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<!>COMPUTATIONAL METHODOLOGY<!>Mechanism of the topochemically controlled regiospecific C 60 fullerene-anthracene transfer reaction<!>Structure and electronic properties of the intermediate INT Mono<!>Reaction mechanism<!>The planar intermediate INT Mono with double decker p-p stacking interactions<!>Corresponding Author
<p>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 creation of exohedrally functionalized fullerene derivatives. 8,[14][15][16][17] Polycyclic aromatic hydrocarbons, such as anthracene, 8,[17][18][19][20][21] other acenes, [22][23][24][25] and derivatives thereof, 26 were found to represent surprisingly suitable diene-components for functionalization of C 60 by [4+2]   cycloaddition reactions. The experimental work on the fullerene functionalization has been accompanied and guided by insightful theoretical studies. [27][28][29][30] Suitably functionalized fullerenes have been widely applied as key components, [31][32][33][34] in photovoltaic devices, [35][36][37][38][39] in artificial photosynthesis, 40,41 drug delivery, 32,42 bio-and nanomedicine, 41,42 in material science, 31,[43][44][45][46][47][48] and as self-healing polymers. 49,50 The molecular features of the fullerenes as polyunsaturated spherical carbon compounds have attracted particular attention to the synthesis of di-and multi-functionalized derivatives with high regio-and stereo-control. 8,[51][52][53][54][55][56][57] Sequential addition reactions to create multi-adducts with exceptional architectures were presented, [57][58][59][60][61][62][63] including reactions between C 60 and anthracenes, where mono-, 16-18, 21, 26, 64 bis-, 19,[64][65][66][67][68] and specific tris-adducts were reported. 63,69 The kinetic and thermodynamic driving forces for the formation of specific bis-and tris-adducts has become a much discussed issue. 8 Thermolysis of the crystalline mono-adduct of C 60 and anthracene has provided a strikingly efficient means for achieving regiospecific antipodal bis-addition. 65 The exquisite selectivity in this process was proposed to result from topochemical control in the solid state, 20,65 because the alternative solution chemistry led to a mixture of anthracene adducts, among them the antipodal bis-adduct as only a minor component. 19,70 The (thermal) DA reaction has become a fundamental synthetic method for the stereo-controlled formation of two new C-C bonds in a 6-memberd ring structure, and a mechanistic textbook topic of (orbital and state) symmetry control, [71][72][73][74] thoroughly investigated in experimental and theoretical studies. [75][76][77][78] For typical hydrocarbons the two new C-C bonds formed by the DA reaction are made in a concerted and thermally reversible process. [79][80][81][82][83][84] Quantum chemical studies have fully verified these 'basic rules' of the thermal [4+2]-cycloaddition chemistry. [85][86][87][88][89][90] The spherical architecture of the fullerenes induces pyramidalisation of the unsaturated carbon centers, 91 rendering the C 60 electrophilic and specifically dienophilic -an early recognized factor for further enhancing reactivity in exohedral addition reactions, 8,92,28,93 decreasing the activation barrier in DA reactions. 94 Aromatic hydrocarbons first associate with C 60 to a non-covalently bound intermediate complex. 95 Recent studies with the example of benzene and C 60 shed light on the interaction of a planar aromatic compound and a curved fullerene surface, 74 which was shown to be different in nature from π-π stacking interactions between two planes.</p><p>Regioselectivity of the DA cycloaddition with C 60 has also been computationally investigated, 57,66,[96][97][98][99] for example, revealing the preference of additions to the [6,6]-bond over the [5,6]-position to be attributed to more favourable interactions between the reactants in the transition state. 12 A finding later confirmed by decomposition of the electron activity 13 and also put forward by Garcia-Rodeja et al. to rationalize the regio-selectivity of bis-cycloaddition reactions to fullerenes. 11 The regiospecific formation of the antipodal bis-adduct from the crystalline mono-adduct of C 60 and anthracene in the solid state suggested a topochemically control. 65 Potentially, the anthracene transfer between two pre-aligned mono-adducts, takes place in a synchronous fashion. However, the detailed reaction mechanism of this anthracene transfer was not established. Formally, this reaction could be achieved by a complete dissociation of the anthracene moiety from one monoadduct by a retro-DA reaction, followed by the highly regio-selective DA-cycloaddition at another one. Alternatively, the anthracene transfer could proceed via a direct one-step reaction, where the transition state would represent a planar anthracene molecule interacting similarly with both fullerenes, or via a synchronous two-step reaction, where in a retro-DA step an intermediate is first formed that is stabilized by two neighbouring fullerene moieties, followed by an addition at the back of mono-adduct to generate the antipodal bis-adduct. Unravelling this reaction mechanism is of significant interest, as it implies a correlated defunctionalisation of one mono-adduct molecule, 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.