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Molecular Dynamics
v2011.09.20 FI3102 Computational Physics 1
Sparisoma Viridi
Nuclear Physics and Biophysics Research Division
Institut Teknologi Bandung, Bandung 40132, Indonesia
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Outline
• Molecular dynamics
• The use of molecular dynamics
• Experiment using simulation
• Molecular scale, human scale, planetoid
v2011.09.20 FI3102 Computational Physics 2
• Molecular scale, human scale, planetoid
• MD algorithm and example
• Is MD so perfect?
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Molecular dynamics
• Molecular dynamics (MD) is a computer
simulation of physical movements of
atoms and molecules (Wikipedia, 2011)
• MD simulation consists of the numerical, • MD simulation consists of the numerical,
step-by-step, solution of classical equation
of motion (Allen, 2004)
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Molecular dynamics (cont.)
• It is a computer simulation technique
where the time evolution of a set of
interacting atoms is followed by integrating
their equations of motion (Ercolessi, 1997)their equations of motion (Ercolessi, 1997)
• MD simulations can provide the ultimate
detail concerning individual motions as a
function of time (Karplus and McCammon,
2002)
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The use of MD
• It can be used from atomic scale until
planetoid scale -- amazing
• To calculate electronic ground state as
function of time of liquid metal (Kresse and function of time of liquid metal (Kresse and
Hafner, 1993)
• Motion of n-Alkanes molecules (Ryckaert,
Ciccotti, and Berendsen, 1977)
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The use of MD (cont.)
• Nanodroplet on a surface (Sedighi, Murad,
and Aggarwal, 2010)
• Grain of in mm and cm size (Gallas,
Herrmann, Pöschel, and Sokolowski, Herrmann, Pöschel, and Sokolowski,
1996)
• Simulation of asteroids movement (Jaffé,
Ross, Lo, Marsden, Farrelly, and Uzer,
2002)
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Experiment using simulation
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(Allen, 2004)
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Experiment using .. (cont.)
• It is a bridge between microscopic and
macroscopic
• It is also a bridge between theory and
experimentexperiment
• Do the experiment using simulation is a
smart way to reduce the financial problem
• Even all considered nature laws are input
to the system, it could give the unexpected
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Molecular scale
• Lennard-Jones potential:
• Coulomb potential
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Molecular scale (cont.)
• Can you derive the expression for the
forces from both potential?
• MD simulation need expression in term of
force instead of potentialforce instead of potential
• Use the relation
v2011.09.20 FI3102 Computational Physics 10
VF ∇−=rr
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Molecular scale (cont.)
• And the results?
=LJFr
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=LJF
=CFr
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Human scale
• Near on earth surface: gravitational force
Fg = -mg
• Friction force : Ff = -bv
• Magnetic force : FB = qv ×B
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Planetoid scale
• Newton’s law of universtal gravitation
rmm
GFG ˆ21−=r
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rr
GFG ˆ2
21−=
(Wikipedia, 2011)
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MD algorithm
• It is uses Newton’s second law of motion
to get the acceleration a
• It using numerical integration to get the
equation of motion, use the simple method equation of motion, use the simple method
i.e. original Euler method
• New motion parameters will cause new
value of all forces
• Calculate the new forces to get new a
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MD algorithm (cont.)
amFrr
=∑
..++++=∑ FFFFFrrrrr
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..++++=∑ LJfBG FFFFF
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MD algorithm (cont.)
• Euler method:
tavv iii ∆+=+
rrr
1
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tvrr iii ∆+=+
rrr
1
ttt ii ∆+=+1
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MD algorithm (cont.)
• You must pay attention to the outside
influence that changes with order of
magnitude of chosen ∆t
• Normally it is chose that ∆t must be 100 • Normally it is chose that ∆t must be 100
times smaller than that change
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Example
• Write the numerical expression for a
parabolic motion when air friction is
considered
• g = - g j• g = - g j
• r0, v0
• b is for Ff = - bv
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Example (cont.)
