Software to simulate and visualize atoms?

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 to add: See giant list of software applications for Quantum Chemistry