I was reading this question and the answer by user EricBrown to it, and this got me thinking about covalent chemical bonds.
The way I was always taught is that a single bond contains 2 paired electrons, a double bond 4 etc (The Lewis dots drawings always show this nicely). In his answer Eric mentions that the whole definition of single, double etc bonds is ambiguous because there haven't been measurements of the electron density. This notion strikes me as odd, because a simple googling gives me articles like this: How similar is a molecule to another? An electron density measure of similarity between two molecular structures Int. J. Quantum Chem. 1980, 17 (6), 1185–1189. But it did make me think about the way the different types of bonds are defined.
I read up a bit on the Theory of atoms in molecules and indeed this theory only specifies 1 bond type: the line with maximum electron density between two nuclei. According to the theory this line is unique for a given pair of nuclei in a given molecule. I could imagine that a molecule which has a triple bond (6 bonding electrons in the 'classical' theoretical sense) would have a relatively high electron density along this maximum line as compared to e.g. a single bond.
My question is: if we would be able to measure the electron density in a molecule (are we?) couldn't we use this to define a relation between the value of the maximum electron density and the notion of a single, double or triple bond? Or perhaps use the spread in electron density between the nuclei for this?