Ground state isoconfigurational mixing in the V2, VNb, and Nb2 molecules

Abstract

Ground state spin–orbit effects in the molecules V2, VNb, and Nb2 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 3Σ− ground state of each molecule were obtained using a CI treatment designed to isolate essential correlation of the ground state and the isoconfigurational Σ+1 state causing the splittings. Energies computed for the Σ+1 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 V2 as the Σg+1 state is not supported. Additional results on excited states of VNb have also been obtained. A Σ-3←X Σ-3 transition observed experimentally for VNb is assigned as a σ*←σ promotion, and the presence of a second excited Σ-3 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.

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

“…Initially it was expected that INDO/S calculations on the cations would be similar to the earlier efforts with the neutrals, giving reasonable agreement with the empirical predictions and CASSCF calculations, but certain discrepancies were found. These included larger disagreement between empirical and INDO/S energies than found for the neutrals, and quartet contamination of both excited doublet states.…”

“…Two related approximations were made in previous derivations. , The first is neglect of overlap integrals in evaluating spin−orbit matrix elements, which omits terms proportional to ζ ( n - 1)d S, where S is the delta-symmetry overlap integral. The second is neglect of the extensive CI of the (dπ u ) 4 (dσ g ) 2 (sσ g ) 2 (dδ g ) 2 and (dπ u ) 4 (dσ g ) 2 (sσ g ) 2 (dδ u ) 2 configurations, which is known to be large for V 2 and Nb 2 . ,,,, This CI imparts local character to the delocalized MO description of the δ g orbitals. It was previously assumed that the δ g MOs are completely local, , but this is only partially true for these molecules.…”

“…The ground states of V 2 , VNb, and Nb 2 have unusually large spin−orbit splittings, − 75 cm -1 for V 2 , 230 cm -1 for VNb, and 410 cm -1 for Nb 2 . (These experimentally determined splittings are henceforth referred to as Δ.)…”

Semiempirical local spin: Theory and implementation of the ZILSH method for predicting Heisenberg exchange constants of polynuclear transition metal complexes

“…This is convenient for calculations of Heisenberg coupling constants as described above, in which a number of calculations for the different spin flips must be run. All of the calculations described in this article used the INDO/S model (intermediate neglect of differential overlap model parameterized for optical spectroscopy), which is known to provide reasonable approximations of the energies of ground and excited states of open‐shell transition metal complexes 4, 8–11, 15, 16, 52–60, in particular those of Fe +3 4, 9, 52, 60. The values used for all parameters in the model were those originally suggested by Zerner et al 9.…”

Investigation of the use of density functionals in second‐ and third‐row transition metal dimer calculations

“…It is an interesting theoretical topic because the metalmetal bond cannot be accurately calculated without taking the neardegeneracy of outermost s and d orbitals into account. 1 The neardegeneracy causes the multiple bond and a number of low-lying excited states. Dimer calculations using the ab initio molecular orbital (MO) method requires a computationally demanding multiconfigurational treatment.…”