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Non-Adiabatic Effects in Quantum-Classical Molecular Dynamics

Please always quote using this URN: urn:nbn:de:0297-zib-3817
  • In molecular dynamics applications there is a growing interest in mixed quantum-classical models. The article is concerned with the so-called QCMD model. This model describes most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of a wavefunction. We review the conditions under which the QCMD model is known to approximate the full quantum dynamical evolution of the system. In most quantum-classical simulations the {\em Born-Oppenheimer model} (BO) is used. In this model, the wavefunction is adiabatically coupled to the classical motion which leads to serious approximation deficiencies with respect to non-adiabatic effects in the fully quantum dynamical description of the system. In contrast to the BO model, the QCMD model does include non-adiabatic processes, e.g., transitions between the energy levels of the quantum system. It is demonstrated that, in mildly non-adiabatic scenarios, so-called {\em surface hopping} extensions of QCMD simulations yield good approximations of the non-adiabatic effects in full quantum dynamics. The algorithmic strategy of such extensions of QCMD is explained and the crucial steps of its realization are discussed with special emphasis on the numerical problems caused by highly oscillatory phase effects.

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Author:Christof Schütte, Peter Nettesheim
Document Type:ZIB-Report
Tag:Schrödinger equation; adiabatic limit; highly oscillatory phase; non-adiabatic processes; quantum adiabati; quantum-classical molecular dynamics
MSC-Classification:81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q15 Perturbation theories for operators and differential equations
81-XX QUANTUM THEORY / 81Qxx General mathematical topics and methods in quantum theory / 81Q20 Semiclassical techniques, including WKB and Maslov methods
81-XX QUANTUM THEORY / 81Sxx General quantum mechanics and problems of quantization / 81S25 Quantum stochastic calculus
81-XX QUANTUM THEORY / 81Vxx Applications to specific physical systems / 81V55 Molecular physics [See also 92E10]
92-XX BIOLOGY AND OTHER NATURAL SCIENCES / 92Exx Chemistry (For biochemistry, see 92C40) / 92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
Date of first Publication:1998/12/21
Series (Serial Number):ZIB-Report (SC-98-38)
Published in:Appeared in: F. Keil, W. Mackens et al. Scientific Computing in Chemical Engineering II, Computational Fluid Dynamics, Reaction Engineering and Molecular Properties. Springer (1999) pp. 42-56
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