Lecture 11. First Midterm Exam Review.

OK so my plans for today is to go over the example Seehofer we get all of that could have any questions before we start yes I don't know when you figure expect so also here's how it works we agreed that the not quite done that they're almost and I left at 11 30 Friday nite trading and stuff like there it's a lot of people in the class of these things are really difficult agreed and there was a lot of perfect credit so it takes a really long time and we will finish it today then we're going to send it to the army service that standard and that will be it will be sent there today and then after goes there I have no control over what happens to it takes some however long it takes and I know the next question you can ask is willing to give you the scorers no because here's what happens then I give you score and you find out that you got 98 per cent and then you e-mail me and say Why did I miss 2 points and I don't know that exam and so on you know it just we just have to wait for the standard and it takes like takes over all my impression from you from reading it is that yeah there were some things that most people really got and there were some things that you know maybe not so much but you know overall it seems pretty reasonable given that it was a very blond exams so anyway let's talk about that any more questions before we do that and so on can we enlarge the image of the army I don't know how to do that by

anyone who knows how to use this thing is welcome to come and try there are some extremely cryptic menu options maybe there work we had Weldon sir so now the other thing is so now that this is large it's going to be our young have to move this remedy but on the screen and I can't see it so please tell me if it's if it's not visible OK so

we start with the short answer questions these are pretty straightforward a sinus molecule to appoint the DOH 3 on the assumption that it's really cold is important because that means that you have to the strongest thing and assume that everything is rigid and so that means that year .period group and C 3 H and I know that this exact example was done in discussion so that the discussion it's important OK so the next 1 he lets the maximum the generous orbitals for of molecule in the US standpoint the highly this anybody know yes that's right for you so you look on the character table which on behalf of 1 year and this particular character table doesn't have the Ostend .period route which is why I had to put it up for you but what Stewart for yes 8 so here goes see that character table and you look at the cemetery species Europe that is in the use and ease but no teaser anything else we know that some tree species there called me something are doubly degenerate so the highest illiteracy phenomenon is too so really straightforward if you know how to do it and otherwise not all right so next 1 what symmetry species present as orbital warned in Indian Finnerty age .period so this is another 1 where you just go look at the character table so that the Infiniti age .period group In the end if you look it up on the character table what you see is what you know as we known as orbital is spherical and so it's going to be invariant to any transformation and so it should just have ones for Everything under that symmetry species and so we look at the top 1 here we have 1 1 1 1 it's invariant to every transformation and here it's called Sigma G

plus so we've seen those being called you know a 181 new prime fairy AG things like that in this case it's called synergy plus and again that you just get that from looking at the at the character table and you know I gave you .period group were you haven't you haven't looked at it much probably and it has a bunch of crazy stuff that you don't recognize but it doesn't matter how you look for is what specific species that invariant every transformation OK and on an army version be there was seeing the so similarly you just check out the character table and here it's a one-word signal lost and so even 1 of those was accepted because the equivalent arrange the last 1 of these was just testing your ability to use directors station and so the question is we want greater expression for the probability that and that assistance in some states with new equals 0 in Tables 1 will later be in estate near equals 1 Jaipal 0 and so on all I need to do is put this indirect irritation and that's it we accepted various other variants of that like if you put new equals 1 G equals 0 India In the brackets that was also fined so there were there were certain trivial variations of that we accepted that that's a good question OK question why do we not include the dipole operator and because we didn't say that those 2 states were connected by the cooperate so this is just this is just a production and if if we were talking about a particular type of spectroscopy then we might say that they're connected by the Eiffel operator or connected by a you know some of the operator but here that wasn't specified so that's just not that's not part of problem so this is this is really general and we're talking about would be for the particular case of of vibrational spectroscopy I see where you're coming from because that's a reasonable thing to do he was back yeah we didn't we didn't specify that are so now we get to matrix representations so you're given some information here about the molecule on you're told that it's square planar you know what shape it and your basis is the PC orbitals on all the other islands and notice it's not a linear combination of so we're talking about the individual pieces Keesee orbitals and not the molecular orbital and so the 1st stages to just this molecule and drier PC orbitals when we said all in phase with each other so you really have to draw this to to get credit as long as the answer was right but it was certainly easier to see what you did if so and we can label them and then we need to look at what happens when you do different things to the the molecule OK so for Sigma being we start out with vector being the and we end up with so I am taking this through an access that's cutting through 1 and 3 that's the vertical plane that I'm using there was the whole bunch of different ways to do this depending on where you put your vertical plane and John Marks sat there forever working out every possible the way to do it so no we did said at 4 various ways that you can set up we actually give people credit for me doing it with the died he broke planes as well just because it's kind of a individualized so no good enough because the idea was you know I do you know how to do it and we didn't we didn't really penalized for for that OK so in order to do this we have to enforce switching places and nothing changes sign so if you do like this we get 1 stays the same 2 ends were for what 3 stays the same and for and support to was and that's