04 molecular dynamics

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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

[email protected]

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Outline

• Molecular dynamics

• The use of molecular dynamics

• Experiment using simulation

• Molecular scale, human scale, planetoid


• 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


(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


VF ∇−=rr

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Molecular scale (cont.)

• And the results?

=LJFr


=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


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


..++++=∑ LJfBG FFFFF

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• Euler method:

tavv iii ∆+=+

rrr

1


tvrr iii ∆+=+

rrr

1

ttt ii ∆+=+1

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• 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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• Granular oscillation (Chen, Lin, Li, and Li,

2009):


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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


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)


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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)


(for your patience)

Education

04 molecular dynamics