Spectroscopy of C₁₂₀⁻ and larger fulleride cluster monoanions in the mid-infrared

Abstract

An optical spectrum of the singly charged anionic dimer of C₆₀, the C₁₂₀⁻ anion, is reported for the first time. This spectrum, recorded in the mid-infrared and extending from 800 cm⁻¹ through to 2200 cm⁻¹, shows a mixture of discrete peaks and broader features. An assignment of this spectrum poses a major challenge for theory. A broad feature observed above 1600 cm⁻¹ can be unambiguously assigned to one or many electronic transitions. However, it is not clear which isomer is responsible for it, as many isomers show electronic transitions in this spectral range. The origin of peaks below 1600 cm⁻¹ in the experimental spectrum remains uncertain, as calculations predict both electronic and vibrational transitions in this spectral range for various isomers. The proximity of several electronic and vibrational transitions suggests a breakdown of the Born–Oppenheimer approximation. This suspicion is supported by the fact that the vibrational spectrum is very dependent on the computational method, much more than expected for small molecules in the gas phase. All in all, C₁₂₀⁻ seems to be at the brink of what is computationally feasible with current methods of quantum chemistry. We also report mid-IR spectra for the larger cluster anions, C₁₈₀⁻ and C₂₄₀⁻, whose spectra show significant similarities to that of C₁₂₀⁻.

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I. Introduction

Ever since the discovery of the bulk synthesis of fullerenes, there has been much interest in the anions of fullerenes, the fullerides. That interest derives from the fact that many chemical compounds containing fullerenes come in the form of metal-containing salts, in which the fullerene is anionic.^1,2 Good examples are the salts provided by the combination of alkali atoms (M) with C₆₀. These can have a variety of stoichiometries, M_xC₆₀, where x can be as low as 1 (RbC₆₀) and as large as 12 (Li₁₂C₆₀), although the latter are better viewed as intercalated compounds rather than conventional salts. Nevertheless, C₆₀ is clearly a strong electron acceptor and the charge on the C₆₀ⁿ⁻ anion can vary depending on the identity of the metal counterion. Perhaps the most intriguing of all of the alkali fullerides are the M₃C₆₀ salts, which have been found to be (relatively) high temperature superconductors.^3–5 Critical to the superconductivity in these salts is the role of the half-filled conduction band arising from the periodic array of C₆₀³⁻ ions and the resulting electron–phonon coupling.⁴

C₆₀ is a highly symmetric molecule (I_h point group symmetry) with closed electronic shells in its ground electronic state. Its lowest unoccupied molecular orbital (LUMO) has t_1u symmetry, so when C₆₀ acquires a single additional electron, it enters this triply-degenerate orbital in the electronic ground state of the anion. The electron affinity of C₆₀ is high, 2.6835 ± 0.0006 eV,⁶ and so the electron in the t_1u LUMO is more tightly bound to the C₆₀ core than the LUMO in many other anions. Unlike most anions, C₆₀⁻ has several bound electronic excited states and electron correlation is critical for a realistic description of these states, i.e. they are unbound at the Hartree–Fock level of theory.^7–10 Furthermore, the nominal high symmetry of C₆₀⁻ delivers multiple electronic and vibrational degeneracies, which are removed by the Jahn–Teller effect.^11–14 Understanding the behaviour of C₆₀⁻ therefore requires a detailed grasp of both electron behaviour and the impact of Jahn–Teller dynamics.

There have been several experimental studies of isolated C₆₀⁻. Early work using photoelectron spectroscopy was limited in its resolution, largely because of the residual temperature resulting from the need to evaporate C₆₀, which causes the population of many low-lying vibrational states.^15–17 However, with the introduction of cryogenic cooling, the resolution can be improved significantly and, along with providing new information on the vibrational states in the anion and neutral molecule, such studies have also provided more detailed probes of the vibronic coupling in the electronic ground state of C₆₀⁻.^6,18 Studies of the laser-induced electron detachment from C₆₀⁻ ions following tuneable near-infrared excitation have provided some experimental information on the excited electronic states of C₆₀⁻.^19,20 Subsequently, using two-colour time-resolved photoelectron spectroscopy, the lifetime of one of those states, identified as the B̃²E_g state, was found to be 2.2 ps.²¹ These investigations in the gas phase complement earlier work on C₆₀⁻ trapped in rare gas matrices, where near-infrared absorption features have been assigned to electronic excitation.^22,23

