Enhanced terahertz (THz) wave generation is demonstrated in nonlinear organic crystals through refractive index engineering, which improves phase matching characteristics substantially. Unlike conventional low-bandgap nonlinear organic crystals, the newly designed benzimidazolium-based HMI (2-(4-hydroxy-3-methoxystyryl)-1,3-dimethyl-1H-benzoimidazol-3-ium) chromophore possesses a relatively wide bandgap. This reduces the optical group index in the near-infrared, allowing better phase matching with the generated THz waves, and leads to high optical-to-THz conversion. A unique feature of the HMI-based crystals, compared to conventional wide-bandgap aniline-based crystals, is their remarkably larger macroscopic optical nonlinearity, a one order of magnitude higher diagonal component in macroscopic nonlinear susceptibility than NPP ((1-(4-nitrophenyl)pyrrolidin-2-yl)methanol) crystals. The HMI-based crystals also exhibit much higher thermal stability, with a melting temperature T-m above 250 degrees C, versus aniline-based crystals (116 degrees C for NPP). With pumping at the technologically important wavelength of 800 nm, the proposed HMI-based crystals boost high optical-to-THz conversion efficiency, comparable to benchmark low-bandgap quinolinium crystals with state-of-the-art macroscopic nonlinearity. This performance is due to the excellent phase matching enabled by decreasing optical group indices in the near-infrared through wide-bandgap chromophores. The proposed wide-bandgap design is a promising way to control the refractive index of various nonlinear organic materials for enhanced frequency conversion processes.