Ground state spin-orbit effects in the molecules V-2, VNb, and Nb-2 have been investigated using self-consistent field configuration interaction (SCF/CI) calculations based on the intermediate neglect of differential overlap Hamiltonian parameterized for optical spectroscopy (INDO/S). Accurate results for the spin-orbit splittings of the X (3)Sigma(-) ground state of each molecule were obtained using a CI treatment designed to isolate essential correlation of the ground state and the isoconfigurational (1)Sigma(+) state causing the splittings. Energies computed for the (1)Sigma(+) states are compared to energies obtained from simple two-state perturbative models. It is observed that the consideration of only two states is a large source of error. Previous assignment of a low-lying excited state observed for V-2 as the (1)Sigma(g)(+) state is not supported. Additional results on excited states of VNb have also been obtained. A (3)Sigma(-)<--X (3)Sigma(-) transition observed experimentally for VNb is assigned as a sigma*<--sigma promotion, and the presence of a second excited (3)Sigma(-) state of VNb that has not been observed is suggested. An analysis of correlation effects in the INDO/S model is given based on a comparison of results obtained with the approximate essential correlation CI calculations and with larger restricted active space full CI calculations.