Not sure if this is a physics or chemistry question. But if the motion of atoms and it's particles can be described by quantum mechanics, then is there a software that simulate full atoms and it's boundings, in a way you can visualize them, and that can be used, for instance, to throw 2 molecules together and watch them reacting?
There are many, many algorithms and pieces of software to do this. In addition to Molecular Dynamics, there are also methods based on statistical simulations in Quantum Monte Carlo, and density functional theory as implemented in programs like Quantum Espresso. It is a simple and worthwhile exercise to program these things yourself - if you wish to study the oscillatory behavior of a molecule subject to some arbitrary external potential, you can do this quite readily using basic programming and visualization tools provided you establish the proper functions and equations to describe your system.
I will note that these algorithms all have explicit ranges of validity and underlying assumptions, and one must very carefully understand the limitations before interpreting the results. In many cases, the accuracy and precision of the algorithms will be questionable, because assumptions at some level have to be made to reduce the system size since not even the most powerful supercomputer can handle a calculation with anything approaching a macroscopic number of particles. Nevertheless, they can provide some sense of the starting point and can give insight into trends.
EDIT: Car Parrinello Works!
The criticism below applies only to the type of molecular dynamics done using molecular potentials, as exemplified by CHARMM. This is the only molecular dynamics I had been exposed to, and it is total crap.
There is a second kind of Molecular dynamics which includes the valence electrons, a core potential, and an clever algorithm to update the valence electron fluid. This is the Car Parrinello method. The Car Parrinello method contains just the right amount of information to do a quantitatively correct simulation, it is the ideal computational dynamics, and I am stunned to learn about it. Thanks to Richard Terrett for pointing it out.
EDIT: Answer to Question
Use CPMD. If your molecule is in solution, use CPMD plus a brownian random force representing the effects of the solute.
Criticism of everything else
There is software which claims to do this, it is called (non CPMD) Molecular Dynamics, and Molecular Dynamics is often used in Chemistry and material science to produce simulations which the proponents claim are quantitatively accurate to predict the detailed microscopic motion of say organic molecules.
The principles behind this software are fundamentally deeply flawed, and, without huge modifications, it simply does not give quantitatively accurate results. Molecular dynamics doesn't quantitatively work for anything at all beyond the homogenous non-conducting solids and small molecules it is calibrated to match.
I consider this a big problem, since a lot of research money goes towards producing this software and calibrating it, and there are a lot of people involved in promoting this stuff, which is a total waste of time and money.
What is Molecular Dynamics?
The idea is to model each atom as a point, and to give a force-law between adjacent atoms, of each different type. So that there is a C-C force law, which models the preferred bond-angles, and a H-C force law, and and O-C and an O-O force law. Then you add up the forces. Then you correct the model for three-nucleus interactions, like a H-H-O interaction which fixes the water bond angle, and so on, until you get a reasonable match to a large swath of experimental data.
Then you take a molecule where you know the structure, and you simulate the atoms using these force laws derived from simple molecules and monatomic solids. The idea is that you are getting some approximate picture of the dynamics from the structure only. This allows you to get a dynamical picture of chemistry
Molecular Dynamics Is A Complete Fake
The reason Molecular Dynamics fails is that the relevant electronic and electromagnetic forces between atoms and molecules are not at all local, not even to a good approximation, and the fundamental approximation in Molecular dynamics is that you can model them using local forces, local pushes and pulls that don't depend on the global positions of far away atoms. These forces are assumed to be mechanical, like the forces in a tinkertoy model, and this means that forces transmitted like sound waves between atoms, while in actual molecules the relevant forces are often purely electronic and grossly nonlocal.
It is simple to illustrate this using symmetric molecules: if you have a Benzene ring, the electrons propagate around the ring, like a wire conducting a current, and these electron currents give the ring rigidity, like a microscopic stiff metal wire. The mechanical properties of Benzene cannot be approximated by a model which does not take into account the delocalized electrons in the ring. The electronic currents is disrupted by moving the carbons, and they transmit forces at the speed of electron-density-variations (the orbital speed of electrons in the Bohr model, much greater than the sound speed).
This is not an atypical situation. The molecular backbones of DNA, RNA contain delocalized electrons, and the mechanical properties of the molecules are determined by the regions where the electrons delocalize. You just can't predict the stiffness of DNA by knowing the stiffness of two-atom or three-atom sub-parts, without knowing the easy paths for electron delocalization.
This problem is nearly impossible to fix, because adding more nonlocal forces requires sophisticated calculations which are fundamentally different type than 2-body and 3-body potentials. They require a seperate fluid flow model over the atoms at the very least, which will give the delocalized electron flow.
Is it fixable?
I think that the fundamental idea of MD is wrong, so I don't hold out any hope for it being useful at any time, ever. But a different idea might do the same thing correctly.
In order for something like MD to work, it must take into account at least:
Most importantly, even if you know the exact forces, the idea of simulating molecular motion by accelerations and collisions is simply idiotic. The simulation should be at the very least stochastic, not deterministic, so that the momentum flows through each local region is found by Monte-Carlo, while only the slow global variables (like the overall shape of the molecules) are simulated by stochastic dynamics. The little things are always either frozen out (like electrons) or in thermal equilibrium (like jiggling nuclei or small molecules).
CPMD fixes the main issue, of electronic delocalization. This issue is so pressing, because without it, molecular simulations are basically fraudulent.