On the Induced Magnetic Field of Fullerenes. Role of Ï- and Ï

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C: Physical Processes in Nanomaterials and Nanostructures

On the Induced Magnetic Field of Fullerenes. Role of #- and #- contributions to Spherical Aromatic, Non-Aromatic and Antiaromatic Character in C (q = +10, 0, -6, -12), and Related Alkali-Metal Decorated Building Blocks, Li C and NaC 60 q

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60

6

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Nickolas D Charistos, and Alvaro Muñoz-Castro J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b02419 • Publication Date (Web): 18 Apr 2018 Downloaded from http://pubs.acs.org on April 19, 2018

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The Journal of Physical Chemistry

On the Induced Magnetic Field of Fullerenes. Role of σ- and π- contributions to Spherical Aromatic, Non-Aromatic and Antiaromatic Character in C60q (q = +10, 0, -6, -12), and Related Alkali-Metal Decorated Building Blocks, Li12C60 and Na6C60 Nickolas D. Charistosa,*, Alvaro Muñoz-Castrob,* a

Aristotle University of Thessaloniki, Department of Chemistry, Laboratory of Quantum and Computational Chemistry, Thessaloniki, Greece, 54 124. b

Grupo de Química Inorgánica y Materiales Moleculares, Facultad de Ingeniería, Universidad Autonoma de Chile, El Llano Subercaseaux 2801, Santiago, Chile. [email protected] [email protected]

Abstract The induced magnetic field of fullerenes is strongly dependent on the charge state, where C60 is depicted as a non-aromatic species, in contrast to C6010+ which exhibits a strong spherical aromatic character. Here, we account for the response of relevant charged stable building blocks for novel extended networks with variable applications, as observed in A12C60 and A6C60 phases (A=alkali metal), given by, Li12C60 and Na6C60, as well as four different charge states of C60q (q = +10, 0, -6, -12), to an external magnetic field is studied in detail, focusing on the contributions from the π and σ systems to the induced magnetic field. C60, C606- and C6012- accounts for the variation of their isolated species upon addition of charge, whereas C6010+, is an hypothetical highly aromatic counterpart. Our results show that each spherical shell and each canonical MO, exhibits characteristic patterns, revealing the direct dependence of the magnetic response, and therefore of spherical aromatic character, with regard to electron configuration. In particular, low-lying S, P, D and F π-type shells exhibit identical strong and long-ranged shielding character among the four charge states. The G shell exhibits a weak shielding response, precluding the strong deshielding contribution from high-lying H and I shells. A similar analysis is given for σ-type orbitals. Thus, the aromatic, non-aromatic and antiaromatic character of C60 among the different charge states is ruled by the population of the high-lying π-shells, which is explained in terms of π→π* excitations of high lying canonical MOs. Hence, in spherical aromatic fullerenes, the formation of a shielding cone is given mainly by the π-type shells, extending characteristic features from planar aromatics to three dimensional structures, which is useful for further rationalization and characterization of spherical/non-aromatic and antiaromatic spherical structures.

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Introduction The fascinating spherical structure of buckminsterfullerene, C60,1,2 has delighted the scientific community since the few past decades, resulting in an extensive and continuous growth leading to interdisciplinary applications of technological interest in a wide variety of fields.3–8 Its icosahedral cage composed of 12 pentagonal and 20 hexagonal faces, is the smallest example of fullerenes, obeying the isolated-pentagon rule (IPR).9,10 Owing to its unsaturated π-orbital system, C60 exhibits noticeable chemical and physical properties,11–14 where several efforts has been devoted to the understanding of the structural-stability relationship and related features.11,14–19 In addition, charged fullerenes ions found in alkali-metal fullerene phases (AnC60) in different stoichiometry exhibits metal-insulator transitions and superconductivity properties,20–23 where A6C60 and A12C60 bearing C606- and C6012- fullerides, appears as particularly stable building blocks with further applications.24–35 Moreover, lithium-doped fullerenes have been found to display increased reactivity with regard to pristine C60.36 The early claim of superaromatic behaviour for C601,37,38 has been the object of large controversy, which is best described as a non-aromatic system18,39–44 exhibiting a polyenic structure with formal double-bonds located between hexagons and single bonds between pentagon-hexagon junction. This is the result that a global response is a defining feature of fullerene aromaticity, instead of local response in each constituent rings.44 Accordingly, both single- and double-bond characteristics account for the character of C60 which cannot be considered as a superaromatic structure, but rather an electron-deficient polyene.11 The Hirsch 2(N + 1)2 rule for spherical aromaticity,18,45 as relevant extension of the concept of aromaticity,46,47 is particularly useful to evaluate the expected aromatic behavior of threedimensional molecules, in terms of the shell closing of spherical harmonics (l = 0, 1, 2, 3, 4, 5... or s, p, d, f, g, h... shells). In this sense, for C60, the sixty π-electron fulfills the S, P, D, F and G shells leaving incomplete the H shell (l = 5). In contrast to C60, a truly spherical aromatic counterpart is expected for the hypothetical C6010+ structure with 50 π-electron system, showing a complete filled S P D F and G shell structure, thus, favouring electron delocalization and bond equalization.42 An indubitable characteristic of aromatic systems, is the capacity to exhibit a free π-electron precession under an external applied magnetic field, as widely explored in planar rings.48–53 This current circulation of electrons, builds up an induced magnetic field shielding (opposing) the external field at the center of the ring, as rationalized through the early Pople ring current model.54,55 The resulting shielding region,49,56–63 builds up the characteristic shielding cone of the aromatic rings, which exhibits a long-range feature leading to changes in the nuclear shielding of neighbour molecules, as characterized from regular NMR experiments.64–66 Recently, this property has been discussed for spherical aromatic fullerenes,67–69 unraveling a direct correlation between planar and spherical aromatic behaviour. As a result, an enhancement of the endohedral shielding response is expected in C6010+, as has been evaluated by a single NICS probe at the center of the structure, increasing from nearly zero for C60 to approximately -80 ppm,42,70 in line to the expected for spherical aromatic 2 ACS Paragon Plus Environment

