Molecular Dynamics, Car-Parrinello

The idea of simulating the microscopic behavior of matter by directly solving Newton’s equations on the computer for a collection of atoms was first proposed by E Fermi in the 1940s. The technique is generally referred to as ‘‘molecular dynamics (MD).’’ The exponential increase of computer power and the continuous refinement of simulation techniques have turned molecular dynamic simulations from a toy model of statistical physics into an extremely valuable and predictive tool nowadays. The application of molecular dynamics is widespread in many fields of condensed matter physics, materials science, chemistry, and molecular biology. Evolving Newton’s equations (Formula presented) for a collection of N atoms with positions {R₁, R₂,…, R_N} and masses {M₁, M₂,…, M_N} implies that the potential V(R₁, R₂,…, R_N) of interaction among them must be given. Determining the interatomic potential is one of the more challenging problems in molecular dynamic simulations, as discussed in detail in Colombo’s contribution. In this article, the focus is on how to determine the interatomic potential V from ‘‘first principles,’’ based on the laws of quantum mechanics, and without any empirical input. By doing so, the computational complexity of a molecular dynamic simulation increases dramatically, implying, for example, that a much smaller number of atoms can be simulated and for much shorter times than conventional molecular dynamic simulations. First-principle (or ab initio) molecular dynamics combines the advantages of conventional molecular dynamics in terms of statistical sampling with the accuracy of quantum mechanical methods in describing electronic structure and chemical bonding in condensed....