Crystallographic studies of [Fe(SR)(4)](2-) (R is an alkyl or aryl residue) have shown that the Fe(II)S(4) cores of these complexes have (pseudo) D2d symmetry. Here we analyze the possibility that these structures result from a Jahn-Teller (JT) distortion that arises from the e(3z(2) - r(2), x(2) - y(2)) orbital ground state of Fe(II) in T(d)symmetry. Special attention is paid to the influence of the second-nearest neighbors of Fe, which lowers the symmetry and reduces the full JT effect to a smaller, pseudo JT effect (PJT). To estimate the size of the PJT distortion, we have determined the vibronic parameters and orbital state energies for a number of [Fe(SR)(4)](2-) models using density functional theory (DFT). Subsequently, this information is used for evaluating the adiabatic potential surfaces in the space of the JT-active coordinates of the FeS(4) moiety. The surfaces reveal that the JT effect of Fe(II) is completely quenched by the tetrathiolate coordination.