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species.53 Moreover, the analysis of the induced magnetic field at the molecular surroundings is able to recover the long-range characteristics of the shielding cone in three-dimensional structures,67,68 where the external field is applied from a specific orientation. In addition, the magnetic behaviour of the C606- and C6012- fullerides is of interest, owing its further application as charged building blocks in the formation of extended networks and their application as hydrogen-storage materials.24–34 Herein, we account for the contribution and relevance of valence and core electron kernels to the global magnetic response, paying particular interest to the behavior and characteristic patterns attributed to σ− and π-electron systems to the induced magnetic field and the resulting shielding cone in spherical structures, which accounts to both tangential (aligned with the cage surface) and radial (directed toward the center, or perpendicular to the cage surface) set of molecular orbitals of the icosahedral C60 cage, respectively. To explore different electronic shell scenarios, ranging from a closed-shell situation to an incomplete or partially filled shell structure, C6010+, C60, C606- and C6012- were studied via density functional theory (DFT) calculations, as relevant fullerene charged ions accounting for a SPDFG closed shell configuration, an incomplete H shell, and incomplete H and I shells. The analysis of the induced magnetic field was extended to related alkali-metal decorated fullerenes Li12C60 and Na6C60 characterized as relevant building blocks in AnC60 phases.24–34 The global response, and its further deconstruction into σ−, π−, and core-electrons unravels the changes that govern the particular induced field features from different charged fullerenes, in order to extend our understanding of the magnetic behavior of such prominent spherical structures by varying the electron population of different electronic shells, contributing to further characterization and design of spherical/non-aromatic and antiaromatic spherical structures.



Computational Methods Geometry optimizations and chemical shielding calculations were performed employing the Perdew–Burke–Ernzerhof (PBE) exchange–correlation functional71 within the generalized gradient approximation (GGA), as implemented in ADF201772,73 package, similarly to previous studies.67,69 All electron triple-ζ Slater basis set with two polarization functions for valence electrons (STO-TZ2P) was used. Both singlet and triplet spin states of Li12C60 and Na6C60 were optimized and the singlet states were identified as the ground states. The stability of the wavefunction for singlet states of Li12C60 and Na6C60 was tested and confirmed with Gaussian0974 at the PBE/6-311++G(d,p)/def2tzv level of theory employing the Stable keyword. Chemical shielding calculations were performed with the GIAO procedure as implemented by Schreckenbach75–77 in the EPR module78 of ADF. Within this DFT-GIAO treatment, the chemical shielding is calculated as the sum over the occupied canonical MOs (CMOs), thus enabling the dissection of the total value into contributions from individual CMOs. The CMO-NICS technique, initially introduced by Heine and coworkers,79,80 is applicable within an uncoupled treatment of Kohn-Sham DFT perturbation theory where the single-determinant wavefunction allows the identification of single MO contributions, but not for correlated wavefunction methods such as MP2 (second order Møller−Plesset perturbation theory) and CASSCF (complete-active-space self-consistent field).81 Additional CMO-NICS calculations were performed with BP8682,83 and PW9184 functionals for Li12C60 and Na6C60. The shielding tensor of each canonical MO (σCMO) is derived from the sum of a diamagnetic (σdia) and three paramagnetic components, according to GIAO formalism:85,86 σCMO = σdia + σgauge + σocc-occ + σocc-unocc The two paramagnetic parts represent contributions from gauge transformation (σgauge) and interactions among occupied orbitals (σocc-occ). The last paramagnetic term, σocc-unocc, accounts for the paratropic contributions of rotationally allowed excitations from occupied to unoccupied orbitals and is the determinant factor that shapes the overall magnetic response.87 The chemical shielding of the π and σ systems was derived from the sum of canonical π and σ orbitals, which were manually separated and selected according to their radial or angular nodal structure respectively. It should be noted that since fullerenes are not planar, the separation to π and σ contributions is only an approximation. The induced magnetic field (Bind), was derived in ppm from the chemical shielding, according to the following equation: Biind (r ) = −σ ij (r ) B j

