Introduction

CE 056388
Introduction to Molecular Simulation
systems at equilbrium
Dr. Simcha Srebnik
Room 377
Tel. 3584
[email protected]
TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY
Chemical Engineering – Molecular Simulation
‫הפקולטה להנדסה כימית‬
‫מכון טכנולוגי לישראל‬
Syllabus
‫מבוא לסימולציות מולקולריות‬
‫הטכניון‬
30 March 2015
056388
2015 '‫סמסטר ב‬
simchas@tx
zadoki@tx
3584 :'‫טל‬
366 ‫חדר‬
‫ד"ר שמחה סרבניק‬
:‫מרצה‬
‫ ישראל צדוק‬:‫בודק תרגילים‬
50%
‫תרגילים‬
50%
‫עבודה סופית‬
: ‫ציון‬
:‫ספר לימוד‬
Richard L. Rowley, Statitical mechanics for Thermophysical Property calculations, Prentice
Hall, 1994.
email ‫ של הקורס או ישלחו ב‬Moodle ‫שקפי ההרצאות יופיעו על אתר ה‬
AVOGADRO, VMD, JMOL, LAMMPS :‫מקורות עזר נוספים‬
Allen, M.P. and Tildesley, D.J., “Computer Simulation of Liquids”, Clarendon Press,
Oxford (1987). h/p://www.ccl.net/cca/so=ware/SOURCES/FORTRAN/allen-­‐Fldesley-­‐book/index.shtml Frenkel, D. and Smit, B., "Understanding Molecular Simulation: From Algorithms to
Applications", Academic Press (2002). h/p://www.acmm.nl/molsim/frenkel_smit/README.html TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY
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Chemical Engineering – Molecular Simulation
Frenkel, D. and Smit, B., "Understanding Molecular Simulation: From Algorithms to
Applications", Academic Press (2002).
30 March 2015
Syllabus
:‫נושאי הלימוד‬
‫פרק בספר הלימוד‬
Rowley
1-3
5
7
8
9
‫נושא‬
‫מבוא‬
‫עקרונות מכניקה סטטיסטית‬
‫הגדרת כוחות‬
‫שיטת מונטה קרלו‬
‫שיטת דינמיקה מולקולרית‬
‫חישובי תכונות תרמודינמיות‬
‫הידרודינמיקה‬
‫מידול עם תוכנות מסחריות‬
1.
1
2.
3.
4.
5.
6.
7.
8.
1
2
3
4
5
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Chemical Engineering – Molecular Simulation
Process Scales
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Spanning the Scales
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Chemical Engineering – Molecular Simulation
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Simulation Scales
Based on SDSC Blue Horizon (SP3)
512-1024 processors
1.728 Tflops peak performance
CPU time = 1 week / processor
TIME
/s
100
(ms)
Continuum
Methods
Atomistic
Simulation
Methods
10-3
Mesoscale methods
Lattice Monte Carlo
Brownian dynamics
Dissipative particle dyn
(µs) 10-6
(ns) 10-9
(ps) 10-12
Semi-empirical
methods
Ab initio
methods
tight-binding
MNDO, INDO/S
(fs) 10-15
10-10
10-9
Monte Carlo
molecular dynamics
10-8
10-7
(nm)
6
The general procedure is to average out
10-6
10-5
10-4
(µm)
LENGTH/
fastChemical
degrees
ofMolecular
freedom.
Engineering – meters
Simulation
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Ab Initio
Electron localization function
for (a) an isolated ammonium
ion and (b) an ammonium ion
with its first solvation shell.
From Liu & Tuckerman, J.
Phys. Chem. B 105, 6598 (2001)
Mesoscale
7
Semi-empirical
Structure of an oligomer of
polyphenylene sulfide
phenyleneamine.
From Giro & Galvão, Int. J.
Quant. Chem. 95, 252 (2003)
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Atomistic
Structure of solid LennardJones CCl4 molecules confined
in a model MCM-41 silica
pore. From Hung, Siperstein,
& Gubbins
Continuum
Temperature profile on a laserheated surface obtained with
the finite-element method.
