My question is related to the edge between Subatomic Physics and Chemistry, but I decided that here is the best place to discuss it.
As we all know, Theoretical Physics is a well developed field of knowledge, able to describe the very tiny forms of interactions. However, after some researches for some kind of formula to perfectly describe the interactions on the atomic level (not subatomic), more specifically, a way to calculate the strength of chemical bounds, I keep comming across frustrating highschool explanations, such as
ionic > covalent > H-bond > dipole-dipole > van der Waals
The most precise data that I was able to find comes at page number 20 and 21 of this pdf, that apparently shows some experimental results (I'm guessing).
So here is my question: is there really a unified formula? What if I want to simulate chemical interactions (proton-by-proton, electron-by-electron) on a computer, is it that complex to do, even assuming that I want a simple simulation of about 20 atoms?
Edit: When I reffer to calculating chemical bonds strength, I also include predicting many other chemical properties, as electron affinity or reactivity of the elements, which are all related.
Note: I can accept as answer any pdf that clarifies my question, because I wasn't able to find. Maybe I'm looking it with the wrong key-words.