  Based on Takayama-Lin-Liu-Maki model, analytical expressions for the
third-harmonic generation, DC Kerr effect, DC-induced second harmonic optical
Kerr effect, optical Kerr effect or intensity-dependent index of refraction and
DC-electric-field-induced optical rectification are derived under the static
current-current($J_0J_0$) correlation for one-dimensional infinite chains. The
results of hyperpolarizabilities under $J_0J_0$ correlation are then compared
with those obtained using the dipole-dipole ($DD$) correlation. The comparison
shows that the conventional $J_0J_0$ correlation, albeit quite successful for
the linear case, is incorrect for studying the nonlinear optical properties of
periodic systems.
