The intermolecular anthracene-transfer in a regiospecific antipodal C 60 difunctionalization

Ever since the discovery of fullerenes, their mono- and multi-functionalization by exohedral addition chemistry has been a fundamental topic. A few years ago, a topochemically controlled regiospecific difunctionalization of C 60 fullerene by anthracene in the solid state was discovered. In the present work, we analyse the mechanism of this unique reaction, where an anthracene molecule is transferred from one C 60 mono-adduct to another one, under exclusive formation of equal amounts of C 60 and of the difficult to make, highly useful, antipodal C 60 bis-adduct. Our herein disclosed dispersion corrected DFT studies show the anthracene transfer to take place in a synchronous retro Diels-Alder/Diels-Alder reaction: an anthracene molecule dissociates from one fullerene under formation of an intermediate, while undergoing stabilizing interactions with both neighbouring fullerene molecules, facilitating the reaction kinetically. In the intermediate, a planar anthracene molecule is sandwiched between two neighbouring fullerenes and forms equally strong “double-decker” type π - π stacking interactions with both of these fullerenes. Analysis with the distortion interaction model shows that the anthracene unit of the intermediate is almost planar with minimal distortion. This analysis highlights the existence of simultaneous noncovalent interactions engaging both faces of a planar polyunsaturated ring and two convex fullerene surfaces in an unprecedented ‘inverted sandwich’ structure. Hence, it sheds light on new strategies to design functional fullerene based materials.


INTRODUCTION
Fullerenes, the spherical molecular carbon allotropes first discovered in mass-spectrometric experiments in 1985, 1, 2,3 open up exciting fields of chemical research. [4][5][6][7] The unique properties of the icosahedral C 60 molecules have particularly inspired a multitude of studies concerning the functionalization of this polyunsaturated carbon compound by the means of addition reactions. 2, 5, 8 Early on, a range of cyclopropanations 4, 8,9 and pyrrolidine forming reactions 8,10 as well as other formal cycloaddition reactions 8 were used very effectively. The synthetic interest in the chemistry of C 60 was further boosted by its pronounced and theoretically rationalized selectivity for cycloaddition reactions at its so called [6,6]-bonds. 6,8,[11][12][13] Indeed, the thermally reversible [4+2]cycloaddition (Diels-Alder, DA) reaction has become a most versatile methodology for the coupled with functionalization of a neighbouring mono-adduct molecule. Hence, a thorough computational analysis of this anthracene transfer between two fullerenes was carried out, in order to gain insights into the simultaneous interaction of two spherical and one planar poly-unsaturated carbon molecules.
We investigated the topochemically controlled regiospecific anthracene transfer by two model reactions: Reaction A describes the transfer of one anthracene molecule from one C 60 fullerene mono-adduct to a 2 nd C 60 fullerene (Scheme 1, panel A), while reaction B describes the transfer of one anthracene from one C 60 fullerene mono-adduct to another C 60 fullerene-anthracene mono- Reaction B depicts the anthracene transfer from one C 60 :anthracene mono-adduct to another, resulting in the creation of one trans antipodal bis-adduct and one C 60 fullerene. A.