</p><!><p>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][103][104][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.</p><p>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 .</p><p>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.</p><p>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.</p><p>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.</p><p>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.</p><p>Assuming (hindered) rotation of the nonfunctionalized C 60 fullerene in INT Bis , TS(INT Bis -3) and 3, results in additional contributions to the rotational entropy. To approximately account for these stabilizing effects, the structures were split up into two moieties -a C 60 fullerene and a bis-adductlike structure and the rotational entropy was calculated for each moiety separately. The resulting contributions were summed up and replaced the rotational entropy contributions of the full complex in the Gibbs energy calculation, thereby, taking additional stabilizing effects due to the (hindered) rotation of the nonfunctionalized fullerene into account.</p><p>The 2D potential energy surfaces (PES) scans were obtained by modifying the structure along the chosen degrees of freedom, then subsequently calculating single point energies of each resulting structure. The resulting PES is visualized with Origin 2018b. 114 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).</p><p>All structures were visualized using PyMol, 117 except for those depicting non-covalent interactions, which were displayed with VMD. 118</p><!><p>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 .</p><p>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. The proposed reaction pathway for the anthracene transfer as modelled by reaction A (see Scheme 1) is shown in Figure 1, depicting educts, products, intermediates as well as transition states.</p><p>Relative electronic energies (BP86/def2-TZVP/D3//BP86/def2-SVP/D3) are given in red and reaction Gibbs energies in green. For sake of comparison, B3LYP/def2-TZVP/D3//BP86/def2-SVP/D3 are listed in blue.</p><p>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.</p><p>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.</p><p>The second transition state, TS(INT Mono -1'), lies above the intermediate state, with ΔE ‡ =57.6 kJ mol -1 , ΔG ‡ =62.0 kJ mol -1 , and ΔE ‡ B3LYP =85.0 kJ mol -1 , exhibiting energy values identical to the reversed reaction to TS(1-INT Mono ). The product compound (1') is chemically identical to the educt 1 (ΔE=0.0 kJ mol -1 ). Compared to BP86, for B3LYP somewhat higher electronic energies were found. Nevertheless, both are in good agreement with each other. 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.</p><p>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), a hindered rotation of C 60 in INT Bis , TS(INT Bis -3) and 3 could be anticipated resulting in additional rotational entropy. This contribution lowered the total Gibbs energy of 3 by about 39 kJ mol -1 , whereas a smaller stabilising effect is expected for INT Bis and TS(INT Bis -3) due to more pronounced rotational hindrance.</p><p>To further analyse the reaction, we used the distortion interaction model/activation strain model independently developed by Houk and Bickelhaupt 93,119,120 to characterise all stationary points in the reaction including intermediates and product/educt structures. As results are expected to be similar, we restrict our analyses to reaction A only.</p><p>We intended to quantify the effects of the deformations exerted by the weak, non-covalent interactions and to characterise the planar anthracene molecule in the intermediate structure. In our distortion interaction analysis along the reaction coordinate, the interactions on both sides of the anthracene were considered by taking the unperturbed fullerene and anthracene molecule as reference structures.</p><p>The deformation and interaction energies can be computed using the following equations, Δ𝐸 #$%&'()*+& = Δ𝐸 -%.. + Δ𝐸 1*'.</p><p>(</p><p>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.</p><p>By summing up the deformation energies and subtracting them from the electronic energy, we obtain the total interaction energy as ). The interplay of distortion and interaction results in a striking stabilization of INT Mono in unprecedented 'inverted sandwich' structure with ΔE Electronic =-80.7 kJ mol -1 , when assembled from two fullerenes and an anthracene.