In a MD simulation, we follow exactly the same a prepare a sample: select a model system consisting of N particles; Interaction energy potential, pair potential is frequently used Second, solve Newton’s equation of motion until the properties of the system no longer change with time. Equilibrate the system After equilibration, perform 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.
N kBT (t ) N mi vi2 (t ) mi vi2 (t ) Nf T (t ) 2 2 i 1 i 1 k B N f The relative fluctuations in the temperature will be of order 1/ N f . As Nf is typically of the order of 102-103, the statistical fluctuations are of the order of 5-10%.
How to 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 over all degrees of freedom, Nf, we have: Average over many fluctuations
In which case 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.
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:
Means that the nuclear motion of the constituent particles obeys the laws of classical mechanics.
Newton’s law, Lagrangian equation, and Langevin equation.
References for Molecular Dynamics
He, H2, D2, etc. Of course, our course of this vast subject is incomplete. If you need the knowledge beyond the course, you can read the references on the coming slide.
Chapter 3 Molecular Dynamics Simulation
3.1 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.
Preparing a sample of the material studied;
Connecting the sample to a measuring instrument;
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. e.g., a thermometer, manometer, or viscometer, etc.