ISSN:
0945-3245
Keywords:
Mathematics Subject Classification (1991): 34C15, 34C40, 70F20, 81Q15, 81V55
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 $\mu$ , 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 ${\cal O}(\mu^{1/2})$ – 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002110050316
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