Solid-state molecular phonons play a crucial role in the performance of diverse photonic and optoelectronic devices. In this work, new organic terahertz (THz) generators based on a catechol group that acts as a phonon suppressing intermolecular adhesive are developed. The catechol group is widely used in mussel-inspired mechanical adhesive chemistry. Newly designed organic electro-optic crystals consist of catechol-based nonlinear optical 4-(3,4-dihydroxystyryl)-1-methylpyridinium (DHP) cations and 4-(trifluoromethyl)benzenesulfonate anions (TFS), which both have multiple interionic interaction capability. Interestingly, compared to benchmark organic crystals for THz generators, DHP-TFS crystals concomitantly achieve top level values of the lowest void volume and the highest crystal density, resulting in an exceptionally small amplitude of solid-state molecular phonons. Simultaneously achieving small molecular phonon amplitude, large optical nonlinearity and good phase matching at infrared optical pump wavelengths, DHP-TFS crystals are capable of generating broadband THz waves of up to 16 THz with high optical-to-THz conversion efficiency; one order of magnitude higher than commercial inorganic THz generators.