Investigating novel materials under high pressure presents a challenge in condensed matter physics. In this study, we examine \(\hbox {LiB}_{{2}} \hbox {N}_{{2}}\) and \(\hbox {LiC}_{{2}} \hbox {N}_{{2}}\) , materials identified through an evolutionary algorithm, which exhibit thermodynamic stability up to at least 100 GPa. Our findings reveal that \(\hbox {LiB}_{{2}} \hbox {N}_{{2}}\) exhibits a rhombohedral structure ( \(R\bar{3}m\) ) at pressures ranging from 0 GPa to 25 GPa, transitioning to a hexagonal structure ( \(P\bar{6}m2\) ) between 50 GPa and 100 GPa. In contrast, \(\hbox {LiC}_{{2}} \hbox {N}_{{2}}\) is predicted to have a monoclinic structure (C2/m) at low pressures and a hexagonal structure ( \(P6_{3}/mmc\) ) at higher pressures. Notably, both materials are dynamically stable within the harmonic approximation at pressures beyond 15 GPa for \(\hbox {LiB}_{{2}} \hbox {N}_{{2}}\) and beyond 25 GPa for \(\hbox {LiC}_{{2}} \hbox {N}_{{2}}\) . Furthermore, accurately capturing the thermal lattice vibrations of these materials under strong quantum anharmonicity requires advanced methods. Using a stochastic approach to self-consistent harmonic approximation (SSCHA), we introduce anharmonic corrections to further explore lattice dynamics. For superconducting properties, \(\hbox {LiB}_{{2}} \hbox {N}_{{2}}\) shows a remarkable critical temperature ( \(T_{\textrm{c}}\) ) of 44.5 K at a pressure of 25 GPa, as predicted within the harmonic approximation. In comparison, \(\hbox {LiC}_{{2}} \hbox {N}_{{2}}\) achieves a \(T_{\textrm{c}}\) of approximately 13 K at a pressure of 50 GPa when anharmonic corrections are applied using the Allen-Dynes modified McMillan equation. Our findings bridge a gap in understanding electronic band structure, phonon linewidth impacts, and vibrational modes under pressure, offering key insights into phase stability and superconducting mechanisms. These findings introduce a promising new class of materials, emphasizing their potential to enrich superconductivity research by advancing previously overlooked substances.
