**3. Molecular Dynamics (MD) modeling**

Molecular dynamics is nothing but classical dynamics. Indeed classical dynamic equations of motion are valid for slow and heavy particles, with typical velocities *υ*<<c, (where *c* is the speed of light) and masses *m*>>*m*e, (where *m*e is the electron mass). Therefore, we can use them for atoms, ions, and molecular mass only in slow motion (slower than thermal vibration).

This technique is based on computing potential energy that is typically considered only as a function of the system spatial configuration and is described by means of interatomic poten‐ tials. These potentials are considered as known input information; they are either found experimentally or are computed by averaging over the motion of the valence electrons in the ion's Coulomb field by means of quantum ab initio methods.

The main equation that we utilize in this technique is the Lagrange equations of motion. For a system of *N* interacting monoatomic molecules, the Lagrange equation turns Newtonian equations divided into "Dissipative equations" and "Generalized Langevin equations."

Integrals of motion are more functions that are useful for modeling in MD technique. Their notable property is depending only on the initial conditions and staying constant in time. Some of these equations are as follows:

$$\frac{dE}{dt} = 0\tag{1}$$

$$\frac{d\mathbf{P}}{dt} = 0\tag{2}$$

$$\frac{d\mathbf{M}}{dt} = 0\tag{3}$$

where *E* is the total energy, *P* is the total momentum, and *M* is the total angular momentum in a system with only conservative forces.