ext

where Bext is the external magnetic field. For the calculation of the induced magnetic field the geometrical center of each molecule was placed on the origin of the Cartesian axes. The external field, Bext, was applied parallel to the two-fold rotation axis C2 of C60 framework, which was considered as the z Cartesian axis 4 ACS Paragon Plus Environment

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(Scheme 1). Calculation of through-space chemical shielding was performed in square twodimensional grids of points with a side of 18.0 Å and a step of 0.6 Å on xz, yz and xy planes taking into account the molecular symmetry to reduce the calculation points to a quarter of the plane. The induced magnetic field was visualized as Bzind maps, which correspond to the z-component of the magnetic field and are equal to NICSzz, and as magnetic field lines. NICSπzz scans were computed in one dimensional grids of points, starting from the center of the cage along the C3 and C5 symmetry axes until a distance of 8.0 Å with a step of 0.2 Å, passing through the centers of 6MR and 5MR respectively. In this case the external field was applied parallel to the corresponding symmetry axis (Scheme 1.b and 1.c). Input preparation, output data processing and visualization of the induced magnetic field was performed with custom MIMAF code.88

Scheme 1

Results and Discussion Magnetic response of the π system The magnetic response of the π system of Ih-C60q (q = +10, 0, -6, -12) fullerenes is presented in Figure 1 as Bπzind maps and as magnetic field lines in Figure S1. According to the orientation depicted in Scheme 1.a, the xz plane dissects the six-membered rings (6MR) on the poles of the sphere and yz plane dissects the five-membered rings (5MR) bilaterally to the poles of the spherical structure. Under this orientation the 6MRs and 5MRs on the poles form an angle of 21o and 12o respectively, with respect to the external field. The shielding cone of benzene’s π system preserves its characteristic long-range shape until a an angle of 36o with regard to the external field’s direction.48 Hence, the xz and yz visualization planes are appropriate to illustrate any potential local magnetic response of 6MRs and 5MRs respectively. Dissected NICS values of the π system and of each spherical shell in cage center are provided in Table 1, whereas the corresponding NICSzz values at ring centers of 6MR and 5MR are presented in Table 2. The CMO-NICS values are in very good agreement with previous reported values at the GIAO-PW91/6-31G*//B3LYP/6-31G* level.42 Additionally, CMO-NICS values for Li12C60 and Na6C60 employing BP86 and PW91 functionals were found in complete agreement with the PBE results (Tables S1 and S2). 5 ACS Paragon Plus Environment


Figure 1

C6010+ and C606The overall π magnetic response of C6010+ displays a strong and long range diatropic response, which encapsulates the whole cage (Figures 1 and S1), adopting the characteristic shape of shielding cone representative of π aromatic species as expected by the 50-π electron count (2(N+1)2, with N=4). The shielding cone retains its long range feature both on xz and yz planes, denoting a global spherical π electron delocalization. Interestingly, a similar long range shielding response is observed for the hexaanion C606-, which exhibits a 66-π electron count avoiding the Hirsch rule. While the Bπzind maps provide an accurate qualitative depiction of the long range magnetic response, NICSπzz scans (Chart 1), provide a more quantitative description. The NICSπzz scans indicate that the decacation C6010+ is much more diatropic inside the cage than the hexaanion C606-. The corresponding NICSπ values at the cage center are -59.2ppm and -28.8ppm, respectively (Table 1).

Table 1

The NICSπzz scans of C6010+ reveal a slight difference of the shielding response between a field oriented along the 6MRs and 5MRs, respectively, and small local effects of 5MRs. The magnetic response of C6010+ is uniform and constant inside the cage until a distance of ~1.2Å above the cage center. Above that distance the NICSπzz profiles along each ring type, diverge. The diatropicity of along the 6MRs, slightly increases (gaining 1ppm) until ~2.2Å above the cage center and then decreases, retaining a strong diatropicity outside the cage. On the other hand, diatropicity along the 5MRs decrease above ~1.2Å from the cage center until a distance of ~2.8Å (or ~0.6Å below the 5MR center), and then remaining constant until ~1.0Å (or ~0.5Å above the center of 5MR). Above that distance the NICSπzz values on both orientations gradually converge. Hence, the NICSπzz scans reveal local decrease of diatropicity in the vicinity of 5MRs, especially in the interior of the cage, denoting weaker diatropic currents in 5MRs with regard to 6MRs of C6010+. The corresponding NICSπzz values at centers of 6MR and 5MR are -53.6 ppm and -43.5ppm respectively (Table 2).

