Carbon Nano-onions as Photosensitizers: Stacking ... - ACS Publications

Article Cite This: J. Phys. Chem. C 2018, 122, 2422−2431

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Carbon Nano-onions as Photosensitizers: Stacking-Induced Red-Shift Muhammad Ali Hashmi† and Matthias Lein*,†,‡ †

School of Chemical and Physical Sciences (SCPS), Victoria University of Wellington, Wellington, New Zealand Centre for Theoretical Chemistry and Physics (CTCP), New Zealand Institute for Advanced Study, Massey University, Auckland, New Zealand

‡

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S Supporting Information *

ABSTRACT: We have investigated the double-layered carbon nano-onions (CNOs) C20@C60, C20@C80, C60@C180, C60@C240, C80@C240, and C240@C540 as well as their triple-layered analogues C60@C240@C540 and C80@C240@C540 with high-level electronic structure calculations. We were able to show that earlier work, which showed the free rotation of the inner fullerene in a CNO, does not extend to multilayered CNOs. We show that the likely reason for this immobility of the outer layers is the superadditivity of the interaction energies between individual shells, i.e., the total interaction energy of all shells is larger than the sum of all individual interaction energies between pairs of shells. We also show how the electronic states of individual fullerenes are polarized but essentially preserved in CNOs and how charge-transfer excitations between layers arise, which are significantly red-shifted to lower absorption energies compared to those of the free fullerenes. This allows CNOs to be utilized as photosensitizers in nanotechnology applications.

1. INTRODUCTION Carbon nano-onions (CNOs) are nanoparticles of pure carbon made from stacked fullerene shells and are variously known in the literature as carbon nano-onions, onion-like carbon, onionlike fullerenes, multishell fullerenes, hyperfullerenes, and nested fullerenes. These nanoparticles may be spherical or polyhedral in shape and are often smaller than 10 nm in diameter.1 CNOs were first discovered by Iijima,2 several years before Kroto and Smalley’s seminal synthesis of buckminsterfullerene3 (see Figure 1), and later described in detail by Ugarte.4 Since their discovery, CNOs have been prepared in a number of experiments,5−10 and their structure,11 morphology,12 and other properties have been investigated systematically.13−17 CNOs have been suggested for use in applications like energy storage,18,19 high-performance wear resistance materials,20,21 superconductive materials,22−24 and biomaterials.20,25−27 Their synthesis, chemistry, and applications have been reviewed in detail.28 Even though an economical method that allows the synthesis of CNOs from nanodiamond particles with high yields exists,29 it is still experimentally diffcult to synthesize large quantities of double- and triple-layered CNOs selectively. Hence, these are usually explored in more detail using theoretical studies. Highlevel theoretical studies on CNOs are also limited because of © 2018 American Chemical Society

their larger number of constituent atoms. The literature contains few density functional theory (DFT) studies on CNOs. The first report on the total energy of C60@C240@C540 using DFT calculations was published in 1998 by Terrones et al.30 Later, Türker studied the bucky onion of C20@C60 at semi empirical calculations and showed that it is a highly endothermic system.31 He further studied the formation and stability of the C60@C180 system on AM1 level and showed that the structure is stable in terms of total energy, but its formation is endothermic.32 Zheng et al. studied C20@C60 at the DFT-B3LYP/3-21G* level of theory and reported the same results that the system is stable but highly exothermic.33 The reason for that is the shorter intershell distance than the observed average interlayer distance in C60@C240, which is 3.4 Å.34 Zope and Dunlap developed an analytical variant of DFT called grid-free ADFT which can study larger fullerenes at the all-electron level.35 Zope studied the electronic structure and static dipole polarizability of C60@C240 using the ADFT/6-311G** level of theory and determined that the outer C240 almost completely shields the inner C60 from the applied Received: November 20, 2017 Revised: January 3, 2018 Published: January 4, 2018 2422

DOI: 10.1021/acs.jpcc.7b11421 J. Phys. Chem. C 2018, 122, 2422−2431

Article

The Journal of Physical Chemistry C

Figure 1. Structures of fullerenes optimized at the RI-PBE0-D3/def2-SVP level of theory: (a) C20, (b) C60, (c) C80, (d) C180, (e) C240, and (f) C540.

