Professor M. Tuckerman Office: 1001L Main Phone: 998-8471 E-mail: mark.tuckerman@nyu.edu
Books
There is no book per se for the course. Much of our initial
work will be based on the treatment of classical mechanics found
Herbert Goldstein's Classical Mechanics. References for
discussions on modern molecular dynamics techniques and applications
will come mostly from the recent literature. There are, however,
several books that have short sections on molecular dynamics,
which I list below:
D. Frenkel and B. Smit Understanding molecular simulation: from
algorithms to applications.
T. Schlick, Molecular Modeling and Simulation.
M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids.
Course Outline
I.
The microscopic dance: What can we study with classical mechanics? (Examples):
A.
Biology: Protein Folding.
B.
Biology: Proton channels.
B.
Chemistry: Proton conduction in liquids - Water and Methanol.
C.
Surface Chemistry: Diels Alder reactions on Silicon (100)-2 .
D.
Physics: Proton-conducting crystals.
II.
Underpinnings: Introduction to Classical Mechanics
A.
Newton's Laws of motion.
B.
Systems that can be solved analytically.
1.
The free particle.
2.
The harmonic oscillator.
C.
Naïve numerical approximations.
III.
Classical Mechanics in Greater Depth.
A.
Lagrangian formulation of classical mechanics.
B.
The classical action and extremization principle.
C.
Hamiltonian formulation of classical mechanics.
D.
Conservation laws.
E.
Phase space.
1.
Incompressible vs. compressible systems.
2.
Conservation of phase space volume.
3.
The symplectic property.
F.
Constrained systems.
G.
Rigid body motion.
1.
Euler's equations.
2.
Quaternions.
H.
Non-Hamiltonian dynamics.
IV.
Operators and numerical methods
A.
The Liouville operator and the classical propagator.
B.
Trotter's Theorem.
C.
Symplectic decompositions of the propagator.
D.
The ``direct translation'' technique.
E.
Multiple time scale decompositions.
V.
Calculating observables.
A.
Introduction to the ensembles.
B.
Ergodicity: Time averages as phase space averages over ensembles.
C.
Static vs. Dynamic observables.
VI.
Designing Equations of Motion
A.
Microcanonical Ensemble.
B.
Canonical Ensemble.
C.
Isothermal-isobaric Ensemble.
D.
Beating the conformational sampling problem.
VII.
Elements of Force Fields
A.
What is a force field?
B.
Intramolecular interactions.
C.
Intermolecular interactions.
D.
Handling long range force (Ewald summation).
VIII.
Introduction to electronic structure and ab initio
molecular dynamics
A.
Basics of density functional theory.
B.
Kohn-Sham formulation of density functional theory.
C.
Basis sets.
D.
The Car-Parrinello algorithm.
IX.
Monte Carlo Methods
A.
Markov Chains.
B.
Sampling and importance sampling.
C.
The Metropolis Algorithm.
D.
Force bias and other ``smart'' Monte Carlo methods.
E.
Hybrid Monte Carlo.
Grading basis
Homework:..............20%
Midterm Project.....40%
Final Exam:............40%
Notes for all lectures can be found on the course web page:
http://www.nyu.edu/classes/tuckerman/mol.dyn
.