</p><!><p>To shed light on the nature of the unprecedented intermediates, INT Mono and INT Bis , where the anthracene lies almost perfectly planar between the two curved fullerenes, potential energy surfaces as well as non-covalent interactions were investigated.</p><p>Two 2D potential energy surface (PES) scans were performed at the example of INT Mono , see Figure 3. On the left-hand side (A.), the PES for the displacement of the left C 60 fullerene along the y-axis and its rotation around the x-axis is depicted. On the right-hand side (B.), the rotation of the anthracene around the x-axis and its tilt, i.e., its rotation around the z-axis is shown. As evident from the plot, the PES is rather flat allowing for a wide range of motion of the anthracene and fullerene without significant increase in energy. The energy minimum, as verified by analysis of the harmonic frequencies, was determined for a conformation, where -compared to an idealized C 2v symmetric complex -the anthracene is rotated by 32.5° around the x-axis and rotated around the z-axis by 8° resulting in a tilt. Last, the two fullerenes are oriented with their centre of mass above and below the xz-plane (see Figure 3). Consequently, this anthracene orientation maximizes attractive interactions with the neighbouring fullerenes. While the dispersion corrections become more favourable when the anthracene-fullerene distance is minimized (see x-axis in the dispersion energy surface shown in Figure 3C), it can also be seen that these interactions depend on the rotation of the fullerene (see y-axis in Figure 3C).</p><p>We also tested replacement of anthracene by smaller rings such as naphthalene and benzene in  given in kJ mol -1 , calculated with BP86/def2-SVP/D3.</p><p>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   Most notable differences in the transition states can be seen in the C1-C10' and C9-C9' bond lengths. With TS Butadiene being a somewhat different case due to the absence of an aromatic ring, it can be seen the C1-C10' and the C9-C9' bond lengths increase with increasing ring size and further increases in the presence of a 2 nd fullerene. In addition, the transition states become more asymmetric in TS(1-INT Mono ), TS(2-INT Bis ) and TS(INT Bis -3). As the TS of the mono-adduct and of the antipodal bis-adduct (see Supplementary Information Figure S7) are almost perfectly symmetric, this asymmetry likely arises due to interaction with the 2 nd fullerene, which is aligned slightly off axis.</p><p>Considering the energy barriers, when the non-covalently bound intermediate is taken as a reference (see Figure S16 for structures), it can be seen that TS(1-INT Mono ) and TS(2-INT Bis ) not only have very similar barrier heights but also the lowest energy barriers for this set of structures (57.6 and 57.7 kJ mol -1 ). The formation of the bis-adduct in TS(INT Bis -3) has a higher energy barrier with ΔE ‡ Barrier = 65.6 kJ mol -1 as expected, which is very similar to that of the antipodal bisadduct (67.2 kJ mol -1 , see S. I. Table S2), slightly surpassing the activation energy necessitated by the formation of the C 60 :anthracene mono-adduct at ΔE ‡ Barrier =62.4 kJ mol -1 . The energy barrier for the formation of mono-adducts increases as the diene gets smaller, ΔE ‡ Barrier = 100.9 kJ mol -1 for TS Naphtalene , ΔE ‡ Barrier = 128.1 kJ mol -1 for TS Benzene , with the notable exception of TS Butadiene , where the energy is the lowest out of all investigated transition states, at only 30.5 kJ mol -1 .</p><p>We also performed a distortion-interaction analysis 93,119,120 on the transition states depicted in Figure 5, for details see illustration in Figure S13 in the Supplementary Information. It can be seen from Table 3, that the total deformation energy is smallest (115.9 and 113.6 kJ mol -1 ) for the two transition states TS(2-INT Bis ) and TS(1-INT Mono ), where a C 60 :anthracene mono-adduct is formed in the presence of a second fullerene. The deformation energy increases slightly when we look at the mono-adduct, at 119.2 kJ mol -1 as well as when reducing the size of the added molecule. Thus, it reaches 159.2 kJ mol -1 naphthalene for and 186.6 kJ mol -1 for benzene. Butadiene, requires a minimal amount of deformation energy compared to the other transition states, with a total of 67.7 kJ mol -1 . The interaction energy of the transfer reactions is consistent amongst all transition states involving aromatic hydrocarbons showing little variation, with TS(INT Bis -3) having the least favourable energy, -52.4 kJ mol -1 , and TS(2-INT Bis ) the most favourable one, at -58.3 kJ mol -1 .</p><p>The deformation energy largely correlates with the barrier height with the exception of TS(INT Bis -3), where the less favourable interaction energy and higher C 60 deformation energy can be considered the cause for the high transition-state energy.