Polarizability and hyperpolarizability of BN zigzag nanotubes calculated by the coupled perturbed Kohn-Sham scheme

Linear and nonlinear electric dipole susceptibilities are evaluated for infinite periodic zigzag BN nanotubes utilizing primarily the coupled perturbed Kohn-Sham scheme recently implemented in the crystal code. The effect of different functionals, basis set, and computational parameters is examined. Most of the calculations are done at the B3LYP/6-31G* level. For electronic linear polarizabilities, substantial differences compared to the uncoupled sum-over-states scheme are found. Much larger radii were considered than in earlier studies, thereby permitting accurate comparison with corresponding properties of the hexagonal monolayer. In addition, we confirmed the dielectric shell model for the linear polarizability, but with a significantly different shell thickness than previously thought. Vibrational (ionic) contributions to the nonlinear susceptibilities are calculated. In doing so, the finite-field–nuclear-relaxation (FF–NR) method was employed for the transverse components of the (6,0), (9,0), and (12,0) nanotubes. Aside from being computationally more efficient than other procedures, this method includes anharmonicity effects through first order and, as shown, is readily applied to key dynamic as well as static properties (and yields the static linear polarizability as well). Our calculated nonlinear vibrational susceptibilities sometimes exceed, or even greatly exceed, the corresponding static electronic susceptibility. In such cases, the relative magnitude of the vibrational contribution grows substantially with tube radius over the range considered. Future plans include extending these FF–NR calculations to large nanotubes and to the longitudinal (periodic) direction as well.