 All right, so if we want to know what point group a molecule belongs to, the procedure we have at the moment is first we identify all the symmetry elements that the molecule has and then we can go searching in this table and find which of these lines corresponds to the symmetry elements of the molecule and then we've identified the point group. That's fine, it works just fine, can be a little annoying to have to identify all the symmetry elements and it's particularly error prone because if you miss one of the symmetry elements then you won't perhaps identify the right line on the table. So it turns out there's an easier, more convenient, less error prone way to identify a point group and you can tell that from looking at this chart and seeing, let's say we found not all the symmetry elements, let's say we found a sigma v symmetry element in the molecule. Certainly not all of these point groups have a sigma v, the c and v point group does, here's another sigma v, so this point group does, but only a few of these point groups have a sigma v. So if we've already identified a particular symmetry element we've already eliminated many of the point groups in this table. So what that means is instead of looking through the entire list, there's, if we bring up a different approach for finding the point groups, this flow chart gives us an easier way to find the point group. So let me show you how that works with an example. So let's say we have a molecule, one that we haven't talked about yet. So there's an ethylene molecule, planar molecule, so I've written it in the plane of the board here, so let me, just so we can picture it in 3D, let me draw some 3D axes. So there's a z-axis and an x-axis and the y-axis, each of which bisects the molecule in a particular way and this molecule would be in the xz plane the way I've drawn it. So now let's go ahead and start using this flow chart to try to figure out what the point group is of this molecule. So just follow the steps on the chart. We ask first is it a linear molecule? No, the atoms of the molecule aren't all on a straight line. It's a planar molecule. Don't get planar confused with linear, but it's not a linear molecule. So no it's not linear, so we go down to this step, find the principal axes. So the principal axis, what that means is we're looking for a cn, we're looking for a rotational axis with the largest value of n. So we can find some c2 axes for this molecule. For example, the z-axis is a c2 axis. If I spin the molecule by 180 degrees around the z-axis, I get the same molecule back. So the z-axis is a c2, the x-axis is also a c2. If I rotate the molecule in this direction, it's not changed. Even the y-axis is also a c2. That would correspond to spinning the molecule in the plane of the board 180 degrees. But there's no higher n c-axis. There's no c4 axis or no c3 axis. You might be tempted to think that the y-axis is a c4. But if I rotate the molecule by 90 degrees, then that double bond is pointing up and down instead of sideways. So that's not a c4 axis. So our largest cn axis, our principal axis, is the c2. Any one of these c2 axes, we can take our pick. So then we have a choice. Did we find no rotation axes? Did we find a single cn axis of some sort? Or did we find more than one cn? Yes, we did. With n larger than 3, larger than or equal to 3? No. The rotational axes we found were c2's. If we had more than one c3, then we'd have one of these tetrahedral or octahedral or icosahedral point groups, perhaps. But instead, we just found some c2's. So we follow this line. c2 axis that we found, the n that we found was a c2. So we found an n equals 2 c2 axis for our molecule. So n is 2. Are there two additional c2's perpendicular to the one that we found? And yes, that's exactly what we saw. If our principal axis is the z-axis, let's say that c2 axis, are there two additional c2's perpendicular? Sure, that x-axis and the y-axis, as we've seen, are c2 axes. And they're perpendicular to the one that we're calling the principal axis. So yes, we do have two additional c2's. So we follow this line. Then it asks, is there a sigma h? Is there a horizontal reflection plane? So if this, if we've identified this as our principal c2 rotation axis, it's asking, is there a horizontal reflection plane perpendicular to that principal axis? So the perpendicular plane would be the xy plane. So if I take this molecule on the plane of the board, I reflect it in the xy plane. Is that a symmetry element? Sure. This h will reflect onto this h. This h will reflect onto this h. The two carbons are in that plane. So that is a sigma h symmetry element. So the answer is yes. And then we've gotten as far as obtaining an answer to the question, our value of n was two. So we've identified that the symmetry, I'm sorry, the point group of this molecule is d2h. So c2h4 ethylene is in the d2h point group. And that was a little bit easier just having to answer these few questions than having to identify all the symmetry elements. For example, there's some other sigma planes. There's some sigma v planes that we didn't have to bother to find because once we had answered these questions, we knew the point group had to be d2h. So using this approach to finding the point group tends to be a little less error prone because you can answer specific targeted questions. You don't have to find all the symmetry elements of the molecule. So hopefully that makes it easier to identify point groups.