static electric field.36 Another study on nested fullerenes described the movement of C20 inside C240 and C60 inside C540 in potential wells in C20@C240 and C60@C540, respectively, and concluded that C20 is neither necessarily positioned in the center of outer C240 shell nor attached to its walls. It has been shown that C20 moves with a regularity inside the outer shell of C240 even at low temperatures.37 Recently, Salcedo et al. studied two complexes of nested fullerenes, i.e. C20@C116 and C60@C180, using the m05-2X/6-31G** level of theory. It was concluded that the former system has a lot of interactions between the two cages, but the latter was thermodynamically not feasible and high energy. It has also been proposed that electrons can move between the two cages of the nested fullerene in the form of free radicals. Very recently, Zope et al. studied the site-specific atomic polarizabilities of CNOs including C60@C180 and C60@C240 and concluded that the encapsulation of C60 inside these fullerenes reduces its polarizability by 83% and 75%, respectively. It has been proposed that the outer atoms in the fullerene shell have major contribution toward the fullerene polarizability.38 In the present work, we studied the structural properties of C20@C60, C20@C80, C60@C180, C60@C240, C80@C240, C240@ C540, C60@C240@C540, and C80@C240@C540 CNOs using stateof-the-art DFT calculations and the energetics of the gyroscopic motion of the inner fullerene cage. The stability of these systems alongside their interaction energies and formation energies per carbon atom have also been studied and discussed. Single-point energy calculations were also performed on the optimized geometries to shed light on frontier orbitals of these systems.

efficiency. Alrichs double-ζ basis set54−59 (def2-SVP) was used for structural optimization throughout. Frequency calculations were carried out for the smaller systems (i.e., those with fewer than 200 atoms, cf. Results and Discussion) at the same (density functional) level of theory to confirm the nature of the stationary points. All examined structures were identified as minima on the potential energy hypersurface by the absence of imaginary frequencies. We abbreviate these levels of theory as RI-PBE0-D3/ def2-SVP and RI-MP2/def2-SVP, respectively. Single-point energy calculations were carried out with a larger basis set of triple-ζ quality54−59 (def2-TZVP) using the previously obtained structures at the RI-PBE0-D3/def2-TZVP or RI-MP2/def2-TZVP level of theory with a very fine grid for the numerical integration and very tight SCF convergence criteria in order to achieve greater numerical accuracy. Excited-state spectra were calculated with the ZINDO/S method60−63 at the previously obtained geometries. These calculations were performed using the quantum chemical methods described above as implemented in ORCA 3.0.3.64 Frontier molecular orbital (FMO) visualizations were produced with GaussView 5.0.965 and are based on single-point PBE0-D3/ def2-SVP calculations using Gaussian 09 (revision D.01)66 with the previously obtained geometries. Molecular structures were visualized using CylView.67

3. RESULTS AND DISCUSSION Of all possible carbon nano-onions, only a few have been characterized and studied experimentally. Among those that we were able to identify in the literature are the doubly layered C60@ C240 and C240@C540, as well as the triply layered C80@C240@C540 and C60@[email protected],69 Hence, we base our theoretical investigation on these experimentally confirmed systems as well as a few others that are structurally similar. CNOs with many more than three layers have been observed with high-resolution transmission electron microscopy (HRTEM), and we aim to shed light on the interaction of these larger systems through accurate computation of smaller analogues and subsequent extrapolation. The main difficulty from a computational perspective is the relatively large number of electrons in the systems. Currently, the

2. COMPUTATIONAL DETAILS Computations have been carried out using Adamo and Barrone’s hybrid formulation of Perdew, Burke, and Ernzerhof’s GGA density functional39−41 (PBE0) in conjunction with Grimme empirical dispersion correction (D3)42 for structural optimizations. Secondorder Møller−Plesset perturbation theory (MP2) calculations were carried out for selected single-point energy calculations.43−46 The resolution of the identity (RI) approximation47−49 within the chain of spheres (COS) approximation50−52 was employed with the corresponding auxiliary basis set53 for computational 2423


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Figure 2. Structures of double-layered CNOs optimized at the RI-PBE0-D3/def2-SVP level of theory: (a) C20@C60, (b) C20@C80, (c) C60@C180, (d) C60@C240, (e) C80@C240, and (f) C240@C540.