Very recently, the same electronic absorption features have been recorded at higher resolution in the gas phase using helium-tagged C₆₀⁻ ions.²⁴ This study employed electron attachment to create negatively charged helium droplets, which were then used to capture C₆₀ molecules. By allowing the helium droplets to collide with a metal surface, anions tagged with one or more loosely bound helium atoms could be produced in the gas phase. Optical spectra were then recorded by vibrational predissociation spectroscopy. The benefit of this approach is that helium is a weak perturber of the spectrum of C₆₀⁻ and so these measurements could potentially form the basis for astronomical searches for this anion.

C₆₀⁻ has also been studied in the mid-infrared. Early work exploiting a neon matrix to isolate the ions revealed a number of peaks between 1100–1450 cm⁻¹, which were assigned to vibrational transitions.²³ Subsequently, Kern et al. were able to obtain cleaner spectra by externally generating ions and then, using a mass filter, co-depositing these ions with the desired matrix material.²⁵ The advantage of this approach, as opposed to the more usual matrix deposition without a mass filter, is that it removes contributions from neutral C₆₀. Good agreement was obtained between the IR spectrum and density functional theory predictions and a Jahn–Teller distorted ground electronic state with D_3d point group symmetry was inferred from the spectrum. Two of the bands seen in the matrix work have also been recorded in a gas phase IR spectrum of C₆₀⁻.²⁶

Although much is now known about C₆₀⁻, almost nothing is known about the corresponding singly charged anionic clusters. The anionic dimer, (C₆₀)₂⁻, was once postulated²⁷ as a possible source of a sharp line persistently seen in the EPR spectra of solutions containing the C₆₀⁻ anion.^28,29 However, subsequent work has shown that the impurity species, C₁₂₀O⁻, is responsible for that sharp feature,³⁰ and so the singly charged dimer anion remains an unknown entity. If formed, it could be expressed as (C₆₀)₂⁻ or C₁₂₀⁻, depending on whether it consists of two recognisable C₆₀ units, as implied in the case of (C₆₀)₂⁻, or is very heavily coalesced into a single fullerene unit, in which C₁₂₀⁻ would be a more appropriate label. We will tend to avoid this distinction and will just refer to the ion as C₁₂₀⁻.

In recent work we reported the first IR spectrum of the cationic equivalent, C₁₂₀⁺, presenting evidence for a peanut-shaped structure in our experiments.³¹ Here we address the corresponding anion formed under similar experimental conditions, alongside the trimer and tetramer, recording the first optical spectra of these ions. As will be seen, the spectra of these cluster anions are challenging to assign because of the complexity of the potential energy landscape and the likelihood of a serious breakdown of the Born–Oppenheimer approximation.

II. Experimental and computational details

Full details of the experimental setup can be found elsewhere,³² so only a brief account is provided here. Central to the experiment is the production of negatively charged helium nanodroplets, which was achieved using electron impact at ca. 22 eV. This leads to the formation of He*⁻ anions within helium droplets,^33,34 which can act as powerful reducing agents.³⁵ The negatively charged helium droplets were then doped with C₆₀ molecules by passage of the droplets through the vapor emanating from a resistively heated oven containing solid C₆₀. The average number of C₆₀ molecules acquired by a helium droplet is dictated by the size of the droplet (collision cross section), the partial pressure of C₆₀ vapor in the oven, and the length of the pickup zone (which is fixed). Collision of these charged droplets with a stainless-steel surface leads to splashing and extraction of lower-mass ions.³² In addition to bare anions such as C₆₀⁻ and its dimer C₁₂₀⁻, some of the fulleride anions are ejected into the gas phase with one or more helium atoms attached.

Optical spectra were then recorded by monitoring the production of excess bare anions induced by photodissociation (loss of all helium atoms) from the helium-tagged anions as a function of laser wavelength. The laser system used was the Ekspla model NT273 XIR (bandwidth <10 cm⁻¹, 833–2230 cm⁻¹). The recorded absorption features were corrected for changes in laser power as a function of wavelength. Note that, because we are potentially seeing signal from anions with different numbers of attached helium atoms, an inhomogeneous broadening effect will result as each of these ions will absorb at slightly different frequencies.

