Ab initiocalculation of optical second harmonic generation at the rutileTiO2(110)surface

Optical second harmonic (SH) response of rutile $\mathrm{Ti}{\mathrm{O}}_2\left(110\right)$ surface was studied by the self-consistent full potential linearized augmented plane-wave method within the local-density approximation. The calculated SH response of the relaxed surface agrees with the measured SH intensity as a function of the excitation photon energy and the sample rotation angle around its surface normal. In order to clarify the origin of the large surface SH response at the SH photon energy of about $2\hslash \omega =4\mathrm{eV}$, SH intensities from various Ti-O bonds on the surface were calculated. The result revealed that the zigzag chains consisting of bridging oxygen and neighboring sixfold coordinated titanium atoms on the top surface layer dominantly contribute to the SH response of the $\mathrm{Ti}{\mathrm{O}}_2\left(110\right)$ surface.