Ab initio molecular dynamics: Theory and Implementation

AB INITIO MOLECULAR DYNAMICS:THEORY AND IMPLEMENTATIONDOMINIK MARXLehrstuhl für Theoretische Chemie, Ruhr–Universität BochumUniversitätsstrasse 150, 44780 Bochum, GermanyE–mail: dominik.marx@theochem.ruhr-uni-bochum.deJÜRG HUTTEROrganisch–chemisches Institut, Universität ZürichWinterthurerstrasse 190, 8057 Zürich, SwitzerlandE–mail: hutter@oci.unizh.chThe rapidly growing field of ab initio molecular dynamics is reviewed in the spiritof a series of lectures given at the Winterschool 2000 at the John von NeumannInstitute for Computing, Jülich. Several such molecular dynamics schemes arecompared which arise from following various approximations to the fully coupledSchrödinger equation for electrons and nuclei. Special focus is given to the Car–Parrinello method with discussion of both strengths and weaknesses in additionto its range of applicability. To shed light upon why the Car–Parrinello approachworks several alternate perspectives of the underlying ideas are presented. Theimplementation of ab initio molecular dynamics within the framework of planewave–pseudopotential density functional theory is given in detail, including diagonalizationand minimization techniques as required for the Born–Oppenheimervariant. Efficient algorithms for the most important computational kernel routinesare presented. The adaptation of these routines to distributed memory parallelcomputers is discussed using the implementation within the computer code CPMDas an example. Several advanced techniques from the field of molecular dynamics,(constant temperature dynamics, constant pressure dynamics) and electronicstructure theory (free energy functional, excited states) are introduced. The combinationof the path integral method with ab initio molecular dynamics is presentedin detail, showing its limitations and possible extensions. Finally, a wide range ofapplications from materials science to biochemistry is listed, which shows the enormouspotential of ab initio molecular dynamics for both explaining and predictingproperties of molecules and materials on an atomic scale.1 Setting the Stage: Why Ab Initio Molecular Dynamics ?Classical molecular dynamics using “predefined potentials”, either based on empiricaldata or on independent electronic structure calculations, is well establishedas a powerful tool to investigate many–body condensed matter systems.The broadness, diversity, and level of sophistication of this technique is documentedin several monographs as well as proceedings of conferences and scientificschools 12,135,270,217,69,59,177 . At the very heart of any molecular dynamics schemeis the question of how to describe – that is in practice how to approximate – theinteratomic interactions. The traditional route followed in molecular dynamics is todetermine these potentials in advance. Typically, the full interaction is broken upinto two–body, three–body and many–body contributions, long–range and short–range terms etc., which have to be represented by suitable functional forms, seeSect. 2 of Ref. 253 for a detailed account. After decades of intense research, veryelaborate interaction models including the non–trivial aspect to represent them1