Potential-energy calculations of the mechanisms of self-diffusion in molecular crystals. Part 2.—Naphthalene

Abstract

Self-diffusion in crystalline naphthalene has been investigated by calculation of the activation energies for various postulated mechanisms. A first-order ‘rigid-lattice’ calculation is first performed in which only the diffusing molecule is allowed to move. This yields several conclusions: (1) self-diffusion normal to the ab plane occurs only by vacancy exchange between sixth-nearest-neighbour sites; (2) diffusion along the a-direction occurs by the same mechanism and also by vacancy exchange between nearest-neighbour sites; (3) diffusion along the b-direction occurs by the nearest-neighbour mechanism; and (4) the molecular trajectories in both mechanisms apparently do not cross saddle points on their respective potential surfaces. It is then postulated that diffusion occurs without rotation of the diffusing molecule when its initial and final lattice sites belong to the same sublattice (the sixth-nearest neighbour mechanism) and with a single, direct rotational flip of the diffusing molecule while it is translating between lattice sites when the sites belong to different sublattices (the nearest-neighbour mechanism). The theoretical activation energies for these trajectories in the rigid lattice model are twice as large as the experimental values, but most of the barrier comes from just four (sixth-nearest neighbour mechanism) or two (nearest-neighbouring mechanism) nearby molecules in the lattice. A second-order ‘relaxed-lattice’ calculation is then performed in which these ‘blocking’ molecules are allowed to rotate, and good agreement with experiment is found for both mechanisms when the blocking molecules rotate ca. 10–15° to their ‘equilibrium’ orientations in the ‘transition state’. The tentative conclusion that the operative trajectories in naphthalene do not cross saddle points is of considerable theoretical interest.