Band Structure of Circumanthracene

The band structure and mobility tensors of circumanthracene have been calculated by the tight-binding band approximation. The total bandwidths of the compound have been found to be slightly larger than those of anthracene; the total widths of the electron and the hole band being 0.82 kT and 1.22 kT room temperature. The values of the calculated mobilities for the electron and the hole are comparable in the b and the c′ directions, but the corresponding values in the a direction are smaller by a factor of about 30∼40, reproducing the anisotropy properties of the bandwidths in the reciprocal lattice directions. Thus, the anisotropy of the band structure of the compound is considerably different from that of anthracene. This behaviour may be associated with the differences in their crystal geometry and molecular structure. The magnitude of the mobility is three times larger than that of anthracene in the b direction, and two or three times larger in the mean, the calculated ratio being roughly in agreement with the experimentally-estimated one. Hence, it has been concluded the sharp drop in the resistivity in going from anthracene to circumanthracene is due mostly to the great increase in the concentrations of charge carriers, 107 times, as a result of the lowering of the energy gap value. Finally, it has been pointed out that, although circumanthracene is among the largest polycyclic aromatics, judging from the estimated magnitude of the mobility (several cm2/V.sec), the band model may be not satisfactory enough for us to understand the conduction in the crystal.