## Adaptive Integration of Multidimensional Molecular Dynamics with Quantum Initial Conditions

Please always quote using this URN: urn:nbn:de:0297-zib-6967
• The paper presents a particle method framework for resolving molecular dynamics. Error estimators for both the temporal and spatial discretization are advocated and facilitate a fully adaptive propagation. For time integration, the implicit trapezoidal rule is employed, where an explicit predictor enables large time steps. The framework is developed and exemplified in the context of the classical Liouville equation, where Gaussian phase-space packets are used as particles. Simplified variants are discussed shortly, which should prove to be easily implementable in common molecular dynamics codes. A concept is illustrated by numerical examples for one-dimensional dynamics in double well potential.

Author: Illia Horenko, Martin Weiser ZIB-Report adaptivity ; classical Liouville equation ; molecular dynamics; particle methods 65-XX NUMERICAL ANALYSIS / 65Jxx Numerical analysis in abstract spaces / 65J10 Equations with linear operators (do not use 65Fxx) 65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M99 None of the above, but in this section 81-XX QUANTUM THEORY / 81Sxx General quantum mechanics and problems of quantization / 81S30 Phase-space methods including Wigner distributions, etc. 2002/07/26 ZIB-Report (02-29) Appeared in: J. Comput. Chem. 24 (2003) 1921-1929

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