Negative g factors, berry phases, and magnetic properties of complexes

It is shown that the sign of the product of three Zeeman splitting factors corresponding to the main magnetic axes defines the sign of the Berry phase of a (pseudo) spin in an applied magnetic field. Ab initio calculations show that g(X)g(Y)g(Z)< 0 is often the case for lanthanide and transition metal complexes, while we prove that it is never achieved in S complexes with dominant second-order magnetic anisotropy. In the case of polynuclear compounds, it is argued that the signs of individual g(i), i=X, Y, Z, on each metal site can be extracted from experiment.