  Based on the hybrid functional, we find that at 0 GPa, the pristine
CsV$_{3}$Sb$_{5}$ has local magnetic moment of 0.85 $\mu_B$ /unit cell, which
is suppressed at pressure of 2.5 GPa resulting in a spin-crossover. Since the
ground sate of CsV$_{3}$Sb$_{5}$ with charge density wave (CDW) distortion is
non-magnetic state, the local magnetic moment of pristine CsV$_{3}$Sb$_{5}$
will be suppressed by temperature-induced CDW transition at 94 K. The schematic
evolution of magnetic moments as functions of pressure and temperature are
presented. At low temperature, CsV$_{3}$Sb$_{5}$ is a rare example of materials
hosting pressureinduced local magnetic moment, and we suggeste that the effects
of local magnetic moments should be considered for understanding its
properties.
