Modelação e Simulação de Sistemas para Micro/Nano Tecnologias

Transcription

1 Modelação e Simulação de Sistemas para Micro/Nano Tecnologias Alberto José Proença, António Joaquim Esteves 2011/12 Mestrado em Micro/Nano Tecnologias ESCOLA DE ENGENHARIA UNIVERSIDADE DO MINHO Motivation Scaling! Pillars of S&T: (i) theory, (ii) experiments, (iii) mod & sim! Levels: (i) quantum, (ii) nano-micro / atomic/molecule, (iii) meso,... Modelling (of molecular mechanics)! Levels: (i) physical, (ii) math, (iii) numerical, (iv) computational Simulation methods! Deterministic: molecular dynamics (MD) methods! Stochastic: Monte Carlo (MC) methods Simulation tools! GROMACS

2 Motivation Scaling! Pillars of S&T: (i) theory, (ii) experiments, (iii) mod & sim! Levels: (i) quantum, (ii) nano-micro / atomic/molecule, (iii) meso,... Modelling (of molecular mechanics)! Levels: (i) physical, (ii) math, (iii) numerical, (iv) computational Simulation methods! Deterministic: molecular dynamics (MD) methods! Stochastic: Monte Carlo (MC) methods Simulation tools! GROMACS

3 Weeks 1-6 Lectures, discussion/lab classes, papers presentation/discussion Weeks 8-11 Lectures, invited talk, tutorial class, project presentation Week 12 Written test Weeks GROMACS tutorials and Project Week 17 Individual discussion of the Project

4 ! Written test [ 30% - 40% ]! Paper analysis and public presentation [ 10% - 20% ]! Project with a Mod&Sim tool, GROMACS [ 50% - 60% ]! teamwork 2-3 students! writing of a Technical Report (teamwork)! individual work assessment! Context: modelling, simulation, scale, math/numerical, computation! Useful concepts in molecular modelling! Force Field models: molecular mechanics! Energy minimization! Computer simulation techniques in molecular modelling! Molecular dynamics simulation methods! Monte Carlo simulation methods! From HPC to commodity computing Relevant chapters will be online From the Preface: Most molecular modelling studies involve three stages. In the first stage a model is selected to describe the intra- and inter- molecular interactions in the system. The two most common models that are used in molecular modelling are quantum mechanics and molecular mechanics. These models enable the energy of any arrangement of the atoms and molecules in the system to be calculated, and allow the modeller to determine how the energy of the system varies as the positions of the atoms and molecules change. The second stage of a molecular modelling study is the calculation itself, such as an energy minimisation, a molecular dynamics or Monte Carlo simulation, or a conformational search. Finally, the calculation must be analysed, not only to calculate properties but also to check that it has been performed properly. Selected chapters: 1. USEFUL CONCEPTS IN MOLECULAR MODELLING 4. EMPIRICAL FORCE FIELD MODELS: MOLECULAR MECHANICS 5. ENERGY MINIMISATION AND RELATED METHODS FOR EXPLORING THE ENERGY SURFACE 6. COMPUTER SIMULATION METHODS 7. MOLECULAR DYNAMICS SIMULATION METHODS 8. MONTE CARLO SIMULATION METHODS

5 " Slides from the lectures/tutorials " Molecular Modelling: Principles and Applications, Andrew R. Leach, Pearson Education, 2 nd edition, January 2001 " Computational Materials Science: The Simulation of Materials Microstructures and Properties, Dierk Raabe, Wiley-VCH, 1998 " Understanding Molecular Simulation: From Algorithms to Applications, Daan Frenkel and Berend Smit, Academic Press, 2nd edition, October 2001 " GROMACS User Manual, Version 4.0! Useful concepts in molecular modelling! Coordinate systems! Potential energy surfaces! Molecular graphics! Surfaces! Mathematical concepts! Series expansions! Vectors, matrices, eigenvectors and eigenvalues! Some basic elements of statistics! The Fourier series, Fourier transform and fast-fourier transform! Force Field models: molecular mechanics! Some general features of molecular mechanics force fields! Bond stretching! Angle bending! Torsional! Introduction to non-bonded interactions! Electrostatic interactions! van der Waals interactions! Many-body effects in empirical potentials! Effective pair potentials! Hydrogen bonding in molecular mechanics! Force field models for the simulation of liquid water! Energy minimization! Statement of the problem! Non-derivative minimization methods! Introduction to derivative minimization methods! First-order minimization methods! Second derivative methods: the Newton-Raphson method! Quasi-Newton methods! Which minimization method! Applications of energy minimization

6 ! Computer simulation techniques in molecular modelling! Time averages, ensemble averages and some historical background! A brief description of the molecular dynamics method! The basic elements of the Monte Carlo method! Differences between the molecular dynamics and Monte Carlo methods! Calculation of simple thermodynamic properties: Energy, Heat capacity, Pressure, Temperature, Radial distribution functions! Practical aspects of computer simulation! Boundaries! Monitoring the equilibration! Truncating the potential and the minimum image convention! Long-range forces! Analysing the results of a simulation and estimating errors! Molecular dynamics simulation methods! Molecular dynamics using simple models! Molecular dynamics with continuous potentials! Finite difference methods! Setting up and running a molecular dynamics simulation! Constraint dynamics! Molecular dynamics at constant temperature and pressure! Monte Carlo simulation methods! Calculating properties by integration! Some theoretical background to the Metropolis method! Implementation of the Metropolis Monte Carlo method! Monte Carlo simulation of molecules! 'Biased' Monte Carlo methods! Monte Carlo sampling from different ensembles! Calculating the chemical potential! Monte Carlo or molecular dynamics?