Complete theory of Ni(II) and V(III) in cubic crystalline fields

Abstract

The generalized crystal field theory of Finkelstein and Van Vleck is augmented by the introduction of spin-orbit coupling and an attempt is made to thus account for both the spin-allowed and the spin-forbidden d n , ( n = 2, 8), spectral transitions of Ni(II) and V(III) complexes. The secular equations are derived by the use of functions which span, in both the weak and strong crystalline field pictures, the proper spin-coordinate cubic symmetry classification of Bethe. These secular equations were solved numerically on the IBM 704 data processing machine at the Murray Hill Bell Telephone Laboratories and the results are illustrated by suitable graphs. The existing spectral data on tetrahedral and octahedral complexes of Ni(II) and V(III) have been interpreted theoretically and it is found that the calculations do not support Jørgensen's assignment of the double-peaked red band of hexaquo nickel systems. Spinallowed infrared transitions are predicted at ∼350, 1000, 1100, and 5300 cm −1 for tetrahedral Ni(II) complexes and at ∼1.6, 168, and 250 cm −1 for octahedral V(III) complexes. Low's spectral data on divalent nickel dissolved in magnesium oxide and trivalent vanadium dissolved in aluminum oxide are given a rigorous theoretical interpretation. Some comments on the applicability of the derived transformation and energy matrices to the related magnetic problems (paramagnetic resonance and magnetic susceptibilities) and spectral problems (energy level splittings due to fields of lower symmetry) are given in the appendices. In particular, it is shown that the ground electronic state splitting of 0.49 cm −1 found by Holden et al. in nickel fluosilicate hexahydrate implies a 50-cm −1 trigonal field splitting of certain of the excited electronic states.