Lattice theory of C36:: A carbon ellipsoidal cell

An ellipsoidal differential lattice structure is developed for studies of the structures, energy bands, and electronic characteristics Of C-36. Constraint numbers are introduced into the wavenumbers of k(phi) in the longitudinal direction of the prolate ellipsoidal lattice. Under these constraints, the structure of the C-36 molecule is demonstrated to be an ellipsoidal cell, where the lengths of major and minor axes are the intermolecular spacing and diameter of C-36. This approach also indicates that the intermolecular interactions of two C-36 molecules are the interactions of the valence electrons in 2p(z) state which is perpendicular to the surface of the ellipsoid. The C-36 molecules join together at the endpoint of the major axis through interactions of the covalence electrons in the intermolecular region, where the electrons are transferred from one C-36 molecule to the other. The ellipsoidal structures of C-36 are isoenergetic and semiconducting. Also, some isomers of C-36 can be narrow semiconducting. Predictions of this theory agree well with the results of the simulations and published measurements, paving the way for the design of practical nanodevices.