Vibronic Splitting and Zeeman Effect in Octahedral Molecules: Odd-Electron Systems

A theoretical investigation of the low-field vibronic Zeeman effect in octahedral molecules with odd-electron central atoms is presented. Such systems are of interest because the vibronic $g$ values differ from those of the parent electronic level and provide a means of studying the vibronic interaction. Only ${\Gamma }_8$ parent electronic states are of interest, and the vibronic multiplet splitting is derived for these states in terms of a minimum number (two) of vibronic interaction parameters. The Zeeman splitting of the vibronic multiplet is determined in terms of the parent electronic Zeeman effect, and for ${\Gamma }_8$ vibronic states, in addition, in terms of the vibronic interaction parameters. It is shown that that in spite of anisotropy in the Zeeman splitting of ${\Gamma }_8$ electronic or vibronic levels and the tumbling of free molecules, the observed Zeeman splitting should appear as four resolvable bands or lines except in certain limiting cases, but in all cases the information on $g$ values can in principle be determined from experiment.