If you wanted to do that, you would have to assume that the positron has a classical trajectory which is of course a severe deviation from the fundamentals of quantum mechanics unless you want to work within the framework of the fringe De Broglie-Bohm theory (https://en.wikipedia.org/wiki/De_Broglie%E2%80%93Bohm_theory).

If we ignore this major caveat for a moment, you can in principle treat a positron like a "very light cation" with a mass of 5.5E-4u and calculate an "MD trajectory" with the interactions you get along the way; former colleagues of mine tried that for electrons when they wanted to estimate the height of repulsive coulomb barriers in multianions, but the result was not particularly satisfying, as far as I've been told.

An additional problem would of course be the neglegt of annihilation probabilites in that process.

We do only for small molecules for positron and other particles it not possible

Yes, you can but not with standard MD codes. You may want to use something like quantum trajectory (Bohmian dynamics) or Path Integrals to recover quantum character of your positron. Also, there is a question of you care about electron-positron processes or not. Overall, one can come up with a decent model for simulation of positron. You probably will need to do adapt some code to allow treatment of your problem. I think that you best bet is to go into path integrals methods, as there are some free codes available.