Although density functional theory is rigorously a ground-state formalism, there has recently been considerable progress in developing methods to calculate optical properties using density functional results as the starting point [19]. As a first step toward investigating the optical properties, we have calculated the imaginary part of the dielectric constant from the self-consistent LAPW wavefunctions and one-electron eigenvalues E_{nk}, using the code developed by Abt and Ambrosch-Draxl [20]. There are of course no excitonic effects included in these calculations. Taking the Kramers-Kronig transform of _{2}, we obtain the calculated spectrum of _{1} after adjusting the calculated band gap and calculated visible refractive index to agree with experiment. [21 ] Our calculated reflectivity was compared to the experimental measurement by Shpinkov et al [22] in Refs. [2,3]. The agreement between the measured and calculated reflectivity for PbWO_{4} is surprisingly good. The sharp peak in the calculated spectrum at the band edge is due to a near singularity in the joint density of single-particle states. Since no lower-energy discrete features are found in the experimental spectrum, we conclude that whatever exciton discrete states are observable in the absorption spectrum should have a low binding energy compared to the 0.3 eV width of the experimental reflectivity peak. The suggestion of a small exciton binding energy in PbWO_{4} was supported by consideration in Ref. [3] of the measured optical and static dielectric constants for PbWO_{4} which are quite large -- _{1}(1.9 eV) ε_{opt} = 5.06 [21] and _{1}(0 eV) ε_{static} = 23.6, respectively, for a-axis polarization.