COMPUTATIONAL METHODOLOGY
As no high resolution X-ray crystal structures were available, the initial structures for the C 60 fullerenes and C 60 :anthracene mono-adduct were set-up using Gaussview 4.1.2. 100 All subsequent structure optimizations and harmonic frequency calculations were performed using Turbomole 7.3 101 and were done in C1 symmetry. Structure optimizations have been carried out with Density Functional Theory (DFT) utilizing the GGA density functional BP86 102-105 in combination with the def2-SVP basis set. 106 As shown in previous studies, empirical dispersion corrections, that are not intrinsically dealt with in DFT, are essential to obtain reliable structures in such extended psystems and to localize reaction intermediates. 95 Therefore, Grimme's empirical dispersion corrections with Becke-Johnson damping of the DFT-D3 107 type were employed in all calculations.
Selected structures were re-optimised with BP86/def2-TZVP 108 /D3 but structural differences were found to be small. Reported electronic energies were calculated as single points BP86/def2-TZVP/D3 on the BP86/def2-SVP/D3 optimized structures. An even larger def2-QZVP 109 basis set yielded very similar single point energies with differences less than 2 kJ mol -1 compared to def2-TZVP. Hence, the triple-zeta def2-TZVP basis set was considered accurate enough. To test the effect of the density functional, single point calculations with B3LYP 102, 105, 110, 111 /def2-TZVP/D3 were computed on the BP86/def2-SVP/D3 optimized structures too. To validate our chosen methodology (density functional/basis set), we compared both structural parameters with known experimental data. As to our knowledge, currently no crystal structure of the C 60 : anthracene mono-adduct exists, we compare our calculated structures to the available experimental C 60 :antracene bis-adducts ("edge" and "trans-4") structures. 67 Through the comparison with the trans-3 and edge C 60 :anthracene bis-adducts, it is shown that the methods chosen offer accurate structures, as the bond lengths deviate less than 0.01 Å from their crystal counterparts, while the angles and dihedrals are within 0.1 o .
To further test our methodology, we also calculated the formation of the C 60 :anthracene monoadduct (see also Table S6 and Table S7 in the Supplementary Information), for which experimental data is available. In their 2004 paper, Sarova et al 24 reported an activation enthalpy of DH ‡ =57 kJ mol -1 and a Gibbs energy of DG ‡ =93 kJ mol -1 in toluene. While this enthalpy is very close to our BP86 calculated value of DH ‡ =59.4 kJ mol -1 , the Gibbs energy was with DG ‡ =72.6 kJ mol -1 a bit underestimated. B3LYP values, however, overestimated the reaction barrier compared to experiment, DH ‡ B3LYP =86.2 kJ mol -1 and DG ‡ B3LYP =114.6 kJ mol -1 . The experimental reaction energy was found to be DH=-81 kJ mol -1 and DG=-23 kJ mol -1 . BP86 underestimated these values (DH=-54.5 kJ mol -1 and DG=7.4 kJ mol -1 ) and the trend got worse for B3LYP (DH=-31.4 kJ mol -1 and DG=31.7 kJ mol -1 ). Full optimisations and calculation of thermodynamic corrections at the BP86/D3/def2-TZVP level alleviated these shortcomings to some extend and correctly predicted the reaction to be exergonic with DG=-5.2 kJ mol -1 (see also Table S7) but are not feasible given the size of the investigated structures. In our view BP86 yielded a better overall performance although barriers are likely to be underestimated.
As the initial reaction is in solid-state, involving no charged species, no long-range interactions were expected. Indeed, taking the effect of the crystal environment into account by a dielectric constant, we chose e=4 here, 112 in agreement with previous studies, had little effect on the resulting energies. As can be seen from Table S5 in the Supplementary Information, the electronic energies decreased by less than 2 kJ mol -1 . Thus, modelling the reaction in gas phase is adequate.
The correct stationary points were identified through harmonic frequency calculations, by examining the eigenvalues of the Hessian corresponding to each structure. Minima show only positive eigenvalues, while a transition state shows exactly one imaginary eigenvalue and its associated eigenvector corresponds to the reaction coordinate.
To obtain Gibbs energies, zero-point energies and thermal corrections at 298.15K were calculated via approximation of the partition function by the standard rigid rotator and harmonic oscillator model using Turbomole's "freeh" tool. Obtained harmonic frequencies were scaled with a factor of 0.9914 113 to increase the accuracy. These corrections were calculated with BP86/def2-SVP/D3 and added to the BP86/def2-TZVP/D3 electronic energies. To highlight the non-covalent interactions, NCIPLOT was used, 115 where the second eigenvalue of the electron-density Hessian matrix, sign(l 2 )r, is depicted on an isosurface of the reduced gradient s. 116 Areas with (weak) non-covalent interactions are characterized with a low (reduced) electron density gradient and a sign(l 2 )r close to zero (depicted in green). Large negative values of sign(l 2 )r are indicative of attractive interactions (depicted in blue), whereas large positive values of sign(l 2 )r indicate non-bonding repulsive interactions (depicted in red).
All structures were visualized using PyMol, 117 except for those depicting non-covalent interactions, which were displayed with VMD. 118

