Stereochemical dependences of vicinal fluorine-fluorine nuclear magnetic resonance coupling constants ((3)J(FF)) have been studied with the multiconfigurational self-consistent field in the restricted active space approach, with the second-order polarization propagator approximation (SOPPA), and with density functional theory. The SOPPA results show the best overall agreement with experimental couplings. The relationship with the dihedral angle between the coupled fluorines has been studied by Fourier analysis, the result is very different from that of proton-proton couplings. The Fourier coefficients do not resemble those of a typical Karplus equation. The four nonrelativistic contributions to the coupling constants of 1,2-difluoroethane configurations have been studied separately showing that up to six Fourier coefficients are required to reproduce the calculated values satisfactorily. Comparison with Fourier coefficients for matching hydrogen fluoride dimer configurations suggests that the higher order Fourier coefficients (C(n)greater than or equal to3) originate mainly from through-space Fermi contact interaction. The through-space interaction is the main reason (3)J(FF) do not follow the Karplus equation. (C) 2004 American Institute of Physics.