Bestand wählen
Merken

# Lecture 04. Group Theory Applications.

Embed Code
DVD bestellen

#### Automatisierte Medienanalyse

Beta
Erkannte Entitäten
Sprachtranskript
are so here's our full reducible representation for a binding question because when we do the C 3 rotation all although little vectors swap places right and so they each contribute 0 2 the character you can also write on the full matrix you see that you get 0 for the character various so let's move on OK so I want to point out here's how we would do this if we didn't have to deal with the basis being on the x y and z axis I'm doing this for completeness if so so it's a little bit confusing right now don't worry about it we're going to go through it again later on but the point is we have to use those rotation matrices and actually put in the signs and coastlines of the angles in order to deal with the the case where the elements that you're using do not exactly not onto to each other so I drew this this molecule you differently with respect to the access system or my basis were the unit vectors I would have to set up my rotation matrix In this way will still get the same answer for the character but we have to to do a little bit differently we can't use the heuristic if we don't have an object that were everything maps onto another element of the basis when you do the operation OK so again that's just for completeness of it we're going to go on if it's not 100 per cent clear right now don't worry we'll do more examples like that later so now let's go back to our original problem that was we want to understand the bonding in the small terms of symmetry so we have a
let's say we have an 0 3 -minus so that not only has the signal was playing but it's got some pie bonding perpendicular to it we know it's perpendicular to it is we know some chemistry OK so here's archive bond and I'm going to go through this because it just did it again it helps you build intuition from some of these problems but they still want talk about the symmetry of the pipeline so we want set this up in a way that it's easy to visualize saw pipelines is it has a at the age the nuclei and we know that it's it's got intensity above and below and it's it's it's a positive on 1 side negative on the other and so we can represent its symmetry it's just a little arrow pointing perpendicular to the signal and so now are basis is going to be 6 directors representing the possible orthogonal so why do we have 6 matters because it's in a three-dimensional space right we could have the pipeline's perpendicular in 1 of 2 ways you could imagine that sticking up out of the plane and molecule which of course we know is the right answer or by symmetry arguments we can also look at the Taiwan's that perpendicular to the single bonds but in the plane so here's where basis looks like again were doing this not because we expect to be surprised by the answer but as practice for some of these kind of problems OK so we wanna know by symmetry which orbitals
conform our and so we're going to consider the In Plain and the of out-of-plane sat separately because it can be both at once right so 1st wearing a look at the ones that are pointing out in this picture out of plane the reducing thing in go through cemetery operations and set up matrices so here is our identity operation unsurprisingly that gives us a character of 3 and looks like it always does and now we do see 3 rotation which in this case everything changes places and we did it in the correct direction it's counterclockwise and so we know that it's going to have a character of 0 because everything changed places c 2 now we have to be careful because were working with objects that can change sign and so we have to pay attention to that so rumor we we represented the direction of the bond with the Alero and so we have to pay attention to the fact that we do see each irritation not only did to haven't switched places but you're turning it over so the change sign and we have to keep track of that In case so if we had that up its character is minus 1 and again we can get that using the shortcut we can say to haven't changed places so they contribute 0 come and the 3rd 1 changes signs that contributes minus 1 yes pursuant to the decision to use the also I have my little arrows all pointing out right they're all the same direction you well so it was so my basis it is those orbitals better going to make a pipe bomb inside represented that symmetry of the pipe bombs as just boleros pointing in the same direction because if the orbitals or out of phase with each other it could make a pipeline rate they have to be all the same direction for that to work and so what we're doing is we're starting with the symmetry of the object that we want to see that being the pipe bombs and were saying which orbitals can contribute to that symmetry and so the other the other thing that's important is remember that I said OK in principle we could have perpendicular ones in the plane but we can't have both at once right because something like this in something like that can make a pipeline together so we're considering 1 said at the time just to make our lives easier I could set up a 6 by 6 matrix for all them but it would be harder that needs to be so we're not going to OK so we need to consider are signs and again if we do a Sigma H. reflection now so again that's perpendicular to the principal access if I do that all 3 of unchanged sign so again we see that the matrix you get totally depends on the basis of depends on what you're applying the operation to so the last time we had these sigma bond vectors but couldn't change when we did that because they don't really have a sign now we're dealing with something that structural and so for -minus once instead of ones on the diagonal there so its characters minus-3 OK so we're almost there to setting up reducible representation for the army out of place and then
