The calculations of frequency-dependent second hyperpolarizabilities for the (static) electric field induced second harmonic generation (ESHG) [gamma(-2 omega;omega,omega,0)] of the FH, H2O, CO, and NH3 molecules in the second-order Moller-Plesset perturbation theory (MP2) based on the quasienergy derivative (QED) method are performed by numerical differentiation of frequency-dependent first hyperpolarizabilities for the second harmonic generation (SHG) [beta(-2 omega;omega,omega)] with respect to static electric fields. The QED-MP2 values of the ESHG second hyperpolarizabilities gamma(parallel to)(-2 omega;omega,omega,0) of the H2O, CO, and NH3 molecules show good agreement with the experimental values.