  Using density functional theory (DFT) within the local density approximation
(LDA), we calculate the physical and electronic properties of PbTiO3 (PTO) and
a series of hypothetical compounds PbTiO3-xSx x = 0.2, 0.25, 0.33, 0.5, 1, 2,
and 3 arranged in the corner-sharing cubic perovskite structure. We determine
that replacing the apical oxygen atom in the PTO tetragonal unit cell with a
sulfur atom reduces the x = 0 LDA calculated band gap of 1.47 eV to 0.43 - 0.67
eV for x = 0.2 - 1 and increases the polarization. PBE0 and GW methods predict
that the hypothetical compositions x = 0.2 to x = 2 will have band gaps in the
visible range. For all values of x < 2, the oxysulfide perovskite retains the
tetragonal phase of PbTiO3, and the a-lattice parameter remains within 2.5% of
the oxide. Thermodynamic analysis indicates that chemical routes using high
temperature gas, such as H2S and CS2, can be used to substitute O for S in PTO
for the compositions x = 0.2 - 0.5.
