7、分子动力学模拟基础汇总课件.ppt
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1、Chapter 3 Molecular Dynamics Simulation3.1 Molecular Dynamics: The Idea What is molecular dynamics ?It is a technique to compute the equilibrium and transport properties of a classical many-body system.Means that the nuclear motion of the constituent particles obeys the laws of classical mechanics.N
2、ewtons law, Lagrangian equation, and Langevin equation. This is an excellent approximation for a wide range of materials.MD simulation is similar to real experiments When we perform a real experiments, we proceed: Preparing a sample of the material studied; Connecting the sample to a measuring instr
3、ument; Measuring the property of interest during a certain time; If the measurements are subject to statistical noise, then the longer we average, the more accurate our measurement becomes. In a MD simulation, we follow exactly the same approach.e.g., a thermometer, manometer, or viscometer, etc.MD
4、approach First, prepare a sample: select a model system consisting of N particles; Second, solve Newtons equation of motion until the properties of the system no longer change with time.Interaction energy potential, pair potential is frequently usedEquilibrate the system After equilibration, perform
5、 the actual measurement. Some of the most common mistakes in MD are similar to the mistakes that may be made in real experiments. The sample is not prepared correctly, the time is too short, the system undergoes an irreversible change during the experiment, or we do not measure what we think. How to
6、 measure an observable quantity ? To measure an observable quantity in a MD simulation, we must first of all be able to express this observable as a function of the positions and momenta of the particles in the system. Let us take temperature as an example. Making use of the equipartition of energy
7、over all degrees of freedom, Nf, we have: 21( )( )22NiiBfimv tk T tN21( )( )NiiiBfmv tT tk NThe relative fluctuations in the temperature will be of order . As Nf is typically of the order of 102-103, the statistical fluctuations are of the order of 5-10%.1/fNAverage over many fluctuations In which c
8、ase should we worry about quantum effects?When we consider the the translational or rotational motion of light atoms or molecules, or vibrational motion with a frequency such that h kBT.He, H2, D2, etc. Of course, our course of this vast subject is incomplete. If you need the knowledge beyond the co
9、urse, you can read the references on the coming slide. References for Molecular Dynamics MP Allen & DJ Tildesley, 1987, Computer Simulation of Liquids. HC Berendsen & WF van Gunsteren, 1984, Molecular Dynamics Simulations: Techniques & Approached, NATO ASI Series C123. CL Brooks et al., 1988, Protei
10、ns. A Theoretical Perspective of Dynamics, Structure and Thermodynamics. Advances in chemical Physics. Volume LXXI. JM Haile, 1992, Molecular Dynamics Simulation. Elementary Methods.4.2 Molecular Dynamics: A ProgramThe best introduction to MD is to consider a simple program. We keep it as simple as
11、possible to illustrate some important features of MD. It is constructed as: read in the parameters that specify the conditions of the run (e.g., initial temperature, number of particles, density, time step, etc.); Initialize the system (select initial ri and vi); Compute the energy and forces on all
12、 particles; Integrate Newtons equations of motion; measure the quantities in the present time;After completion of the central loop, compute and print the averages of measured quantities, and stop. Central loop, the core of the simulationA simple MD programProgram MD simple MD programcall init initia
13、lizationt=0 set timedo while (t.lt.tmax) MD loop call force(f,en) determine the forces call integrate(f,en) integrate equations of motion t=t+delt update time call sample sample averagesenddostopSubroutine init, force, and integrate will be described later. Subroutine sample is used to calculate ave
14、rages of quantities of interest like pressure and temperature, etc.4.2.1 Initiallization To start the simulation, we should assign initial positions and velocities to all particles in the system. Often this is achieved by initially placing the particles on a cubic lattice.Avoiding positions that res
15、ult in an appreciable overlap; choose positions compatible with the structure that we are aiming to simulate.As the equilibrium properties of the system do not depend on the choice of initial conditions, all reasonable initial conditions are in principle acceptable.Initial positions To simulate a so
16、lid state of a model system, it is logical to prepare the system in the crystal structure of interest. If we are interest in the fluid phase, we simply prepare the system in any convenient crystal structure. If the density close to the freezing, selection of crystal structure is unwise: meta-stable
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