From Rajadhyaksha &
Michaleris, Int. J. Numer.
Meth. Eng. 47, 1807 (2000)
Phase equilibrium between a lamellar surfactantrich phase and
a continuous
surfactant-poor
phase
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in supercritical CO2, from a lattice MC simulation.
Chemical Engineering – Molecular Simulation
J. Chem. Phys. 122, 094710 (2005)
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Why do modelling?
•  Point is not (just) to reproduce the results of experiments
•  Aim to
–  Gain confidence to calculate quantities that cannot easily be
measured
–  Gain understanding of relationships between physical quantities in
situations too complicated to treat by analytical theory
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Chemical Engineering – Molecular Simulation
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Why do simulations?
•  Simulations are the only general method for “solving” manybody problems. Other methods involve approximations and
experts.
•  Experiment is limited and expensive. Simulations can
complement the experiment.
•  Simulations are easy even for complex systems.
•  They scale up with the computer power.
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Chemical Engineering – Molecular Simulation
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The idea of (atomistic) simulation
• 
This course is about structure of
materials and its relationship to
properties
• 
The simulation approach: start from
atoms and the interactions between
them
• 
Deduce the equilibrium structure of
the system, and other properties:
–  Macroscopic variables (e.g.
pressure, volume)
–  Measurable structural parameters
for comparison with experiment
(e.g. structure factor for a liquid,
lattice vectors for a crystal)
–  Quantities not directly related to
structure (e.g. electrical properties)
+
Interactions
Structure
Properties
e.g.
S(q,ω),
p(V,T), σ
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Chemical Engineering – Molecular Simulation
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Definition of Simulation
•  What is a simulation?
–  An internal state “S”
–  A rule for changing the state Sn+1 = T (Sn)
–  We repeat the iteration many time.
•  Simulations can be
–  Deterministic (e.g. Newton’s equations=MD)
–  Stochastic (Monte Carlo, Brownian motion,…)
•  Typically they are ergodic: there is a correlation time T. for
times much longer than that, all non-conserved properties are
close to their average value. Used for:
–  Warm up period
–  To get independent samples for computing errors.
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Chemical Engineering – Molecular Simulation
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A Molecular Experiment
• 
Molecular simulation is a computational
“experiment” conducted on a
molecular model.
10 to 100,000 or more
atoms are simulated
(typically 500 - 1000)
• 
Many configurations are generated, and averages
taken to yield the “measurements.” One of two methods is used:
–  Molecular dynamics
•  IntegraFon of equaFons of moFon
•  DeterminisFc
•  Retains Fme element
Monte Carlo
Ensemble average StochasFc No element of Fme • 
Molecular simulation has the character of both theory and experiment
• 
Applicable to molecules ranging in complexity from rare gases to
polymers to electrolytes to metals
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Chemical Engineering – Molecular Simulation
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Challenges of Simulation
Physical and mathematical underpinnings:
•  What approximations come in:
–  Computer time is limited _ few particles for short periods of
time.
•  Systems with many parFcles and long Fme scales are problemaFc. •  Hamiltonian is unknown, until we solve the quantum many-body
problem!
•  How do we estimate errors? Statistical and systematic.
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Chemical Engineering – Molecular Simulation
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Warnings !!!
•  Simulation can be deceptively easy to do
•  Results are entirely dependent on
–  Choosing a good enough form for the interatomic interactions
–  Using a suitable simulation algorithm to extract the physics one is
interested in
•  Garbage in, garbage out!
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Chemical Engineering – Molecular Simulation
Some Examples of Molecular
Simulations …
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Chemical Engineering – Molecular Simulation
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LJ liquid simulation
http://www.chemistry.wustl.edu/~gelb/gchem/materials/lve/
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LJ chains adsorbing on carbon nanotube
•  Flexible
•  Stiff
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•  Assignment #1: Look for paper on simulation for final project.
–  Points to look for:
•  MC or MD
•  Small system (O(103) particles)
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