The expression for the analytical derivatives of the second-order correlation energy was derived for a system under the spin-dependent perturbations, and it was applied to the correlated calculation of the (3)J(HH)＇s in ethane, methanol, and methylamine. The calculation showed that the addition of tight s-type functions to the basis set considerably affects the Fermi contact (FC) contribution. Furthermore, the third-and fourth-order correlations were also evaluated for the FC contribution with the finite perturbation theory. The three noncontact contributions were computed at the Hartree-Fock (HF) level. The total contribution to the (3)J(HH) in ethane was significantly lower than the experimental value. The calculated (3)J(HH)＇s in methanol and methylamine were nearer to the experimental couplings than in ethane. (C) 2000 American Institute of Physics. [S0021-9606(00)00208-7].