Molecular Dynamics

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Introduction to Mle

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Molecular Dynamics

  1. 1. Molecular Dynamics (Part 1) Sparisoma Viridi* Nuclear Physics and Biophysics Research Division Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia *dudung@gmail.comSK6202 Senin, 4 Februari 2013 1 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  2. 2. Outline• Short history of molecular dynamics (MD)• Introduction to MD• MD Algorithm• Example• AssignmentsSK6202 Senin, 4 Februari 2013 2 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  3. 3. Short history Molecular dynamics Contribution from some worksSK6202 Senin, 4 Februari 2013 3 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  4. 4. History of MD• It was first introduced in studying the interact- ions of hard spheres which exhibits phase transitions (Alder et. al, 1957)• Then, a series of paper led by Alder is then pu- blished during 1959-1980 investigating this methodB. J. Alder and T. E. Wainwright, “Phase Transition for a Hard Sphere System”, Journal of Chemical Physics 27 (5)1208-1209 (1957)SK6202 Senin, 4 Februari 2013 4 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  5. 5. History of MD (cont.)• Studies of Alder and Wainwright in 1957 and 1959 induced other studies concerning beha- ior of simple liquids• Realistic potential for liquid argon is then used (Rahman, 1964)• Simulation of realistic system is conducted for the first time for water (Stillinger et. al, 1974)A. Rahman, “Correlations in the Motion of Atoms in Liquid Argon”, Physical Review 136 (2A), A405-A411 (1964)F. H. Stillinger and A. Rahman, “Improved Simulation of Liquid Water by Molecular Dynamics”, Journal of ChemicalPhysics 60 (4), 1545-1557 (1974)SK6202 Senin, 4 Februari 2013 5 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  6. 6. History of MD (cont.)• The dynamics of folded of globular protein (bovine pancreatic trypsin inhibitor) is the first protein simulation (McCammon et. al, 1977)• Many program and code are released, e.g. Chemistry HARvard Molecular Mechanics (CHARMM) (Stote et. al, 1999)J. A. McCammon, B. R. Gelin, and M. Karplus, “Dynamics of Folded Proteins”, Nature 267 (5612) 585-590 (1977)R. Stote, A. Dejaegere, D. Kuznetsov, and L. Falquet, “Theory of Molecular Dynamcis Simulation ” in Tutori@lMolecular Dynamics Simulation CHARMM, URI http://www.ch .embnet.org/MD_tutorial /pages/MD.Part1. html[2012.02.13]SK6202 Senin, 4 Februari 2013 6 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  7. 7. Alder’s papers• This series of papers published during 1959- 1980, a lot of time of consistency of studying something – I. General Method (1959) – IV. Behavior of a Small Number of Elastic Spheres (1960) – III. A Mixture of Hard Spheres (1964) – IV. The Pressure, Collision Rate, and Their Number Dependence for Hard Disks (1967)SK6202 Senin, 4 Februari 2013 7 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  8. 8. Alder’s papers (cont.) – V. High-Density Equation of State and Entropy for Hard Disks and Spheres – VI. Free-Path Distributions and Collision Rates for Hard-Sphere and Square-Well Molecules (1968) – VII. Hard-Sphere Distribution Functions and an Augmented van der Waals Theory (1969) – VIII. The Transport Coefficients for a Hard-Sphere Fluid (1970) – IX. Vacancies in Hard Sphere Crystals (1971)SK6202 Senin, 4 Februari 2013 8 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  9. 9. Alder’s papers (cont.) – X. Corrections to the Augmented van der Waals Theory for the Square Well Fluid (1972) – XI. Correlation Functions of a Hard-Sphere Test Particle (1972) – XII. Band Shape of the Depolarized Light Scattered from Atomic Fluids (1973) – XIII. Singlet and Pair Distribution Functions for Hard-Disk and Hard-Sphere Solids (1974)SK6202 Senin, 4 Februari 2013 9 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  10. 10. Alder’s papers (cont.) – XIV. Mass and Size Dependence of the Binary Diffusion Coefficient (1974) – XV. High Temperature Description of the Transport Coefficients (1975) – XVI. Fluctuation Driven Resonance (1977) – XVII. Phase diagrams for ’’step’’ potentials in two and three dimensions (1979) – XVIII. The square-well phase diagram (1980)SK6202 Senin, 4 Februari 2013 10 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  11. 11. Introduction Molecular dynamics Definitions, use, and limitationsSK6202 Senin, 4 Februari 2013 11 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  12. 12. Molecular dynamics• Molecular dynamics (MD) is a computer 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)Wikipedia contributors, “Molecular dynamics”, Wikipedia, The Free Encyclopedia, 5 September 2011, 15:49 UTC,oldid:448597141 [2011.09.21]M. P. Allen, “Introduction to Molecular Dynamics Simulation”, in Computational Soft Matter: From Synthetic Polymersto Proteins, Lecture Notes, Norberg Attig, Kurt Binder, Helmut Grubmüller, Kurt Kremer (Eds.), John von NuemannInstitut for Computing, Jülich, NIC Series, Vol. 23, pp. 1-28, 2004SK6202 Senin, 4 Februari 2013 12 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  13. 