Introduction

The first proof that fullerene cages can be filled with atomic or small molecule dopants dates back to the pioneering ion beam studies of H. Schwarz and coworkers in which He@C60+ was generated by colliding hyper thermal fullerene cations with helium atoms [1]. Since then, many different kinds of endohedral fullerene species have been made and studied—not only in gas phase but also in solid state and solution environments [2,3,4]. Early preparative scale examples were the endohedral metallofullerenes containing lanthanide elements, e.g., La@C82 [5, 6] and La2@C80 [7] or scandium, e.g., Sc3@C82 [8]. These were made in low yields by arc-discharge growth using the Krätschmer–Huffman method [9]—typically by adding appropriate dopants, e.g., metal oxides, to the graphite electrodes used for producing fullerenes via electric discharge in an inert gas. This results in a range of products which have to be tediously separated from the discharge soot by multi-step, column-based liquid chromatography to ultimately generate isomerically pure materials in very small amounts. H. Dorn and coworkers [10] showed that the simple expedient of adding some molecular nitrogen to the inert gas used for graphite/metal oxide arc discharge allows the efficient production of “trimetallic nitride templated endohedral metallofullerenes” (TNT-EMFs), M3N@C80, where M = Sc, Y, or lanthanide elements. Driven also by the development of simplified extraction and separation schemes [11], this has resulted in the general availability of TNT-EMF materials, M3N@C80. Consequently, much has been learned about the physical and chemical properties of TNT-EMFs in various phases. In fact, today, they are arguably the best studied endohedral fullerenes.

And yet, there are surprisingly simple questions about these substances which still remain unanswered. One issue common to all endohedral fullerenes is the interaction of the dopant with the cage. This can range from a weak van der Waals like interaction, e.g., for He@C60, to stronger covalent or even ionic interactions. Neutral M3N@C80 molecules can formally be thought of as comprising a (M3+3N3−)6+ unit constrained within a (C80)6− cage. This simple view is consistent, e.g., with photoluminescence spectra of Er3N@C80, which show characteristic Er3+ emission upon visible-UV absorption [12]. However, DFT calculations of the corresponding electronic ground states suggest that far fewer than six electrons are in fact transferred from the N-centered trigonal M3N unit to the fullerene cage [11]. Instead, M3N@C80 species (preferentially consisting of an Ih symmetry fullerene cage—see Figure 4) manifest a significant degree of covalent interactions between the endohedral metal ions and those sections of the cage adjacent to them—much like the behavior of transition metal coordination complexes, e.g., ferrocene. Various experimental studies in condensed phase have attempted to quantify the associated charge transfer. For instance, the observed regular dependencies of chromatographic retention (observed in separation studies) on both fullerene cage size and endohedral metallofullerene composition have been rationalized in terms of the corresponding van der Waals interactions between fullerenes and apolar column materials (together with additional dipole-induced dipole interactions for those EMFs having permanent dipole moments) [13]. These have been used to estimate average polarizabilities and to infer the extent of charge transfer by comparing the chromatographic retention of empty fullerenes to EMFs of the same cage size [14, 15]. Given the many assumptions inherent in this procedure, the numbers obtained must be regarded with some caution however. Similarly, quantum chemistry (typically DFT based) in principle allows the determination of charge density distributions from the corresponding ground state wave functions. However, it is unclear which of the several possible methods to assign partial charges to individual atoms should be used, and in fact, large discrepancies between these different methods are observed.

Here, we use a different approach to indirectly probe changes to the electronic and geometric structure of the cage due to endohedral doping. We compare the collision cross sections of isolated EMF anions with those of the corresponding empty cages. At sufficiently high resolution and accuracy, we are able to distinguish effects due to doping. To do this, we use ion mobility spectrometry (IMS), which in analogy to the solution phase work alluded to above, can be regarded as a different type of chromatography. IMS determines the ion mobility and from this, the thermally averaged collision cross section of a mass-to-charge selected ion as it passes through a neutral collision gas. In the most straightforward and best-known IMS configuration, the mobility of an ion is obtained by measuring its drift time (cf. retention time) through an inert gas filled drift tube under the influence of an applied electric field. Drift tube IMS in helium can achieve a mobility resolving power in excess of 120 and in an early pioneering study, such a custom high-resolution setup was in fact used to probe EMF cations laser desorbed from a soot extract containing a mixture of different Sc-based EMF species [16]. The interest back then was in exploring the global geometry of the new molecules generated (in part by laser desorption) rather than in delving into structure change and charge transfer. For this, even higher resolving powers turn out to be necessary.

