Molecular dynamics (MD) is a computer simulation technique used to model physical movements of atoms and molecules over time. MD simulations involve numerically solving classical equations of motion to simulate interactions between atoms at different scales, from molecular to human to planetary. While MD can provide detailed atomic-level insights, it has limitations such as potential issues with numerical integration accuracy at small time steps.

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Molecular Dynamics
Sparisoma Viridi
Nuclear Physics and Biophysics Research Division
Institut Teknologi Bandung, Bandung 40132, Indonesia
dudung@fi.itb.ac.id
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0110001 Outline
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• Molecular dynamics
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• The use of molecular dynamics
• Experiment using simulation
• Molecular scale, human scale, planetoid
• MD algorithm and example
• Is MD so perfect?
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0110001 Molecular dynamics
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• Molecular dynamics (MD) is a computer
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simulation of physical movements of
atoms and molecules (Wikipedia, 2011)
• MD simulation consists of the numerical,
step-by-step, solution of classical equation
of motion (Allen, 2004)
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0110001 Molecular dynamics (cont.)
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• It is a computer simulation technique
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where the time evolution of a set of
interacting atoms is followed by integrating
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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0110001 The use of MD
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• It can be used from atomic scale until
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planetoid scale -- amazing
• To calculate electronic ground state as
function of time of liquid metal (Kresse and
Hafner, 1993)
• Motion of n-Alkanes molecules (Ryckaert,
Ciccotti, and Berendsen, 1977)
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0110001 The use of MD (cont.)
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• Nanodroplet on a surface (Sedighi, Murad,
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and Aggarwal, 2010)
• Grain of in mm and cm size (Gallas,
Herrmann, Pöschel, and Sokolowski,
1996)
• Simulation of asteroids movement (Jaffé,
Ross, Lo, Marsden, Farrelly, and Uzer,
2002)
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0110001 Experiment using simulation
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(Allen, 2004)
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0110001 Experiment using .. (cont.)
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• It is a bridge between microscopic and
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macroscopic
• It is also a bridge between theory and
experiment
• 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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0110001 Molecular scale
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• Lennard-Jones potential:
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• Coulomb potential
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0110001 Molecular scale (cont.)
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• Can you derive the expression for the
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forces from both potential?
• MD simulation need expression in term of
force instead of potential
• Use the relation
r r
F = −∇V
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0110001 Molecular scale (cont.)
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• And the results?
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r
FLJ =
r
FC =
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0110001 Human scale
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• Near on earth surface: gravitational force
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Fg = -mg
• Friction force : Ff = -bv
• Magnetic force : FB = qv ×B
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0110001 Planetoid scale
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• Newton’s law of universtal gravitation
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r m1 m 2
FG = −G 2 r ˆ
r
(Wikipedia, 2011)
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0110001 MD algorithm
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• It is uses Newton’s second law of motion
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to get the acceleration a
• It using numerical integration to get the
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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0110001 MD algorithm (cont.)
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r r
0
∑ F = ma
r r r r r
∑ F = FG + FB + F f + FLJ + ..
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0110001 MD algorithm (cont.)
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• Euler method:
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r r r
vi + 1 = vi + ai ∆t
r r r
ri + 1 = ri + vi ∆t
t i +1 = t i + ∆t
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0110001 MD algorithm (cont.)
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• You must pay attention to the outside
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influence that changes with order of
magnitude of chosen ∆t
• Normally it is chose that ∆t must be 100
times smaller than that change
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0110001 Example
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• Write the numerical expression for a
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parabolic motion when air friction is
considered
• g=-gj
• r0, v0
• b is for Ff = - bv
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0110001 Example (cont.)
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• Write the numerical expression for a
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charged particle that moves perpendicular
to external magnetic field B, initial velocity
is v0 at r0
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0110001 Is MD so perfect?
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• Unfortunately not
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• It has problem even all forces are already
considered
• It can produce unreported results or
unexpected (wrong) results
• It has problem in time stamp
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0110001 Time stamp problem
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• Nanodroplet (Sedighi, Murad, and
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Aggarwal, 2010):
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0110001 Time stamp problem (cont.)
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• continue from previous
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• Granular oscillation (Chen, Lin, Li, and Li,
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2009):
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0110001 Time stamp problem (cont.)
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0110001 References
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1. Wikipedia contributors, “Molecular dynamics”, Wikipe-
0 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
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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0110001 References (cont.)
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3. Furio Ercolessi, “A Molecular Dynamics Primer”, Spring
0 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
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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6. Jean Paul Ryckaert, Giovanni Ciccotti, and Herman J.
0 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)
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)
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0110001 References (cont.)
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8. Charles Jaffé, Shane D. Ross, Martin. W. Lo, Jerrold
0 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,
“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)
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Thank you
(for your patience)
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