  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.
