Electronic and geometric structures of ${\mathrm{C}}_{76}$ and ${\mathrm{C}}_{84}$

We report electronic and geometric structures of four main candidates for ${\mathrm{C}}_{84}$ obtained by using quantitatively reliable models. From a comparison to the recent photoemission spectra (PES), we show that a rather round fullerene with ${\mathit{D}}_2$ symmetry proposed by Achiba et al. is the most abundant ${\mathrm{C}}_{84}$ cluster in the graphite-arc soot. Other ${\mathrm{C}}_{84}$ clusters with ${\mathit{T}}_{\mathit{d}}$ and ${\mathit{D}}_{6\mathit{h}}$ symmetries are also expected to be present. The previously proposed rather flat ${\mathit{D}}_2$-symmetry ${\mathrm{C}}_{84}$ is found to be unfavorable. The electronic structure of ${\mathit{D}}_2$${\mathrm{C}}_{76}$ is also obtained and the agreement with PES is found to be excellent.