 2 was reported by Mislow et al. utilizing empirical force eld (EFF) computations that revealed a very long central R CC of 1.64Å in H-1 2 due to the repulsion between the trityl moieties. 17 The D 3 symmetric structure was found to be 2.6 kcal mol À1 more stable than the S 6 structure. A QM/MM (ONIOM) study of 2002 favoured the S 6 form and gave a BDE ¼ 16.6 kcal mol À1 for H-1 2 and a central bond length of 1.72Å. 18 The rst isolation of an unbridged HPE derivative was achieved by Rieker in 1978 through the introduction of tert-butyl groups in all 2-and 6-positions onto the Schlenk (tri(4biphenyl)-methyl) radical. 4,5 The previously reported introduction of t Bu groups onto the trityl radical H-1$ yielded tris(3,5-ditert-butylphenyl)methyl ( t Bu-1$) that was found to be monomeric in benzene 19 and Rieker concluded that [.] steric hindering of formation of the Jacobson-Nauta structure [R-2] by incorporation of bulky groups [in meta and/or para positions], [R-1$] must then either be persistent as the monomer-or dimerize to [R-1 2 ]. 4,5 Indeed, "poor, colourless crystals" could be grown from the orange cyclohexane solution consisting of the rst unbridged HPE derivative 1,1,1,2,2,2-hexakis(2,6-di-tertbutyl-[1,1 0 -biphenyl]-4-yl)ethane ( t Bu-4 2 ). 4,5 The dimer crystallized in S 6 symmetry with an astonishingly short experimental R CC of only 1.47Å. Mislow responded with improved EFF and MNDO SCF-MO computations that gave a R CC between 1.62 and 1.68Å. 20 Finally, a central bond length of 1.67Å was determined from a new crystal structure of t Bu-1 2 ; 6 magic angle spinning (MAS) nutation experiments gave R CC ¼ 1.64-1.65Å, 21 con-rming the earlier bond distance and refuting Rieker's structure. Our recent computational reinvestigation of the "HPE riddle" with the modern DFT implementations conrmed these results. 22 Both H-2 and t Bu-1 2 afford yellowish-orange, EPR active solutions, in line with very low computed dissociation energies. 22 The equilibrium constants for radical formation form the dimers should therefore be accessible by variable temperature NMR spectroscopy despite Rieker's notion that "Because of the high degree of dissociation and the sensitivity of the radical towards traces of oxygen no denite proof of the structure of [ t Bu-1 2 ] can be obtained with 1 H-NMR, 13 C-NMR, and mass spectroscopy, [.]". 4 The stronger magnetic elds available with current NMR spectrometers together with sophisticated techniques encouraged us to investigate the dissociation/association equilibrium of t Bu-1 2 .
The precursor tris(3,5-di-tert-butylphenyl)methyl chloride (5) was synthesized from benzene (6) via Friedel-Cras alkylation with t BuCl, ipso-bromination followed by lithiation at À78 C, subsequent triple addition to diethylcarbonate and chlorination of the central methyl carbon with acetyl chloride (Scheme 2). The classic reduction of 5 to t Bu-1$ with silver in benzene 1,21,23 under Scheme 2 Synthesis of t Bu-1 2 : (a) t BuCl, AlCl 3 , (À40) / (À15) C, 81% (b) Br 2 , Fe, CCl 4 , rt, 86% (c) 1. t BuLi, Et 2 O, À78 C / rt 2. (EtO) 2 CO, 78% (d) AcCl, n-hexane, 95% (e) Zn(Cu), C 6 D 6 or C 6 D 12 , rt (f) only in C 6 D 12 . meticulous exclusion of oxygen was slow and mainly yielded bis(tri(3,5-di-tert-butylphenyl)methyl) peroxide (7). Even silver derived from reduction of silver nitrate seemed to introduce a signicant amount of oxygen. Using the zinc-copper couple instead gave rapid quantitative conversion. The reduction in benzene-d 6 resulted in an orange solution with a 1 H-NMR spectrum that contained, besides several sharp signals, a very broad peak at d ¼ 1.88 ppm with a total width of 3 ppm (Fig. 1a,  top). The sharp signals were assigned to 7, tris(3,5-di-tertbutylphenyl)methane (8) and tris(3,5-di-tert-butylphenyl)methanol (9) by comparison with the NMR spectra of the pure compounds (cf. ESI †). The sample gave an EPR signal featuring the known spin pattern. 19,24 This, together with the known NMR lifetime broadening of organic radicals 25 as well as the r À6 line width dependence of the NMR signal with respect to the radical centroid in the molecule, 26 made it possible to identify the broad peak as the tert-butyl group hydrogen resonance of t Bu-1$.