Supporting the experimental findings about C₁₂₀⁻ with theoretical calculations is complex, not least because there are multiple potential isomers that must be considered, which we distinguish here into four classes, namely as fully reconstructed buckyball (B), peanut-shaped (P), covalently bound dimers (C) and van der Waals (V) structures (see SI for all calculated stable isomers, i.e. isomers whose energy lies below the energy of C₆₀⁻ + C₆₀); the structures were taken from our C₁₂₀⁺ study,³¹ and based also on previous work by Onoe and co-workers.^36,37

We have performed density functional theory (DFT) calculations on 29 isomers of C₁₂₀⁻ with the BP86/def2-SVP method to obtain geometries and vibrational frequencies, and TD-BMK/6-31+G* to calculate electronic excitations. For benchmarking purposes, we also calculated structures and vibrational frequencies of C₆₀, C₆₀⁻ and the four isomers B1, P1, C1 and V1 of C₁₂₀⁻ using eight further methods of quantum chemistry, namely ωB97XD/def2-SVP, BHandHLYP/def2-SVP, BMK/def2-SVP, M06L/def2-SVP, B3LYP/def2-SVP, BLYP/def2-SVP, BP86/def2-TZVP and PBE/def2-SVP. Where possible, we applied density fitting and Grimme's empirical dispersion correction D3.³⁸ To calculate electronic excitations of C₆₀⁻ and the four isomers B1, P1, C1 and V1 of C₁₂₀⁻, we used five different DFT methods, namely TD-BHandHLYP/6-31+G*, TD-BHandHLYP/def2-TZVP, TD-BMK/6-31+G*, TD-BMK/def2-TZVP and TD-CAM-B3LYP/6-31+G*, which were applied to geometries obtained from BP86/def2-SVP, BP86/def2-TZVP and B3LYP/def2-SVP, making a total of 15 calculations for each of these five molecules. Wave function stabilisation³⁹ was performed prior to every calculation, to make sure that the electronic wave function, which was used for geometry optimization or as a starting point for calculation of electronically excited states, is the wave function of the electronic ground state.

To compare structures in the excited state to the ground state structure, we used root mean square displacement (RMSD) as a measure of structural similarity. For example, an RMSD of 0.01 Å means that, on average, every nucleus in the excited electronic state is 0.01 Å away from its original position in the ground electronic state. All calculations were performed in Gaussian 16.⁴⁰

III. Results and discussion

1. Infrared spectroscopy of C₆₀⁻

Initial work started with an attempt to record a spectrum of C₆₀⁻ in the mid-IR by monitoring wavelength-dependent changes in the anion signal at m/z 720. Spectra in this region have been successfully recorded previously in a neon matrix^23,25 and in the gas phase.²⁶ A number of discrete bands have been seen in these spectra which have been attributed to vibrational transitions. However, and in contrast to the previous work, we were unable to see any absorption features between 800–2200 cm⁻¹ when monitoring C₆₀⁻. We assume that this is because the vibrational transitions of C₆₀⁻ are too weak for us to observe in our current experiments. We will return to this in the next section.

We performed DFT calculations to predict the IR vibrational spectrum of C₆₀ and C₆₀⁻, as can be seen in Fig. S1. In the case of the vibrational spectra of C₆₀, all methods provide very similar results. It is, however, interesting that there is such a quite strong method-dependence for the calculated vibrational spectrum of C₆₀⁻. By comparing our results to an experimental spectrum of C₆₀⁻ in the mid-IR from Kern et al.,²⁵ we identify BLYP/def2-SVP, BP86/def2-SVP, BP86/def2-TZVP and PBE/def2-SVP, as the most reliable methods among those investigated, because the vibrational spectra from these methods match very well with the experimental one. In the case of the calculated spectrum, only two electronic transitions are predicted for C₆₀⁻ in the measured energy range covered in the present work (see Fig. S2), both of which are forbidden by symmetry.

