Is there such thing as well defined physics and math for atomic interactions?

We have a lot of good Newtonian physics simulation software out there (Bullet, PhysX, Havok, etc.), but I see none good for simulating atomic interactions (going deeper). I like to build one for educational and gaming purposes, but I need some good references (book, paper, ...) to implement the logic. Any suggestions, critics, etc. are welcome. For now, I have been looking into dozens of WIKI papers, but all speak about the atomic structure and not about their interactions.

• Thank you for the insights. Will start with something. Basic rules for atom interactions is Exactly what I need. Like if I put 2 atoms besides - do they repel or attract based on their properties and what happens when I smash 2 atoms together at current speed, and so on. I think the phet simulation gets close to what I need, but it's not complete and miss the theory behind that simulation. – John T Aug 16 '20 at 12:16