Theoretical Equations of Zeeman Energy Levels for Distorted Metal Complexes with 3T1 Ground Terms

Hiroshi Sakiyama

doi:10.3390/magnetochemistry5010017

Abstract

The theoretical equations of Zeeman energy levels, including the zero-field energies and the first- and second-order Zeeman coefficients, have been obtained in closed form for nine states of the 3 T 1 ( g ) ground term, considering the axial ligand-field splitting and the spin-orbit coupling. The equations are expressed as the functions of three independent parameters, Δ , λ , and κ , where Δ is the axial ligand-field splitting parameter, λ is the spin-orbit coupling parameter, and κ is the effective orbital reduction factor, including the admixing. The equations are useful in simulating magnetic properties (magnetic susceptibility and magnetization) of the complexes with 3 T 1 ( g ) ground terms, e.g., octahedral vanadium(III), octahedral low-spin manganese(III), octahedral low-spin chromium(II), and tetrahedral nickel(II) complexes.

Highlights

Magnetic properties of metal complexes with T ground term is difficult to be interpreted because of the spin-orbit coupling
This paper reports theoretical expression of Zeeman energy levels for distorted metal complexes with 3T1 ground terms for the purpose of simulating the magnetic properties at high speed
In order to obtain magnetic susceptibility and magnetization equations for the metal complexes with 3T1(g) ground terms, the zero-field energies and Zeeman coefficients were obtained in closed form by solving the secular matrices

Summary

Introduction

Magnetic properties of metal complexes with T ground term is difficult to be interpreted because of the spin-orbit coupling. Since the orbital angular momentum depends on the symmetry around the central metal ion, the distortion effect should be considered in addition to the spin-orbit coupling. This paper reports theoretical expression of Zeeman energy levels for distorted metal complexes with 3T1 ground terms for the purpose of simulating the magnetic properties at high speed. Concerning the T-term magnetism, Figgis successfully simulated the temperature dependence of the effective magnetic moment of the metal complexes with 2T2 ground terms [1], considering both the axial distortion and the spin-orbit coupling. The secular matrices were to be solved each time to simulate the magnetic properties. Simulation can be freely performed only by those who can use programs to solve matrix equations, and simulation output can only be performed within the programmed range

Methods

Results

Discussion

Conclusion