Unique determination of localized basis in molecular spin

Localized basis plays an important role in comprehending the magnetic dynamics in molecular spins from a physics perspective. Nonetheless, the uniqueness and rigor of its determination have received limited attention. In this study, we propose a new determination of the localized basis applicable to both non-Kramers and Kramers molecular spin systems, leveraging the time-reversal symmetry of the spin Hamiltonian and the molecular spin's main magnetic axis. By introducing this, we establish a distinct and practical means of determining the localized basis, enabling the association of a molecular spin wave function with either an "up" or "down" magnetic moment orientation in molecular spins. This finding facilitates a comprehensive interpretation of magnetic dynamics and simplifies the construction of theoretical models for materials analysis.