# Ordinary differential equation for molecule collision

I have no background in chemistry.

But, I have a good background in mathematics and computer programming.

I have planned to simulate the collision of two simple molecules $\ce{Br2}$ and $\ce{H2}$ just for fun and using state space and Ordinary Differential Equation (ODE) to simulate.

I have considered 24 states for simulations of their collision. The state vector is X, and the state space representation is:

X'=f(X,t)


Atom numbering

1: Br
2: Br
3: H
4: H


The 24 states for vector X are:

x1, x2, x3:  position of atom 1 in x, y, z axis
x4, x5, x6:  position of atom 2 in x, y, z axis
x7, x8, x9:  position of atom 3 in x, y, z axis
x10,x11,x12: position of atom 4 in x, y, z axis
x13,x14,x15: velocity of atom 1 in x, y, z axis
x16,x17,x18: velocity of atom 2 in x, y, z axis
x19,x20,x21: velocity of atom 3 in x, y, z axis
x22,x23,x24: velocity of atom 4 in x, y, z axis


To make a simulation, I need to know two things:

1. Are the mentioned states enough to describe the entire system? Are there more states to be added?
2. What are the forces applied to each atom at each moment?

$\frac{d x_1}{d t}=x4$ (derivative of position is velocity)

$\frac{d x_4}{d t}=\frac1{m_{Br}}(???????)$ (derivative of velocity is acceleration)