Hydrogen Bonding described with Words (physicists, please ignore)

 I've been reading "Chemistry Essentials for Dummies," just to get back up to speed on basic chem. I just passed the halfway marker, and thus far, I think the book is a bit too facile in its approach. Specifically, it focuses quite a bit on chemistry conventions, like compound nomenclature, but there are some interesting sections.

At some point, I can delve into the nuclear chemistry section toward the beginning of the book, which is definitely the most worthwhile portion in my opinion. However, there's a section on molecular interactions and bonding that I can briefly discuss. Once you get past the imperative covalent/ionic bonding section, the author discusses some of the electromagnetic interactions between molecules that I'll briefly detail here.

I should first note that this explanation is going to seem silly and handwavy, but that's kind of the point of chemistry. These are really just intuitive explanations more than anything. That will likely give you more insight than writing code to approximate solutions to the Schrodinger equation would. Perhaps we can do a blog post on that, but for now, just deal with it.

Well, firstly, we're going to need to establish the concept of electronegativity. Electronegativity is an element's ability to attract electrons toward it when those electrons are part of a molecular bond. Assume we have a full valence shell. So, the number of electrons won't change, though some of them may be shared with another element. As we move across a period in the periodic table, the number of protons in the nucleus of the element increases. Thus, ceteris paribus, the shared electrons are more likely to shift in the direction of greater positive charge. So, moving across a period will increase the element's electronegativity.

However, as we move down a group, the valence shell ends up being farther and farther away from the nucleus. Again, ceteris paribus, by Coulomb's Law, we would expect the attraction between the protons and the bonding electrons to drop off with distance faster than it would increase with increasing protons.

Well, maybe I should unpack that. Let's make a really dumb assumption; we can make a more sophisticated one later. Let's assume that we only have one electron in the entire atom. If we increase the number of protons without changing the radius of the atom by adding more shells (empty shells in this case), then the electron is going to be more attracted to the nucleus. However, if we increase the number of protons by a factor of n and increase the radius by a factor of n, we're going to get 1/n of the force we had previously.

F = k*q0*q1 / r^2 -> k*n*q0*q1 / (nr)^2 = (k*q0*q1 / r^2) * (n/n^2) = F/n

Now, does the number of protons increase by the same factor as the radius as we move down a group? No, that's another dumb (actually quite dumb) assumption I subtly made haha. But it is telling. Without doing calculations, it's probably good to intuit that distance from the nucleus causes the attractive force to drop off faster than adding protons causes it to increase.

Again, these aren't hard and fast rules. You CAN find exceptions. For instance, there are some for the transition metals. Gold's electronegativity is higher than silver's. This approximation seems to hold pretty well for nonmetals, metalloids, and halogens. But again, this is a simplified model that allows us to lets us understand things without touching the Schrodinger equation. We can make our assumptions a bit better by accounting for the other electrons in the atom (we could use Gauss's Law to estimate field strengths), but I doubt we'll really gain more insight from this.

Anyhow, if there's a sufficiently large difference in electronegativity between two atoms in a molecule, they'll likely form an ionic bond. The electron will be so much more attracted to the more electronegative atom that it will be ripped off one atom and move to the other. Less of an electronegativity gradient leads to a polar covalent bond, where a nonuniform effective charge gradient develops over the molecule. The more electronegative atom will better attract electrons, leading to a slight negative charge in a sense on that portion of the molecule. And of course, a small electronegativity gradient leads to a nonpolar bond.

Let's assume we have two molecules with a huge EN difference (I'm going to start using this acronym to save having to write "electronegativity" and opt for writing long explanatory parentheticals instead). We can get this by using hydrogen and one of the high EN elements, like oxygen or fluorine. The EN gradient will be so large that a polarized bond, perhaps even an ionic bond, will form. Thus, the slightly positive hydrogen atom and the slightly negative fluorine/oxygen on separate molecules have such a large charge gradient that they're attracted to one another in a "hydrogen bond".

These are quite weak, less than an order of magnitude weaker than a covalent bond, but they have noticeable impacts on molecular behavior. For instance, the base pairs on either side of the DNA double helix are held together via hydrogen bonds. However, we can also get similar interactions with relatively nonpolar molecules.

 Picture the electrons (or electron cloud... wavefunctions... again, not solving the Schrodinger equation) moving around the molecule, subject to some sort of statistically-describable motion as opposed to being fixed in place. Just by sheer chance, a dipole could form. And with a little more chance, the two molecules could briefly be in a dipole-like state and attract one another. Such interactions are known as London forces.

Alright, it's getting late. I might do a Schrodinger blog post at some point...