A Mathematical Investigation of the Car-Parrinello Method

Please always quote using this URN: urn:nbn:de:0297-zib-2302
  • The Car-Parrinello method for ab-initio molecular dynamics avoids the explicit minimization of energy functionals given by functional density theory in the context of the quantum adiabatic approximation (time-dependent Born-Oppenheimer approximation). Instead, it introduces a fictitious classical dynamics for the electronic orbitals. For many realistic systems this concept allowed first-principle computer simulations for the first time. In this paper we study the {\em quantitative} influence of the involved parameter $\mu$, the fictitious electronic mass of the method. In particular, we prove by use of a carefully chosen two-time-scale asymptotics that the deviation of the Car-Parrinello method from the adiabatic model is of order ${\rm O}(\mu^{1/2})$ --- provided one starts in the ground state of the electronic system and the electronic excitation spectrum satisfies a certain non-degeneracy condition. Analyzing a two-level model problem we prove that our result cannot be improved in general. Finally, we show how to use the gained quantitative insight for an automatic control of the unphysical ``fake'' kinetic energy of the method.

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Metadaten
Author:Folkmar A. Bornemann, Christof Schütte
Document Type:ZIB-Report
Date of first Publication:1996/05/31
Series (Serial Number):ZIB-Report (SC-96-19)
Published in:Appeared in: Numer. Math. 78 (1998) pp. 359-376