New Volleyballenes: Y₂₀C₆₀ and La₂₀C₆₀

Abstract

Two new stable Volleyballenes, the Y₂₀C₆₀ and La₂₀C₆₀ molecular clusters, are proposed on the basis of first-principles density functional theory. In conjunction with recent findings for the scandium system, these findings establish Volleyballene M₂₀C₆₀ molecules as a general class of stable molecules within the fullerene family. Both Y₂₀C₆₀ and La₂₀C₆₀ molecules have T_h point group symmetries and relatively large HOMO-LUMO gaps.

Since the first observation of the C₆₀ fullerene molecule¹,², much effort has been invested in the study of this novel molecular cluster. In the fullerenes, all the atoms are C atoms and they form a hollow sphere comprised of pentagonal and hexagonal rings. Very recently, on the basis of density functional theory (DFT) calculations, an exceptionally stable hollow cage, composed of 20 Sc atoms and 60 C atoms, the Volleyballene Sc₂₀C₆₀, was reported³. This molecular cluster has a T_h point group symmetry and a volleyball-like shape. This Volleyballene was the first buckyball to be spiked with metal atoms and is awaiting synthesis⁴,⁵,⁶,⁷,⁸.

If the Volleyballene Sc₂₀C₆₀ does actually exist, it is expected that other early transition metals should be capable of forming molecules of a similar type, and might also display unusual stability. We have therefore extended our work to other transition metal systems, with particular attention to elements with a single d electron: yttrium (Y) and lanthanum (La). As in the case of Sc₂₀C₆₀, the M₂₀C₆₀ (M = Y and La) molecules also are found to display an enhanced stability with the volleyball-like shape. In the following, the stability and electronic properties of the Volleyballenes Y₂₀C₆₀ and La₂₀C₆₀ are investigated through their bonding characters and the vibrational frequencies, as well as through molecular dynamics simulations.

Figure 1 shows the configurations of the two new Volleyballenes M₂₀C₆₀ (M = Y and La), which both have T_h point group symmetries within a tolerance of 0.1 Å. Similar to the case of Sc₂₀C₆₀, the new Volleyballenes are composed of six M₈C₁₀ subunits arranged in a crisscross pattern. In each M₈C₁₀ subunit, 10 carbon atoms form two head-to-head connected carbon pentagons (C-pentagon), and 8 transition-metal atoms form a single transition-metal octagon (M-octagon). The two connected C-pentagons are surrounded by the M-octagon, to give a structure that resembles the panels of a volleyball.

Figure 1. The configurations and deformation electron densities of Y₂₀C₆₀ and La₂₀C₆₀.

The isosurface is taken to be 0.01 e/ų.

The 20 transition metal atoms link to form 12 suture lines with the average distances between transition-metal atoms being 3.411 Å for Y-Y and 3.617 Å for La-La. For the C-pentagons of the Y₂₀C₆₀ molecule, the lengths of the C-C bonds lie in the range 1.449–1.460 Å. Along with a 1.485 Å C-C bond connecting the two C-pentagons, the average C-C bond length is found to be 1.455 Å. The average Y-C bond length is 2.396 Å.

For La₂₀C₆₀, the C-C bond lengths are in the range 1.450–1.456 Å and the C-C bond connecting the two C-pentagons has a length of 1.490 Å, resulting in an average C-C bond length of 1.457 Å. The La-C bond length is 2.565 Å. Both the average C-C and M-C bond lengths, as well as the average M-M distance, in La₂₀C₆₀ are larger than the corresponding distances in Y₂₀C₆₀, indicating a larger-sized cage for La₂₀C₆₀. The reason may lie with the relatively larger atomic radius of La. All the calculated data including the binding energies per atom, are listed in Table 1. For the new Volleyballenes, the binding energies per atom are 6.622 and 6.565 eV, for Y₂₀C₆₀ and La₂₀C₆₀, respectively. For more details see Section I of the Supplementary Information.

Table 1. Summary of the calculated results for M ₂₀C₆₀ (M = Y and La).

	Sym.	d1	d2	QM	QNPA	Eb	Eg
Y20C60	Th	1.455	2.396	0.953	0.921	6.622	1.395
La20C60	Th	1.457	2.565	0.693	0.779	6.565	1.254

The data include the symmetry group (Sym.), the average C-C (d₁) and M-C (d₂) bond lengths, the average charge transfer from M to carbon atoms (Q_M for Mülliken analysis and Q_NPA for NBO analysis), the binding energy per atom (E_b), and the HOMO-LUMO energy gap (E_g) in units of Å for the lengths and eV for energy.

The bonding characters of the Volleyballene M₂₀C₆₀ (M = Y and La) molecules were investigated by analyzing their deformation electron densities. The Volleyballenes Y₂₀C₆₀ and La₂₀C₆₀ have similar bonding characteristics, mainly due to their similar electron configurations, 4d¹5s² for the Y atom and 5d¹6s² for the La atom. On the whole, there is electron transfer from the transition metal atoms to the C atoms. Mülliken population analysis showed an average charge transfer of 0.95e from each Y atom to the neighboring C atoms for Y₂₀C₆₀, while for La₂₀C₆₀, the average charge transfer is 0.69 e. To better understand the chemical bonding, natural bonding orbital (NBO)⁹ analysis was employed, and it was found that the results of the natural population analysis (NPA) are in accord with those of Mülliken population analysis (Table 1). The NPA showed an average charge transfer of 0.92 e from each Y to the neighboring C atoms in Y₂₀C₆₀, while the charge transfer for La₂₀C₆₀ was 0.78 e. For the C atoms, there are obvious characteristics of sp²-like hybridization, and each C atom has three σ bonds. As with the Sc atoms in the Volleyballene Sc₂₀C₆₀, there are four lobes for each M atom in Volleyballene M₂₀C₆₀ (M = Y and La) molecules, pointing to the four neighboring C atoms. This strengthens the link between the M₈C₁₀ subunits.

