Spin−Orbit Effects in the Ground States of Singly Positive and Neutral V2, VNb, and Nb2:  INDO/S and Empirical Model Calculations

Ground-state spin−orbit splittings in V2 +, VNb+, and Nb2 + were investigated with spin−orbit configuration interaction (SOCI) calculations using the intermediate neglect of differential overlap method for optical spectroscopy (INDO/S). Splittings found for the X4Σ- ground states of V2 + and VNb+ using a CI treatment isolating essential correlation of the ground and isoconfigurational a2Σ+ and b2Σ- state wave functions agreed well with experiment. The size of the splitting for Nb2 + was predicted. In all three cases the a2Σ+ and b2Σ- states were found to be strongly coupled by the spin−orbit operator. Several perturbative models for predicting energies of interacting excited states based on measured splittings were analyzed by comparing to SOCI results for V2, VNb, and Nb2. Second-order perturbation theory, treating only the isoconfigurational states, and neglecting overlap and CI in computing couplings was the best choice of approximations due to cancellation of errors. An empirical model treating the isoconfigurational states of the cations was developed within these guidelines and agrees well with SOCI calculations for V2 +. The empirical wave functions were divergent for Nb2 + due to similar energies of the doublet states. Analysis of correlation effects in the INDO/S model indicates that a charge-iterative method could be effective for systematically correlated semiempirical calculations on metal cluster ions.