Chart 1.

In the case of the hexaanionic C606-, the magnetic response is almost uniform with regard to the external field’s direction. Only a marginal deviation is observed between the two orientations in the region of 2.0Å - 4.0Å above the cage center, which leads to a maximum difference of 3ppm at ~3.4Å above the cage center, practically at ring centers. The corresponding NICSπzz values at centers of 6MR and 5MR are -31.0 ppm and -28.3ppm 6 ACS Paragon Plus Environment

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respectively. Hence, the 5MRs of C606- exhibit a marginal local reduction of diatropicity with regard to 6MRs.

Table 2

C60 and C6012Unlike the decacationic and the hexaanionic species, the π system of neutral C60 displays a short range response, which is paratropic inside the cage and presents local paratropic and diatropic areas in the close vicinity outside the cage. The magnetic response does not adopt the shape of a long range (de)shielding cone, denoting the absence of global delocalization. The different response of 5MRs and 6MRs is revealed by inspecting the yz and xz planes respectively. The 5MRs display local paratropic response (yz plane, Figure 1), forming deshielding cones perpendicular to the ring plane, extending both to the inner and the outer of the cage. This picture is representative of strong local paratropic currents in 5MRs. On the other hand, the 6MRs display weak diatropic response outside the cage (xz plane, Figure 1), while the response remains paratropic inside the cage. The obtained response of 6MRs is representative of weak local diatropic currents, and not support a long range shielding cone. A Bπzind map (±25ppm) reveals that the paratropicity inside the cage is not homogenous, but it is significantly augmented in the interior vicinity of 5MRs (yz plane, Figure S2). The augmented paratropicity follows the shape of 5MR’s deshielding cones denoting stronger paratropic currents of 5MRs in the interior of the cage, in agreement with reported ring current analysis44,89,90. On the contrary, the paratropicity weakens in the interior of the cage close to the 6MRs (xz plane, Fig S2) indicating an absence of paratropic currents at the 6MRs. The above remarks are quantitatively depicted in NICSπzz-scan profiles (Chart 1). In the case of C60, the paratropicity inside the cage is uniform and constant (~21.5ppm) until ~1.0Å above the cage center. Above that distance the magnetic response totally diverges when the Bext is applied parallel to the C5 and C3 symmetry axis. When the Bext is applied parallel to the C5 axis, then the paratropicity dramatically increases above the distance of 1.0Å from cage center, to reach a maximum value (77.9ppm) at 3.0Å from cage center (or ~0.4 Å below the 5MR center) and then decreases to zero at a distance above 6.6Å from the cage center (or ~3.2Å above the 5MR center). The antiaromaticity of 5MRs is comparable to cyclobutadiene in terms of NICSπzz values at ring center (55.3ppm for 5MRs of C60 and 59.7ppm for cyclobutadiene at the same level of theory). Contrarily, the paratropicity along the C3 axis decreases monotonically inside the cage, whith a greater slope close to the 6MR center and then becomes diatropic 0.2Å above the 6MR center reaching a maximum (-7.3ppm) at ~1.1Å above the 6MR center. According to the above analysis, the neutral C60 is classified as non-π-aromatic, because its paratropic response is confined inside the cage and does not exhibit a long range deshielding 7 ACS Paragon Plus Environment


cone. Instead, isolated deshielding cones are observed at the 5MRs denoting strong local antiaromaticity. This observation is the main contribution to the earlier description of the isotropic induced magnetic field given by Kleinpeter and co-workers for C60 and C606-,90 who also identified the deshielding above the 5MRs of C60 as the result of the local antiaromaticity. The π system of dodecaanion C6012- presents a strong paratropic response inside the cage, which is considerable stronger than the paratropic response of neutral C60, and also presents different topology. In this case, the magnetic response of 5MRs and 6MRs is reversed with regard to the neutral C60: the 6MRs induce strong long-range paratropic response outside the cage (xz plane, Figure 1) representative of strong paratropic currents in 6MRs, while the 5MRs (yz plane, Figure 1) display short-range diatropic response outside the cage. The rescaled at ±60ppm Bπzind map reveals that the paratropic response in the interior of the cage is augmented at the vicinity of 6MRs (xz plane, Fig S2), while it weakens at the vicinity of 5MRs (yz plane, Fig S2). These findings indicate strong paratropic currents in 6MRs and weak diatropic currents in 5MRs of C6012-. The NICSπzz-scan profiles of C60-12 reveal the reversed orientation depentence of its magnetic response. The strong deshielding character inside C60-12 cage (+57.9ppm) is about the triple of C60 and remains uniform and constant until ~1.0Å above the cage center, indicating a paratropic behavior. Above that distance the deshielding features along the C3 axis increases to reach a maximum of +72.0ppm at 0.75Å below the 6MR center and then decreases, retaining however its paratropic sense at long range. Contrarily, the deshielding response along the C5 axis decreases radically above ~1.0Å of the cage center and becomes weak above the 5MR center. Hence, the deshielding features of C60-12originates from the strong paratropic response of the twenty 6MRs. The long range deshielding response of C60-12 denotes an antiaromatic character of this charge state. Magnetic response of σ valence and core electrons

