Unique definition of localized states in molecular spin

Although localized basis plays an important role in providing a physics picture of the magnetic dynamics in molecular spins, little attention has been given to the uniqueness and rigor in its definition. Here we propose a new definition of the localized basis for both non-Kramers and Kramers system based on the time-reversal symmetry of the spin Hamiltonian and the easy magnetic axis of the molecular spin. Given this definition, a unique and practical determination of the localized basis is achieved, which allows to associate a wave function with either "up" or "down" magnetic moment orientation in molecular spins. This facilitates a comprehensible interpretations of magnetization dynamics and eases the process of building simplified theoretical models involving the materials.