In the present study, quantum chemical investigations were carried out on our previously reported co-crystal based on 1,3,5-tris(4-hydroxyphenyl)benzene and 2,4,6-trimethoxy-1,3,5-triazine, which showed CH center dot center dot center dot pi and pi center dot center dot center dot pi interactions driven layer-by-layer self-assembly of hydrogen-bonded hexagonal blocks in the solid state. Using the DFT/B3LYP calculation method with 6-311++G(d,p) basis set in the ground state, the optimized molecular geometric parameters, conformational analysis, vibrational wavenumbers and their assignments, the HOMO-LUMO analysis, molecular electrostatic potential, thermodynamic properties, and atomic charges were calculated to understand various structural features that are playing an important role in its packing. Furthermore, the simulated infrared and Raman spectra of the co-crystal are plotted using the calculated results. The calculated results are in a good agreement with experimental data. The study with constructive propositions may be helpful in understanding complex self-assembled systems and in the construction of similar molecular self-assemblies.