Figure 2

The magnetic response of the σ valence and core electrons of Ih-C60 at different charge states show the same characteristics (Figure 2). The sum of 120 core electrons exhibit a uniform long range diatropic response, while the sum 180 σ valence electrons display a long range paratropic response which is augmented close to the carbon skeleton and weakens inside the cage. As a result, the contribution from both core and σ valence sets of MOs exhibits a short range diatropic response confined inside the cage and local short range isolated paratropic areas close to the carbon skeleton. That is because the diatropicity of core electrons inside the cage overwhelms the paratropicity of σ valence electrons (Table 1), whereas the diatropic and 8 ACS Paragon Plus Environment

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paratropic effect of core and σ valence MOs cancel each other at long range. Hence the response of core and σ valence MOs is practically identical among the four studied charge states of C60 and the variation of the magnetic response among these species is ruled from the different population of π-orbitals.

Magnetic response from spherical shells

Figure 3

The variation of the magnetic response along the studied series can be elucidated by dissecting the total magnetic response to contributions from spherical shells of the π-system (Figure 3). The magnetic response of inner shells (S, P, D and F) is identical among the studied molecules, showing a long range shielding response which is homogenous inside the cage and adopts the typical shape of shielding cone, with a short range deshielding torus encircling the cage. The G shell displays a different magnetic response from the other inner shells. Its response is slightly shielding and not homogenous, as it declines inside the cage and it is augmented in the vicinity of carbon skeleton. Among the four molecules, the shielding contribution from the G shell increases with increasing number of electrons (Figure 3, Table 1) but retain its characteristic topology. Hence in C6010+ every spherical shell is of diatropic nature, resulting in an overall strong long range shielding magnetic response of the π system. Actually the sum of S, P, D, F and G shells exhibit identical shielding response among the four molecules. The high lying H shells in C60q (q=0, -6, -12) and I shell in C6012- contribute strongly with a deshielding response, owing to its paratropic character, which rule the respective overall magnetic response. In C60 the H shell, which is filled with 10 out of 22 electrons, displays a very strong and long range deshielding response (NICS(H)zz = +81.8 ppm at cage center) that overwhelms the shielding contribution from the inner shells (NICS(S+P+D+F+G)zz = -60.2 ppm at cage center) resulting in the short range deshielding response of the total π system.90 As expected, the paratropicity of H shell increases at the 5MRs (NICS(H)zz5MR = +100.7 ppm) and decreases at the 6MRs (NICS(H)zz6MR = +59.5 ppm). In C606- the deshielding response of H shell weakens significantly (NICS(H)zz = +30.7 ppm at cage center) and loses the strong long range effect. As a consequence in C606- the strong diatropic response of the inner shells is able to overwhelm the moderate and short ranged paratropicity from the H shell, leading to a reduced overall diatropic response with regard to the strongly diatropic C6010+ (Figure 1). The next six electrons of C6012- do not fill the H shell but occupy the first triply degenerate set of MOs that belong to the I shell. Consequently the paratropic response of the H shell remains identical to both C606- and C6012-. The I shell exhibits a very strong and long range deshielding response which is the main source of the of the overall paratropicity of C60129 ACS Paragon Plus Environment


