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 2 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 TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 3 Chemical Engineering – Molecular Simulation Process Scales 30 March 2015 TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY Chemical Engineering – Molecular Simulation Spanning the Scales 30 March 2015 TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 5 Chemical Engineering – Molecular Simulation 30 March 2015 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 TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 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) 30 March 2015 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 TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY in supercritical CO2, from a lattice MC simulation. Chemical Engineering – Molecular Simulation J. Chem. Phys. 122, 094710 (2005) 30 March 2015 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 TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 8 Chemical Engineering – Molecular Simulation 30 March 2015 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. TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 9 Chemical Engineering – Molecular Simulation 30 March 2015 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 TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 10 Chemical Engineering – Molecular Simulation 30 March 2015 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. TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 11 Chemical Engineering – Molecular Simulation 30 March 2015 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 TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 12 Chemical Engineering – Molecular Simulation 30 March 2015 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. TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 13 Chemical Engineering – Molecular Simulation 30 March 2015 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! TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 14 Chemical Engineering – Molecular Simulation Some Examples of Molecular Simulations … TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY Chemical Engineering – Molecular Simulation 30 March 2015 LJ liquid simulation http://www.chemistry.wustl.edu/~gelb/gchem/materials/lve/ TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 16 Chemical Engineering – Molecular Simulation 30 March 2015 LJ chains adsorbing on carbon nanotube •  Flexible •  Stiff TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 17 Chemical Engineering – Molecular Simulation 30 March 2015 •  Assignment #1: Look for paper on simulation for final project. –  Points to look for: •  MC or MD •  Small system (O(103) particles) TECHNION – ISRAEL INSTITUTE OF TECHNOLOGY 18 Chemical Engineering – Molecular Simulation