Mapping the correlations between bandgap, HOMO, and LUMO trends for meta substituted Zn-MOFs

Bandgap is a key property that determines electrical and optical properties in materials. Modulating the bandgap thus is critical in developing novel materials particularly semiconductors with improved features. This study examines the bandgap, highest occupied molecular orbital (HOMO), and lowest unoccupied molecular orbital (LUMO) energy level trends in a metal organic framework, metal-organic framework 5 (MOF-5), as a function of Hammett substituent effect (with the constant σ_m in the meta-position of the benzene ring) and solvent dielectric effect (with the constant ε). Specifically, experimental design and response surface methodologies helped to assess the significance of trends and correlations between these molecular properties with σ_m and ε. While the HOMO and LUMO decrease with increasing σ_m, the LUMO exhibits greater sensitivity to the substituent's electron withdrawing capability. The relative difference in these trends helps to explain why the bandgap tends to decrease with increasing σ_m.