Introduction to density-functional theory and ab-initio molecular dynamics

Density-Functional-Theory (DFT) provides a general framework to deal with the ground-state energy of the electrons in many-atom systems. Its history dates back to the work of Thomas [1], Fermi [2] and Dirac [3] who devised approximate expressions for the kinetic energy [1, 2] and the exchange energy [3] of many-electron systems in terms of simple functionals of the local electron density. These ideas were further elaborated in the Xα method of Slater [4], until finally, the foundations of the modern theory were laid down in the mid-sixties by Kohn and collaborators [5, 6]. Since then but particularly in the last two decades the number of applications of DFT to electronic structure problems has grown dramatically. Today DFT is the method of choice for first-principles electronic structure calculations in condensed phase and complex molecular environments. DFT based approaches are used in a variety of disciplines ranging from condensed matter physics, to chemistry, materials science, biochemistry and biophysics. There are several reason for this success: (i) DFT makes the many-body electronic problem tractable at a numerical cost of self-consistent-field single particle calculations; (ii) despite the severe approximations made to the exchange and correlation energy functional, DFT calculations are usually sufficiently accurate to predict materials structures or chemical reactions products; (iii) currently available computational power and modern numerical algorithms make DFT calculations feasible for realistic models of systems like e.g. an interface between two crystalline materials, a carbon nanotube, or the active site of an enzyme.