produced by stacking the optimized structures of the individual fullerenes and subsequent structural optimization. In this procedure, the two constituent fullerenes were aligned along their respective principal axes of inertia in all three possible orientations. In this work, we report only the lowest-energy structure that was obtained for each CNO (see Figure 2).

only quantum chemical method that allows the routine calculation of systems of this size is density functional theory in the Kohn−Sham formulation (KS-DFT). This particular approach of density functional approximations (DFA) has long been known to suffer from a poor description of dispersion interactions of the type that can be expected to be of significance in the kind of stacked or nested π-systems that we are investigating here. However, we and others were able to demonstrate that the combination of a hybrid-DFA (like PBE0) with an empirical correction for dispersion interactions (like D3) can successfully describe the intra- and intermolecular forces even with a moderately sized basis set (like def2-SVP).70−73 In order to explore the systematic error that is associated with the RI-PBE0-D3/def2-SVP and RI-PBE0-D3/def2-TZVP methods that we use in our discussion, we also calculated the interaction energies of some smaller CNOs with a highly accurate ab initio method, RI-MP2/def2-TZVP. This method includes a much more accurate treatment of the intermolecular dispersion forces between the different shells of the CNO as an implicit part of its treatment of dynamic electron correlation through manybody perturbation theory. It has been described in the literature that CNOs stabilize the inner fullerene cage, which plays the role of a guest in these cages.74 The electronic behavior, structural changes during the formation of onions, the gyroscopic movement of the guest cages, and the volume of these CNOs are discussed in detail below. 3.1. Structural Properties of Carbon Nano-onions. Initial structures for the C20, C60, C80, C180, C240, and C540 fullerenes were obtained from the online database of the Michigan State University Computational Nanotechnology Lab.75 While all, apart from C80 (which has D5h symmetry), fullerene starting geometries possess high (icosahedral) symmetry, they were optimized without any symmetry constraints in either the SCF or the geometry optimization cycles. Nevertheless, all structures that were obtained after optimization had retained the same point group symmetry (see Figure 1). In the next step, the doubly layered structures for C20@C60, C20@C80, C60@C180, C60@C240, C80@C240, and C240@C540 were

Figure 3. Structures of triple-layered CNOs optimized at the RI-PBE0-D3/ def2-SVP level of theory: (a) C60@C240@C540 and (b) C80@C240@C540.

Finally, the triply layered structures C60@C240@C540 and C80@C240@C540 were produced and then optimized in the same fashion (see Figure 3). To compare all fullerenes and CNOs on the same basis, we calculated their energies of formation (Eform) per atom (see eq 1), with respect to the energy of a single free carbon atom (EC).

Eform =

Etotal − nEC n

(1)

The resulting values of Eform (see Table 1) confirm that all systems considered in this study are indeed thermodynamically stable. Table 1 also shows that fullerenes with a number of carbon atoms in the range of n = 20−540, the formation is more exothermic for larger fullerenes than for smaller ones. The relationship between size and interfullerene interaction in the CNOs is more complicated but not counterintuitive. 2424


