 So as we talk about vibronic transitions, transitions that change the vibrational and the electronic state of the molecule simultaneously, there's one more piece of the puzzle we need to consider. Remember for row vibrational transitions, there were some selection rules for simultaneously changing the rotational state and the vibrational state of the molecule, the selection rules were that the vibrational state had to change by plus or minus one and the angular momentum quantum number that defined the rotational state, rotational energy level has to change by one and the magnetic quantum numbers not allowed to change. So those were our selection rules for the row vibrational transitions. If we're simultaneously changing electronic states of a molecule and vibrational states, there's also selection rules to worry about. They're somewhat similar in this case, the vibronic selection rules are that the spin state of the molecule can't change. We haven't talked about spin in this sense, spin for the molecular spin for a molecule, electrons in a molecule. We'll talk more about that when we talk about the quantum mechanics of electrons in molecules. For now though, I'll just say that those molecules have a property called spin. The spin is not allowed to change and you may or may not have heard of this idea of molecular spin in perhaps an organic chemistry class or maybe even an analytical chemistry class. If you've heard molecules referred to as singlet, being in a singlet state or triplet state, for example, that's talking about the spin of the molecule. So all we need to know for right now is if two of these electronic states have the same spin. For example, if the spin for this electronic state is s equals zero and the spin for this electronic state is s equals zero, then transitions between these levels and these levels are allowed. On the other hand, if there were some other state somewhere, if this was a spin one state, which we would call a triplet state as opposed to a singlet state, if there's another electronic state with spin one, then transitions between this singlet state, s equals zero state, and this triplet state are not allowed. So what that means is transitions between s equals zero states are okay. Transitions between, for example, an s equals zero and an s equals one state, that would be not allowed. That's forbidden by the selection rule. There's another restriction, however, now that we've got this idea of these vibrational energy levels stacked on top of an electronic, different potential energy surface for this electronic state and for this electronic state, remember that what this diagram is telling us is how the potential energy depends on bond length or distance between distance of the bond in this diatomic molecule. Another feature that determines whether a transition absorbs light, remember, is that intensity ends up being proportional to the transition dipole moment. So for some initial state i, going to some final state j, we need to calculate this transition dipole moment and if that's large, or in fact even nonzero, the molecule can absorb light to make that transition. If this integral is zero, it cannot absorb light to make that transition. It's forbidden. So this is for the transition from initial state i to final state j. So recalling that fact, this integral needs to be nonzero and fairly large in order for the transition to happen. It tells us another feature about these vibronic transitions. These vibrational states, this would be the ground vibrational state, first excited, second excited, various other excited vibrational states. The wave functions for those states, the ground state looks like a Gaussian. The excited states, I'll go ahead and just draw, let's see, the 1, 2, 3, 4, 5th state will have five lobes, so that's going to look something like this. Likewise, up in this excited electronic state, it has a ground vibrational state that looks like a Gaussian, 1, 2, 3, 4, 5, the sixth vibrational state is going to look something like that. So let's think now about the transition dipole moment and how it affects which of these various transitions are possible. If I imagine making a transition between this state, the ground state in the ground vibrational state of the ground electronic state, if I want to make a transition up to this state, so this is my i and this is my j, ground vibrational state in the excited electronic state, if I imagine what happens as I compute this integral, this wave function of the ground state, the Gaussian down here, doesn't have much overlap at all with the Gaussian up here in the excited electronic state. Everywhere I multiply those two functions together, either the ground state or this destination state is going to be small or zero. Everywhere that the ground electronic state is zero in this region, the wave function in the upper state is zero. On the other hand, everywhere that this wave function is non-zero in this region of bond links, the lower wave function is zero. So the product of those two wave functions is zero and that's going to ensure that this integral will come out, if not zero, very, very small. So that transition does not happen. The transition between this ground state and the ground vibrational state of that upper manifold doesn't happen. On the other hand, I can make a transition up to this vibrational excited state in the electronic upper well. And that's because the wave function I've drawn here does have some support, does have some non-zero values of the wave function in the same place as the ground state has some non-zero regions of the wave function. So the product between this ground state and this excited state is going to be non-zero. Some area of those two wave functions overlap and that transition is allowed. So this one is okay. This transition that I'd have to draw with a tilted, a slanted line. That one is forbidden because the transition dipole moment would turn out to be very small. So what that tells us is this general idea is called the Frank Condon principle. So I can phrase that in a couple of different ways. Connecting it to this equation, what it means is that a transition between a vibronic transition between some vibrational state in some electronic state and a different vibrational state in a different electronic state, that transition is going to happen only if there's a good overlap between the two wave functions. So a vibronic transition that only occurs if the initial and the final wave functions have some overlap. A simpler way of phrasing that same principle, this Frank Condon principle, the way most people think of it after they've learned it, is notice that the transition that was allowed in this case is a transition that goes straight up. When this molecule, if I draw a line straight up, I can encounter the wave function above here. If I have to draw a line that's not vertical, if I have to draw a line that's diagonal in order to reach the other wave function, that's a transition that cannot happen because I've had to draw the line diagonally to reach a different portion of the bond length axis. So essentially what that means is transitions that allow the bond length to remain constant and move vertically up this diagram are allowed. Transitions that are not vertical are not allowed. So a different phrasing of this Frank Condon principle would be that only these vertical transitions on this Vibronic energy level diagram are the ones that occur. So that's very helpful in telling us what transitions are allowed, and in fact if we look a little more closely at which transitions are allowed both in excitations, how to get from the ground electronic state up to some vibrationally excited state in the upper electronic potential energy well, and also what energy levels, what transitions are permitted as we fall back down to the lower energy level, that's going to teach us something very interesting about the types of light that's absorbed and emitted by different types of molecules.