The rapidly growing field of ab initio molecular dynamics is reviewed in the spirit
of a series of lectures given at the Winterschool 2000 at the John von Neumann
Institute for Computing, J¨ulich. Several such molecular dynamics schemes are
compared which arise from following various approximations to the fully coupled
Schr¨odinger equation for electrons and nuclei. Special focus is given to the Car–
Parrinello method with discussion of both strengths and weaknesses in addition
to its range of applicability. To shed light upon why the Car–Parrinello approach
works several alternate perspectives of the underlying ideas are presented. The
implementation of ab initio molecular dynamics within the framework of plane
wave–pseudopotential density functional theory is given in detail, including diag￾onalization and minimization techniques as required for the Born–Oppenheimer
variant. Efficient algorithms for the most important computational kernel routines
are presented. The adaptation of these routines to distributed memory parallel
computers is discussed using the implementation within the computer code CPMD
as an example. Several advanced techniques from the field of molecular dynam￾ics, (constant temperature dynamics, constant pressure dynamics) and electronic
structure theory (free energy functional, excited states) are introduced. The com￾bination of the path integral method with ab initio molecular dynamics is presented
in detail, showing its limitations and possible extensions. Finally, a wide range of
applications from materials science to biochemistry is listed, which shows the enor￾mous potential of ab initio molecular dynamics for both explaining and predicting
properties of molecules and materials on an atomic scale.