Mechanism of the topochemically controlled regiospecific C 60 fullerene-anthracene transfer reaction
Prior to investigating the C 60 fullerene-anthracene transfer reaction, we evaluated the reaction energies associated with the formation of an isolated C 60 :anthracene mono-adduct, see Scheme 2 (panel A), for which we found a stabilizing energy of DE= -62.4 kJ mol -1 and DG= 7.4 kJ mol -1 .
Comparing this value to the experimentally found one of DG= -23 kJ mol -1 , 24 we see that the Gibbs energy is underestimated in our calculations (see also Computational methodology). However, the reaction is correctly predicted to be exergonic (DG= -5.2 kJ mol -1 ), when structures and thermodynamic corrections were calculated with a larger basis set (see also Table S7 in the Supplementary Information). The formation of the complex 1 from the constituents yields an energy gain of DE= -123.7 kJ mol -1 and DG= 3.2 kJ mol -1 (see panel B). Therefore the coordination of a 2 nd C 60 fullerene to the C 60 :anthracene mono-adduct to form 1, exerts a stabilizing effect of DE= -60.1 kJ mol -1 and a Gibbs reaction energy of DG= -4.2kJ mol -1 (panel C). Similarly, aligning two C 60 :anthracene mono-adducts, to form the complex 2, also results in a stabilization of DE= -58.5 kJ mol -1 and DG= -7.8 kJ mol -1 . It is noteworthy here that the stabilization energy of the second reaction partner to form the stable complexes 1 and 2, is roughly the same as the formation energy of the C 60 :mono-adduct, -60.1/-58.5 kJ mol -1 vs. -62.4 kJ mol -1 .

