**2.1. Classical mechanics approach**

The physical properties of matter are associated with its structure and the movement of its basic constituents, nuclei and electrons. In principle, the evolution of a system of particles—a many-body problem—can be obtained by solving the Schrödinger equation dependent on time, which gives the probability of finding the particles in any position of space in a given time. In many cases, it is possible to decouple the wave function of the electrons from the wave function of the nuclei, following the Born-Oppenheimer approach (due to mass difference). However, even considering this approach, it is impossible, in practice, to solve the Schrödinger equation numerically and further approaches must be used (Hartree Fock, density functional theory, etc.). In particular, for biological systems (where thousands of nuclei and electrons), its resolution is impossible even under such approximations.

In this direction, molecular dynamics simulation could help to study problems of many bodies at the atomistic level, based on classical mechanics. Within this approach, Newton's equations are solved numerically. The main advantage is the realistic simulation of materials through the simplification by potentials with analytical form.

Although it is quantum mechanics, instead of classical mechanics, which describes the fundamental physics of condensed matter, the validity of the classical approximation can be evaluated based on the Broglie thermal wavelength defined by

$$
\Lambda = \left(\frac{2\pi\hbar^2}{mk\_\flat}\right)^{1/2} \tag{1}
$$

where *ħ* is the Plank constant, *m* the atomic mass, *kb* the Boltzmann constant, and *T* the temperature. The classic approach is valid for Λ < <a, being the separation of the nearest neighbor. Under this condition, the entire system can be treated as a diluted gas model based on the formulation of classical kinetic theory [9]. In this case, each atom can be considered as a particle. Many biomolecular processes can be addressed by semi-empirical parameterizations that describe the interactions of pairs between the particles of the system with classic effective potentials. In addition to having a lower computational cost, the classic models offer an adequate description of the processes and interactions. Chemical reactions (formation and breaking of bonds) and vibrations of bonds and angles with very high frequencies are excluded from the classical treatment.

Through MD simulations, information of positions and velocities of each particle is obtained, from which macroscopic observables could be calculated, such as pressure and energy.
