First of all, H2 molecule is not classical system. You have to take considerations of quantum theory. But depending on what you want to study, you can use classical models to approximate. For example, if you want to study the properties near equilibrium, you can assume a harmonic potential or Yukawa potential (definitely not coulomb potentials, they diverge!) between the two H atoms, you can see the vibration and rotation of the molecule nicely. But if you want to study how the H2 is formed by two protons and two electrons, you just cannot do classically.

Zhaorang

What do you mean with the vibrations can be treated classically? They are quantized

Or do you mean the BO approximation, by first separating electronic and atomic motion?

The problem is that I have to treat the collision He2+ + H2 at low energy (30keV). With quantum mechanics, this problem is just impossible to treat. Zhaorong, there already exist some classical models using Morse potentials to treat such collisions. However, an attractive potential is completely unrealistic. With my model, using only Coulombic potentials, my molecule stays stable during about 500a.u. (~25nm), which is comfortable since the collision distance for He2+ + H2 is of the order of 1 or 2 nm. I would like to extend the model to have a stability under 5000 a.u. !

Harry,

Yes, BO approximation can treat nucleus classically but electron quantumly. If one only cares about the movement of nucleus, it is a good model to use.

François,

30keV? You are probably dealing with scattering problem. You can look up the scattering cross section as a function of energy, between He2+ and H2 molecule. I feel like this process is highly classical because of the high energy of He2+. H2 can be easily ionized.

Zhaorang

Why does one want to assume that the vibration/rotation is classical? In all interactions these two motions are quantized

Any update on the topic? It seems interesting.

I just began the problem by treating the collision H+ + H classically. Even with such a simple collision system, the answer is not simple. At high projectile energy, the ionization and capture cross section agrees with experiment. At low energy (under 20keV), the calculation for electron capture underestimates the experimental one. In fact, to treat H2 molecule or He atom, so with two electrons, one way is to take into account classically the Heisenberg principle and the Pauli principle. This was done many years ago by introducing additional potentials to the coulombic ones.

Do you have some paper relevant on that application? I did know about it. I know about some scattering codes to performs collisions, with some approximations done o ease the calculations.

Yes, I have some. Try Cohen, Phys. Rev. A in 1996 if I remember

It was Michael Gryzinski who did most calculations on the classical molecular systems, starting from early 50-ies. One may try 

. Petar Grujić and Nenad Simonović

      INSIGHTS FROM THE CLASSICAL ATOM

      Physics Today, 65, No 5 (2012) 41-46.

      Corrigendum

      Physics Today, 65, No 8 (2012) 12.

as the starting point.