**10. Conclusion**

In this chapter, we have introduced the general method of calculating the ground state energy of a crystalline solid by application of DFT. We have just described how it is possible to determine the energy of the ground state of a solid by studying a fictitious system of independent particles giving rise to the same density as the real electronic system. On the other hand, we have highlighted the approximations necessary to be able to apply this theory. Despite the importance of the DFT to find the exchange-correlation energy, but this quantity remains inaccurate to describe the elastic properties. So we have to go beyond DFT with RPA to correct this handicap. In this direction, we have shown that RPA is a good description of electronic correlation energy.

*The Density Functional Theory and Beyond: Example and Applications DOI: http://dx.doi.org/10.5772/intechopen.100618*
