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In Physics, Newton's laws are enough for many applications. Sometimes, relativity must be used instead or complementary, and sometimes, Quantum Mechanics.
Is this the same case with Chemistry? Are there areas of Chemistry where the simplification of electrons as little particles orbiting the nucleus at distances proportional to their energy level is possible? Or does all of modern Chemistry must use Quantum Mechanics? At what point Chemistry "breaks" if the particles and orbits model is used?
There are two distinct approaches to model chemical systems, namely Molecular Mechanics (MM) and Quantum Mechanics (QM).
QM uses quantum physics principles to predict the behavior of molecules. this approach is more accurate and more computationally expensive.
MM models molecules as balls connected with springs. This approach is relatively cheap, but less accurate. It requires calibration (you need to have experimental data for distances, angles, dihedrals for atoms you want to model). It cannot model transition states. But again, it is very cheap.
Molecular Dynamic simulations (MD) studies big molecules over long periods of time (long is just microseconds, but for a molecular simulation it is long). You have to use MM here, because you cannot afford QM.
So, if you want to model a small molecule (like acetone) you should use QM. But if you want to model a large molecule such as protein folding, or docking (of a small molecule to a protein active site for example), then you have to use molecular mechanics.
You can also use a QM-MM approach when you model a small and important part of a protein with an accurate QM method and the rest of the protein with cheap MM method. ONOIM is a common approach to do that.
So, do chemists use non-quantum mechanics representation of atoms and their interactions? Yes they do. Whenever they use MM they ignore quantum effects.
Do they use point particles orbiting nuclei as the model? Not really, they use springs connecting balls in these models.
Bohr model of atom was accurate enough to produce valid predictions. So in that field you can use Bohr's model. But in practice this is rarely needed.
Organic chemists (usually) don't care about the "implementation" of the reaction. For ethanol dehydratation reaction all they use is:
(1) Ethanol is an alcohol with a structure R2CH-CR2 OH (important parts are bold, not important parts are labeled as R) without any cycles (cycles might prevent dehydration sometimes). It doesn't have any other active groups (no esters, amids, thiols, double bonds to worry about).
(2) Alcohols that fit R2CH-CR2 OH template react with H2SO4 in three ways: (a) dehydration (2) formation of ether (3) formation of R-O-SO3H (at low temperature).
(3) Yes, I can dehydrate ethanol using sulfuric acid. I need to run the reaction at higher temperatures. I don't know how to decrease yield of ether. I will google the procedure (or check it in scifinder).
So, organic chemists just accept the rules and combine them to get the desired result. They don't really care what exactly was electron doing when all this stuff was happening.
More advanced chemists use reaction mechanisms, but there they operate such concepts as "acid", "base", "nucleophile" "electrophile", "anion", "cathion", "radical". They ignore the quantum physics behind the process. They just say: "this is a strong nucleophile, so we should protect it first". If they want to know they can talk to theoretical chemists.
When the fixed-orbit particle model is taught in general chemistry classes, it is usually presented as Bohr's fixed circular orbit model.
However, this was not the culmination of the deterministic-orbit particle model. In 1916 Sommerfeld expanded the model to include precessing elliptical orbits, and made the theory relativistic. The varying of the eccenticity of the ellipses permits multiple angular momentum values for a given energy.
The Sommerfeld relativistic model correctly predicts the fine structure of the hydrogen atom.
In this one aspect, the deterministic-orbit particle model is superior to the non-relativistic Schrodinger model. The Sommerfeld model correctly predicts the fine structure, whereas the Schrodinger model does not.