Recently, great progress has been made towards further raising the intrinsic mobility resolution of IMS-based methods. In particular, two IMS variants, “trapped ion mobility spectrometry” (TIMS) [17] and “structures for lossless ion manipulations” (SLIM) [18] have been developed and optimized to the point that collision cross sections of charged molecular species in gas-phase can now be routinely determined with unparalleled absolute and relative accuracies. In this study, we have used a commercial TIMS setup to determine and compare the collision cross sections of empty fullerene monoanions C80− with those of the EMFs La2@C80−, Sc3N@C80−, and Er3N@C80− in molecular nitrogen at room temperature. We find that the relative accuracy of TIMS is sufficient to allow us to observe slight changes in collision cross sections due to incorporation of finite sized molecular dopants.

Methods

Substances and Instrumental Methods

The endohedral fullerenes Sc3N@C80 and Er3N@C80 were purchased from SES Research (95% purity) and used as is. Based on the literature [10], we expect each TNT-EMF sample to consist primarily of the Ih-fullerene cage isomer. For C80 and La2@C80, we used a fullerene mix sample obtained by extraction of pure carbon and lanthanum oxide doped carbon arc-discharge soots with o-dichlorobenzene. It has been chromatographically enriched in higher fullerenes (thus containing mostly C84, but also minor amounts of smaller and larger fullerenes as well as some lanthanum containing EMFs). Based on our previous work [19], we expect the C80 component of this fullerene mix to consist primarily of the D2 cage whereas La2@C80 is known to comprise primarily the Ih-fullerene cage [7].

The mass spectra were obtained with a Thermo LTQ Orbitrap XL, the ion mobilities with a Bruker timsTOF mass spectrometer equipped with an electrospray ionization source. For electrospray, the fullerene and EMF samples were dissolved in o-dichlorobenzene and diluted with acetonitrile (TNT-EMFs) or a 1:1 mixture of toluene and acetonitrile (fullerenes), respectively, to a concentration of approximately 0.1 mg/ml. To enhance signal in electrospray ionization (ESI) we added a roughly equimolar amount of Tetrakis(dimethylamino) ethylene (TDAE (Sigma)) to the solutions as reducing agent [20] and operated in negative mode, with typically 3.5 kV spray voltage. The ion mobility data were determined in the high-resolution mode (“ultra” or “custom” with 500 ms ramp time and 1/K0 interval width of 0.05 Vs/cm2) of the timsTOF instrument. Under these conditions, the instrumental resolving power (determined as CCS/ΔCCS) was typically 200. The relative accuracy with which CCS values for two closely related species could be determined was significantly better as will be described in more detail below. For ion mobility calibration, we used the low concentration ESI tunemix (Agilent), a mixture of phosphazene derivatives with cross sections determined by Stow et al. [21]

Computational Methods

Starting geometries were obtained from ref. [22] for Sc3N@C80 with an Ih symmetry cage and by the FULLFUN [23,24,25] software for the fullerenes. For Er3N@C80, the optimized Sc3N@C80 geometry is used as starting geometry; for La2@C80, we started with the structure of Akasaka et al. [7] All fullerene anion geometries were fully optimized, i.e., without any symmetry restrictions (Note that planar Er3N is larger than planar Sc3N; however, some degree of pyramidal distortion may be present) [26]. We used the density functional method (DFT) with the BP-86 functional [27, 28] and the def-SV(P) basis set [29] as implemented in the TURBOMOLE [30] package. We assigned partial charges on each atom based on a Mulliken population analysis [31]. Compared to the starting neutral geometries, the structures of the optimized anions differ only slightly. Therefore, for simplicity, we refer to them as “D2”-C80− and “Ih”-C80− as well as “Ih”-La2@C80−, “Ih”-Sc3N@C80−, and “Ih”-Er3N@C80− below, where necessary.

