New Volleyballenes: Y20C60 and La20C60

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 Th point group symmetries and relatively large HOMO-LUMO gaps.

shows the configurations of the two new Volleyballenes M 20 C 60 (M = Y and La), which both have T h point group symmetries within a tolerance of 0.1 Å. Similar to the case of Sc 20 C 60 , the new Volleyballenes are composed of six M 8 C 10 subunits arranged in a crisscross pattern. In each M 8 C 10 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.
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 Y 20 C 60 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 La 20 C 60 , 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 La 20 C 60 are larger than the corresponding distances in Y 20 C 60 , indicating a larger-sized cage for La 20 C 60 . 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 Y 20 C 60 and La 20 C 60 , respectively. For more details see Section I of the Supplementary Information.
The bonding characters of the Volleyballene M 20 C 60 (M = Y and La) molecules were investigated by analyzing their deformation electron densities. The Volleyballenes Y 20 C 60 and La 20 C 60 have similar bonding characteristics, mainly due to their similar electron configurations, 4d 1 5s 2 for the Y atom and 5d 1 6s 2 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 Y 20 C 60 , while for La 20 C 60 , 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)   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 (Y 20 C 60 and La 20 C 60 ). These results indicate that the two new Volleyballenes, both have good kinetic and thermodynamic stabilities. Figure 2 shows the calculated Raman spectrums of Y 20 C 60 and La 20 C 60 . 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.
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 M 8 C 10 subunit, four transition metals have d z 2-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 M 8 C 10 subunit thus playing the role of a connection between M 8 C 10 subunits. There is sp-d hybridization for the LUMO orbital. Noted that the LUMO of La 20 C 60 is slightly different from that of Y 20 C 60 at the same isosurface (0.015 e/Å 3 ). For La 20 C 60 , the d z 2-like orbital has obvious hybridization characteristics, with one pear-shaped region above the torus being larger than the one below the torus, while for Y 20 C 60 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 M 20 C 60 (M = Y and La).
For the Volleyballenes Y 20 C 60 and La 20 C 60 , relatively large HOMO-LUMO gaps were found, as listed in Table 1. The HOMO-LUMO gaps are 1.395 eV for Y 20 C 60 and 1.254 eV for La 20 C 60 . 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 Y 20 C 60 and La 20 C 60 should be stable fullerene variants with moderately high chemical stability.
In summary, first-principles studies have identified two new stable Volleyballenes, Y 20 C 60 and La 20 C 60 . In an initial report on the stability of Sc 20 C 60 3 , we speculated that Sc 20 C 60 might comprise one member of a Volleyballene family, and that other transition or rare-earth metals could also form stable M 20 C 60 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 DMol 3 package 13 .  Table 1. Summary of the calculated results for M 20 C 60 (M = Y and La). The data include the symmetry group (Sym.), the average C-C (d 1 ) and M-C (d 2 ) 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.