(NICS(I)zz = +86.0 ppm at cage center). The observed paratropicity of I shell is retained at the 6MRs (NICS(I)zz6MR = +83.3 ppm) but decreases significantly at the 5MRs (NICS(I)zz5MR = +36.2 ppm). A similar analysis concerning the σ orbitals, is presented in Figure S3 showing the magnetic response of each σ spherical shell of C60. The Bzind maps reveal that the paratropicity of σ orbitals originates from the high energy incomplete L shell and the complete K shell which both present a very strong and long range deshielding response. A deeper dissection to individual σ CMOs, given in Figure S4, shows that each σ CMO of K and L shell exhibit strong paratropic character. On the contrary, the J shell exhibits a weak short ranged diatropic response, whereas the lower level shells (S, P, D, F, G, H and I) present strong and long ranged shielding response, owing to its diatropic character. The dissection to individual σ CMOs (Figure S4) shows that each σ CMO belonging to J shell displays a very weak magnetic response, whereas all the lower energy σ CMOs present strong and long range diatropic response. Magnetic response of high-lying canonical π-MOs. Paratropic contributions from π→ →π* excitations The varying magnetic response of the outer π-shells can be rationalized by examining the πCMO contributions, given in Figure S5, and especially the paratropic contributions arising from rotationally allowed π→π* excitations85–87, shown in Figure 4. A π→π* excitation is rotationally allowed when the direct triple product of the occupied and unoccupied orbitals’ irreducible representations with the irreducible representation of the rotation around the direction of the applied field, which in the case of Ih symmetry is the t1g, contains the totally symmetric representation. The magnitude of the paratropic contribution depends on the energy gap and the overlap of occupied and rotated unoccupied orbitals87. The overlap depends on the shape and number of nodal planes of interacting orbitals. Accordingly, an excitation between different spherical shells results in small overlap due to different number of nodal planes, and consequently produces weak paratropic response. On the contrary an excitation within the same shell would give strong paratropic response due to favored overlap between orbitals with similar nodal structure. In such a case the paratropicity arising from the π→π* excitation can be strong enough to dominate on the total response of the π system. Thus the magnetic response of individual MOs, as well as of spherical shells in fullerenes can be explained by inspecting the symmetry and energy levels of high lying occupied and unoccupied π MOs.

Figure 4

In C6010+ the G shell is fully filled with 18 electrons that occupy the quintuply degenerate hg HOMO-1 and the quadruply degenerate gg HOMO. The HOMOs display a very weak shielding response inside the cage (+0.5ppm per MO at cage center) which is responsible for the reduced diatropicity of the G shell. The weak paratropicity of HOMOs originates from the 10 ACS Paragon Plus Environment

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gg→hg excitation to LUMO+4 (+1.3ppm per MO at cage center). All the other lower level excitations of HOMO are rotationally forbidden and thus do not contribute sizably to the deshielding character. The weak paratropic response is due to the high energy gap (5.02 eV) and small overlap because the hg LUMO+4 belongs to the I shell. In C60 only the first set of quintuply degenerate hu MOs of the H shell are occupied. The hu HOMOs allow two rotational excitations to LUMO(t1u) and LUMO+2(t2u) both belonging to the H shell. Therefore the magnitude of the deshielding response strongly depends on the energy level. The HOMO(hu)→LUMO(t1u) excitation produces +10.4 ppm per MO and HOMO(hu)→LUMO+2(t2u) +4.0 ppm per MO at cage center. These two excitations are responsible for ~88% of H shell’s paratropicity at cage center. By adding 6 electrons to form the hexaanion C606-, the next set of triple degenerate t1u orbitals of H shell are occupied. Consequently the strongly paratropic hu→t1u excitation of C60 disappears in the hexaanion and only the hu→t2u from HOMO-1 to LUMO+1 is preserved. Additionally the paratropic contribution of hu→t2u excitation slightly increases in the hexaanion (+4.5 ppm per MO at cage center) due to small decreasement in the energy level. On the other hand, the rotationally allowed excitation of HOMO is a t1u→hu excitation and the next unoccupied hu orbital (LUMO+4) belongs to the J shell. Due to small overlap this excitation results in negligible paratropic contributions (+0.6 ppm per MO at cage center), although the calculated energy level is comparable to the hu→t2u excitation. Hence in the hexaanion the HOMOs exhibit a very weak magnetic response and the moderate paratropic response of H shell arises from the hu→t2u excitation of HOMO-1. In the dodecaanion C6012- the same hu→t2u excitation of HOMO-2 to LUMO of H shell is observed and gives slightly increased paratropic response (+4.9 ppm per MO at cage center) in comparison to the hexaanion, due to smaller energy gap. Moreover, the HOMO of C6012- is the triple degenerate t1g that belong to I shell and allows a t1g→hg excitation within the same shell. Hence this excitation induces a strong deshielding response (+23.4 ppm per MO at cage center) due to small energy gap and favored overlap, producing the 82% of the paratropicity of I shell in cage center. Induced magnetic field of Li12C60 and Na6C60 The optimized ground state geometries of Li12C60 and Na6C60 are shown in Figure 5. In Li12C60 the lithium atoms are homogenously distributed on the 5MR sites retaining Ih symmetry, whereas in Na6C60 the sodium atoms are binded on 6MR sites trying to keep the maximum distance between them adopting S6 point group symmetry91,92. In both cases the singlet states were found ~10kcal/mol more stable than their triple states.