• Write the numerical expression for a
charged particle that moves perpendicular
to external magnetic field B, initial velocity
is v0at r
0is v
0at r
0
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Is MD so perfect?
• Unfortunately not
• It has problem even all forces are already
considered
• It can produce unreported results or • It can produce unreported results or
unexpected (wrong) results
• It has problem in time stamp
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Time stamp problem
• Nanodroplet (Sedighi, Murad, and
Aggarwal, 2010):
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Time stamp problem (cont.)
• continue from previous
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Time stamp problem (cont.)
• Granular oscillation (Chen, Lin, Li, and Li,
2009):
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Time stamp problem (cont.)
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References
1. Wikipedia contributors, “Molecular dynamics”, Wikipe-
dia, The Free Encyclopedia, 5 September 2011, 15:49
UTC, oldid:448597141 [2011.09.21 09.34+07]
2. Michael P. Allen, “Introduction to Molecular Dynamics
Simulation”, in Computational Soft Matter: From
v2011.09.20 FI3102 Computational Physics 25
Simulation”, in Computational Soft Matter: From
Synthetic Polymers to Proteins, Lecture Notes, Norberg
Attig, Kurt Binder, Helmut Grubmüller, Kurt Kremer
(Eds.), John von Nuemann Institut for Computing,
Jülich, NIC Series, Vol. 23, pp. 1-28, 2004
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References (cont.)
3. Furio Ercolessi, “A Molecular Dynamics Primer”, Spring
College in Computational Physics, ICTP, Trieste,
9/10/1997 URI http://www.fisica.uniud.it/~ercolessi/md
/md/node6.html [2011.09.21 09.51+07]
4. Martin Karplus and J. Andrew McCammon, “Molecular 4. Martin Karplus and J. Andrew McCammon, “Molecular
Dynamics Simulations of Biomolecules”, Nature
Structural Biology 9 (9), 646-653 (2002)
5. G. Kresse and J. Hafner, “Ab Initio Molecular Dynamics
for Liquid Metals”, Physical Review B 47 (1), 558-561
(1993)
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References (cont.)
6. Jean Paul Ryckaert, Giovanni Ciccotti, and Herman J.
C. Berendsen, “”Numerical Integration of the Cartesian
Equations of Motion of a System with Constraints:
Molecular Dynamics of n-Alkanes”, Journal of
Computational Physics 23 (3), 327-341 (1977)Computational Physics 23 (3), 327-341 (1977)
7. Jason A. C. Gallas, Hans J. Herrmann, Thorsten
Pöschel, and Stefan Sokolowski, “Molecular Dynamics
Simulation of Size Segregation in Three Dimensions”,
Journal of Statistical Physics 82 (1-2), 443-450 (1996)
v2011.09.20 FI3102 Computational Physics 27
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References (cont.)
8. Charles Jaffé, Shane D. Ross, Martin. W. Lo, Jerrold
Marsden, David Farrelly, and T. Uzer, “Statistical
Theory of Asteroid Escape Rates”, Physical Review
Letters 89 (1), 011101 (2002)
9. Nahid Sedighi, Sohail Murad, and Suresh K. Aggarwal, 9. Nahid Sedighi, Sohail Murad, and Suresh K. Aggarwal,
“Molecular Dynamics Simulations of Nanodroplet
Spreading on Solid Surfaces, Effect of Droplet Size”,
Fluid Dynamics Research 42 (3), 035501 (2010)
10. Kuo-Ching Chen, Chi-Hao Lin, Chia-Chieh Li, and Jian-
Jhih Li, “Dual Granular Temperature Oscillation of a
Compartmentalized Bidisperse Granular Gas”, Journal
of the Physical Society of Japan 78 (4), 044401 (2009)v2011.09.20 FI3102 Computational Physics 28
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Thank you (for your patience)
v2011.09.20 FI3102 Computational Physics 29
(for your patience)
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