Kohn-Sham density functional theory is the most widely-used method of electronic-structure calculation in materials physics and chemistry, because it reduces the many-electron ground-state problem to a computationally tractable self-consistent one-electron problem. Exact in principle, it requires in practice an approximation to the density functional for the exchange-correlation energy. Common approximations fall on one of the five rungs of a ladder, with higher rungs being more complicated to construct but potentially more accurate. The first three or semi-local rungs are important, because (a) they are computationally efficient, (b) they can be constructed non-empirically or with minimal empiricism, and (c) they can serve as input to fourth-rung functionals including hybrid functionals, or as a correction to the fifth-rung Random Phase Approximation. The third-rung meta-generalized gradient approximation can recognize and describe covalent, metallic, and weak bonds , providing a good description of the equilibrium properties of many molecules and solids.
 J. Sun, B. Xiao. Y. Fang, R. Haunschild, P. Hao, A. Ruzsinszky, G.I. Csonka, G.E. Scuseria, and J.P. Perdew, Phys. Rev. Lett. 111, 106401 (2013).