Figure 5



The π-magnetic response of Li12C60 and Na6C60 reproduces precisely the corresponding response of C6012- and C606- ions respectively, as shown by maps of the total π sytem (Figure 5) and of each spherical π shell (Figure S6). Accordingly the π system of Li12C60 sustains a long range paratropic response presenting identical topology with the C6012- anion. However, as shown in Chart 1, the paratropicity of Li12C60 is considerable weaker (~20ppm inside the cage). This reduction originates from the I shell, which displays weaker paratropic contributions from t1g→hg excitations (+14.2 ppm per MO at cage center) due to increment of the energy gap (Figure 4). On the other hand Na6C60 displays a uniform long range diatropic response, which is somewhat less diatropic than C606- (~10ppm inside the cage), as shown in Chart 1. In Na6C60 the lowering of symmetry splits orbital degeneracy, but however orbitals of H shell retain their paratropic contributions (33.3ppm at cage center), as shown in Figure S6. The small reduction of diatropicity in Na6C60 originates from the lower energy F and D shell orbitals. In summary, Li12C60 is antiaromatic due to strong paratropicity of 6MRs, whereas Na12C60 is spherically aromatic.


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Conclusions The induced magnetic field of four charge states of Ih-C60q (q = +10, 0, -6, -12) fullerenes, as well as alkali decorated Li12C60 and Na6C60, has been studied in detail by dissecting the total magnetic response into contributions of the total π and σ systems, each spherical shell and each canonical MO, revealing the direct dependence of the magnetic response, and therefore of aromaticity, with regard to electron configuration, where C606- and C6012- are relevant charged building blocks for novel extended networks with variable applications. Neutral C60 is non-aromatic because its π system sustains only a short range deshielding magnetic field confined inside the molecular cage. Local antiaromaticity of 5MRs has been identified as its characteristic feature, portraying local deshielding cones perpendicular to the ring plane both outside and inside the cage. The through-space depiction of the π magnetic response elucidates the moderate paratropic NICSπ value at cage center of C60, which may be erroneously interpreted as a result of antiaromaticity.42 On the other hand C6012- presents a strong long ranged deshielding magnetic field, as a result of strong paratropic response of the twenty 6MRs, and hence it is classified as spherically antiaromatic. Interestingly, from C60 to C6012-, the antiaromatic faces shifts from the twelve 5MRs to the twenty 6MRs. On the contrary, both C6010+ and C606- are spherical aromatic because their π system exhibits a uniform long range shielding cone which encapsulates the whole cage. Li12C60 and Na6C60 reproduce the magnetic response of antiaromatic C6012- and aromatic C606- anions respectively, with identical topology but weaker magnitude. The varying π magnetic response is explained on the basis of incompleteness of spherical shells and π-π* excitations of high lying canonical MOs. Incomplete shells display strong paratropic response originating from π-π* rotationally allowed excitations between occupied and unoccupied MOs that belong in the same shell. The magnitude of paratropicity is enhanced by increased overlap between MOs with similar nodal structure and small energy gap. In contrast complete shells do not display significant paratropic contributions from π-π* excitations due to small overlap and large energy gap of MOs that belong in different shells. Accordingly C6010+ with complete G shell obeying Hirsch’s rule, displays diatropic response from all shells leading to a long range shielding magnetic field, whereas the other charge states of C60q (q = 0, -6, -12) display paratropic response of incomplete H and I shells which diminish (in C606-), annihilate (in C60) or overwhelm (in C6012-) the long range diatropic response of inner shells. The current approach can be useful to rationalize and evaluate the shielding and deshielding contribution according to the different population of electronic shells in smaller and larger fullerenes, among other functionalized species, varying the electron population of different electronic shells, contributing to further characterization and design of spherical/non-aromatic and antiaromatic spherical structures.



Supporting Information CMO-NICS values at different levels of theory, field lines of the induced magnetic field, maps of σ spherical shells and individual CMOs. The Supporting Information is available free of charge on the ACS Publications website at DOI:

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TABLES AND FIGURES

Scheme 1. Schematic representation of Ih C60 orientations under an external magnetic field Bext. a) Bext is applied parallel to the C2 rotation axis, b) Bext is applied parallel to the C3 rotation axis, and c) Bext is applied parallel to the C5 rotation axis. The red dotted lines in (a) represent the xz and yz visualization planes of Bπzind maps. Green dots in (b) and (c) represent the points of NICSπzz-scan calculations.



