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

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Abstract

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. Very often one is interested in modeling atoms that are not static but in motion. This is the case in fluid systems, but even in crystalline materials atoms move at finite temperature. Furthermore structural changes in materials or molecular changes due to chemical reactions are inevitably associated to atomic motions. A dynamic approach is needed in such situations. Assuming that classical mechanics is adequate to describe atomic motion, atomic trajectories can be calculated numerically by solving the corresponding classical equations of motion. This approach is called molecular dynamics (MD) and was pioneered [7, 8] after the advent of modern digital computers. Today it is a highly successful computational approach widely used in many fields of science to model the dynamics and the statistical properties of classical many-body systems. Usually in MD simulations empirical force fields are used to describe the inter-atomic interactions. Although the accuracy of the force fields is often remarkable, it cannot match the accuracy and the predictive power of quantum mechanical calculations based on DFT, particularly when changes in the electronic structure play a crucial role, like e.g. in chemical reactions. To address this issue a new molecular dynamics scheme was formulated [9] in which the potential energy surface is generated "on the fly" from the instantaneous ground state of the electrons within DFT. This approach, called ab-initio (or first-principles) molecular dynamics (AIMD), is now used with success to model atomistic processes in materials physics, chemistry and biology. Many applications of DFT and AIMD are reviewed in this special issue of QSAR, spanning from studies in physical chemistry to examples in biological and life sciences. It is the purpose of these notes to provide an introduction accessible to the non-specialist to some of the ideas and concepts behind DFT and AIMD.

Original languageEnglish (US)
Pages (from-to)97-104
Number of pages8
JournalQuantitative Structure-Activity Relationships
Volume21
Issue number2
DOIs
StatePublished - Aug 15 2002

All Science Journal Classification (ASJC) codes

  • Pharmacology

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