Orientational vibrations of 2D molecular layers with quadrupolar interaction

Molecular layers with rotational degrees of freedom and quadrupolar interaction between linear molecules are investigated theoretically. Rotation of the molecules in the plane of an adsorbing surface is considered; centers of gravity of the molecules are pinned to sites of a rectangular lattice. The energy of the system contains an additional parameter rho (ratio of the lattice constants of a 2D system), in comparison with the I D case. It is found that alternating orientation of the adsorbed molecules along both sides of the rectangular unit cell corresponds to the minimum of the energy. Equations of rotational movement are derived for linear oscillations of molecules near the equilibrium positions in a 2D lattice. Dispersion relations are obtained and analyzed. The Brillouin zone cannot be divided as in the ID case after unit-cell doubling. The parameter B(k), which describes the topology of the dispersion surfaces, is introduced. It is shown that both branches of the spectrum have optical behavior. The gaps and bandwidths are found as functions of p. The method of calculation of the density of states (DOS) for translational oscillations of a 2D rectangular lattice with one atom per unit cell is generalized for rotational oscillations of a 2D two-sublattice molecular lattice. The diagram describing three regions with different analytical properties of the DOS which correspond to different topologies of the isofrequency lines is introduced. This diagram is a portrait in the plane of the parameters B and rho. The DOS is found in terms of complete elliptic integrals of the first kind.