we have to deal with the S-3 3 so let's check that I actually do it counterclockwise and I did so were in good shape but again when we do that workstation a couple of them swap places where they may also places sorry and then only do the reflection perpendicular To that they'll change sign then again that is the heart of the improper rotation is the hardest when visualize so it it's going to take practice OK so now we're left with just the signal being so the same thing as before to them change places but because we're doing a reflection not turning it over now nothing changes sign and so that gives us a character at once so we here's are complete reducible representation pipelines In out of playing set saw next step is to reduce it and again reviews the reduction formula that we weren't and I'm going to go through quickly yeah actually looks like I opted to not go through so that is left is as an exercise in student but again news the the formula I had the sliding here I think I decided it was 94 OK so what we get for Dennis Michael that O'Keefe rout of plane we get to double prime and the double prime and I encourage you to you know go through and do this and confirm that you get that make sure that you understand how to use the reduction formula
and now it's considerably in playing set so these are the blue ones so these are the ones that are perpendicular to the sigma bond but they're in the plane of the molecule and we're going to go through quickly so here a C 3 rotation doesn't change the sign of anything it just makes stuff switch places so it's character is 0 again c 2 and then we have to foot the worst thing is signed Sigma each would he think anything change sign no right is now everything is on the same plane as reflected and so that gives us a character of 3 and yes on the other hand if you think of way we need to let's see well so you have to flip it over and so the errors that were pointing this way enough pointing out way the principal axis is the principal axis movie the axis the year that sticking out at you if you do well so you have to you have to rotate about the sea to access which is perpendicular to that yet got so even these these are now in in In that plane when you do this each irritation yourself over so the ones that were this way another when the C 2 is not the principal axis that's right the C 3 is the principal axes the highest water access is always the principal axis OK so let's
style let's try to finish up this example sleeping at least see what the answer is to for practice purposes OK so again U.S. 3 so we rotated 120 degrees counterclockwise and reflected In that horizontal plane which doesn't change the sign of everything so that just gives us a position swap and are vertical planes following a change society because stuff is the plane that were there were reflecting about and so we get minus 1 for the vertical planes and so again we need you to use the reduction formula and reduce said and I'm not going to do it because I think I correctly calculated that we would run out of time if we if we did all that class and so what we find is that we get free the inflamed 8 2 prime plus the prime so homework number 1 next class is actually do those so go through reducing yourself verify that this is what you get and then proved yourself that the orbitals that are involved are the ones that you expect to see involved in that once said OK so I think that's where we are now is worth finished up with what we're going to do with group theory for the moment we're going to see it later in the quarter because it's going to come up we talk about vibrational spectroscopy actually will come up we talk about selection rules preparing regional officer consists of a few minutes left it's distracting when everyone is is packing up and and rustling around all OK Serena secret .period again we talk about selection rules were going to talk about how you know that enables them to 0 in a particular place so 1 way to prepare for that if you don't remember it is know look up the Wikipedia page on even on rule that that's 1 case of this on that's something that is very useful in terms of being able look at intervals and to say that they go to Zurich revealing that's it's something that is very helpful to be able to do so next time when you start talking about rotational spectroscopy so we moved on to the next chapter on right I will see you either at the office hours of exports
Hydroxybuttersäure <gamma->
Single electron transfer
Screening
Oktanzahl
Quelle <Hydrologie>
Explosivität
Altern
Redoxsystem
Chemische Bindung
Watt
Optische Aktivität
Alkoholgehalt
Operon
Molekül
Aktives Zentrum
Metallmatrix-Verbundwerkstoff
Potenz <Homöopathie>
Quellgebiet
Reflexionsspektrum
Erdrutsch
Azokupplung
Vektor <Genetik>
Expressionsvektor
Chemische Bindung
Chemischer Prozess
Oktanzahl
Metallmatrix-Verbundwerkstoff
Computeranimation
Atom
Stockfisch
Spezies <Chemie>
Reduktionsmittel
Chemische Formel
Optische Aktivität
Gezeitenstrom
Molekül
Operon
Paste
Chemie
Systemische Therapie <Pharmakologie>
Expressionsvektor
Redoxsystem
Periodate
Aktives Zentrum
Pipette
Chemische Forschung
Fleischersatz
Kryosphäre
Transformation <Genetik>
Schönen
Orbital
Computeranimation
Transformation <Genetik>
Altern
Nucleolus
Spezies <Chemie>
Sense
Vektor <Genetik>
Bukett <Wein>
Elektronegativität
Krankheit
Molekül
Operon
Orbital
Chemie
Chemischer Prozess
Pipette
Phasengleichgewicht
Metallmatrix-Verbundwerkstoff
Oktanzahl
Gangart <Erzlagerstätte>
Reflexionsspektrum
Computeranimation
Azokupplung
Reduktionsmittel
Redoxsystem
Chemische Formel
Optische Aktivität
Operon
Expressionsvektor
ISO-Komplex-Heilweise
Sekret
Reduktionsmittel
Fülle <Speise>
Chemische Formel
Optische Aktivität
Nitrate
Alkoholgehalt
Wasser
Periodate
Computeranimation