2. Infrared spectrum of C₁₂₀⁻

In contrast to the null spectrum for C₆₀⁻, a variety of absorption features are seen in the IR spectrum detected at m/z 1440, which corresponds to the C₁₂₀⁻ anion. The spectrum obtained is shown by the black trace in Fig. 1. Discrete structure is more evident at lower frequencies while in the higher frequency part of the spectrum there is some broad structure built upon a rising absorption background. The low-frequency structure shows a strong resemblance to the vibrational features observed in the IR spectra of C₆₀⁺ and C₆₀⁻,^23,25 as well as the C₁₂₀⁺ ion.³¹ We therefore consider whether vibrational structure might be responsible for the peaks below 1600 cm⁻¹ in the spectrum for C₁₂₀⁻.

Fig. 1 IR spectrum of helium-tagged C₁₂₀⁻ ions alongside those of C₁₈₀⁻ and C₂₄₀⁻. The photofragment yield has been corrected for both variations in the laser power and the background signal in the absence of the laser.

To assist, we have performed DFT calculations for a variety of representative structures, ranging from a fully-fused ‘buckytube’ structure all the way through to a simple dimer structure held together by dispersion forces. One representative structure for each class of isomers is shown in Fig. 2, along with vibrational spectra obtained through the four most reliable methods, as derived from benchmarking calculations on C₆₀⁻. In all, 29 distinct isomers were considered, as detailed in the SI (Fig. S3; see Fig. S4 and S5 for further benchmarking and direct comparison with the experiment).

Fig. 2 Calculated spectra of C₁₂₀⁻ for four different isomers labelled as B₁, P₁, C₁ and V₁ from top to bottom. The structures and symmetries of the isomers are also shown in the upper right of each panel. The vibrational spectra from four different DFT-based methods are shown, as indicated by the legend at the bottom of the figure. To calculate the electronic spectra, TD-BMK/6-31+G*//BP86/def2-SVP methodology was employed and the resulting electronic transitions are identified in the insets in the upper left side of each panel (electronic excitations). The stabilisation energy in eV with respect to dissociation into C₆₀⁻ + C₆₀ at the BP86/def2-TZVP level of theory is also shown beneath each structure in each panel. Vibrational and electronic transitions are shown within the spectral region covered within Fig. 1. The vertical scale for the vibrational spectra is the absorption cross section, σ, and an empirical broadening of 50 cm⁻¹ has been applied to the vibrational frequencies to generate the calculated spectra shown. For the electronic spectra, each electronic excitation is marked with a blue “x” together with its oscillator strength f.

Three things become clear from all of these calculations. First, for most isomers of C₁₂₀⁻, the vibrational absorption cross sections are up to one order of magnitude higher than those calculated for C₆₀⁻(see Fig. 2 and Fig. S1, S3–S5). This might be seen as a possible explanation for our inability to observe a spectrum of C₆₀⁻ in the mid-IR. However, a second point of note is that none of the calculated vibrational spectra for C₁₂₀⁻ produce vibrational bands that match those seen in the observed experimental spectrum, even if multiple isomers are considered to be present simultaneously. This is seen most clearly in the absence of intense absorption bands below 1300 cm⁻¹ in the calculated spectra of these isomers, which is not consistent with the observed experimental spectrum. A detailed comparison can be made by accessing the full set of calculated spectra in Fig. S3. Thirdly, even more than in the case of C₆₀⁻, the calculation of vibrational spectra is unexpectedly method-dependent (see Fig. S4). Even though BLYP/def2-SVP, BP86/def2-SVP, BP86/def2-TZVP and PBE/def2-SVP show good agreement with the experiment in the case of C₆₀⁻, and these methods are very consistent with each other in the case of C₁₂₀⁻, we cannot rule out that the calculated vibrational spectra are considerably flawed, as other methods predict considerably different vibrational spectra. Our conclusion is therefore that either the vibrational calculations are unexpectedly wrong, or that pure vibrational transitions are not the source of the discrete absorption bands of C₁₂₀⁻ lying below 1600 cm⁻¹.

The alternative explanation is that one or more electronic transitions, or a combination of vibrational and electronic transitions, are responsible for the experimentally observed peaks. Electronic transitions in the mid-infrared are indeed predicted for C₁₂₀⁻, as illustrated in Fig. 2 for the four selected structures. The energies and intensities of these electronic transitions are very robust with respect to changing the computational method (see Fig. S6). Interestingly, the electronic transitions seem to be more consistent among different methods than the vibrational ones.

