How do we know ##BF_3## has Lewis structure but ##Al_2S_3## does not?

The first thing we notice is that we have a metal and a nonmetal, so we would think about an ionic model.

These elements form the ions ##Al^{3+}## and ##S^{2-}##.

These ions form a lattice structure and we get an ionic crystal.

But apparently no bond is perfectly ionic or covalent.

The electronegativities of aluminium and sulfur are 1.6 and 2.6, respectively. The difference is 1, which is a relatively low value, indicating a high covalent character to the bond formed. However, I am not sure if this difference in electronegativity is relevant when we are analyzing an ionic compound. I learned it in the context of ascertaining the ionic character of a covalent bond.

However, if we think in terms of polarization and polarizing power, then we have an ion with a relatively small radius and high charge (##Al^{3+}##) and an anion (##S^{2-}##). We should expect some distortion in the electron cloud of the anion and this occurrence means the bond has relatively high covalent character. This covalent character would be even larger if the anion were a larger, heavier atom. Such atoms have lower effective nuclear charge and more shells and their electron clouds are more easily distorted.

Question 1: Does any of this mean we can form a Lewis structure for a compound like ##Al_2S_3##?

After all, there is a Lewis structure for ##BF_3##, and ##B## forms ##B^{3+}## ions.

Instead of being an ionic compound it is covalent with a central boron that has an incomplete octet. It does, however, have high ionic character since the difference in electronegativity is ##\chi_{F}-\chi_{B}=2##.

Question 2: How do we know we can't have the same thing for ##Al_2S_3##?

Now, I'm asking this from the point of view of Lewis Structures and VSEPR.

It has been frustrating to study these topics because many things seem ad-hoc.

Here is another example

##N_2O##

One rule of thumb is to assume the central atom is of the element with the lowest ionization energy. That would be oxygen.

Apparently (by way of googling this molecule), another rule of thumb is to choose the element with the lowest electronegativity. That would be nitrogen.

So, how in the heck do we ever know, given a formula, what Lewis structure to build?

My guess is that these are all experimental results, and actually there is nothing that tells you whether oxygen or nitrogen is the central atom other than listing out exceptions upon exceptions to basic rules of thumb.

EDIT: just after writing this I realized that ##O## can't be the central atom because of another rule of sorts. If ##O## were the central atom it would have expanded valence. But only p-block atoms of elements in period 3 or later can have expanded valence because these elements have empty d-orbitals.

I just want to make sure that this is really the way to study this stuff. I'm self-studying Chemistry. It seems like a bunch of cases and some rules.

Question 3: Is there a light when one learns about quantum mechanics?

I do have one more question though. When we do write out the Lewis structure of ##N_2O##, we get



Question 4: Now, ##N## has five valence electrons. It appears only four are being shared in the structures above, and the fifth one went over to the oxygen. Either that or three electrons are being shared, and the fourth bond uses both electrons from ##N##.

Basically you are discovering that simplified models fail when analyzed too deeply.

At the same time you are using intuitions you have built thanks to these simplified models, so they served their purpose.

And yes, in the end QM should give the final answer. To some extent it does - but you may not like the way it does. With exception of the simplest cases solving Schroedingers equation can be done in two ways - exact (which produces numbers, but no insight) and approximate - which produces insight and generalizations, but in the end they are always limited in their applicability, just like models you are using now.