Scheme 2.
Formation of the C 60 :anthracene mono-adduct (A) from isolated C 60 and anthracene, formation of complex 1 (B) from two isolated C 60 molecules and anthracene, interaction of C 60 with the C 60 :anthracene mono-adduct to form complex 1 (C), interaction of two C 60 :anthracene mono-adducts to form complex 2 (D). Relative Gibbs energies (DG) as well as relative electronic energies (DE) of the reactions are given in kJ mol -1 and were obtained with BP86/def2-TZVP/ D3//BP86/def2-SVP/D3. While the formation of complex 1, from two fullerenes and an anthracene molecule is energetically favoured, the most stable conformation of 1 was determined by a potential energy scan of the rotation of the 2 nd fullerene as depicted in the Supplementary Information in Figure S12.
In the initial reaction step, complex 1 undergoes a Retro-Diels-Alder type process, in which the anthracene separates from the fullerene moiety, while still being trapped between and stabilized by the two fullerene species. The transition state TS(1-INT Mono ) for this reaction step has a barrier of ΔE ‡ =79.4 kJ mol -1 , ΔG ‡ =62.8 kJ mol -1 and ΔE ‡ B3LYP =94.7 kJ mol -1 . The reaction then proceeds to reach a stable intermediate structure (INT Mono ). This energy minimum structure is less stable than the educt, 1, by ΔE=21.8 kJ mol -1 (ΔG=0.8 kJ mol -1 , and ΔE B3LYP =9.7 kJ mol -1 ). Remarkably, the anthracene molecule lies completely flat between the two fullerenes experiencing interactions with both sides. The reaction then continues in a mirrored fashion, with a [4+2] cycloaddition step.  has a relative electronic energy ΔE=19.1 kJ mol -1 (ΔE B3LYP =9.5 kJ mol -1 ) and a Gibbs energy of ΔG=2.8 kJ mol -1 , indicating the stabilizing effect of the neighbouring fullerenes on the anthracene.
INT Bis then reaches a 2 nd transition state TS(INT Bis -3) with a relative energy of DE ‡ =84.7 kJ mol -1 , a relative Gibbs energy of DG ‡ =72.0 kJ mol -1 (ΔE ‡ B3LYP =110.0 kJ mol -1 ) before forming the antipodal bis-adduct in complex with C 60 , denoted as 3. The 2 nd transition state is less favourable than TS(2-INT Bis ), but the barrier is with DE ‡ =65.6 kJ mol -1 (DG ‡ =69.2 kJ mol -1 ΔE ‡ B3LYP =100.4 kJ mol -1 ) slightly lower due to the higher energy of INT Bis . In the initial calculations, the formed antipodal C 60 :anthracenes bis-adduct in complex with C 60 (3) is with a relative electronic energy of 7.9 kJ mol -1 (DG=7.2 kJ mol -1 and ΔE B3LYP =7.6 kJ mol -1 ) thermodynamically slightly less favoured than 2. However, as shown by low barrier to rotation of the C 60 moiety in 1 (see Figure   S12) (1) where ΔE Electronic represents the electronic energy of the structure with reference to isolated C 60 fullerene and anthracene molecules. The deformation energy can be defined as the energetic difference between the individual molecule fragments and their isolated, optimized structures. In the case of reaction A, the molecule fragments are represented by two C 60 fullerenes and one anthracene.
By summing up the deformation energies and subtracting them from the electronic energy, we obtain the total interaction energy as When looking at the deformation energies for the C 60 fullerene along the reaction coordinate of reaction A as listed in Table 1 Figure 3C), it can also be seen that these interactions depend on the rotation of the fullerene (see y-axis in Figure 3C).
We also tested replacement of anthracene by smaller rings such as naphthalene and benzene in INT Mono. Both, naphthalene and benzene assume positions very close to that of the anthracene, being tilted by 8° (rotated by 8° around the z-axis) and rotated by 32.5°around the x-axis, even though the arrangement of the acene over the ring slightly differs (see Figure S15 S.I.). To further elucidate the interactions between the anthracene and their two neighbouring fullerenes, the non-covalent interactions were visualized using NCIPLOT as depicted in Figure 4. 115,116 Here, the electronic density is examined as a function of an isosurface of the reduced gradient, thus allowing for a quantitative assessment on the non-covalent interactions. Red areas in Figure 4 denote strong repulsive interaction, whereas green denote weakly attractive regions, typical for van der Waals interactions or dispersive interactions. These are found between the upper and middle C 6 -ring of anthracene and the closest C 6 -ring of the left fullerene as well as between the middle and lower C 6 -ring of anthracene and the closest C 6-ring of the right fullerene, showing symmetric p-p double decker interactions in this 'inverted sandwich' structure.  functionalization. Distances are given in Å, angles, and dihedrals in °. ΔE ‡ Barrier represents the energy barrier between the noncovalently bound intermediate (see Figure S16 for structures) and their respective transition state in kJ mol -1 calculated as single points (BP86/def2-TZVP/D3) on the fully optimized BP86/def2-SVP/D3 structures.  We also performed a distortion-interaction analysis 93, 119, 120 on the transition states depicted in  Table 3. Distortion-Interaction energies for the transition states depicted in Figure 5. ΔE C60 Def represents the deformation energy of the fullerene/C 60 :anthracene mono-adduct, when compared with the corresponding intermediate C 60 fullerene/ C 60 :anthracene mono-adduct structure; ΔE Diene Def. represents the total energy difference of the diene, when compared with the corresponding intermediate structure molecule; ΔE Total Def. represents the sum of all deformation energies; ΔE Total Int. represents the difference between the barrier energy and the total deformation; ΔE Barrier represents the electronic energy difference between the transition state and the corresponding intermediate structure.

