Electron spin resonance (ESR) spectroscopy of the transition-metal complexes and clusters I.: Systematic investigations of real- and complex-orbital methods for calculating the d-orbital energies of a low-spin(S=1/2) nd5(t25, 2T2)(n=3,4,5) system (II) mathematical relation between real- and complex-orbital methods of calculating the d-orbital energies for a low-spin nd5(t25, 2T2)(n=3,4,5) system

On the basis of the first paper's theoretical derivations and concrete-instance calculations of the energies of the d orbitals for a low-spin (S=1/2)nd(5)(t(2)(5) T-2(2)) (n=3, 4, 5) system, the major results reported in this paper contain the following two respects: explicit relationships between the coefficients of the real and complex Kramers doublets have been derived by using two types of the expressions of the principal components of the g tensors in real- and complex-orbital representations obtained in the first paper; the use of these relationships of the real- and complex-orbital coefficients has carried out a series of mathematical demonstrations on the agreement of the real- and complex-orbital methods.