The MD idea

Molecular dynamics is a remedy. The idea is very simple. 

If we knew the potential energy K as a function of the position (R) of all the atoms (whatever force field has been used for the approximation ), then all the forces the atoms undergo could be easily computed. If / = (Xj, X2, denotes the coordinates of all the N atoms (Xi, X2, X3 are the x, y, z coordinates of atom 1, X4, X5, Xe are the x, y, z of atom 2, etc.), then — is the x component of the force atom 1 undergoes, — is the y component of the same force, 

Our immediate goal is collecting the atomic positions as functions of time, i.e. the system trajectory. 

The Newton equation tells us that, knowing the force acting on a body (e.g., an atom), we may compute the acceleration the body undergoes. We have to know the mass, but there is no problem with that. Hence the i-th component of the acceleration vector is equal to 

let us assume that at i = 0 all the atoms have the initial coordinates Rq and the initial velocities wo- Now we assume that the forces calculated act unchanged during a short period At (often 1 femtosecond or 10 s). We know what should happen to a body (atom) if under influence of a constant force during time At. Each atom undergoes a uniformly variable motion and the new position may be found in the vector 

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