*2.2. Mathematical Model Construction*

This simulation used an all-atom molecular dynamics simulation approach, and the Newton's Equation of motion (1) was used during the simulation:

$$F\_i(t) = m\_i a\_i(t) \tag{1}$$

where: *Fi* is combined force on the molecule, *mi* is relative molecular mass, *ai* is the acceleration of the molecule. The force on the atom can be obtained from the potential energy concerning the position in the coordinate system as Equation of motion (2):

$$-\frac{\partial V}{\partial r\_i} = m\_i \frac{\partial^2 r\_i}{\partial t^2} \tag{2}$$

Because there are no charged molecules in the system, the potential energy function [23] discards electrostatic interactions and constructs a potential energy function that includes inter-bonding atomic interactions and van der Waals forces, with the specific functional relationship shown in Equation (3):

$$V = \sum\_{bonds} k\_r (r - r\_{\text{eq}})^2 + \sum\_{angles} k\_\theta (\theta - \theta\_{\text{eq}})^2 + \sum\_{dihdral} k\_\theta (1 + \cos[n\phi - \gamma]) + \sum\_{i < j}^{\text{atoms}} \varepsilon\_{ij} \left[ \left( \frac{r\_m}{r\_{ij}} \right)^{12} - 2 \left( \frac{r\_m}{r\_{ij}} \right)^6 \right] \tag{3}$$

where: *kr* is force constant, *req* is equilibrium bond length, *θeq* is equilibrium bond angle, *εij* is van der Waals force constant between atoms, *rm* is the minimum distance between atoms, and *rij* is the distance between atoms at equilibrium.

The integration process uses the Verlet (1967) integral equation of motion algorithm. The advantages of the Verlet integrator are that it has only one energy evaluation per step, requires only a modest amount of memory, and allows relatively large time steps to be used. The Verlet velocity algorithm overcomes the disadvantages of the Verlet step-over method, which is not synchronous. The Verlet velocity algorithm is provided in Equations (4)–(6):

$$r(t + \Delta t) = r(t) + \Delta t v(t) + \frac{\Delta t^2 a(t)}{2} \tag{4}$$

$$a(t + \Delta t) = \frac{f(t + \Delta t)}{m} \tag{5}$$

$$v(t + \Delta t) = v(t) + \frac{1}{2}\Delta t[a(t) + a(t + \Delta t)]\tag{6}$$

where: *r*(*t*) is relative position, *v*(*t*) is relative velocity, and *a*(*t*) is the acceleration of the atom.