The in situ radical generation in cylohexane-d 12 through reduction with Zn(Cu) is slower as compared to benzene-d 6 but gave the same orange solution and a similar 1 H-NMR spectrum with ve additional peaks at d ¼ 7.75, 7.19, 6.02, 0.98 and 0.95 ppm in a ratio of 1 : 1 : 1 : 9 : 9, respectively (Fig. 1a,  middle). This indicates a highly symmetric structure that would be incompatible with a less symmetric quinoid structure for which an allylic resonance at 5 ppm and a vinylic resonance at 6.4 ppm in a 1 : 2 ratio would be expected. 3,27 The spectrum is also in excellent agreement with the B3LYP-D3(BJ)/6-31G(d,p) C-PCM:cyclohexane computed spectrum of t Bu-1 2 (Fig. 1a,  bottom).
This rst 1 H-NMR spectrum of an unbridged HPE derivative features a signicant chemically inequivalence of the ortho or meta phenyl nuclei (for the 13 C-NMR spectrum see the ESI †). The fast inversion of the local helical chirality of an individual trityl group through a two-ring ip mechanism 28-30 that makes the two ortho or meta nuclei appear as a single signal at rt is blocked in t Bu-1 2 . That is, one edge of the phenyl ring points outside and the other inside towards the S 6 axis. While the phenyl groups in the X-ray crystal structure are indistinguishable due to the superposition of four disordered t Bu-1 2 arrangements, 6 the computed structure (Fig. 1b) nicely features this structural difference between inside (o 0 ) and outside (o) protons (Fig. 1a, bottom). Fortunately, the equilibrium between the t Bu-1$ radical and t Bu-1 2 revealed a strong temperature dependence (Fig. 2a), allowing us to determine parameters to calculate the equilibrium constant K at a particular temperature through integration of with I being the 1 H-NMR integrals, x the molar fraction, 1$ the radical monomer and 1 2 the dimer (for the derivation see the ESI †). The van't Hoff plot (Fig. 2b) shows a good linear correlation and DG 298 d ¼ À1.60(6) kcal mol À1 for the homolysis of t Bu-1 2 into two radicals reveals a very low dissociation energy. This DG 298 d value agrees reasonably well with computational predictions of DG 298 d ¼ À3 to +1 kcal mol À1 in cyclohexane with PWPB95-D3/TZV(2d,2p), 22 and it is in the range of the weakest experimentally determined DG 298 d of À0.2(1) kcal mol À1 for a C-C single bond reported for the 2,6-di-tert-butyl-4-methoxyphenoxyl dimer (12, Fig. 3). 31 As found for 12, DH 298 d of 6.1(5) kcal mol À1 is outbalanced by TDS 298 d ¼ 6.3 kcal mol À1 (298 K). We nd a similar enthalpy-entropy compensation for t Bu-1 2 with DH 298 d ¼ 7.94(3) kcal mol À1 and TDS 298 d ¼ 9.5(3) kcal mol À1 (298 K); this compares well with other weakly bonded hydrocarbons (cf. ESI †).
The dissociation enthalpy of t Bu-1 2 is 2.8 kcal mol À1 smaller than the 10.7(2) kcal mol À1 DH 298 d of H-2, 32 while the entropy contribution in t Bu-1 2 is signicantly larger (TDS 298 d ¼ 6.0 kcal mol À1 ). This is not surprising because covalent t Bu-1 2 requires much more ordering of the t Bu-groups for optimizing the LD interactions, leading to a large, counteracting DS contribution. This is likely to be a general phenomenon for structures with large LD contributions because the DEDs oen require optimal structural alignment for maximizing the LD interactions.
Differences in LD contributions between gas phase computations and solution experiments were rationalized with a di-n- Fig. 2 (a) Variable temperature 1 H-NMR spectra of the equilibrium between t Bu-1$ ( ) and t Bu-1 2 ( ) and (b) the corresponding van't Hoff plot (see ESI † for complete spectra). Fig. 3 The experimental bond lengths R CC do not correlate well with the bond dissociation enthalpy, entropy, and free energy. Bond lengths given inÅ, enthalpies and energies in kcal mol À1 , entropies in cal K À1 mol À1 . Bold numbers are from this work. a No error given. t Bu-1 2 ; 6 H-2; 32, 33 12. 31 hexyl substituted Wilcox-type balance by Cockro and coworkers. 34,35 Another approach outlined here is the use of the radical dimerization energies to determine the effect of DEDs on chemical equilibria. While large, polarizable electron donor substituents stabilize the dimers and the free radicals to different degrees, the radicals are stabilized mostly by conjugation. Depending on which radical stability scale one uses, meta alkyl substitution of benzyl radicals may be slightly stabilizing [36][37][38] or destabilizing, 39,40 but it is small in all cases. That is, the increased stability of t Bu-1 2 relative to parent H-1 2 must originate from the LD contributions of the t Bu groups.
