Structure–Performance Relationship of Novel Azo-Salicylaldehyde Disperse Dyes: Dyeing Optimization and Theoretical Insights

High yields of three novel azo disperse dyes based on the diazonium salt of sulfonamides-azo-salicylaldehyde were successfully synthesized. These dyes were structurally characterized by using spectroscopic techniques, including FTIR, 1H NMR, and MS. The fundamental goal of the research was to determine the optimal dyeing parameters, such as temperature, pH, and time, to understand the behavior of dispersed dyes 13–15 during the dyeing of polyester materials. The results showed that increasing the dyeing temperature from 100 to 130 °C significantly improved the dyed polyester’s color strength (K/S values). The colored polyester samples’ hues ranged from beige to yellowish brown to dark brown due to the coupler molecules and other parameters such as temperature, duration, and pH. Moreover, the substituents of the main dye structures were investigated by studying the change in color data using (CILAB), reflectance, and color strength (K/S) evaluations of polyester-dyed fabrics. Experimental results indicate that dye 15 achieves the highest color intensity and reflectivity, correlating with its narrower band gap and enhanced electrophilic/nucleophilic reactivity, as revealed by DFT and TD-DFT calculations. The findings highlight the relationship between the dye structure and performance, demonstrating that superior dye–fiber interactions and stability contribute to improved performance. The synthesized dispersed dyes present promising candidates for imparting diverse, stable colors and excellent fastness to wash, light, and crock to polyester fabrics.