The methodology of ab initio molecular dynamics, wherein finite-temperature dynamical trajectories are generated by using forces computed ''on the fly'' from electronic structure calculations, has had a profound influence in modern theoretical research. Ab initio molecular dynamics allows chemical processes in condensed phases to be studied in an accurate and unbiased manner, leading to new paradigms in the elucidation of microscopic mechanisms, rationalization of experimental data, and testable predictions of new phenomena. The purpose of this work is to give a brief introduction to the technique and to review several important recent developments in the field. Several illustrative examples showing the power of the technique have been chosen. Perspectives on future directions in the field also will be given.M odern theoretical methodology, aided by the advent of high speed and massively parallel computing, has advanced to a level that the microscopic details of chemical processes in condensed phases can now be treated on a relatively routine basis. One of the most commonly used theoretical approaches for such studies is the molecular dynamics (MD) method, in which the classical Newtonian equations of motion for a system are solved numerically starting from a prespecified initial state and subject to a set of boundary conditions appropriate to the problem. MD methodology allows both equilibrium thermodynamic and dynamical properties of a system at finite temperature to be computed. The quality of a MD calculation rests largely on the method by which the forces are specified. In many applications, these forces are computed from an empirical model or ''force field,'' an approach that has enjoyed tremendous success in the treatment of systems ranging from simple liquids and solids to polymers and biological systems including proteins, membranes, and nucleic acids. Since most force fields do not include electronic polarization effects (see, however, ref. 1) and can treat chemical reactivity only through specialized techniques (see, e.g., ref.2), it is often necessary to turn to the methodology of ab initio MD (AIMD).AIMD is a rapidly evolving and growing technique that constitutes one of the most important theoretical tools developed in the last decades. In an AIMD calculation, finite-temperature dynamical trajectories are generated by using forces obtained directly from electronic structure calculations performed ''on the fly'' as the simulation proceeds. Thus, AIMD permits chemical bond breaking and forming events to occur and accounts for electronic polarization effects (3, 4). AIMD has been successfully applied to a wide variety of important problems in physics and chemistry and is now beginning to influence biology as well. In numerous studies, new physical phenomena have been revealed and microscopic mechanisms elucidated that could not have been uncovered by using empirical methods, often leading to new interpretations of experimental data and even suggesting new experiments to perform.In its most ideal form,...

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