Does the common measure for bond strengths, the bond dissociation energy (BDE), still apply here? BDEs were initially developed on the basis of small (oen diatomic) molecules for which LD is a minor component and the overall bond stability reects the covalent bond strength. For larger, crowded molecules as R-1 2 the covalent bond increasingly is inuenced by Pauli repulsion and LD attraction. While for H-1 2 LD attenuates about half of the repulsion, in t Bu-1 2 the increased repulsion must be compensated by LD to a higher degree. 41 The difference between the DG 298 d computed in the gas phase (13.7 kcal mol À1 ) 22 and the experimental DG 298 d value measured here (À1.6 kcal mol À1 ) can be taken as a rough measure of the attenuation of the LD interactions in solution. As the corrections to account for LD effects are large (ca. 60 kcal mol À1 ), 22 a signicant LD contribution must therefore persist also in solution. In light of such large LD contributions (cf. Table S3 †), the BDE does not seem to be a good measure for the covalent bond strength of the central bond.
As large-scale computations including properly computed entropy terms can reproduce DG 298 d reasonably well, 22 we used more approximate DFT computations to make some qualitative predictions regarding other DEDs in R-1 2 as model (Fig. 4). We employed the commonly used alkyl groups Me, i Pr, t Bu, Cy, and 1-Ad as DEDs. With up to 356 atoms in Ad-1 2 only DFT methods are currently feasible; these computations still take a very long time because of the very at potentials caused by the rotations of these groups. The B3LYP 42,43 functional with the Becke-Johnson damped dispersion correction D3(BJ) introduced by Grimme 44,45 as well as the hybrid GGA functional M06-2X 46 of Truhlar et al. were used in conjunction with a cc-pVDZ basis set (Table S3 †). 47 In the HPE derivatives the symmetry was restricted to the S 6 point group 6,18 (as experimentally observed for t Bu-1 2 ) while the radical monomers t Bu-1$ were assumed to have C 3 symmetry. The C-PCM model was employed to account for bulk solvent effects. 48 First of all, the B3LYP-D3(BJ) and M06-2X results with a cc-pVDZ basis set show the same general trends but diverge signicantly as the size of the DED increases (Table S3 †). The M06-2X functional is in good agreement for t Bu-1 2 but the trend is not as smooth as with B3LYP-D3(BJ). 49 Still, the LD contributions are not merely minor corrections but are quite large, exceeding the magnitude of carbon-carbon bond energies for R ¼ 1-Ad (cf. ESI †). There is a large dispersion correction even in the hitherto unobserved parent system H-1 2 that is predicted to dissociate with a DG 298 d of less than À5 kcal mol À1 . Non-covalent interactions can be visualized by plotting the reduced density gradient in regions of low electron density (NCI plot). 50 This enables a qualitative analysis of the balance between repulsive and attractive contact areas. The NCI plots (Fig. 5) of H-1 2 , t Bu-1 2 and Ad-1 2 visually support the general trend obtained for DG 298 d . Parent H-1 2 features repulsive (red) areas between phenyl moieties within and between the trityl  Non-covalent interaction (NCI) plots (s ¼ 0.5 au/À0.01 < r < +0.01 au) are depicted separately on the left from the molecular structure on the right for clarity. Repulsion is colour-coded red, "strong" attraction blue and weak interactions in green. groups and few attractive (C-H/p) interactions (blue). Substitution with t Bu groups leads to signicant growth of both attractive and repulsive regions in the periphery of the HPE core structure but scattered weak interactions (green) also appear. Finally, Ad-1 2 clearly shows a dense, weakly interacting region between the substituted trityl moieties. Hence, although the 1-adamantly moieties are even larger than the t Bu groups, they exhibit a huge noncovalent contact area that maximizes attractive LD interactions visually outweighing the repulsive regions.

Conclusions
We re-synthesized t Bu-1 2 , a member of the elusive class of HPE derivatives, and were able to obtain its dynamic NMR spectrum in equilibrium with the corresponding free radical t Bu-1$. The dissociation free energy of DG 298 d (exp.) ¼ À1.60(6) kcal mol À1 conrms computational pre-dictions and is composed of nearly equally large enthalpy and entropy contributions at 298 K. Computations suggest that substitutions with isopropyl and cyclohexyl DEDs also are accompanied by large unfavourable entropy contributions so that it is imperative to use rigid hydrocarbon moieties as DEDs. As a consequence, the introduction of sterically even more demanding 1-adamantyl substituents predicts an even further reduction the central bond length and a signicant increase in stability as compared to t Bu-1 2 . Counterintuitively, Ad-1 2 should therefore be an isolable HPE derivative despite the use of even bulkier groups. Hence, large, highly polarizable and rigid hydrocarbon moieties are the most effective DEDs.