**5. Random phase approximation**

Despite the DFT is relevance in determining the exchange-correlation energy, it is still insufficient to characterize elastic characteristics. To rectify this amount, we must go beyond DFT. This is due to the random phase approximation as a method for calculating the electronic correlation energy accurately. RPA appears in the 1950s' [7–10] as a method of solving the N-body problem and arises from the desire to describe better (i.e. better than in a mean-field approximation) the physics of uniform electron gas, where the correlation between the positions of long-range electrons is important. In fact, collective oscillations (called plasma oscillations) are observed in an electron gas, which is the direct consequence of the long-range correlation between the electrons. Bohm and Pines, who introduced RPA, propose to place these collective oscillations at the center of solving the N-body problem, hoping that a good description of one will provide a good understanding of the other. RPA has been used with some success in the literature to describe systems containing Van der Waals interactions and in particular involving [11] scattering forces, which are known to be difficult to process. RPA introduced within the framework of DFT via the fluctuation-dissipation theorem with adiabatic connection (ACFDT).