the matrices do that again you could go the other way and that's equally correct if you went in between like this axis that actually the the usual claim but we give you credit for anyway but that OK so the next 1 is to and I prefer to set this up on and on said Agassi 2 is the same as the principal axis of course there are 2 other C to Accies that perpendicular to that and we give you credit for so if it wasn't so you know ideally you should set up so that seek to is the 1 that coincides with the principal axis than the other 2 were C to primacy to double prime but we don't worry about it credit if you set up any reasonable C 2 operation RE N if from if you set it up on your principal axis you get something like this so 1 swap places as a radius of OK 10 again there are different ways to do it depending on how you define your seat to access you could define it perpendicular to your principal axis and faltered over you know that's where this way in the plane that was also fined a case of than the last 1 is to just find the arm the characters for these matrices that we found and of course you that I just adding up the diagonal so for for that 1 it's 1 wants to your right I carried my handwriting and that 1 is 0 this 1 is to Wunnicke adjusted by just 1 glance at it too quickly OK so that's he said of the Matrix representations of Everybody OK with that women have questions the right call for the most part people did reasonably well with that there were you know once a while there was somebody mistaking the operation but mostly they're pretty well but I think we should look at the other version too because there were different different operations given OK so are basis is the same but we also did the inversion so if we do new inversion then 1 and 3 swap places and to enforce what places the 2 groups so one-in-three swap 2 for staff so that's the inversion and nothing changes signed here were just workers flipping workers in Burgundy the positions of the objects this is virgin In yeah I was just thinking about that I realized the signs do change and again again John market right on the it's just it's it's hard to win it up in front of everybody and it takes manages to think about a case so you're right beside you change and we did get that right so you understand why rightly the take the coordinates of each position and X to minus X for each 1 miners wives egos magazine so they do change like OK so now we for rotation and if you do it counterclockwise you get you get this and your character for that equals 0 of course you can also do it clockwise and we can that too if you do it do it clockwise he just get this matrix reflected about the diagonal wants the same thing yes he has made it all it does yeah because yeah it does all yeah adjusted and you end up with With the column beginning actually you have to think about that for a 2nd OK so if we inverted and they're all the same phase then yeah we end up with the same thing in all negative OK so now let's move on to the island the matrix representation earlier the is a theory the applications OK so these were this OK so the group theory representations this is where we set up a basis for our problems and to learn about bonding and the Roman active modes From the symmetry and so the 1st part Is that so this best thing work it says brother Lewis structure and double check it and what is the hybridization of the central and that's just a hint for you to make sure that you draw the thing right and you then get it on the right .period OK so what we end up with is we have we have a saying so when the other 1 the army on the other 1 the molecule was was chlorine into fluoride which some people don't read the name and interpreted as CIA 5 years lucky people because you get in the same quarter you that so if it turned out basically OK I'm so we we countered that but you know I get support to read the whole thing carefully like it's a it is you know it is easy to misinterpret that's that's why also rapped name OK so and this is a real molecule it does really exist here's are the principal axis and the reason I wanted to draw the Lewis structure and look at it is 1st of all you have to count electrons to know that you get that lone-parent flooring and that tells you the shape of the bottle and also we want know the hybridization of central and because that's going to help us check check answers and so that's the hybridization right because we have you know we've got the we have 6 orbitals and play on the bromine and so we have the US and the 3 peas and to duties and this is you know just from general chemistry knowledge OK so now does that mean that all the baubles there are involved in the bombing no right because 1 of them is taken up by a lone pair so the answer that we expect to get to involving sorrel 3 keys and ID but the extra duty is taken up by the lone pair so it's not going to be involved in the bomb OK so having a set this up and drawn molecule we find that it's in the .period Group C 4 B and so if you got it wrong .period group the rest of this is really really hard because bad things happen and it doesn't work out right and you get fractions and things like that but so here is what we get for it Bob reducible representation OK so if we look at this and use the shortcut for figuring out you know what the characters are for this molecule are basis is the 5 bonds since that's all were asking about that's what we wanna know and so for the identity we get 5 if we do a C for rotation so that's like I'm holding the top flooring and rotated 90 degrees to the top 1 changes the site atop 1 stays the same and all the rest us block so that's 1 behind USC the same thing happens the 1 the 101 the principal access doesn't change in the restaurant and so now here's the hard part figuring out what is saying Monday in what is Sigmund so these are all vertical planes but meaning they contain the principal access by the definition of a day he'd role-playing is that it is oriented perpendicular to some C 2 axes and so that means that the vertical plane is the 1 that cuts through 3 of these missed 3 of the Florence and indicted or 1 is the 1 that goes in between because it goes with that sure so where were assuming that our C to access coincides with the see for access to the principal axis break and and ask you in this case because there's no ability to access their images to Obama but they're they're both the Orient about right and then on the vertical plane you goes along that ended that the definition of a dying he drove claim is that its purpose is bisects 2 perpendicular C 2 axes so that's why it goes between me and the other and so on without I want you to know you have to because it is you can go this way way so so I'm saying that so my my 6 signal the goes through it these for Adams and Sigmund the cuts between the Florence so like if I want to thank all this acts and that's why I can rotate 180 degrees