  A systematic first-principles study within density functional theory on the
geometrical structures and electronic properties of unconventional fullerene
C64 and its derivatives C64X4 (X = H; F;Cl;Br) has been performed. By searching
through all 3465 isomers of C64, the ground state of C64 is found to be
spherical shape with D2 symmetry, which differs from the parent cage of the
recently synthesized C64H4 that is pear-shaped with C3v symmetry. We found that
the addition of the halogen atoms like F;Cl;Br to the pentagon-pentagon fusion
vertex of C64 cage could enhance the stability, forming the unconventional
fullerenes C64X4. The Mulliken charge populations, LUMO-HOMO gap energies and
density of states are calculated, showing that different halogen atoms added to
C64 will cause remarkably different charge populations of the C64X4 molecule;
the chemical deriving could enlarge the energy gaps and affect the electronic
structures distinctly. It is unveiled that C64F4 is even more stable than
C64H4, as the C-X bond energy of the former is higher than that of the latter.
The computed spectra of C64H4 molecules agree well with the experimental data;
the IR, Raman, NMR spectra of C64X4 (X = F;Cl;Br) are also calculated to
stimulate further experimental investigations. Finally, it is uncovered by
total energy calculations that C64X4 could form a stable hexagonal monolayer.