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interact in a stabilizing fashion. The C20 fullerene is, for example, too large to fit into the cavity of the C60 fullerene. This results in a very large repulsive interaction energy. This repulsion is an indication that while the C20@C60 CNO is thermodynamically stable, it is unlikely to be formed because of the kinetic barrier that would have to be overcome. A similar situation can be observed when the C60@C240 CNO is compared to C80@C240. Both CNOs interact attractively, and their Eform values differ by less than 0.1%, but the smaller C60 fullerene fits much better inside the cavity of C240; hence, the interaction energy of C60@ C240 is 43% larger than that of C80@C240. Second, larger fullerenes interact more strongly than smaller fullerenes in size-matched CNOs. For example, the interaction between C240 and C540 in C240@C540 is more than three times larger than the interaction of C60 and C240 in C60@C240. This is the result of the fact that the dispersion interactions between the CNO layers scale with the size of the surface area of the constituent fullerenes. Third and most importantly, the interactions between individual layers of CNOs are superadditive. This means that the overall interactions of all layers are larger than the sum of the individual interactions between separate layers. Table 2 shows that the interaction of C60 and C240 in C60@C240 amounts to −143.96 kcal/mol, and the interaction of C240 and C540 in C240@ C540 amounts to −489.62 kcal/mol. However, the interaction of the C60@C240 CNO with its C540 outer shell in the C60@C240@ C540 CNO amounts to −658.26 kcal/mol, which is 25 kcal/mol higher than the sum of the two individual interactions. The same is true, to an even greater extent, for the other triply layered CNO, C80@C240@C540, as well. We believe that this cumulative effect explains the observed thermodynamic stability of CNOs with many layers. In effect, every additional layer of a growing CNO should be at least as stable as the previous layer, which indicates that the energetics of spherical CNO growth are somewhat analogous to the energetics of crystal growth in general, although the mechanism is radically different.76 In order to validate the DFT results, we also carried out correlated wave function calculations at the MP2 level of theory. The corresponding interaction energies are shown (in parentheses) in Table 2. Although different in detail, the overall trends of the MP2 results agree with the DFT calculations. The MP2 calculations indicate, in general, even stronger binding interactions than the DFT calculations. Hence, the MP2 results suggest that C60@ C180 has a stabilizing interaction energy, whereas DFT predicts that the interaction in C60@C180 is, in fact, destabilizing. Whether this is an artifact of the well-known tendency of MP2 to overbind or a real property of the system is beyond the scope of this investigation77 Most importantly, the MP2 results agree with the overall conclusion that the larger CNOs are well-stabilized. As far as the average distances between the individual CNO layers are concerned, it is apparent that all CNOs whose formation is predicted to be kinetically inhibited, i.e., C20@C60, C20@ C80, and C60@C180, exhibit shorter distances than the experimentally observed 3.35 Å for a five-layered CNO.15 This lends further credence to our prediction of the large kinetic barrier to their formation. The larger CNOs all show longer interlayer distances than experimentally predicted. We believe that this is mostly due to the relatively high uncertainty that is inherent in HRTEM measurements for materials such as CNOs. We have also calculated the diameters across (see Tables 3 and 4) and volumes enclosed by (see Table 5) the individual constituent fullerenes in CNOs. This allows us to examine the effects of the pressure build-up as subsequent layers of the CNOs form.

Table 1. Fullerene and CNO Formation Energies Per Atom at the RI-PBE0-D3/def2-TZVP Levela

a

fullerene/CNO

Eform

C20 C60 C80 C180 C240 C540 C20@C60 C20@C80 C60@C180 C60@C240 C80@C240 C240@C540 C60@C240@C540 C80@C240@C540

−126.075 −145.640 −146.708 −150.704 −151.634 −153.164 −128.817 −139.771 −148.886 −151.007 −150.878 −153.284 −152.959 −152.916

All energies are in kilocalories per mole.

The sterically crowded systems C20@C60 and C20@C80 show values for Eform that are much closer to the value of C20 than to the much more stable C60 or C80. This is an indication that the interaction between the two fullerenes in the two CNOs is repulsive, which is a likely consequence of the close approach of the two nested fullerenes. The C60@C180 CNO shows a value of Eform that is a little higher than the arithmetic mean of the (unweighted) Eform values of the individual fullerenes. Once the number of atoms in the two constituent fullerenes (i.e., 60 and 180) are considered, it becomes clear that the loss incurred for the 180 carbon atoms of C180 is not compensated by the gain of the 60 carbon atoms of C60, and we can conclude that C60@C180 is also a system that is dominated by repulsion between the two layers. The remaining doubly and triply layered CNOs all show Eform values that are large enough to indicate attractive interlayer interactions. This data is confirmed once interaction energies Eint are calculated (see eq 2) directly from the total energies of the CNOs (ECNO) and the total energies of the inner and outer layers (Eouter and Einner). E int = ECNO − (Eouter + E inner)

(2)

