The ultimate goal of ab initio calculations is to obtain the value of a physical quantity by solving fundamental equations of physics without empirical approximations. In the case of a material, this goal can be achieved by solving the Schrödinger equation for the system of interest, as composed of electrons and nuclei, where the only input parameter is the atomic number of the chemical elements present.
However, this problem is generally unsolvable and must be simplified. The most effective technique, nowadays routinely used for ab initio calculations in materials science, is the application of density functional theory. DFT is an exact one-body reformulation of the many-body quantum mechanical problem governed by the Schrödinger equation, which can be used effectively (after introducing a number of approximations) to determine the ground-state energy of a system of interacting particles.
They require large computer resources but allow to quantitatively determine characteristics, properties and behaviors of atoms (energy of interaction, migration energy…). In addition, difficulties arise when handling concentrated random alloys, especially with more than two chemical elements, because with a limited amount of atoms it is difficult to reproduce a realistic random distribution of species.