Can we (in principle) obtain molecular bound systems by modelling fundamental particles and their interactions? Is it possible, at least in principle, to start with the Schrodinger/Dirac/Klein-Gordon equations to model elementary particles and their interactions and to obtain in the end molecular bound systems? In other words, is it possible (in principle) to deduce the laws of chemistry starting from the laws of elementary particles?  
 A: In principle, yes, this is done in theory of atoms and molecular bonds, also known as quantum chemistry. One can begin with Schroedinger's equation and derive much of the observed properties of atoms and molecules - their energy, spectra, bond lengths and stable arrangements of atoms in space (shape of molecules) which reproduce some chemical ideas of molecules (say, the typical angles between C-H bonds - for example, 120 degrees in methane, which is a tetrahedron).
In practice, the calculations get too demanding to do exactly for small molecules, so there are approximate methods, which have some success, but not always. Chemistry is still not merely 'applied theory of Schroedinger's equation' and probably won't be for a long time.
A: Yes, but due to the difference in time and space scales, we have specific models for specific problems to model. Some examples are: First principles modelling (ab-initio approaches), DFT, molecular dynamics; the first two start with Schrodinger's equations and work their way up, molecular dynamics is used in bigger systems using data from the DFT or first principles (usually as a bridge to scale size and time).
