A novel method for the calculation of the dynamic polarizability (alpha) of open-shell molecular systems is developed based on the. quantum master equation combined With the broken symmetry (BS) time dependent density functional theory within the Tamm-Dancoff approximation, referred to as the BS-DFTQME method. We investigate the dynamic alpha density distribution obtained from BS-DFTQME calculations in order to analyze the spatial contributions of electrons to the field-induced polarization and clarify the contributions of the frontier orbital pair to alpha and its density. To demonstrate the performance of this Method, we examine the real part of dynamic alpha of singlet 1,3-dipole systems having a variety of diradical characters (y). The frequency dispersion of a, in particular,in the resonant region, is shown to strongly depend on the exchange-correlation functional as well as on the diradical character Under sufficiently off-resonant condition, the dynamic alpha is found to decrease with increasing y and/or the fraction of Hartree-Fock exchange in the exchange correlation functional, which enhances the spin polarization, due to the decrease in the delocaliztion effects of pi-diradical electrons in the frontier orbital pair. The BS-DFTQME method with the BHandHLYP exchange-correlation functions.. also turns out to semiquantitatively reproduce the a spectra calculated by a strongly correlated ab initio molecular orbital method, i.e., the spin-unrestricted coupled-cluster singles and doubles.