  We theoretically investigate the size-, shape-, and composition-dependent
polarizabilities of the SimCn (m, n = 1 - 4) clusters by using the density
functional based coupled perturbed Hartree-Fock method. The size-dependence of
the polarizabilities of the SimCn (m, n = 1 - 4) clusters is more complicated
than that of pure Sim and Cn (m, n = 1 - 8) clusters because for a given
cluster size the heteroatomic clusters have more isomers than the homoatomic
ones. For the shape-dependence, we consider three kinds of shape, linear
(chain), prolate, and compact. For most clusters, we can clearly observe orders
of {\alpha}(linear) > {\alpha}(prolate) and {\alpha}(prolate) >
{\alpha}(compact) for a given composition. The composition-dependence of
polarizabilities reveals that the linear clusters have an obvious larger
polarizability than both the prolate and the compact clusters especially for a
given m/n value. The shape effect makes a main contribution to determine the
size of the polarizability. To understand the size of polarizability and the
evolution of polarizability, we have tried many factors, such as the energy gap
and binding energy, and defined a new parameter ({\Delta}q) that characterizes
the redistribution of charge in cluster. We find that both the binding energy
and the {\Delta}q are more available than the energy gap for reflecting the
evolution of polarizabilities provided that both the cluster shape and one of
the components in cluster are fixed. The correlation between the polarizability
and the energy gap is poor, in agreement with the previous results.
