Molecular Dynamics

Recommended Prerequisites

Classical Mechanics, Thermodynamics, Quantum Mechanics.

Teaching Methods

The subject matter will be presented in the theoretical classes. These presentations will be complemented with practical and theoretical problems given as homework and discussed afterwards in the tutorial classes.

Learning Outcomes

After completion of this course, the student should be able to:

i) assess all factors that affect the accuracy of MD simulations;

ii) understand the algorithms and computational cost of MD simulations;

iii) assess the quality of sampling and of the methods used to improve sampling;

iv) set up classical or ab-initio MD simulations;

v) set up free energy calculations;

vi) analyse structural and dynamical properties.

The following competences will also be developed:

- Competence in analysis and synthesis;

- Competence in problem solving;

- Competence in critical reasoning;

- Competence in autonomous learning;

- Competence in research.

Work Placement(s)

No

Syllabus

Statistical mechanics review: ensembles, fluctuations, correlation functions and transport coefficients.

Empirical and semi-empirical pair- and inter-molecular potentials.

Classical molecular dynamics: equations of motion, simulation initialisation, algorithms for integration of the equations of motion, Liouville formulation.

Simulations at constant temperature or pressure: Andersen and Nosé-Hoover thermostats and barostats.

Free-energy calculations: thermodynamic integration, chemical potential, Gibbs ensemble, free energies of solids, non equilibrium systems.

Technical details: long-range interactions, rare events, supercomputers.

Ab-initio molecular dynamics: Born-Oppenheimer, Ehrenfest, Car-Parrinello, QM/MM.

Applications.

Head Lecturer(s)

Fernando Manuel Silva Nogueira

Assessment Methods

Assessment
Synthesis work: 20.0%
Project: 30.0%
Resolution Problems: 50.0%

Bibliography

Understanding Molecular Simulation: From Algorithms to Applications
Daan Frenkel and Berend Smit
Academic Press (2002)

Computer Simulation of Liquids
M. P. Allen and D. J. Tildesley
Oxford University Press (1987)

Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods
Dominik Marx and Jürg Hutter
Cambridge University Press (2009)

The Art of Molecular Dynamics Simulation
D. C. Rapaport
Cambridge University Press (2004)

A molecular dynamics primer
Furio Ercolessi
http://www.fisica.uniud.it/~ercolessi/md/md/

Molecular dynamics without effective potentials via the Car-Parrinello approach
Dahlia K. Remler , Paul A. Madden
Molecular Physics 70 (1990) 921-966

Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients
M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos
Rev. Mod. Phys. 64 (1992) 1045-1097