Lattice Theory of : A Carbon Ellipsoidal Cell

An ellipsoidal differential lattice structure is developed for studies of the structures, energy bands, and electronic characteristics of C₃₆. Constraint numbers are introduced into the wavenumbers of k_rho in the longitudinal direction of the prolate ellipsoidal lattice. Under these constraints, the structure of the C₃₆ molecule is demonstrated to be an ellipsoidal cell, where the lengths of major and minor axes are the intermolecular spacing and diameter of C₃₆. This approach also indicates that the intermolecular interactions of two C₃₆ molecules are the interactions of the valence electrons in 2p_z state which is perpendicular to the surface of the ellipsoid. The C₃₆ 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 C₃₆ molecule to the other. The ellipsoidal structures of C₃₆ are isoenergetic and semiconducting. Also, some isomers of C₃₆ 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