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
© Copyright 2024