  We compute from first principles the infrared dispersion of the nonlinear
susceptibility $\chi^{(2)}$ in zincblende semiconductors. At terahertz
frequencies the nonlinear susceptibility depends not only on the purely
electronic response $\chi^{(2)}_{\infty}$, but also on three other parameters
$C_1$, $C_2$ and $C_3$ describing the contributions from ionic motion. They
relate to the TO Raman polarizability, the second-order displacement-induced
dielectric polarization, and the third-order lattice potential. Contrary to
previous theory, we find that mechanical anharmonicity ($C_3$) dominates over
electrical anharmonicity ($C_2$), which is consistent with recent experiments
on GaAs. We predict that the sharp minimum in the intensity of second-harmonic
generation recently observed for GaAs between $\omega_{\rm TO}/2$ and
$\omega_{\rm TO}$ does not occur for several other III-V compounds.
