Vibrational contribution to static and dynamic (Hyper)polarizabilities of zigzag BN nanotubes calculated by the finite field nuclear relaxation method

The vibrational contribution to static and dynamic (hyper)polarizabilities for the zigzag (n,0) family of BN nanotubes, with n ranging from (6,0) to (36,0), has been obtained. Calculations were done by the finite field nuclear relaxation (FF-NR) method for periodic systems, newly implemented in the CRYSTAL code, using the Coupled Perturbed Kohn-Sham (CPKS) scheme at the B3LYP/6-31G* level for the required electronic properties. Both transverse and transverse-longitudinal tensor components are determined by applying finite, i.e. static, fields in the transverse direction. The magnitude of the vibrational term increases with the radius of the nanotube as determined by the increase in the field-induced geometric deformation. The resulting vibrational (hyper)polarizability varies from being dominant to negligible, when compared with the corresponding static electronic contribution. This depends upon the radius, as well as the property and the component, in a systematic manner. The extension to longitudinal components, not yet available, will be implemented next.