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Table 1. Total and dissected NICSiso values to contributions from π, σ, core and spherical shells at cage center of C60q (q = +10, 0, -6, -12) fullerenes. Values in parentheses correspond to the contributions of π→π* excitations. Values are in ppm computed at the PBE/TZ2P level. Molecule

total

σ

core

π

S

P

D

F

G

-77.2

6.8

-24.8

-59.2

-4.3

-13.1

-18.8

-20.6

-2.3 (8.8)

2.5

6.7

-25.8

21.6

-4.5

-12.9

-108.8

-20.8

-3.2 (9.2)

81.8 (75.9)

-51.1

4.3

-26.6

-28.8

-4.7

-12.5

-18.0

-20.6

-3.7 (9.7)

30.7 (31.6)

Na6C60

-48.3

-2.9

-26.8

-18.6

-4.5

-11.1

-15.4

-15.8

-3.3 (10.9)

31.6 (33.3)

C6012-

34.6

2.1

-25.4

57.9

-4.8

-11.8

-17.1

-19.9

-6.8 (7.5)

32.4 (33.1)

86.0 (76.4)

Li12C60

9.2

-1.6

-28.7

39.5

-4.4

-11.9

-14.8

-16.8

-3.3 (11.1)

33.1 (34.5)

57.5 (50.6)

C60

10+

C60 C60

6-


H

I

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Table 2. Total and dissected NICSzz values to contributions from π and spherical shells at ring centers of six- and five-membered rings of C60q (q = +10, 0, -6, -12) fullerenes. Values in parentheses correspond to the contributions of π→π* excitations. Values are in ppm computed at the PBE/TZ2P level. Molecule

Ring

total

π

S

P

D

F

G

C6010+

6MR

-37.6

-53.6

-3.5

-10.6

-15.6

-18.4

-5.5 (8.7)

5MR

-29.4

-43.5

-3.3

-10.3

-15.7

-16.8

2.6 (12.8)

6MR

19.5

4.8

-3.6

-10.7

-16.0

-18.6

-5.8 (9.0)

59.5 (58.2)

5MR

66.6

55.3

-3.5

-10.1

-15.7

-17.7

1.2 (13.1)

100.7 (94.0)

6MR

-19.5

-31.0

-3.7

-10.6

-15.6

-18.6

-6.1 (9.4)

23.6 (27.3)

5MR

-17.4

-28.3

-3.6

-10.2

-15.2

-17.2

-0.4 (13.2)

18.4 (23.6)

6MR

-17.9

-22.8

-3.4

-9.1

-12.7

-14.9

-6.1 (10.0)

23.4 (28.4)

5MR

-16.5

-20.8

-3.4

-9.3

-12.8

-13.1

0.3 (14.2)

17.5 (23.4)

6MR

62.8

55.0

-3.8

-10.3

-14.6

-18.1

-7.1 (8.4)

25.7 (28.8)

83.3 (74.3)

5MR

10.5

0.1

-3.8

-9.6

-15.1

-16.8

-9.6 (8.8)

18.8 (25.2)

36.2 (32.9)

6MR

39.8

38.0

-3.5

-10.1

-12.7

-14.9

-3.5 (11.8)

27.2 (30.4)

55.6 (48.6)

5MR

2.7

4.8

-3.5

-9.3

-10.5

-11.8

-3.6 (11.8)

18.6 (24.7)

24.8 (23.7)

C60

C60

6-

Na6C60

C60

12-

Li12C60


H

I


Figure 1. Bπzind maps of the total π system of C60q (q = +10, 0, -6, -12) fullerenes. Blue hues represent diatropicity and red hues represent paratropicity. The dimensions of each map are 18 × 18 Å.


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Chart 1. NICSπzz-scan profiles (ppm) of C60q (q = +10, 0, -6, -12), Li12C60 and Na6C60 fullerenes starting from the center of the cage through the center of 6MRs (filled circles) and through the center of 5MRs (white circles). Black crosses denote the center of each ring.



Figure 2. Bzind maps core MOs, σ valence MOs and their sum of C60q (q = +10, 0, -6, -12) fullerenes. Blue hues represent diatropicity and red hues represent paratropicity.


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Figure 3. Bzind maps of the π spherical shells of C60q (q = +10, 0, -6, -12) fullerenes. Blue hues represent diatropicity and red hues represent paratropicity.


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Figure 4. Relative energy levels and significant paratropic contributions of rotational π→π* excitations computed at the PBE/TZ2P level. Filled arrows represent excitations within the same shell and dashed arrows represent excitations between different shells. The width of the arrows are proportional to the paratropic contributions per MO. Values of paratropic contributions (red numbers) refer to the cage center and are given in ppm.



Figure 5. a) Optimized ground state geometries of Na6C60 (S6) and Li12C60 (Ih). b) Bπzind maps of the total π system of Na6C60 and Li12C60. Blue hues represent diatropicity and red hues represent paratropicity.


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