The Continuous Movement of Molecules

Even at 0 K, molecules do not stand still. Quantum mechanically, this unexpected behavior can be explained by the existence of a so-called zero-point energy. Therefore, simplifying a molecule by thinking of it as a collection of balls and springs which mediate the forces acting between the atoms is not totally unrealistic, because one can easily imagine how such a mechanical model wobbles aroimd, once activated by an initial force. Consequently, the movement of each atom influences the motion of every other atom within the molecule, resulting in a com- 

In this case, F is the force acting on the Cartesian coordinate X for j = 3,. .., 3JV for the N atoms in the molecule or molecular system, m, is the atomic mass of atom i, U is the potential energy function given in Eq, (32), and t is the time. The total energy E of the system is the sum of all kinetic (Va and potential 

If we wish to know the position, (t+ At) of an atom i at the time t + At, it can be calculated based on the known position Xj t) at the time t, e.g., by the Leapfrog algorithm [9] (which is a modification of the well-known Verlet [10] algorithm) given in Eq. (35). 

The temperature T of a system is related to the mean kinetic energy of all atoms N via Eq. (36), where kg is the Boltzmann constant and Vf the average of the squared velocities of atom i. 

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