Two new Cu(II) carboxylate complexes, Cu-NTA and Cu-DNTA, were prepared by treating 2-nitroterephthalic acid with CuSO4·5H2O at room temperature. The synthesized complexes were characterized by elemental (CHN), FT-IR, and thermogravimetric analysis. The crystal structures of both complexes were explored by single crystal X-ray diffraction analysis, which inferred that the coordination geometry is slightly distorted octahedral and square pyramidal in Cu-NTA and Cu-DNTA, respectively. The non-covalent interactions that are the main feature of the supramolecular assembly were investigated by Hirshfeld surface analysis for both complexes. The propensity of each pair of chemical moieties involved in crystal-packing interactions was determined by the enrichment ratio. Quantum chemical computations were performed to optimize the molecular geometry of complex Cu-NTA and compared it with the experimental single crystal structure, which was found to be in sensible agreement with the experimental structure of the complex. The DFT method was used to see the potential of the selected Cu-NTA complex for linear and nonlinear optical properties. The static NLO polarizability <γ> of complex Cu-NTA was calculated to be 86.28 × 10–36 esu at M06 functional and 6-31G*/LANL2DZ basis set, which was rationally large to look for NLO applications of complex Cu-NTA. Additionally, the molecular electrostatic potential and frontier molecular orbitals were also computed with the same methodology to see electronic characteristics and ground-state electronic charge distributions.