Octahedral complexes. Part 2.—The calculation of spin-orbit coupling energies

Abstract

The general form of the matrix of spin-orbit coupling energy between a pair of terms in an S r r l M l coupling scheme is derived. A table is given exhibiting this form explicitly for all terms occurring in t T e n configurations. The complete matrix of spin-orbit coupling is given for d2 and for the lowest terms of d3 to d7, in each case in the strong-field coupling scheme. As applications the crossing of tge2 5T2 by tg1A1 in d6 is discussed and a calculation is made of the zero-field splitting of the ground term of the high-spin chromous ion due to second-order effects of spin-orbit coupling. For the latter no significant disagreement between theory and experiment is found, thus, contrary to a previous view,ZO making it unnecessary to postulate a spin-spin coupling constant significantly different from zero.

Some investigations in the theory of open-shell ions

“…The phases of the coupling coefficients in the latter are the same as in the present series except for coupling of T2T 1 to E, T1E to T 2 and ET,~ to T1, but not the same as in references [3, 7 or 8]. I did not realize when I wrote that paper [6] that I could choose my phases so that W is invariant to odd permutations of its columns. Next we calculate the complete matrix of spin-orbit coupling in a scheme in which the basic states are built up by coupling together one-electron functions which form bases for irreducible spin and space representations.…”

“…Thus for triplet terms we have a new method of calculating the ratios of the c-numbers given in reference [6]. The phases of the coupling coefficients in the latter are the same as in the present series except for coupling of T2T 1 to E, T1E to T 2 and ET,~ to T1, but not the same as in references [3, 7 or 8].…”

“…The order of the representations in the V symbol is important and will always be taken as in equation (1). I adopt the double-barred notation for the reduced matrix element [3,4] rather than Condon and Shortley's four dots notation [5] which I have used previously [2,6,7]. It follows from equation (1) that (c n Tb II a)= (-1)~ (a II Tb I1 ) (2) for Hermitian T b, where (-1) ~ is -1 for a=A 2 or T1 and is + 1 otherwise (see Part II).…”

Van Vleck excitons in Ca2RuO4

“…Valid in the ∆ λ regime where minimal mixing between t and e states occur, the projection of the L = 2 t onto the L = 1 p states greatly simplifies the process of calculating α directly using representation theory. In the case of the orbital triplet ground state of the d 4 configuration, Griffith 57 and Moffitt 58 determined a value of − 1 2 for α in the pure L-S Russell-Saunders coupling scheme.…”

Energy levels of paramagnetic ions: Algebra. III. The case of dN ions in cubical symmetry

“…The starting point of the landmark progress in crystal-field theory lies on the pioneer works of the Japanese school [l] and of Griffith [2]. The greatest part of the papers in Refs.…”