Charge carriers density oscillations or charge density waves (CDW) are observed, described, and defined differently, depending on the context. Any defect -such as a dislocation or an impurity -on the metal surface or in a system with a high electron delocalization gives rise to charge density oscillations. Initially, for metals, we observe so-called Friedel oscillations, which are also defined differently, depending on the context. This phenomenon appears in various fields including low-frequency plasmonics , quantum many-body theory , a surface ordering in chemistry , solitons of charge density and, upon discussion, in some molecular systems with high electron delocalization . Due to the widespread occurrence in condensed matter systems, FOs may be referred to by various names depending on the specific context or field of study. However, they all describe the same underlying phenomenon of electron density modulation (static or dynamic) around impurities or defects. (SCO) and induced-charge density (ICD) oscillations are related to the observation and origin of the charge oscillations, respectively. Finally, the name used the most in the experimental surface science is LDOS (lo-cal density of states) oscillations that point out the nature of FOs -the oscillatory perturbation in the electron charge density around a defect. LDOS refers to the spatial variation of the density of available electronic states at a given energy level within a material, particularly near surfaces or interfaces (see section 1.4.2). These oscillations arise due to interference effects caused by the interaction of electrons with the local environment, such as impurities, defects, or surface roughness. The oscillations in the local density of states have significant implications for electronic properties, such as conductivity, magnetism, and optical response. Charge-density waves (CDW) denote the timedependent case of FOs (for instance, due to the time-dependent external perturbing potential), and acoustic-surface plasmon (ASP) describe collective oscillations of electrons coupled to surface phonons or acoustic phonons at the interface between a metal and a dielectric. The connection between ASP and FOs lies in their shared context of electron-surface interactions. While ASP involves the collective motion of electrons coupled with surface phonons, Friedel oscillations arise due to the scattering of electrons by surface imperfections.