Molecular Dynamics Simulation

      Molecular dynamics (MD) is a computer simulation method to predict the motions of particles with time. The particles can be atoms such as C, molecules (after which the method is named) such as CH4, or clusters. The motions of particles in MD are governed by Newton's laws of motion (force F = ma where m is mass, and a is acceleration). Here we need two more relationships to make the positions of particles and time related with each other. One is based on the conservation of energy, and defines the relation between potential energy (PE) and force as
where rij,k is the k-component of distance between particles i and j. The other is extended by the numerical analysis algorithm solving the derivative relationships
or
where v is velocity, with respect to very small time duration Dt ~ 1 ps (pico second, 10-12 sec). In the first step of MD simulations all the information of system, such as the vectors (coordinates, velocities, accelerations, etc.) of particles, and parameters of potentials equations, are read from input data (or files). During the energy minimization step total energy of the system at initial state is calculated. Then all new vectors at the next time step are predicted by integrator. The integrated potentials and forces between particles are calculated with the predicted vectors. If the thermostat particles are designated, the velocities or accelerations of the particles are modulated according to the types of thermostat, that is, the methods of controlling system temperature. The accelerations calculated from the forces are different with predicted ones. The other vectors are corrected by considering the discrepancies between the predicted and calculated accelerations. The steps from predictor to corrector are repeated for the time enough to observe significant phenomena, such as diffusion, adsorption, deformation, and so on.


Figure 1. General flow chart for classical MD simulations. The loop in the flow is repeated at every time step until wanted number of time steps is reached.