The optimized anion geometries and partial charges (see SI) formed the basis of trajectory method calculations as implemented in the IMoS 1.09 package [32, 33], with a Lennard-Jones (LJ)-type interaction potential

$$ U=\sum \limits_{l=1}^{atoms}{\varepsilon}_l\left({\left(\frac{\sigma_l}{R_l}\right)}^{12}-{\left(\frac{\sigma_l}{R_l}\right)}^6\right)-\frac{1}{8\pi {\varepsilon}_0}\left(\sum \limits_{i=1}^3\alpha {\left(\sum \limits_{l=1}^{atoms}\frac{X_{il}{q}_l}{{R_l}^3}\right)}^2\right)\kern4.25em $$
(1)

with ε and σ representing element-specific LJ parameters (the default C–N2-LJ parameters in IMoS1.09 are ε = 4.65 meV and σ = 3.5 Å, based on a test set of 16 molecular ions) [34]. α is the polarizability of nitrogen, ql the partial charges on each atom, Rl the distance between the respective atom and nitrogen, and Xil its Cartesian component. Based on this interaction potential, the scattering angles (χ) were calculated by a series of trajectory calculations, and finally, the momentum transfer cross section (CCS) was obtained by numerical integration of χ [35]. The parameters used in the simulation were T = 302 K, α = 1.7 Å3. For each system, 5 × 106 trajectories were run.

Results

Typical negative ion mode ESI mass spectra of the samples used for TIMS measurements are shown in Figure 1: (a) fullerene mix (also containing La2@C80), (b) Sc3N@C80, and (c) Er3N@C80. Figure 2 compares TIMS data (i.e., ion signal versus inverse reduced mobility, 1/K0) for C80−, La2@C80−, Sc3N@C80−, and Er3N@C80−. Note, the clear resolution of empty from endohedrally doped C80 cages on the basis of their ion mobilities alone. Applying the Mason-Schamp expression (Eq. (2), with T0 = 273.15 K, p0 = 101,325 Pa, μ reduced mass of ion and N2)

$$ \frac{\varOmega }{z}=\frac{3\cdot e}{16}\cdot \frac{T_0}{p_0}\sqrt{\frac{2\pi \cdot {k}_B}{\mu \cdot T}}\cdot \frac{1}{K_0}\kern1em $$
(2)

to determine the corresponding CCS values shows that this separation is partly due to reduced mass differences. Nevertheless, there remains a clear CCS difference between filled and empty cages. Figure 3 shows all TIMSCCSN2 mobilograms (calibrated against the tunemix CCS values of Stow et al. [21]) obtained in this study for C80−, La2C80−, Sc3N@C80−, and Er3N@C80−. Measurements are grouped according to the experimental runs in which they were taken. The absolute uncertainty is in the order of 1 Å2, due to run-to-run variations in the source conditions such as RF-amplitude, DC voltages, pressure, and temperature. The relative errors (i.e., the CCS differences) are much less, on the order of 0.1 Å2 (see SI) since we always measured both endohedral fullerenes and fullerenes during the same run, immediately after each other, keeping the source conditions constant. The peak widths are between 1 and 1.5 Å2, this is in line with the instrumental resolution which exceeds 200 under these conditions. Deviations from the typical Gaussian peak shape are most likely due to intensity fluctuations, i.e., the shoulder in the Er3N@C80− signal is not significant. For C80−, we obtained an averaged CCS of 244.3 Å2, for La2@C80− 244.5 Å2, for Sc3N@C80− 244.7 Å2, and for Er3N@C80− 244.6 Å2 (based on 5, 5, 3, and 2 independent measurements, respectively). So, the CCS differences of 0.2 Å2 between C80− and La2@C80−, 0.4 Å2 between C80− and Sc3N@C80−, and 0.3 Å2 between C80− and Er3N@C80− are significant. These differences are highlighted by the “relative CCS” plot shown in the bottom right of Figure 3. This indicates the averages of all CCS mobilograms plotted relative to their corresponding C80− measurement centroid.

Figure 1
figure 1

Typical negative ion ESI mass spectra of (a) fullerene mix (note logarithmic intensity scale) with La2@C80, (b) Sc3N@C80 and (c) Er3N@C80. See main text for spray conditions

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Figure 2
figure 2

Ion intensity versus inverse reduced mobility as determined by tims-TOFMS for C80− (black), Sc3N@C80− (green), La2@C80− (red), and Er3N@C80− (blue). Note the clear separability of filled versus empty cages

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Figure 3
figure 3

Mobilograms of C80− (black), La2@C80− (red), Sc3N@C80− (green), and Er3N@C80− (blue), i.e., mass selected ion signal versus TIMSCCSN2. (a)–(e) Separate measurement runs on different days in which EMFs were compared to C80− under the same experimental conditions. (f) Averages of all CCS mobilograms plotted relative to their corresponding C80− measurement centroid highlighting that the filled C80 cages have larger CCS values. See SI for a more detailed error analysis

