The present work addresses the underlying nature of weak noncovalent interactions (NCIs) in the self-assembled dimers of two square planar palladium(II) and platinum(II) complexes trans-[Pd(Hida)2] (1) and trans-[Pt(Hida)2] (2) (Hida = monoprotonated iminodiacetate) within the framework of density functional theory (DFT) in gas phase. Initial geometries of the dimers in different spatial orientations were extracted from the X-ray crystal structures, reported earlier, and optimized with three dispersion-corrected functionals that are frequently used to explore NCIs. The BP86-D3, M062X-D3 and ωB97X-D3 functionals have been used to test their performances over the present systems. The SARC-ZORA-TZVP and ZORA-def2-TZVP basis sets were applied for the metals and the remaining elements, respectively. The optimizations resulted in equilibrium geometries where the monomers are self-assembled through NCIs to form dimers in a cyclic fashion. This type of structural pattern is absent in the crystal structures of both 1 and 2. Physical components of interaction energies were investigated by symmetry-adapted perturbation theory (SAPT). The UV-Vis absorption spectra of the dimers are described by time-dependent density functional theory (TD-DFT). Global reactivity parameters for the dimers have been computed within the framework of conceptual density functional theory (CDFT). Detailed investigations on NCIs were performed for all dimer geometries. Simulated IR and 1H NMR spectra, charge transfer, QTAIM, NCI-RGD, IGM, ETS-NOCV and ELF studies confirmed the presence of intermolecular hydrogen bonds (HBs) and weak van der Waals interactions. Energies of the hydrogen bonds and associated orbital interaction energies were computed by QTAIM and ETS-NOCV methods, respectively.