13. 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)• MD simulations can provide the ultimate detail concerning individual motions as a function of time (Karplus et. al, 2002)F. Ercolessi, “A Molecular Dynamics Primer”, Spring College in Computational Physics, ICTP, Trieste, 9/10/1997 URIhttp://www.fisica.uniud.it/~ercolessi/md /md/node6.html [2011.09.21]M. Karplus and J. A. McCammon, “Molecular Dynamics Simulations of Biomolecules”, Nature Structural Biology 9 (9),646-653 (2002)SK6202 Senin, 4 Februari 2013 13 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  14. 14. Range of use• It is used from atomic until planetoid scale• Calculation of electronic ground state as function of time of liquid metal (Kresse et. al, 1993)• Motion of n-Alkanes molecules (Ryckaert et. al, 1977)G. Kresse and J. Hafner, “Ab Initio Molecular Dynamics for Liquid Metals”, Physical Review B 47 (1), 558-561 (1993)J. P. Ryckaert, G. Ciccotti, and H. J. C. Berendsen, “Numerical Integration of the Cartesian Equations of Motion of aSystem with Constraints: Molecular Dynamics of n-Alkanes”, Journal of Computational Physics 23 (3), 327-341 (1977)SK6202 Senin, 4 Februari 2013 14 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  15. 15. Range of use (cont.)• Nanodroplet on a surface (Sedighi et. al, 2010)• Grains in mm and cm size (Gallas et. al, 1996)• Simulation of asteroids movement (Jaffé et. al, 2002)N, Sedighi, S. Murad, and S. K. Aggarwal, “Molecular Dynamics Simulations of Nanodroplet Spreading on SolidSurfaces, Effect of Droplet Size”, Fluid Dynamics Research 42 (3), 035501 (2010)J. A. C. Gallas, H. J. Herrmann, T. Pöschel, and Stefan Sokolowski, “Molecular Dynamics Simulation of SizeSegregation in Three Dimensions”, Journal of Statistical Physics 82 (1-2), 443-450 (1996)C. Jaffé, S. D. Ross, M. W. Lo, J. Marsden, D. Farrelly, and T. Uzer, “Statistical Theory of Asteroid Escape Rates”,SK6202Physical Review Letters 89 (1), 011101 Senin, 4 Februari 2013 (2002) 15 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  16. 16. Use of MD• There are three main scenarios for the use of MD (Fedman, 2006)• In the first scenario the simulated properties are compared with experimental results, and when the two agree it is reasonable to claim that the experimental results can be explained by the simulation model.F. Hedman, “Algorithms for Molecular Dynamics Simulations: Advancing the Computational Horizon”, Ph.D. Thesis,Avdelningen för fysikalisk kemi, Arrheniuslaboratoriet, Stockholms Universitet, Stockholm, 2006SK6202 Senin, 4 Februari 2013 16 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  17. 17. Use of MD (cont.)• In the second scenario, MD simulations are used to interpret experimental results. In a sense the second scenario is the inverse of the first.• In the third scenario, simulations are used as an exploratory tool to help gain an initial understanding of a problem and give guidance among possible lines of investigation, be it theoretical or experimental.SK6202 Senin, 4 Februari 2013 17 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  18. 18. Experiment using simulationM. P. Allen, “Introduction to Molecular Dynamics Simulation”, in Computational Soft Matter: From Synthetic Polymersto Proteins, Lecture Notes, Norberg Attig, Kurt Binder, Helmut Grubmüller, Kurt Kremer (Eds.), John von NuemannInstitut for Computing, Jülich, NIC Series, Vol. 23, pp. 1-28, 2004SK6202 Senin, 4 Februari 2013 18 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  19. 19. Experiment .. simulation (cont.)• It is a bridge between microscopic and 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 unexpectedSK6202 Senin, 4 Februari 2013 19 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  20. 20. Is MD so perfect?• Unfortunately not• It has problem even all forces are already considered• It can produce unreported results or unexpected (wrong) results• It has problem in time stampSK6202 Senin, 4 Februari 2013 20 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  21. 21. Time stamp problem• NanodropletN, Sedighi, S. Murad, and S. K. Aggarwal, “Molecular Dynamics Simulations of Nanodroplet Spreading on SolidSurfaces, Effect of Droplet Size”, Fluid Dynamics Research 42 (3), 035501 (2010)SK6202 Senin, 4 Februari 2013 21 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  22. 22. Time stamp problem (cont.)SK6202 Senin, 4 Februari 2013 22 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  23. 23. Time stamp problem (cont.)• Granular oscillationK. -C. Chen, C. -H. Lin, C. -C. Li, and J. -J. Li, “Dual Granular Temperature Oscillation of a CompartmentalizedBidisperse Granular Gas”, Journal of the Physical Society of Japan 78 (4), 044401 (2009)SK6202 Senin, 4 Februari 2013 23 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  24. 24. Time stamp problem (cont.)SK6202 Senin, 4 Februari 2013 24 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  25. 