ChemReaX™ is a free web app for modeling and simulating basic chemical reactions. EdSurge and LearnPlatform databases as an online chemistry education. Allows users to construct a virtually unlimited variety of chemical reactions.
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There isn't an easy way to describe all organic reactions, then pile that into a code for people to play with. It ends up being much more complex, and certain codes are good for certain things.With that said if you are still interested, try looking up some information on reactive force fields, that is probably the closest to what you are looking for (ReaxFF or something similar)! You could also check out Chemdraw or VMD which you can use to just draw out structures and do some (very) basic calculations. (VMD will require a formatted input file, but chemdraw is a point click type drawing program)Keep in mind this is an active area of research and requires significant computational resources and time to do accurately. Its really not something that is simple enough to be scripted into a video game.
Sure, you could pre-render movies and play back visuals for selected reactions, but to have customization and have reactions truly calculated on the fly at a high enough level of theory to be accurate for all types of organic reactions is not possible now.W e do not have the storage space or computational resources. As I mentioned above, check out ReaxFF if you are interested in reading further, it seems to be the closest thing to what you are describing.