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What is the reason for this difference? At first sight, the answer is trivial: the two-, resp. four atoms inside the C80 cage stretch the fullerene somewhat and as a consequence, EMFs are a little larger than C80. A closer look shows that the situation is more complicated: the C80 cage has seven possible IPR-isomers (IPR, isolated pentagon rule) [36, 37], i.e., seven conventional fullerene cage isomers in which the 12 pentagons are separated from each other by surrounding hexagons. The stabilizing IPR structural motif is common to all empty fullerene cages which can be chromatographically separated from arc-discharge fullerene soot. Based on NMR measurements, it is well known that the empty C80 cage forms predominantly in the D2-isomer [19] (at least that isomer is predominantly extracted from the arc-discharge soot). On the other hand, the endohedral fullerenes La2@C80, Sc3N@C80, and Er3N@C80 are known to preferentially have a C80-cage with Ih symmetry, see Figure 4 [7, 10]. This cage is somewhat smaller than the D2-cage. Geometrical size is not the only parameter which contributes to the CCS as determined in an ion mobility experiment in nitrogen. The other is the attractive interaction between the drifting ion and the nitrogen molecules, i.e., comprising the 1/r6 term in the LJ-potential as well as a charge-induced dipole interaction (see Eq. (1)).

Figure 4
figure 4

Calculated structures of “D2”-C80−, “Ih”-La2@C80−, “Ih”-Sc3N@C80−, and “Ih”-Er3N@C80−. Note that the Schoenflies symbols refer to the symmetry group of the neutral fullerene cage, which is used as a starting point for the geometry optimization. For the anions, all geometries are fully optimized without symmetry restrictions (see text)

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In order to quantitatively understand the experimentally observed CCS differences, we computed theoretical CCS values based on quantum chemical geometry optimizations of the (endohedral) fullerene monoanions (with TURBOMOLE; see above) and trajectory calculations with IMOS1.09. It should be noted, that none of these methods are perfect: DFT is known to give very reliable fullerene geometries, nevertheless small errors (< 1%, when comparable with X-ray data) in the bond distances have to be accepted, depending on the functional and basis set used. A potentially more severe source of error is the assignment of partial charges to the constituting atoms via population analysis. Several methods exist, among them is the Mulliken method which we use here. The trajectory calculation depends on the partial charges in the calculation of the charge-induced dipole interactions (see Eq. (1), right term). Furthermore, it models the interaction between the drifting ion and the nitrogen buffer gas by a sum of LJ-potentials, centered at each atom [38]. These LJ parameters are element-specific, i.e., they are assumed not to depend on partial charge or hybridization (and thus not on cage size).

In order to gauge the accuracy of the calculated CCS values, we performed test measurements and calculations for some of the other fullerenes present in the mix. C60, C70, C76, and C84 represent ideal benchmarks since their structures are well known: C60 and C70 exist in one isomer only, C76 has two isomers with D2 and Td symmetry, but only the D2 can be extracted from the arc-discharge-soot with o-dichlorobenzene [39, 40]. C84 is known to exist in two closely related isomeric forms with D2 and D2d symmetry. We obtained the experimental values of 211.6 Å2 for C60−, 227.5 Å2 for C70−, 237.8 Å2 for C76−, and 249.2 Å2 for C84− (each based on 8 independent measurements, see Table 1). The statistical error of the absolute numbers is 0.3 Å2; we estimate the total absolute (statistical + systematic) error to 1 Å2, due to uncertainties in the mobility calibrations. The relative errors, i.e., the CCS differences are smaller (on the order of 0.2 Å2), since the fullerene ions were always measured together in the same run with identical experimental parameters.

Table 1 Experimental and calculated CCS for C60‐, C70‐, C76‐, and C84‐
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Using the default Lennard-Jones parameters in IMOS 1.09 for the C–N2 interaction (σ = 3.5 Å and ε = 4.65 meV), we then calculated CCS values based on DFT geometry optimizations for the monoanions. As can be seen, the values for the two C84 isomers are basically identical; therefore, the measured CCS does not depend on their relative concentrations in the extract. However, all values are slightly too large (between 1.1 and 1.7%, see Table 1) compared to the experimental values. Therefore, we decided to reoptimize the LJ parameters using the experimental values for C76− and C84− as calibration points (close neighbors to C80−, since we were mainly interested in highly accurate CCS values for C80−). In a least-squares fit, we adjusted either σ (giving an optimum of 3.457 Å, see Table 1 column 4) or ε (4.386 meV, see Table 1 column 5). As can be seen, the two calibration procedures give almost identical results, and with these adjusted LJ parameters, IMOS predictions are now expected to be accurate to within 0.1% in the CCS region between C76 and C84 (around 240 Å2). We choose in the following the combination σ = 3.457 Å and ε = 4.65 meV.

