 Hi, well, I'm Steven Eschiaveni, and I'm here to tell you a little bit about how wave-like properties of electrons are connected to and lead to covalent bonds. So the first idea that is here is that electrons have wave-like properties. And like any waves, like if you want to think of a water wave, water waves over time, there's a high part of the water wave and a low part and so on, the term that we're going to use for this part of the wave that's above normal, we're going to say that that's a positive phase, if you like. And then there's a negative phase of the wave and a positive phase of the wave. Let's just refer into the amplitude of the wave. And I'm using this symbol psi to indicate the amplitude of that water wave, but it can also be used to indicate the amplitude of the electron wave. And we're accustomed to thinking about these wave-like depictions of electrons as orbitals. That is to say, here's a 1s orbital, and it has this spherical shape. So how do waves manifest themselves in this picture? Well, what happens, what a way to think about it, is that at this point in time, the phase of that orbital is positive, kind of like that. And then later on, the phase of that orbital is negative, and then the phase of the orbital is positive again. And so on. And so we just imagine the phase of all orbitals oscillating from positive, negative, positive. And I've just kind of indicated that here. Same thing happens with a p orbital. In a p orbital, we have two lobes. And what happens is that when one side of the p orbital, one lobe of the p orbital, is in a positive phase like that, then the other one is in a negative phase. So p orbitals, you can kind of think as doing this kind of thing. But just like with any other wave, those phases change over time. So given all that, the question then arises, is what happens when an s orbital from one hydrogen atom, let's say, interferes with the s orbital from another hydrogen atom? And that's what I've kind of drawn here. There's the nucleus of the hydrogen atom right in the center there, and there's another one there. And I've drawn these in a way that they both have positive phase at this particular instant in time. But of course, if they're locked in phase at the same kind of orbital, then what will happen is that when these both go negative, then they will still be in phase. So the overlap of waves when they are in phase kind of has a generic term, and that's called constructive interference. And the same way that you can imagine waves of water which are coincident with each other and in phase, they tend to produce an even bigger wave. That's what's happening right here, especially in the overlap region. So what I've indicated here is that when there's constructive interference between the orbitals of two different atoms, we have a bigger wave amplitude, and that ultimately translates into a higher electron density in between the nuclei. That higher electron density corresponds to electrons having simultaneous attractions to both positive nuclei through Coulomb's law, which in the end is what we understand to be a covalent bond. So there's one more little piece of the story. You can imagine that there could be constructive interference when the orbitals are in phase with each other, the orbitals from the two different atoms. What happens when those orbitals are out of phase? Well, what happens is that they tend to interfere with each other and they produce a, they erode the amplitude of the wave right at the point where they intersect because one wave is high and the other one is low at the same time. And I've kind of drawn that here as a positive phase, negative phase here. That erosion is called destructive interference and it leads to what we call a node between those two orbitals. And these don't lead to bonding because there's not a buildup of electron density in between them. These orbitals end up getting called anti-bonding orbitals, whereas these end up getting called bonding orbitals. Okay.