The extended SSH model and Bogoliubov-de-Gennes (BdeG) formalism are applie
d to investigate the electronic properties and stable lattice configuration
s of C-36 We focus the problem on the molecule's unusual D-6h symmetry. The
electronic part of Hamiltonian without Coulomb interaction is solved analy
tically. We found that the gap between HOMO and LUMO is small due to the lo
ng distance hopping between the 2nd and 5th layers. The charge densities of
HOMO and LUMO states are mainly distributed in the two layers, that causes
a large splitting between the spin triplet and singlet excitons. The diffe
rences of bond lengths, angles and charge densities among molecule and pola
rons are discussed.