Defect engineering and non-covalent interaction strategy allow for dramatically tuning the optoelectronic features of graphene. Herein, we theoretically investigated the intrinsic mechanism of non-covalent interactions between pentagon-octagon-pentagon (5-8-5) defect graphene (DG) and absorbed molecules, tetrathiafulvalene (TTF), perfluoronaphthalene (FNa), tetracyanoquinodimethane (TCNQ) and 2,3,5,6-tetrafluoro-7,7,8,8 –tetracyanoquinodimethane (F4TCNQ), through geometry, distance, interaction energy, Mulliken charge distribution, terahertz frequency vibration, visualization of the interactions, charge density difference, electronic transition behaviour, band structure and density of state. All the calculations were performed using density functional theory including a dispersion correction (DFT-D). The calculated results indicate that the cyano- (CN) group (electron withdraw group) in TCNQ and F4TCNQ, rather than the F group, gain the electron from DG effectively and exhibit much stronger interactions via wavefunction overlap with DG, leading to a short non-covalent interaction distance, a large interaction energy and a red-shift of out-of-plane terahertz frequency vibration, changing the bands near the Fermi level and enhancing the infrared (IR) light absorption significantly. The enhancement of such IR absorbance offering a broader absorption (from 300 to 1200 nm) will benefit the light harvest in the potential applications of solar energy conversion.