Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme

Margaret Mandziuk; Tamar Schlick

doi:10.1016/0009-2614(95)00316-V

Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme

Margaret Mandziuk, Tamar Schlick

Chemistry

Research output: Contribution to journal › Article › peer-review

Abstract

The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- (Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance (Δt ≈ 7 fs here) leads to instability, and higher-order resonances (n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.

Original language	English (US)
Pages (from-to)	525-535
Number of pages	11
Journal	Chemical Physics Letters
Volume	237
Issue number	5-6
DOIs	https://doi.org/10.1016/0009-2614(95)00316-V
State	Published - May 19 1995

ASJC Scopus subject areas

General Physics and Astronomy
Physical and Theoretical Chemistry

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10.1016/0009-2614(95)00316-V

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title = "Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme",

abstract = "The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- (Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance (Δt ≈ 7 fs here) leads to instability, and higher-order resonances (n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.",

author = "Margaret Mandziuk and Tamar Schlick",

note = "Funding Information: We thank Sebastian Reich and Bob Skeel for pointing us to interesting references. This research was generously supported by the National Science Foundation (CHE-9002146, PYI Award ASC-915782, and GCAG ASC-9318159), the National Institutes of Health ( Research Resource RR08102), the Alfred Sloan Foundation and the Howard Hughes Medical Institute.",

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AU - Schlick, Tamar

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PY - 1995/5/19

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N2 - The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- (Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance (Δt ≈ 7 fs here) leads to instability, and higher-order resonances (n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.

AB - The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- (Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance (Δt ≈ 7 fs here) leads to instability, and higher-order resonances (n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.

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Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme

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