The Eint values (see Table 2) show that there are three noticeable trends within the interaction energies. First and most obviously, we can immediately see that there is a certain size match that is necessary for the layers of a nested fullerene to Table 2. Interaction Energies between Individual CNO Layersa cage 1

cage 2

CNO

C20 C20 C60 C80 C60 C240 C60@C240 C80@C240

C60 C80 C180 C240 C240 C540 C540 C540

C20@C60 C20@C80 C60@C180 C80@C240 C60@C240 C240@C540 C60@C240@C540 C80@C240@C540

Eint 1011.68 325.03 195.17 −81.90 −143.96 −489.62 −658.26 −670.18

(933.27) (93.95) (−260.61) (−511.55) (−359.13)

distance 2.94 3.14 3.34 3.48 3.70 3.61 3.69, 3.61 3.49, 3.62

a

Energies were calculated at the RI-PBE0-D3/def2-TZVP//RI-PBE0-D3/ def2-SVP level of theory. C60@C240@C540 and C80@C240@C540 were calculated at the RI-PBE0-D3/def2-SVP level, with energies in parentheses at RI-MP2/def2-TZVP//RI-PBE0-D3/def2-SVP. All energies are in kilocalories per mole, and interlayer distances are in angstroms. 2425


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changes by a maximum of 1.5% (which causes a contraction of less than 6% by volume). The outer fullerenes, C60 and C80, respectively, undergo expansion of a similar magnitude. The changes to the larger CNOs are even smaller than the ones just discussed to the extent that the volume encompassed by the C540 moiety in C80@C240@C540, is just a little more than 0.5% larger than the volume encompassed by a free C540 molecule. 3.2. Internal Rotation of Carbon Nano-onions. Another interesting question about CNOs is whether the individual fullerene layers can rotate feely with respect to each other like the layers of a rolling-element bearing. Because of the noncovalent nature of the interlayer interactions, the barrier to internal rotation is expected to be low,38 at least for systems with reasonable interlayer distances. To shed light on this issue, we performed a scan of the potential energy changes that are associated with the rotation of the inner fullerene with respect to the outer fullerene in C60@C240, C80@C240, and C240@C540. To this effect, a series of structures with the inner fullerene rotated around an arbitrary axis in steps of 10° were created (see Figure S1). It can be seen that the cavity inside the C240 moiety provides ample space for an almost free rotation of both C60 and C80. The potential energy curve for the C60 buckminsterfullerene is essentially flat, and the corresponding curve for C80 does not exhibit a much higher barrier. The curve describing the rotation of the C240 fullerene inside a C540 moiety, however, does provide evidence for a substantial barrier to rotation. To ensure that our choice of axis did not prejudice the outcome, the calculation for the C240@C540 CNO was repeated for two more axes, perpendicular to the first one. The results are essentially identical and are shown in the Supporting Information. Even when we consider the fact that the curves obtained in our calculations provide only an upper boundary to the true value, it appears reasonable to estimate that the barrier to rotation is approximately 30 kcal/mol (see Figure S2). Although more accurate calculations that allow individual structures to relax might resolve to a lower barrier, at this stage we feel confident to predict that there will be no observable rotation between these two fullerenes. Whether this finding extends to larger fullerenes in even bigger CNOs remains to be seen. However, given that the interaction energies appear to be superadditive, we can use this as an indication that the outer layers of larger CNOs might interact strongly enough to make rotation impossible. A related, but separate question is whether any gyroscopic motion would be spectroscopically observable. Traditionally, Raman spectroscopy has been the method of choice for the investigation of CNOs, and the focus has been on distinguishing CNOs from other carbon nanostructures.78−80 The experimental difficulties in producing pure carbon nano-onions (i.e., free from other carbon nanocompounds) with a well-defined monodispersity are often cited as reasons for the use of Raman spectroscopy over other methods.81 All fullerenes in this investigation (and many fullerenes in general) are centrosymmetric and hence have no permanent dipole moment, which means that single-molecule IR spectroscopy is not possible for those species. This is reproduced (to within numerical accuracy) in our calculations (see Table S3), and the double-layer CNO structures we calculate show the same behavior. The only exception is C80@C240, which has a small, nonzero permanent dipole moment. Consequently, as far as the relative rotation of two objects with no (or a very small) permanent dipole moment in objects that themselves have no (or a very small) permanent dipole moment is concerned, it is a priori

Table 3. Diameters of Fullerene Cages Independently and Inside a Double-Layer CNOa diameter in CNOs

C20 C60 C80 C180 C240 C540 a

diameter

C20@ C60

C20@ C80

C60@ C180

C60@ C240

C80@ C240

C240@ C540

406 709 819 1225 1413 2107

406 752 − − − −

400 − 834 − − −

− 696 − 1239 − −

− 710 − − 1411 −

− − 814 − 1418 −

− − − − 1413 2109

All values are in picometers. Note that 1000 pm = 1 nm.