Furthermore, and as expected, the electronic transitions are calculated to be more intense than the pure vibrational transitions (see Fig. S3 in the SI for directly comparable numerical values). In the lower two examples of Fig. 2, we have what could reasonably be described as (C₆₀)₂⁻. Isomer C1 is a dimer of two covalently bound C₆₀ units, while isomer V1 is based on two C₆₀ units held together by dispersion forces. In a simulation that spans the same wavelength region as the experimental spectrum in Fig. 1, we see weak vibrational structure and, at higher frequencies, an electronic absorption band for these two isomers. The electronic absorption prediction could account for the rising background seen in Fig. 1 above 1500 cm⁻¹, lending support to the idea that this arises from electronic absorption. However, as already discussed above, there is poor agreement between the calculated vibrational structure and the sharper bands seen below 1500 cm⁻¹ in the experimental spectrum, both in terms of the band positions and their relative intensities.

Isomer P1 shown in Fig. 2 has more extensive covalent bonding between the two C₆₀ units and has more of a ‘peanut’ shape. Electronic and vibrational features show the same qualitative behaviour as for the other two isomers, but with the electronic excitation at ∼2000 cm⁻¹ being at a lower frequency than for the other two isomers. This shows that, for some structures of C₁₂₀⁻, very low-lying electronic transitions are possible. The fourth representative, isomer B1, is of a buckytube-type, having slightly different vibrational features and no allowed electronic transitions up to 8000 cm⁻¹, making it unlikely that this isomer is the main carrier of the experimental spectrum in Fig. 1. In our calculations we have not attempted to predict the vibrational structure accompanying the electronic transitions due to a very complex potential energy surface (PES), as detailed below.

As can be seen in the SI, we have pursued the same type of analysis for all 29 isomers of C₁₂₀⁻ considered in the present work, including the comparison in intensities between vibrations and electronic transitions, and none of them convincingly account for the experimental spectrum of C₁₂₀⁻. So what can we conclude? First, there is no reason why multiple isomers couldn’t contribute to this spectrum. For example, the electronic transitions identified for the isomers shown in Fig. 2 could account for the experimental spectrum. After all, these span almost the entire range of the absorption features seen in Fig. 2. To account for the spectral structure seen experimentally, we might have to assume that the resolved structure corresponds to excitation of particular vibrations in the electronic band system(s). In any case, the complexity of the potential energy landscape provides a serious challenge to finding one or more specific isomers to account for the observed structure.

The findings of our calculations also point to another serious problem, a possible breakdown of the Born–Oppenheimer approximation. The methodology underlying our calculations makes the standard assumption that the Born–Oppenheimer approximation is valid, so that electronic and vibrational motions are fully separated. However, the examples in Fig. 2 show that this is likely to be a poor approximation, with excited electronic and vibrational states in close proximity. This could result in strong electronic–vibrational state mixing, further complicating attempts to understand the IR spectroscopy of C₁₂₀⁻. Note that this is markedly different from C₆₀⁻, where the vibrational fundamental and electronic transitions are well separated (see ref. 22–24 and Fig. S1, S2), and where the vibrational spectrum from DFT calculations closely matches the experimental mid-IR spectrum (see ref. 25), even though this is only the case for some DFT methods (see Fig. S1).

To further analyse the situation, Fig. 3 includes lower-lying electronic states of isomer C1 of C₁₂₀⁻ along with the respective irreducible representations of the states within D_2h symmetry and the corresponding singly-occupied molecular orbitals. We choose C1 simply as a representative structure to show the impact of electronic excitation on the geometry, but expect similar findings for other isomers. We calculated vertical and adiabatic excitation energies and estimate the difference between two structures through a calculation of the RMSD. Upon optimization, the RMSD value reached 0.006–0.019 Å, showing that the geometrical structure barely changes upon electronic excitation, irrespective of electron localization in a considerably different orbital. The orbitals involved in these excitations are very much delocalized over the entire C₁₂₀⁻ ion. The fact that many electronic states in C₁₂₀⁻ lie close to each other, both energetically and geometrically, strongly influences the potential energy surface of the system and complicates the spectral assignment. Indeed, this phenomenon can also be interpreted as an onset of solid-state behavior, where many electronic states lie close to each other, forming energy bands, and the geometry of the system barely changes upon electronic excitation.

