Here, we perform theoretical investigation using time-dependent density functional theory (TD-DFT) and time-dependent density functional tight binding (TD-DFTB) for the electronic structure and optical properties of silver nanorods. TD-DFTB generally performs well for the accurate description of optical properties with respect to the - m size and type of dimer assembly of silver nanorods compared to TD-DFT. However, the energies and intensities of the longitudinal and transverse peaks of the nanorods are somewhat underestimated with TD-DFTB compared to the values calculated at the TD-DFT level. By exploiting the computational efficiency of TD-DFTB, we also extend our investigation to longer nanorods and their dimers containing up to similar to 2000 atoms. Our results show that the coupling between nanorods and the resulting optical properties of the dimer assemblies are quite dependent on the length of the monomers. In all cases, the energy shifts in dimers as a function of the gap distance deviate significantly from the dipole-dipole interaction model. Moreover, a comparison of the best-fit curves for the dependence of the fractional shifts (Delta lambda/lambda(0)) on nanorod length indicates that the parameters of the plasmon ruler equation depend on the length of the nanorods and the type of the assembly rather than approaching a universal value. These insights are enabled by the computational efficiency of TD-DFTB and its ability to treat quantum mechanical effects in large nanorod dimer systems.