Reaction mechanism
Both investigated reaction A and B (see Scheme 1) follow a synchronous two-step retro DA/DA sequence, where the anthracene dissociates while still being trapped between two fullerenes during the entire reaction to yield a regiospecific difunctionalization.
The starting point of reaction A is represented by a stabilized complex, 1, consisting of a C 60 fullerene and a C 60 :anthracene mono-adduct. The interactions between the mono-adduct and the fullerene, while being favourable, allow for a large rotational movement of the C 60 fullerene as the potential energy surface is very shallow (see Figure S12). This indicates that a pre-alignment in the first reaction step is not immanent to the structures, but facilitated due to the confined arrangement of molecules in the solid state. rotation is potentially more hindered there, hence, we have not assigned any number in Figure 2 but just indicated the stabilising effect. In any case, this correction to the standard model makes 3 the thermodynamically favoured product of reaction B and entropic effects are likely to be the driving force for this reaction. 65 Of course, this also holds for reaction A, but the effect is symmetric and does not affect the relative energy difference between the structures.
Regiospecificity. In the experimental solid-state reaction, exclusively the formation of the antipodal bis-adduct and free C 60 fullerene was observed, a surprising, much commented and further explored process. 65, 96, 121-123 However, when comparing all possible bis-adducts as listed in Table S3 in the Supplementary Information, the antipodal bis-adduct, is the least stable adduct.
In addition, it also has the highest activation energy of 67.2 kJ mol -1 of all bis-adducts. Thus, in the absence of a 2 nd fullerene, the antipodal bis-adduct would not be thermodynamically favoured.
This provides strong evidence that a prealignment of C 60 :anthracene monomers in the crystal structure and a synchronous coupled retro DA/DA reaction facilitates the observed topochemically controlled regiospecific antipodal difunctionalization.

The planar intermediate INT Mono with double decker p-p stacking interactions
INT Mono represents an unprecedented case of non-covalent p-p-stacking interactions between a planar and two curved surfaces.
Being exposed to a convex surface, planar structures such as anthracene tend to deform and adapt to the convex shape to maximize attractive dispersive interactions as indicated by the slight bend in the anthracene when forming a noncovalently bound intermediate with C 60 as depicted in Figure S17. The deformation of the anthracene can be characterized by the bowl depth -calculated according to Ref. 124 , which amounts to 0.14 Å for the C 60 and anthracene intermediate. Such a deformation is also observed for other acenes. 95 In the presence of a 2 nd C 60 fullerene as in INT Mono and INT Bis , the anthracene is almost perfectly planar with minimal distortion from the gas phase geometry. This finding is supported by the distortion-interaction analysis, where for INT Mono a minimal distortion of anthracene was found (3.2 kJ mol -1 ). Thus, an alignment with the two fullerenes stabilizes a planar structure and counteracts the tendency of a large aromatic hydrocarbons to slightly bend towards C 60 surfaces. Concerning the position of the anthracene relative to the two fullerenes, a rotation around the xaxis by 32.5° and a rotation around the z-axis by 8° with respect to an idealized C 2v symmetric molecule maximizes favourable interactions. This orientation is very different from the position an anthracene molecule adopts when interacting with a single C 60 fullerene, where it is aligned directly on top of the bond-to-be-formed, along the common edge formed by two C6 rings on the fullerene. 95,125 When a second fullerene is added, the simultaneous double decker p-p stacking interactions induce a rearranging of the anthracene to stack the 6-membered carbon ring of one C 60 on its upper ring and of the 2 nd C 60 fullerene on the lower ring. In contrast, if two benzene molecules are stacked in parallel, the two rings are slightly shifted so that on carbon atom stands over the centre of the second benzene molecule. 126 In addition, the presented intermediate INT Mono shows with 3.06 Å shorter π-π stacking distances between anthracene and each fullerene (compare also with Ref. 127 ) than found in planar π-π stacking structures, for example in benzene dimers the distance between the two faces is 3.8 Å . 126  Given that in experiment only the formation of C 60 and the antipodal bis-adduct occurs, despite the latter being the thermodynamically least stable of all C 60 :anthracene bis-adducts, strongly suggests that crystal packing pre-aligns the structures to control the regiospecific reaction. These findings encourage new approaches of topochemically steered C 60 multi-functionalization.

CONCLUSION
The intermediate structures INT Mono and INT Bis present a central point of interest, as they are to the best of our knowledge an unprecedented case of a perfectly planar molecule, trapped between equal and opposing π-π stacking interactions with 'curved' fullerenes. Our studies shed more light on the nature of π-π stacking interactions between a planar and (two) curved surfaces, as we report the first example of a double decker type of π-π stacking in an 'inverted sandwich' arrangement.
These findings could open up new possibilities in designing functional fullerene based materials.

Supplementary Information
Detailed information about bis-adduct structures and energetics, comparison with experimental data, details on the Distortion-Interaction Analyses, detailed Energy Decomposition Analyses,