A mathematical investigation of the Car-Parrinello method |
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Authors: | Folkmar A Bornemann Christof Schütte |
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Institution: | (1) Courant Institute of Mathematical Sciences, New York University, 251 Mercer St RM 711, New York NY 10012-1185, USA; e-mail: bornemann@cims.nyu.edu , US;(2) Konrad-Zuse-Zentrum Berlin, Takustrasse 7, D-14195 Berlin, Germany; e-mail: schuette@zib.de , DE |
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Abstract: | 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 quantitative influence of the involved parameter , 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 – 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.
Received June 14, 1996 |
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Keywords: | Mathematics Subject Classification (1991): 34C15 34C40 70F20 81Q15 81V55 |
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