《Simulations Moléculaires》 Cours04I

Simulations moleculaires WeI dong aboratoire de chimie UMR 5182 CNRS-Ecole normale Superieure de lyon, 46, Allee d Italie, 69364 Lyon Cedex 07 france Tel:0472728844 Email: Wei Dong @ens-lyon. fr Bureau: LR6 A008

Simulations Moléculaires Wei DONG Laboratoire de Chimie, UMR 5182 CNRS - Ecole Normale Supérieure de Lyon, 46, Allée d’Italie, 69364 Lyon Cedex 07, France Tél : 0472728844 Email : Wei.Dong@ens-lyon.fr Bureau : LR6 A008

Plan Introduction Brief recall of statistical mechanics and thermodynamics Molecular dynamics method (MD) .Monte Carlo method(MC) .lllustration of a few applications of MD and MC in the research works carried out in our laboratory Tutorials on md and mC

Plan •Introduction •Brief recall of statistical mechanics and thermodynamics •Molecular dynamics method (MD) •Monte Carlo method (MC) •Illustration of a few applications of MD and MC in the research works carried out in our laboratory •Tutorials on MD and MC

What can one do with molecular simulations? Study complex systems i.e. those which cannot be described by simple theories o Calculate thermodynamic properties of complex systems(eg liquids internal energy, pressure, chemical potential, Henrys constant etc o Calculate transport properties, e. g. diffusion coefficient viscosity, coefficient of thermal conduction etc Calculate the rate of different types of chemical reactions .Determine different types of distribution functions

What can one do with molecular simulations? •Study complex systems, i.e., those which cannot be described by simple theories. •Calculate thermodynamic properties of complex systems (e.g., liquids): internal energy, pressure, chemical potential, Henry’s constant etc. •Calculate transport properties, e.g., diffusion coefficient, viscosity, coefficient of thermal conduction etc. •Calculate the rate of different types of chemical reactions •Determine different types of distribution functions

Application domains Simple liquids, molecular liquids .liquid mixtures, electrolyte solutions inhomogeneous fluids(interfaces), fluids confined in porous solids polymers, proteins .self-assembling systems(amphiphile, micelle, micro emulsion )etc

Application domains •Simple liquids, molecular liquids; •liquid mixtures, electrolyte solutions; •inhomogeneous fluids (interfaces), fluids confined in porous solids; •polymers, proteins; •self-assembling systems (amphiphile, micelle, micro emulsion) etc

What is the relation between simulation, theory and experiment? Simulation eory Experiment

What is the relation between simulation, theory and experiment? Simulation Theory Experiment

Difference and relation between molecular Simulation and Quantum Chemistry Different scopes (lenght and time scales Quantum chemistry Electronic level. one or a few atoms or molecules Microscopic length and time scales Bond energy, Transition state etc Molecular simulation Atomic and molecular level, large assembly of atoms and molecules Larger length and time scales Effects of inter-molecular interactions, dynamics(non reacting and reacting systems

Difference and relation between Molecular Simulation and Quantum Chemistry Different scopes (lenght and time scales): - Quantum chemistry Electronic level, one or a few atoms or molecules. Microscopic length and time scales. Bond energy, Transition state etc.. - Molecular simulation Atomic and molecular level, large assembly of atoms and molecules. Larger length and time scales. Effects of inter-molecular interactions, dynamics (non reacting and reacting systems)

What is a molecular simulation or the aim ofit? .generating microscopic configurations or trajectories of model systems sampling phase space to determine structural, thermodynamic and transport properties through calculating averages and probabilities pI What are the main methods Molecular dynamics Monte carlo Molecular mechanics

What is a molecular simulation or the aim of it? •generating microscopic configurations or trajectories of model systems. •sampling phase space to determine structural, thermodynamic and transport properties through calculating averages and probabilities. What are the main methods: •Molecular dynamics •Monte Carlo •Molecular mechanics

Basic principles ofMd and MC. molecular dynamics From a given initial condition(positions and momenta), the trajectories of all the molecules are generated by solving the equations of motion(Newton equation for classical dynamics or time-dependent schrodinger equation for quantum dynamics) onte carlo Different configurations are generated by using a stochastic methods

Basic principles of MD and MC: Molecular dynamics From a given initial condition (positions and momenta), the trajectories of all the molecules are generated by solving the equations of motion (Newton equation for classical dynamics or time-dependent Schrödinger equation for quantum dynamics). Monte Carlo Different configurations are generated by using a stochastic methods

A short history Monte Carlo: N. Metropolis, A W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and e. Teller, J. Chem. Phys. 21,, (1953) Molecular dynamics B.J. Alder and T.E. Wainwright, J. Chem. Phys. 27, 1208 (1957);ibid.31,459,(1959) State of the art Molecular simulation spreads more and more widely in various scientific disciplines, e. g, physics, chemistry, biology chemical engineering etc. Systems tractable nowadays: fluids with a million of particles, b1O-polymers etc

A short history: Monte Carlo: N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller, J. Chem. Phys. 21, 1087, (1953). Molecular dynamics: B.J. Alder and T.E. Wainwright, J. Chem. Phys. 27, 1208, (1957); ibid. 31, 459, (1959). State of the art: Molecular simulation spreads more and more widely in various scientific disciplines, e.g., physics, chemistry, biology, chemical engineering etc.. Systems tractable nowadays: fluids with a million of particles, bio-polymers etc

orce felds Atomic systems. U=∑W)∑∑MGF)∑∑∑vFFF片 j>i k>j> where ul, u, and u3 are respectively one-body two-body three-body interaction potentials Pair potential models are widely used in simulations Model interaction potentials Hard-sphere potential u(r

Force fields ( ) ( , ) ( , , ) ... 1 2 3 = +  +   +     u r u r r u r r r k k j i i j i j i j j i i i i i U       Atomic systems: where u1 , u2 and u3 are respectively one-body, two-body, three-body interaction potentials. Pair potential models are widely used in simulations. Model interaction potentials Hard-sphere potential: u HS(r) =  r s r u(r) s