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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
    Adaptive accuracy control for Car-Parrinello simulations (1999)
    Springer
    Numerische Mathematik 83 (1999), S. 179-186 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65M99, 34C15, 34C40, 70F20, 81Q15, 81V55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. The Car-Parrinello (CP) approach to ab initio molecular dynamics serves as an approximation to time-dependent Born-Oppenheimer (BO) calculations. It replaces the explicit minimization of the energy functional by a fictitious Newtonian dynamics and therefore introduces an artificial mass parameter $\mu$ which controls the electronic motion. A recent theoretical investigation shows that the CP-error, i.e., the deviation of the CP–solution from the BO-solution decreases like $\mu^{1/2}$ asymptotically. Since the computational effort increases like $\mu^{-1/2}$ , the choice of $\mu$ has to find a compromise between efficiency and accuracy. The asymptotical result is used in this paper to construct an easily implemented algorithm which automatically controls $\mu$ : the parameter $\mu$ is repeatedly adapted during the simulation by choosing $\mu$ as large as possible while pushing an error measure below a user-given tolerance. The performance and reliability of the algorithm is illustrated by a typical example.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002110050445
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  • 3
    Electronic Resource
    Electronic Resource
    A theoretical model for molecules interacting with intense laser pulses: The Floquet-based quantum-classical Liouville equation (2001)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 5733-5743 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The Floquet-based quantum-classical Liouville equation (F-QCLE) is presented as a novel theoretical model for the interaction of molecules with intense laser pulses. This equation efficiently combines the following two approaches: First, a small but spectroscopically relevant part of the molecule is treated quantum-mechanically while the remaining degrees of freedom are modeled by means of classical molecular dynamics. The corresponding nonadiabatic dynamics is given by the quantum-classical Liouville equation which is a first-order approximation to the partial Wigner transform of full quantum dynamics. Second, the dynamics of the quantum subsystem is described in terms of instantaneous Floquet states thus eliminating highly oscillatory terms from the equations of motion. The resulting F-QCLE is shown to have a well defined adiabatic limit: For infinitely heavy classical particles and for infinitely slow modulation the dynamics adiabatically follows the Floquet quasi-energy surfaces for a strictly time-periodic field. Otherwise, nonadiabtic effects arise both from the motion of the classical particles and from the modulation of the field which is assumed to be much slower than the carrier frequency. A numerical scheme to solve the F-QCLE is based on a Trotter splitting of the time evolution. The simplest implementation can be realized by an ensemble of trajectories stochastically hopping between different Floquet surfaces. As a first application we demonstrate the excellent agreement of quantum-classical and fully quantum-mechanical dynamics for a two-state model of photodissociation of molecular fluorine. In summary, due to the favorable scaling of the numerical effort the F-QCLE provides an efficient tool for the simulation of medium to large molecules interacting with intense fields beyond the perturbative regime. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.1398577
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  • 4
    Electronic Resource
    Electronic Resource
    Quantum-classical molecular dynamics as an approximation to full quantum dynamics (1996)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 1074-1083 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: This paper presents a mathematical derivation of a model for quantum-classical molecular dynamics (QCMD) as a partial classical limit of the full Schrödinger equation. This limit is achieved in two steps: separation of the full wave function and short wave asymptotics for its "classical'' part. Both steps can be rigorously justified under the same smallness assumptions. This throws some light on the time-dependent self-consistent-field method and on mixed quantum-semiclassical models, which also depend on the separation step. On the other hand, the theory leads to a characterization of the critical situations in which the QCMD model is in danger of largely deviating from the solution of full Schrödinger equation. These critical situations are exemplified in an illustrative numerical simulation: the collinear collision of a classical particle with a harmonic quantum oscillator. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.471952
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  • 5
    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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