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  • Mathematics Subject Classification (1991): 34C15, 34C40, 70F20, 81Q15, 81V55  (1)
  • generalized ensemble  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    A mathematical investigation of the Car-Parrinello method (1998)
    Springer
    Numerische Mathematik 78 (1998), S. 359-376 
    Details
    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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  • 2
    Electronic Resource
    Electronic Resource
    Hybrid Monte Carlo with adaptive temperature in mixed-canonical ensemble: Efficient conformational analysis of RNA (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 19 (1998), S. 1689-1697 
    Details
    ISSN: 0192-8651
    Keywords: hybrid Monte Carlo ; generalized ensemble ; reweighting ; n-butane ; triribonucleotide ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: A hybrid Monte Carlo method with adaptive temperature choice is presented that exactly generates the distribution of a mixed-canonical ensemble composed of two canonical ensembles at low and high temperature. The analysis of resulting Markov chains with the reweighting technique shows an efficient sampling of the canonical distribution at low temperature whereas the high temperature component facilitates conformational transitions, which allows shorter simulation times. The algorithm is tested by comparing analytical and numerical results for the small n-butane molecule before simulations are performed for a triribonucleotide. Sampling the complex multiminima energy landscape of this small RNA segment, we observe enforced crossing of energy barriers.   © 1998 John Wiley & Sons, Inc.   J Comput Chem 19: 1689-1697, 1998
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
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