Table 4. Diameters of Fullerene Cages Independently and Inside a Triple-Layer CNOa diameter in CNOs C60 C80 C240 C540 a

diameter

C60@C240@C540

C80@C240@C540

709 819 1413 2107

710 − 1412 2110

− 817 1419 2111

All values in picometers. Note that 1000 pm = 1 nm.

Table 5. Volumes of Free Fullerenes and Fullerene Moieties Inside CNOsa fullerene/CNO

volume

relative volume

C20 C20@C60 C20@C80 C60 C20@C60 C60@C180 C60@C240 C80 C20@C80 C80@C240 C180 C60@C180 C240 C60@C240 C80@C240 C540 C240@C540 C240@C540 C60@C240@C540 C60@C240@C540 C60@C240@C540 C80@C240@C540 C80@C240@C540 C80@C240@C540

23.61 23.20 22.23 161.66 192.11 153.63 162.70 258.01 272.88 254.06 915.50 949.56 1418.35 1414.59 1437.26 4791.47 1419.96 4805.12 162.43 1417.23 4806.79 256.03 1439.16 4821.04

0.146 0.144 0.138 1.000 1.188 0.950 1.006 1.596 1.688 1.572 5.663 5.587 8.774 8.750 8.891 29.639 8.784 29.724 1.005 8.767 29.734 1.584 8.902 29.822

a Relative volumes are normalized against C60. The volume shown is for the moiety printed in bold. The units are bohr3.

The relatively large interaction energies (specifically those of the smallest CNOs) could potentially be accompanied by large structural changes. Surprisingly, none of the fullerene carbon cages experience much change during the formation of the CNOs. Neither do the inner fullerenes contract by a large amount, nor do the outer fullerenes expand much. Even in the high-energy systems C20@C60 and C20@C80, the diameter of the C20 fullerene 2426


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Figure 4. Frontier orbitals of fullerenes and CNOs calculated at PBE0-D3/def2-SVP. All energies are given in kilocalories per mole.

unclear if the breaking of the symmetry of any CNO through rotation of one fullerene with respect to the other in a CNO is

enough to produce a change in the dipole moment. We have computed the permanent dipole moment of all structures used to 2427


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Figure 5. UV−vis spectra of the C60, C240, and C540 fullerenes and the C60@C240, C240@C540, and C60@C240@C540 CNOs. The black lines indicate the frequencies of individual excitations, and their height is proportional to their oscillator stength. The red line indicates the charge-transfer excitation, and the insets show the molecular orbitals involved in that transition. Note that the spectra of C240@C540 and C60@C240@C540 are truncated at approximately 480 nm because of the limitation to 256 excited states in the ZINDO/S calculations.

changes to the permanent dipole moment upon rotation, it gives an indication that this motion might be able to be spectroscopically probed in an IR experiment. 3.3. Electronic Structure of Carbon Nano-onions. To gain some insight into the electronic structure of CNOs, we compare the frontier orbitals of the constituent fullerenes to the

create the potential energy scans reported in Table S4. From this data, it can be concluded that neither the rotation of C60 inside C240 nor the rotation of C240 inside C540 changes the dipole moment of the CNO to any significant extent. The rotation of C80 inside C240, however, shows variations of up to 0.44 D. While this value may serve as only an upper boundary to the actual 2428


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This means that the previously reported free rotation of the inner fullerene in CNOs is unlikely to occur in the outer shells of CNOs with many layers. We furthermore conjecture that this superadditivity is important for the experimentally observed growth of CNOs with many layers. We also show that the molecular orbitals of individual fullerenes do not mix when CNOs are formed, but the energy levels of these molecular orbitals shift in energy according to their new environment. This is a consequence of the fact that the interaction between individual layers of CNOs is neither covalent nor ionic but dominated by dispersion interactions. Our excited-state calculations confirm that this finding extends to the UV−vis spectra of CNOs, which comprise the spectra of individual fullerenes energy shifted and overlaid on top of each other. The excited states that correspond to charge transfer between different layers of a particular CNO are particularly interesting for applications. We were also able to show that the lowest such transition occurs at much lower energies in C60@C240 and C60@C240@C540 than previously reported for C60@C240.

