A computational laboratory experiment investigating molecular models for hexagonal boron-carbon-nitrogen sheets (h-BCN) was developed and employed in an upper-level undergraduate chemistry course. Students used the Avogadro user interface for molecular editing and the WebMO interface for the quantum computational workflow. Density functional theory calculations were carried out to compare the electronic structures, relative energies, and other properties of mono-, di-, and tetrameric h-BCN molecular models. Experimental precursor molecules and other analogous single-layer two-dimensional (2D) materials were studied as well. These computations exemplified how electronic properties such as the band gaps of potentially useful 2D materials can be finely tuned by varying chemical structure.