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Computational Methods
for
Molecular Dynamics
5 points
Aim:
The aim of the course is to present different problem settings in
modern molecular dynamics and show how modern, efficient and accurate
numerical techniques can be used to solve them. Both classical and
quantum dynamics for the nuclei will be considered. After completion of
the course, the students will be able to select from and use a variety of
computational tools to solve research problems in molecular dynamics.
Lectures: The course consists of 12 lectures, one per week
Time: Mondays 10.15 - 12, first lecture January 31, 2005
Room:Angstrom 64119
Examination: Computer assignments
Target group: Graduate students in physics, chemistry, biochemistry and
scientific computing.
Teachers:
- Sverker Holmgren,[SH], Department of Scientific Computing
- Hans Karlsson, [HK],Department of Quantum Chemistry
- Daniel Spångberg,[DS], Department of Material Chemistry
Applications should be sent to Hans.Karlsson@kvac.uu.se
The course is an "Gemensam forskarutbildningskurs" given within the
framework of Uppsala Multidisciplinary Center for Advanced Computational
Science (UPPMAX)
Content of the lectures
| Date | Lecturer | Content |
| 31/1 | DS | Molecular dynamics and classical mechanics.
Introduction. Overview of the field of molecular dynamics .
Equation of motion. Simple model potential surfaces. Initial conditions |
| 7/2 | SH | Integrating the equations of motion.Sympletic integrators.
Multiple time-scales |
| 14/2 | DS | Many-body and polarizable potentials |
| 21/2 | SH | Evaluation of the force field. Ewald summation. Multipole methods.
Parallelization |
| 28/2 | HK | Molecular dynamics and quantum mechanics.
The time-dependent Schrödinger equation.
Potential energy surfaces. Time-dependent potentials. The time-evolution operator. |
| 7/3 | SH | Representation in space. Pseudo-spectral methods. The Discrete variable
representation. Finite differences. Finite elements |
| 14/3 | HK,SH | Propagation methods for time-independent Hamiltonians.
The split-operator method. Runge-Kutta type methods |
| 21/3 | HK | Polynomial approximation. The Chebychev and Lanczos methods. |
| 4/4 | SH | Explicit time-dependent Hamiltonians.The Magnus approximation. |
| 11/4 | | Molecular dynamics and quantum-classical methods. |
| 18/4 | | Summary. |
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