  The new structures, Cmc2$_1$-Si$_2$P$_2$X (X=S, Se, Te, and Po), are
predicted, and their mechanical, electronic and optical properties are
investigated with the density functional theory, by first principles
calculations. The elastic constants of the four compounds are calculated by the
stress-strain method. The calculations of the elastic stability criteria and
phonon dispersion spectra imply that they are mechanically and dynamically
stable at zero pressure. The mechanical parameters, such as shear moduli $G$,
bulk moduli $B$, Young's moduli $E$ and Poisson's ratios $v$ are evaluated by
the Voigt-Reuss-Hill approach. The Cmc2$_1$-Si$_2$P$_2$X has the largest
hardness due to the largest Young's modulus in the four compounds, and it is a
covalent crystal. The anisotropies of their mechanical properties are also
analyzed. The band structures and densities of states, which are calculated by
using HSE06, show that Cmc2$_1$-Si$_2$P$_2$X compounds are indirect bandgap
semiconductors, and the values of the band gaps decrease with increasing atomic
number from S, Se, Te, to Po. In addition, the longitudinal sound velocity and
transverse sound velocity for Cmc2$_1$-Si$_2$P$_2$X have been investigated. The
dielectric constant, electron energy loss, refractive index, reflectivity,
absorption and conductivity are analyzed to gain the optical properties of
Si$_2$P$_2$X.
