In this study, the structural, electronic, optical, and dynamical properties of C \(_3\) N monolayer substituted with (V, B, Cu) atoms have been studied using the WIEN2K computational package. The results reveal that introducing these guest atoms into the structure alters the bond lengths. The larger the radius of the substituted atom compared to nitrogen, the longer the bond length between the substituted atom and the second-nearest neighbors; this structural modification leads to changes in the physical properties of the material. Among the studied structures, compared to the pristine C \(_3\) N structure, the C \(_3\) N@B shows the highest mechanical stability, while the C \(_3\) N@V shows the lowest. The study of electronic properties reveals that pristine C \(_3\) N is a semiconductor with an indirect band gap of 0.5 eV, while by adding a B atom to C \(_3\) N, it displays a 1.46 eV direct energy gap. Moreover, by substituting V and Cu atoms, this two-dimensional structure exhibits metallic behavior. Phonon dispersion spectra were calculated using the linear response method along high-symmetry directions in the Brillouin zone. The results demonstrate that the absence of negative frequencies in phonon spectra confirms its dynamical equilibrium. However, in the case of Cu and V atoms, it has no dynamical equilibrium due to larger atomic mass and radius with respect to C and N atoms, and negative modes emerge. The optical properties, including the real and imaginary parts of the dielectric function, electron energy loss spectra, absorption coefficient, and reflectance, were investigated for the stable structures using the random phase approximation (RPA).