25. MD Algorithm Trajectory of a particle Potentials, the forms, and their physical meaningSK6202 Senin, 4 Februari 2013 25 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  26. 26. Algorithms• 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 i.e. original Euler method• New motion parameters will cause new value of all forces• Calculate the new forces to get new aSK6202 Senin, 4 Februari 2013 26 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  27. 27. Algorithms (cont.)• Newton’s second law of motion   ∑ F = ma• Left side consists of all considered forcesSK6202 Senin, 4 Februari 2013 27 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  28. 28. Algorithms (cont.)• Euler method:    vi +1 = vi + ai ∆t    ri + 1 = ri + vi ∆t t i +1 = t i + ∆t • Particle position is given by ri at time t iSK6202 Senin, 4 Februari 2013 28 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  29. 29. Algorithms (cont.)• You must pay attention to influence from out- side of the system that changed with order of magnitude of chosen Δt• Normally it is chosen that Δt must be 100 times smaller than that changeSK6202 Senin, 4 Februari 2013 29 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  30. 30. Potentials• Lennard-Jones potential  σ 12  σ  6  U LJ ( r ) = 4ε   −     r   r  • Coulomb potential q1q 2 1 UC (r) = 4πε 0 rSK6202 Senin, 4 Februari 2013 30 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  31. 31. Potentials (cont.)• Gravitation potensial near large object U G ( r ) = −mgr• Gravitation potensial 1 U G ( r ) = −Gm1m2 rSK6202 Senin, 4 Februari 2013 31 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  32. 32. Potentials (cont.)• Morse potential U M ( r ) = De 1 − e [ ] −α ( r − re ) 2• Yukawa potential − kmr e U Y ( r) = −g 2 rSK6202 Senin, 4 Februari 2013 32 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  33. 33. Potentials (cont.)• Harmonic oscillator potential 1 U HO ( r ) = k ( r − r0 ) 2 2SK6202 Senin, 4 Februari 2013 33 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  34. 34. Force• Force can be obtained from potential through   F = −∇USK6202 Senin, 4 Februari 2013 34 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  35. 35. Granular memory device Example Sequence of particle under gravitation potentialSK6202 Senin, 4 Februari 2013 35 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  36. 36. System• Granular device (D), sensor (S), particle sequence (P)• P moves with constant initial velocity before entering DSK6202 Senin, 4 Februari 2013 36 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  37. 37. Typical states• Observed states are: – s10w0r0 (two configurations) – s10w1r0 – s10w1r1SK6202 Senin, 4 Februari 2013 37 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  38. 38. Typical states (cont.)• Writing zero particle and relecting none from ten particles sequence (s10w0r0)• gn = 0, gp = 0, b = 0, v0 = 4SK6202 Senin, 4 Februari 2013 38 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  39. 39. Typical states (cont.)• Writing zero particle and relecting none from ten particles sequence (s10w0r0)• gn = 1, gp = -2, b = 2, v0 = 6SK6202 Senin, 4 Februari 2013 39 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  40. 40. Typical states (cont.)• Writing one particle and relecting none from ten particles sequence (s10w1r0)• gn = 1, gp = -2, b = 2, v0 = 5SK6202 Senin, 4 Februari 2013 40 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  41. 41. Typical states (cont.)• Writing one particle and relecting another one from ten particles sequence (s10w1r1)• gn = 1, gp = -3, b = 2, v0 = 4SK6202 Senin, 4 Februari 2013 41 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  42. 42. AssignmentsSK6202 Senin, 4 Februari 2013 42 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  43. 43. Assignments• Make six groups of 2-3 students• Each group collects only one answer file• Answer file should be sent to dudung@gmail.com with subject [SK6202] MD Assignment 1• The file sould be received before 11 February 2013SK6202 Senin, 4 Februari 2013 43 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  44. 44. Assignments (cont.)• Question 1. Derive force formulation for following potential: (a) harmonic oscillator, (b) Coulomb, (c) gravitation, (d) Lennard-Jones, (e) Morse, (f) YukawaSK6202 Senin, 4 Februari 2013 44 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  45. 45. Assignments (cont.)• Question 2. Describe the physical meaning of parameters used in each force or potential formulation• Question 3. Tell the difference between molecular dynamics and molecular mechanics• Question 4. Find the Euler, Verlet, Gear pre- dictor-corrector, Rattle, and Shake algorithm• Question 5. Find a topic to be solved using molecular dynamics and explainSK6202 Senin, 4 Februari 2013 45 BSC-A Lantai 3Kapita Selekta Sains Komputasi
  46. 46. Thank youSK6202 Senin, 4 Februari 2013 46 BSC-A Lantai 3Kapita Selekta Sains Komputasi

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