</p><!><p>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.</p><p>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.</p><p>By comparing the transition states of reactions A and B, with several transition states for  S9), making the TS more intermediate like (earlier TS for cycloaddition/later TS for cycloreversion). Moreover, the 2 nd fullerene induced a difference in the two bond lengths resulting in more asymmetric transition states, which likely arises because the 2 nd fullerene is located off centre the anthracene-fullerene axis but whether this is a result of the gas phase calculation and whether this also pertains the solid state remains In agreement with other studies on monoadducts, these are concerted transition states as indicated by their symmetric structures. 95 Finding identical barriers for both the retro Diels-Alder reaction to form the intermediate INT Mono and the Diels-Alder reaction to form 1', is in contrast to experimental and theoretical studies of the C 60 :anthracene mono-adduct formation, where the retro Diels-Alder reaction is found to have a significantly higher barrier 24,95 emphasizing once more the effect of the 2 nd fullerene.</p><p>The reaction rate for the elementary cycloreversion step and the according half-life can be calculated using the Eyring equation,</p><p>where k is the reaction rate, κ is the transmission coefficient, here equal to one, k B is the Boltzmann constant, h is the Planck constant, ΔG ‡ is the Gibbs energy barrier, R is the gas constant and T is the temperature in Kelvin.</p><p>At room temperature, for reaction A reaction rate of 6.2 x 10 1 s -1 is obtained for the cycloreversion (t 1/2 =1.1 x 10 -5 s), while heated up to 180 C the reaction rate increases to k=5.4 x10 5 s -1 (t 1/2 =1.3 x 10 -9 s). Similar values are found for reaction B, k= 4.8 s -1 (t 1/2 =1.5 x 10 -1 s) at room temperature and k=1.0 x10 5 s -1 (t 1/2 =6.9 x 10 -9 s) at 180°C. This agrees with the experimentally observed fast reaction at elevated temperatures and shows that the reaction model is indeed plausible. 65 It should be kept in mind, however, that reported calculated values for the energy barriers might be underestimated by several kJ mol -1 (see also Computational methodology and Tables S5-S7 in the Supplementary Information).</p><p>Concerning reaction B, our initial calculations showed structure 3 is slightly less table than the educts. However, thermodynamic corrections are calculated with the standard rigid rotator model/harmonic oscillator model of the entire complex 3. In this model, the rotational entropy is calculated for the whole complex not allowing for individual rotation of the C 60 fullerene.</p><p>If we assume the nonfunctionalized C 60 fullerene to be rotating, the additional rotational entropy lowers DG of INT Bis , TS(INT Bis -3), and 3. In the limit of a freely rotating C 60 , the Gibbs energy of 3 is lowered by approximately 39 kJ mol -1 making it thermodynamically favoured species. The gain in rotational entropy for INT Bis and TS(INT Bis -3) can be expected to be smaller as the C 60 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</p><p>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.</p><p>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][122][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.</p><p>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.</p><p>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.</p><!><p>INT Mono represents an unprecedented case of non-covalent p-p-stacking interactions between a planar and two curved surfaces.</p><p>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.</p><p>Further analysing the interactions between the C 60 :anthracene and the 2 nd fullerene (1, TS(1-INT Mono ), INT Mono ), we see that the calculated the bowl depth 124 of anthracene correlates with the stabilization energy: INT Mono (anthracene is planar) has the smallest stabilization energy (-51.9 kJ mol -1 ) but it gets more favourable for TS(1-INT Mono ), with a bowl depths of anthracene of 0.88 Å and an interaction energy of -57.8 kJ mol -1 . The stabilization energy is with -60.1 kJ mol -1 most pronounced in 1, where a bowl depth of 1.63 Å was determined. This is in line with previous studies, where the bowl depth of hexabenzocorones was found to correlate with C 60 interaction strength, reaching an optimum at 1.5 Å. 124 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</p><p>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  ASSOCIATED CONTENT structures of intermediates with smaller acenes, as well as xyz structure coordinates of all investigated species, their total energies and thermodynamic corrections.</p><!><p>Maren Podewitz*: maren.podewitz@uibk.ac.at</p>