**4.4 Weak interactions**

Over the last two decades, tremendous progress has been made in addressing the challenges associated with weak van der Waals (vdW) interactions. Traditional functionals do a good job at manipulation of covalent, ionic, and metallic interactions due to their semi-local nature, but they fall short when it comes to longer, weaker bonds, and cannot offer weak binding that drops off as a function of R6 (R is the distance among two atoms) [38]. To account these impacts, modifications must be applied to the conventional functionals and this can be accomplished in one of three ways. There is a succession of approximations produced by Langreth and Lundqvist and collaborators [43] for the evolution of explicit non-local functionals of electron density, while these approximations are generated non-empirically, notably beginning with contributions of correlation energy. Additionally, these functionals may be useful for any materials, ranging from solids to molecules, and have been designed by supposing systems that contain a gap [44]. RPA, which incorporates approximations to the vdW forces by default, as well as the Becke and Johnson technique [45], leverages the exchange hole's dipole moment to approximate C6, as well as higher coefficients.

#### **4.5 Gaps of solids**

The inadequacy of traditional approximations to anticipate band gaps of semiconductors and insulators is a critical flaw. The LDA undervalues gap between bulk Si and Ge by a factor of two, making Germanium a metal, whereas GGAs performs a bit good but underestimate as well. The ability to give precise and dependable gaps has always been a strong suit of the GW approach [46]. In the last two decades, precise gap computation utilizing hybrid functionals such as HSE06 [41] has been a huge success, and is accomplished through the use of a generalized KS scheme [47]. In this case, rather than using pure Kohn-Sham theory, the orbital reliant element of the functional is considered as in Hartree-Fork approach to overcome flaws of other Exc functionals [48].
