by Peter Nettesheim, Sebastian Reich
Lecture Notes in Computational Science and Engineering
http://www.mcs.surrey.ac.uk/Personal/S.Reich/97_5.ps
Add To MetaCart
Abstract:
Abstract. The overall Hamiltonian structure of the Quantum-Classical Molecular Dynamics model makes--analogously to classical molecular dynamics-- symplectic integration schemes the methods of choice for longterm simulations. This has already been demonstrated by the symplectic PICKABACK method [12]. However, this method requires a relatively small step-size due to the high-frequency quantum modes. Therefore, following related ideas from classical molecular dynamics, we investigate symplectic multiple-time-stepping methods and indicate various possibilities to overcome the step-size limitation of PICKABACK. 1
Citations
|
308
|
Mathematical methods of classical mechanics
– Arnold
- 1989
|
|
48
|
The life-span of backward error analysis for numerical integrators
– HAIRER, LUBICH
- 1997
|
|
42
|
Backward error analysis for numerical integrators
– Reich
- 1999
|
|
37
|
On the Hamiltonian interpolation of near to the identity symplectic mappings with application to symplectic integration algorithms
– BENETTIN, GIORGILLI
- 1994
|
|
23
|
Dangers of multiple-time-step methods
– Biesiadecki, Skeel
- 1993
|
|
10
|
Quantum-classical molecular dynamics as an approximation to full quantum dynamics
– Schutte
- 1996
|
|
9
|
Preservation of adiabatic invariants under symplectic discretization
– Reich
- 1999
|
|
7
|
On the singular limit of the quantum-classical molecular dynamics model
– Schutte
- 1999
|
|
7
|
An explicit and symplectic integrator for quantum-classical molecular dynamics
– Schutte
- 1996
|
|
7
|
Numerical Hamiltonian Systems
– Sanz-Serna, Calvo
- 1994
|
|
6
|
Quantum simulation of reaction dynamics by density matrix evolution
– Berendsen, Mavri
- 1993
|
|
5
|
Time-dependent self-consistent field approximation for intramolecular energy transfer
– Gerber, Buch, et al.
- 1982
|
|
5
|
Symplectic integrators tailored to the time-dependent Schrodinger equation
– Gray, Manolopoulos
- 1996
|
|
5
|
A bunch of time integrators for quantum/classical molecular dynamics
– Lubich
- 1998
|
|
5
|
Numerical integrators for quantum-classical molecular dynamics
– Schutte
- 1998
|
|
4
|
Mixed quantum wave packet/classical trajectory treatment of the photodissociation process ArHCl
– Garc'ia-Vela, Gerber, et al.
- 1992
|
|
3
|
Discrete time-reversible propagation scheme for mixed quantum classical dynamics
– Schmitt, Brinkmann
- 1996
|
|
2
|
Gemischt klassisch-quantenmechanische Molekulardynamik im Liouville-Formalismus
– Schmitt
- 1997
|