With these optimized parameters, we calculated the CCS for the seven IPR isomers of C80. All isomers span a range of ± 0.6% compared to the experimental value. Note, however, that by far, the best fitting structure is the D2 isomer, which is known be the dominating isomer in the dichlorobenzene extract. The predicted CCS value agrees to within 0.1% or 0.3 Å2 with the experimental value. This shows that by a combination of high-resolution ion mobility and carefully calibrated trajectory calculations, it is possible to identify empty cage fullerene isomers. We will report on this in more detail in a future publication [41].

As for the endohedral fullerenes, we measured cross sections of 244.5 Å2 for La2@C80−, 244.7 Å2 for Sc3N@C80−, and 244.6 Å2 for Er3N@C80−. With the methodology outlined above, we calculate 245.7 Å2, 245.6 Å2, and 246.2 Å2, i.e., our calculated values overestimate the observed CCS slightly, by 0.9–1.6 Å2 (0.4–0.6%), but reproduce the trend that endohedral fullerenes have larger CCS than empty C80 (Table 2).

Table 2 Experimental and calculated CCS of C80‐, La2@C80‐, Sc3N@C80‐, and Er3N@C80‐
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A final question that one might want to address is to what extent the observed CCS differences are due to geometrical or partial charge effects—the interaction potential (Eq. (1)) combines both. The answer is complicated by the fact that the empty and filled fullerene cages are composed of different cage isomers, D2 and Ih, respectively. Filling the smaller Ih cage leads to CCS values which are slightly larger than those of the empty D2 cage. To sort out the relative contributions of geometry and charge, it is helpful to also consider CCS predictions based on the projection approximation (PA) [42]. The geometrical CCS can be easily calculated with the PA, by replacing all atoms by spheres (with element-specific radius) and calculating the projected area, basically as the shadow of the molecule. With PA, we can reproduce the experimental value of C80− (244.3 Å2) using the geometry of the D2 isomer and a C-atom radius of 3.26 Å (strictly speaking the hard-sphere distance between a C-atom and the scattering nitrogen molecule). Using the same distance for the calculation, we obtain for La2@C80− a PA-CCS of 244.7 Å2, 245.1 Å2 for Er3N@C80−, while Sc3N@C80− has a PA-CCS of 244.3 Å2—basically the same value as that of D2 C80−. The empty C80 Ih-isomer has a PA-CCS of 243.6 Å2, 0.8 Å2 smaller than the empty D2-isomer. Filling with 2 or 4 atoms (and the associated stretching of the Ih cage) apparently more or less compensates this difference and the (calibrated) PA-CCS agree within 0.2–0.5 Å2 (< 0.3%) with experiment, even better than the TM-CCS. Obviously, geometric effects account largely for the CCS difference between empty and filled C80. Differences in the partial charge distributions as obtained by Mulliken population analysis lead to a slight TM-CCS overestimation. In summary, geometry effects dominate the differences between experimental TIMSCCSN2 values for “D2”-C80− and the three “Ih”-EMF anions probed.

We note in conclusion that our rationalization of the experimental data based on IMoS 1.09 trajectory calculations has made use of Mulliken partial charges. Other methods for partial charge assignments, e.g., based on Natural [43] or Löwdin [44] population analysis, have not been systematically explored. Similarly, while IMoS 1.09 also allows the inclusion of (additional) ion-N2 quadrupole interaction contributions to scattering trajectories, we have not made use of this capability given the large(r) uncertainties inherent in partial charge assignment. Should it become possible to obtain even more highly differentiated experimental data (e.g., by raising the TIMS ramp time and/or varying the collision gas composition), it would be interesting to explore the added contribution of ion-quadrupole interactions to CCS values.

Summary

We have used a set of structurally rigid, fullerene-based molecular anions to demonstrate that trapped ion mobility spectrometry (TIMS) allows to determine CCS values to very high relative accuracies and to distinguish differences in CCS values as low as 0.1%. In comparing C80−, La2@C80−, Sc3N@C80−, and Er3N@C80−, this capability enabled us to resolve the endohedral fullerenes from the empty cage based on ion mobility alone (1/K0 values of the EMFs are larger by 1.0–1.5%; the corresponding TIMSCCSN2 values are larger by 0.2%). Furthermore, we could show that it is possible to rationalize these observations with a combination of DFT optimized geometries and carefully calibrated CCS calculations as implemented in IMoS 1.09.