The first model describing the metal's electrons was proposed by Paul Drude in 1900 and extended by Hendrik Lorentz in 1905 . It was quite a successful classical model of the electric and thermal conductivity of metals, and after the appearance of the wave and matrix mechanics in 1925 , it was adjusted to the quantum theory by Hans Bethe and Arnold Sommerfeld in 1933 , leading to the Drude-Sommerfeld model. However, the more accurate description of metallic properties appeared in 1970 through the jellium model proposed by Lang and Kohn 36 . Afterward, more sophisticated models based on the matrix expansion of Green's function were developed, e.g. Korringa-Kohn-Rostoker expansion of the matrix elements The traditional definition of a covalent bond, characterized by the sharing of electron pairs between atoms, has evolved with the understanding that electron delocalization can lead to "fuzzy bonds" , where the exact nature and strength of the bond are less defined. This concept, which suggests a continuum of bonding scenarios rather than discrete bond classifications, remains a topic of ongoing discussion in the field of chemical bonding, as highlighted by recent studies on the energy and dynamics of covalent interactions. As it will be shown, in principle, Friedel oscillations can be related to any system with an electron gas. However, complications arise due to the diversity of electron gas models and the variety of systems (3D volumes, 2D surfaces, or 1D atomic chains) that can be involved, making the mathematics behind these seemingly Fig. Scheme showing the dependence of a bandgap on a distance between atoms. It is highly connected to the definition of electron gas . The attempt to classifying the electron gas density depends on the distance between AOs or overlapping electronic levels in crystals. One should note here that a chain of atoms can be considered a 1D, graphene-2D crystal.