Density Functional Theory
One of the most widely used computational methods in the field of materials science—as well as chemistry and physics, more broadly—is density functional theory, or DFT. DFT is a method of computation and calculation based on quantum mechanics; it deals with the smaller end of the length scales studied in materials science, the scale of electrons, atoms, and molecules. More specifically, DFT calculates electronic structures (i.e., the location and energy levels, the quantum states, of the electrons) and uses that to predict properties.
DFT has been used for calculations for many decades, but truly grew in popularity after the 1990s, as refinements to the technique improved its accuracy in the quantum mechanical realm. Even before then, its usage was significant. Walter Kohn received a Nobel Prize in chemistry for his contributions to DFT, including early development of the Hohenberg–Kohn theorems, followed by development of a set of equations with Lu Jeu Sham known as the Kohn-Sham equations. These equations and DFT in general use of functionals of electron density, which is where the technique gets its name.
As with any computational method, DFT does have its drawbacks. It has a low computational cost to performance ratio compared to similar electronic structure methods such as wave function-based methods, but still has a high computational cost in general. It can have trouble describing certain situations, including, sometimes, intermolecular interactions, dopant interactions, and band gap calculations in semiconductors.
Sources/Further Reading: (Matlantis—Image 1) (Wikipedia—Image 2) (2011 article) (Jashore University)