A single model is developed for the different photoelastic response of Ge-family materials and chalcogen-based molecular solids. If ${\ensuremath{\chi}}^{\ensuremath{'}}$ is the "Gr\"uneisen" parameter for the electronic susceptibility, experiment shows that ${\ensuremath{\chi}}^{\ensuremath{'}}<0$ for the former group, while ${\ensuremath{\chi}}^{\ensuremath{'}}>1$ for the latter. In addition, several group IV-VI compounds have $0\ensuremath{\le}{\ensuremath{\chi}}^{\ensuremath{'}}\ensuremath{\le}1$. In our model the dielectric constant is calculated, within the Drude formalism, using one Penn-Phillips oscillator for Ge-family solids and two for molecular chalcogenides. The model predicts that ${\ensuremath{\chi}}^{\ensuremath{'}}$ should depend linearly on $\frac{2\ensuremath{\eta}}{{E}_{g}}$, with ${E}_{g}$ the Penn-Phillips gap and dimension-less $\ensuremath{\eta}$ determined from experiment. Reliable values of ${\ensuremath{\chi}}^{\ensuremath{'}}$, ${E}_{g}$, and other relevant parameters are tabulated for a large number of materials. New experimental results are also presented for ZnTe. The experimental evidence provides support for the model. A plot of ${\ensuremath{\chi}}^{\ensuremath{'}}$ versus $\frac{2\ensuremath{\eta}}{{E}_{g}}$ exhibits the predicted linear correlations for materials with ${\ensuremath{\chi}}^{\ensuremath{'}}<0$ and ${\ensuremath{\chi}}^{\ensuremath{'}}>1$; the slopes are in excellent agreement with measured band-gap volume derivatives. These correlations pertain to amorphous and crystalline solids alike. For the molecular chalcogenides, it is concluded that band-broadening influences ${\ensuremath{\chi}}^{\ensuremath{'}}$ through a uniform "red shift" of the lower-energy oscillator with respect to the stationary upper oscillator. The observed photoelastic trends are related to bonding topology by analogy with arguments previously applied to phonons. ${\ensuremath{\chi}}^{\ensuremath{'}}>1$ follows from the bonding strength dichotomy in (3D)-network structures, whereas ${\ensuremath{\chi}}^{\ensuremath{'}}0$ obtains for covalent 3D-network solids. It is suggested that ${\ensuremath{\chi}}^{\ensuremath{'}}$ can serve as an indicator of network dimensionality for these two cases.