Fig. 3 Left: Electronic states in isomer C1 of C₁₂₀⁻ at the BP86-D3/def2-SVP level of theory. Each energy level corresponds to the lowest energy state for the stated irreducible representation, connecting vertical excitation (RMSD = 0) to structures obtained upon nuclear relaxation (RMSD > 0). Structures marked with an asterisk contain an imaginary vibrational frequency. Right: Singly-occupied orbitals of the six lowest states shown in the energy level diagram.

3. Infrared spectra of C₁₈₀⁻ and C₂₄₀⁻

Fig. 1 also shows a comparison of the IR spectrum of C₁₂₀⁻ with those from C₁₈₀⁻ and C₂₄₀⁻. The C₁₈₀⁻ spectrum has some significant similarities to that of C₁₂₀⁻, with several peaks below 1600 cm⁻¹ matching quite well in the two cases. The spectrum of C₁₈₀⁻ also shows a broadly rising background absorption above 1500 cm⁻¹, with some hints of coarse structure on top of that. For C₂₄₀⁻, absorption falls into similar regions as for C₁₂₀⁻ and C₁₈₀⁻. However, any structure is less pronounced than for the two smaller cluster anions.

We have not attempted any calculations on C₁₈₀⁻ and C₂₄₀⁻. However, the similarities seen between the spectra of C₁₂₀⁻, C₁₈₀⁻ and C₂₄₀⁻ indicate that all three anions have some structural features in common, i.e. in the way each C₆₀ unit is linked to an adjacent one. If that was not the case, we would expect markedly different spectra. One can also expect many low-lying electronic states of the C₁₈₀⁻ and C₂₄₀⁻ anions, complicating the spectral analysis.

IV. Conclusions

Infrared spectra of the fullerene anions C₁₂₀⁻, C₁₈₀⁻ and C₂₄₀⁻, have been recorded for the first time. The spectra show considerable structure, particularly for C₁₂₀⁻ and C₁₈₀⁻, with several well-resolved bands alongside a structured but broad absorption feature extending to higher frequency. Supporting DFT calculations yield many possible structures for C₁₂₀⁻. The rising background above 1600 cm⁻¹ in the experimental spectrum can be attributed to one or many electronic excitations. However, the calculations do not allow for an unambiguous assignment of the experimentally observed features below 1600 cm⁻¹ to either vibrational or electronic excitations of any of the investigated isomers.

The calculations do show that vibrational and the lowest-lying electronic states of C₁₂₀⁻ lie in close proximity. Indeed, for some isomers the lowest-lying electronic transition is calculated to lie below the most prominent vibrational fundamental transitions (although possibly inaccessible by allowed electronic transitions). These findings suggest a likely breakdown of the Born–Oppenheimer approximation, which will mean that standard DFT and ab initio calculations on C₁₂₀⁻ and its larger equivalents will be of limited value. These fulleride monoanion clusters pose a serious challenge to current computational methods in quantum chemistry and we hope that this study will stimulate alternative approaches to try and understand their behaviour.

Conflicts of interest

There are no conflicts of interest to declare.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: method benchmarking via DFT calculations on C₆₀⁻ and C₁₂₀⁻. Electronic and vibrational spectra of all calculated C₁₂₀⁻ isomers, Cartesian coordinates and electronic energies of all calculated structures of C₁₂₀⁻. See DOI: https://doi.org/10.1039/d5cp03392f.

Acknowledgements

The computational results presented have been achieved using the HPC infrastructure LEO of the University of Innsbruck. This research was funded in part by the Austrian Science Fund (FWF) [10.55776/P35013, 10.55776/I6221, 10.55776/V1035]. GS acknowledges receipt of a DOC Fellowship of the Austrian Academy of Sciences. This article is based upon work from COST Action CA21126 – Carbon molecular nanostructures in space (NanoSpace), supported by COST (European Cooperation in Science and Technology). The authors are grateful to Professor Jun Onoe and Dr Toshiaki Nishii for providing them with C₁₂₀ structures from their past work.

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