Second-harmonic generation in boron nitride nanotubes adsorbed with molecular hydrogen*

We present {\it ab initio} calculations for second harmonic response of single wall zigzag pristine and with molecular hydrogen adsorption boron nitride nanotubes. These calculations were performed with density functional theory within the local-density approximation (LDA) and the application of the GW approximation to calculate the band gap GW correction. A length-guage formalism for calculating the nonlinear optical response with the correct implementation of the scissor correction was used to obtain the nonlinear susceptibility $\chi^{(2)}(-2\omega;\omega,\omega)$ of zigzag BN nanotubes. We found that contrary to that reported in the literature, the (5,0) and (9,0) boron nitride nannotubes have a non vanishing SHG response. We also found that SHG is not a suitable thecnique to monitor the physisorption of $H_{2}$ molecules on the external surface of BN nanotubes.