In this study, we employed Density Functional Theory to explore the electronic structure and superconducting properties of pristine LiFeAs and 50% Ru-substituted LiFeAs ( \(\hbox {LiFe}_{0.5}\) \(\hbox {Ru}_{0.5}\) As). The calculations were performed using the Quantum ESPRESSO package with projector-augmented wave pseudopotentials and the Perdew–Burke–Ernzerhof exchange–correlation functional. Superconducting characteristics were evaluated within the framework of Density Functional Perturbation Theory, through which we determined the superconducting transition temperature ( \(\hbox {T}_\textrm{c}\) ), electronic density of states, phonon dispersion relations, electron–phonon coupling constant ( \(\lambda\) ), Eliashberg spectral function [ \(\alpha {^{2}}F(\omega )\) ], and the logarithmic average phonon frequency ( \(\langle \omega_{\log } \rangle\) ). The optimized lattice parameters were determined to be a = 3.34 \(\mathring{A}\) and c = 5.32 \(\mathring{A}\) for LiFeAs, and a = 3.50 \(\mathring{A}\) and c = 5.43 \(\mathring{A}\) for \(\hbox {LiFe}_{0.5}\) \(\hbox {Ru}_{0.5}\) As, in good agreement with previously reported theoretical values. The phonon dispersion curves of both LiFeAs and LiFe0.5Ru0.5 As exhibit no imaginary frequencies, confirming their dynamical stability in this study. Nevertheless, the calculated superconducting transition temperatures ( \(\hbox {T}_\textrm{c}\) ) at 0 kbar and 600 kbar were 0.639 K and 4.38 K, respectively, both significantly lower than experimental measurements. \(\hbox {Ru}_{0.5}\) This discrepancy suggests that, beyond electron–phonon coupling, additional mechanisms particularly spin and orbital fluctuations likely play a significant role in driving superconductivity in Fe-based compounds.