frontier orbitals of the resulting CNOs (see Figure 4). Inspection of the frontier orbital plots immediately reveals that while the individual orbitals adjust their energy in the electrostatic potential the other CNO component creates, very little orbital mixing between the constituent parts of the CNO is happening. This is in a sense unsurprising, because no covalent interaction between individual CNO layers was expected. This also means, however, that the molecular orbital scheme of CNOs consists of a sequence of states that are either localized on the inner or the outer fullerene but not delocalized over both. Those cases where the localization of the HOMO and LUMO alternates between the inner and outer fullerene are promising because they indicate that charge-transfer excited states might be possible within the material as well as through the stabilization of charge-transfer states in donor−acceptor heterojunctions. Recently, Solà and Voityuk published an in-depth analysis of excited states in the C60@C240 CNO that correspond to chargetransfer between the inner and outer shells.82 They found that the structure of CNOs stabilizes charge-transfer states where one electron is promoted from the inner to the outer fullerene forming C60+@C240−. Because they were able to demonstrate the reliability of the ZINDO method for the description of CNO excitations, we have adopted the same methodology and applied it to the CNOs in this investigation. The simulated ultraviolet−visible (UV−vis) spectra that result from these calculations are shown in Figure 5. It can be seen that the optical absorption is more red-shifted the larger the fullerene becomes (left panels). It is also obvious that the main features of the individual spectra transfer directly to the spectra of the CNOs (right panels). For example, the strong absorptions around 450 and 380 nm in the C240 spectrum can be found in the spectrum of the C60@C240 CNO as well. However, two distinct differences can be observed. First, it becomes clear that there is some dispersion of the excitation energies. For example, the strong absorption in the C240 at 542 nm shifts to 473 nm in the spectrum of C60@C240. Second, many new absorptions that are present in neither the C60 nor the C240 spectrum appear. This is partly due to the fact that some formerly forbidden transitions become allowed in the CNO of reduced symmetry, and partly because new excitations from states on C60 to C240 (and vice versa) appear in the spectrum. This aspect of the C60@C240 spectrum has been discussed in detail by Solà and Voityuk.82 The final two panels that show the UV−vis spectra of C240@ C540 and C60@C240@C540 confirm that this is also the case for these two, much larger, carbon nano-onions. It is indeed evident from our data that the lowest charge-transfer excitation (Figure 5, shown in red) is lower in energy than any transition of the individual fullerenes that constitute the two CNOs in question.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b11421. Optimized geometries of all structures and animations (ZIP) Figure S1 and S2 and Tables S1−S5 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Muhammad Ali Hashmi: 0000-0001-5170-1016 Matthias Lein: 0000-0002-5164-8638 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Julia Schacht, Yasir Altaf, Dr. Renee Goreham, Dr. Siobhan Bradley, and Dr. Khurshid Ayub for useful discussions. M.A.H. acknowledges Victoria University of Wellington for a Victoria Doctoral Scholarship. Additional computer time was provided by the Victoria University of Wellington High Performance Computer Facility SciFacHPC and by the New Zealand eScience Infrastructure (NeSI) project NESI181 through the Pan cluster at the Centre for eResearch at the University of Auckland.

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4. CONCLUSIONS We have investigated double-layered carbon nano-onions as well as two triple-layered analogues, C60@C240@C540 and C80@ C240@C540, that can be obtained by stacking two double-layered CNOs. Using high-level electronic structure calculations, we were able to show that the free rotation of the inner fullerene inside a CNO against the outer shell depends on size-matching of the two adjacent pairs and is furthermore restricted to the innermost layer. We have found that the strong dispersion interactions between individual layers of CNOs are superadditive. This means that the total interaction energy of three shells was larger than the sum of the two individual interaction energies of the two doublelayered CNOs that comprise the three-layered CNO. This result was found for both triple-layered CNOs in our investigation.

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