The stability of the M₂₀C₆₀ molecules was further checked using ab initio molecular dynamics (MD) simulations with the constant-energy, constant-volume (NVE) ensemble. The simulation time step was set to be 1.0 fs with a total of 10000 dynamics steps. With initial temperatures of 2200 and 1800 K (~1100 and ~900 K effective temperatures) for Y₂₀C₆₀ and La₂₀C₆₀, respectively, the structures were not disrupted over the course of a 10.0 ps total simulation time. For more details see Section II of the Supplementary Information. Vibrational frequency analysis was also carried out, and no imaginary frequencies were found for either of the two Volleyballenes (Y₂₀C₆₀ and La₂₀C₆₀). These results indicate that the two new Volleyballenes, both have good kinetic and thermodynamic stabilities. Figure 2 shows the calculated Raman spectrums of Y₂₀C₆₀ and La₂₀C₆₀. The temperature was taken to be 300 K, and incident light of wavelength 488.0 nm was chosen in order to simulate a realistic Raman spectrum that can be compared to experimental results. The specific vibrational modes corresponding to the peaks of Raman spectrum are given in Section III of the Supplementary Information.

Figure 2. Simulated Raman spectrums for the Volleyballenes M₂₀C₆₀ (M = Y and La) at a temperature of 300 K and using 488.0 nm incident light.

The Lorentzian smearing was set to be 20.0 cm⁻¹. The labels show the frequencies corresponding to the peaks of the intensities.

We then calculated the partial densities of states (PDOS) and the frontier molecular orbitals, including the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) as shown in Fig. 3. From the contours of the HOMO orbitals, it can be seen that the HOMO orbitals are mostly localized on the C atoms. There is also obvious hybridization between C p and M d orbitals. For the LUMO, the orbital wave functions are mostly localized on the transition metal atoms, and have obvious d orbital characteristics. In one M₈C₁₀ subunit, four transition metals have -like orbital characteristics, and each of the other four has four pear-shaped lobes. The centers of all four lobes lie in one plane, which is perpendicular to the plane of the M₈C₁₀ subunit thus playing the role of a connection between M₈C₁₀ subunits. There is sp-d hybridization for the LUMO orbital. Noted that the LUMO of La₂₀C₆₀ is slightly different from that of Y₂₀C₆₀ at the same isosurface (0.015 e/ų). For La₂₀C₆₀, the -like orbital has obvious hybridization characteristics, with one pear-shaped region above the torus being larger than the one below the torus, while for Y₂₀C₆₀ this situation is not obvious. This may be due to La having a larger atomic radius than that of the transition metal Y. Close examination of the PDOS further confirms the hybridization characteristics of the HOMO and LUMO orbitals. All these results are consistent in demonstrating that hybridization between the M d orbitals and C s-p orbitals is essential for stabilizing the cage structure of M₂₀C₆₀ (M = Y and La).

Figure 3. The HOMO and LUMO orbitals, and PDOS for M₂₀C₆₀ (M = Y and La).

The isosurface for the orbitals is set at 0.015 e/ų.

For the Volleyballenes Y₂₀C₆₀ and La₂₀C₆₀, relatively large HOMO-LUMO gaps were found, as listed in Table 1. The HOMO-LUMO gaps are 1.395 eV for Y₂₀C₆₀ and 1.254 eV for La₂₀C₆₀. The large gaps are due mainly to the energies of the d atomic orbitals being much lower than those of the p orbitals. With relatively large HOMO-LUMO gaps, the two new Volleyballenes Y₂₀C₆₀ and La₂₀C₆₀ should be stable fullerene variants with moderately high chemical stability.

In summary, first-principles studies have identified two new stable Volleyballenes, Y₂₀C₆₀ and La₂₀C₆₀. In an initial report on the stability of Sc₂₀C₆₀³, we speculated that Sc₂₀C₆₀ might comprise one member of a Volleyballene family, and that other transition or rare-earth metals could also form stable M₂₀C₆₀ molecular clusters. This speculation now appears to have been borne out.

Methods

The calculations were carried out with the exchange-correlation potential described by the Perdew-Burke-Ernzerhof (PBE) version of the general gradient approximation (GGA)¹⁰. The double-numerical basis plus polarized functions (DNP)¹¹ was chosen. For the transition metal atoms, relativistic effects in the core were included using the DFT semi-core pseudopotentials (DSPP)¹². All structures were fully relaxed, and geometric optimizations were performed with unrestricted spin and without any symmetry constraints as implemented in the DMol³ package¹³.

Additional Information

How to cite this article: Wang, J. and Liu, Y. New Volleyballenes: Y₂₀C₆₀ and La₂₀C₆₀. Sci. Rep. 6, 30875; doi: 10.1038/srep30875 (2016).