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 magneic 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.