about a liar right and it works and then the dike proclaimed cuts between so that said if you've got these backwards so if you put 1 year and 3 there you get something that works out pretty well and you just get a different and your role involved in the bonding and I think we took up 2 points if you do that you got almost all the points for forgetting that it's easy mistake to make the hard to visualize and you wouldn't know you had done it because you get an answer that looks completely reasonable so that was a very very minor issue .period twice OK so now that we've gotten this far we need to reduce our representation and learn what happened to bond OK so we are going through the on the various symmetry species from the character table and so here we go in case I get to a once and twos everybody remember how I'm getting this I went through fast yeah OK so I got to a ones and then for H E I am not going to work it out but I got 0 the 1 is 1 the 2 equals 0 then he was 1 OK so that's the reducible representation yes We Can you have a different basis definitely not because the whole question is on you know we want to find out about the signal bonds and there's only 1 set of signal once although maybe maybe a misunderstanding your question what what what you mean that is well so let your your basis is what you set up at the beginning that is so we started something that we know the symmetry of that's what we want to to find out about and see you select basis in the directions of all the single bonds and you don't know which your role is going to be involved in match at the beginning right that's the question will it but this year saying you look at the character table and then decide our priority before use of the bases which will going involved on it's not a good idea right because it might work in some cases but it might not work in other cases so you really do need to work through the the you know reducing representation to get your future tree species I'm not saying that whatever work it's just that it will always work so it's it's sort of interest you OK so we have a reusable representation and we reduced it and so now the next step is to look at the character table and see withdrawals are involved in the so this is really important because I was surprised at all you know I know it's at that time pressure situations but a lot of people got this far and did everything exactly right and then put down nonsense for the orbitals which is kind of sad so you know it's in with it's important to go over this because I want to make sure that you that you really get it for the final OK so now it's time to take a deep breath and think about you know what the answer me and does it make any sense OK so we look at the character table we know that from our readers for representation that there have to be to orbitals involved that have anyone symmetry and if we don't look at it from the city therefore seek if we look at our character Table A-1 has disease but we know that they're supposed to be too orbitals there now are there to see orbitals on that central and no so what's the other 1 yes that's right yeah and you have to remember that unless orbital always belongs to the cemetery species that has once for every operation invariant all transformations OK so this 1 give us S & P z and so what I'm saying when you when I when I saw that people Saudi did everything right and then came up with nonsense some people put to PC instead of instead of that member's work that way OK so we don't have anything on to worry about it B 1 if we look at that it has nothing in this column but it does have expedite his wife's work and that is a perfectly acceptable the orbital so this is the expert OK and I mentioned if you got these looked around and worked out that way what you get instead is you get beat 2 which is the X and Yevgeny that most points if that's what happened question I don't know of so by symmetry alone there are d orbitals there but on the reason you don't count them is that you know some chemistry see note that there has to be you know that that the dual roles are much higher in energy and there were there only 2 8 ones and that representation rights and so we taken from lowest energy the highest energy so we have an ass a PC and there aren't any more anyone's there and so you know that those the Peoria law going to participate in bonding before the durables can involve just because you know some chemistry now if we work this out and we got for 81 instead many would say S P and O's the but we don't have enough of them to go around and news that the rebels there and so those those coefficients on under the representations do correspond to the number of orbitals about symmetries pieces that are involved in the bonding and you have to take them from Boston energy highest and again the character table and symmetry arguments on the road don't tell you that you have to you have to know so it's really powerful there are lots of things that you can learn from this kind of symmetry analysis but not everything some things you you have to remember OK so what's next so that the experiments Weisberg and then for we have X and Y and so on that's PX and PY and so the actual answer as he is yet he wired experiments twice for those of the orbitals involved In the bonding and so again there were variations of things that people did that involve getting all this right and then putting down things that don't make sense so other things people that included just writing down every single thing that is you know that was listed under the cemetery species but doesn't work rejected you have to look at it and decide which orbitals are involved also taking into account the energy considerations and not just the cemetery I were another thing that I saw always people just leaving it as the cemetery species but you can do that and that's not an oral you have to go through and look at the character table and see what's actually involved in the bombing OK so let's move on to the next part of the cemetery problems and I want to point out for this thing on I needed to keep this part and I gave tons of partial credit like there are lots of things that you know where like you got some things but not others that there were there were lots of there's lots of partial credit given OK so now the question is 2 we've learned about the bonding now we want to talk about the vibrational modes Of this molecule whether their ire on inactive and so the question is on what basis would you use for this and what its characters so for the bases you just 1 using xyz unit vector any shadow and just writing that was completely acceptable some people drew it that's fine on my gave people partial credit for drying it inappropriately on the previous page where you don't need to use it on anything that indicates that we're looking at displacements of all these Adams so now works the character for the identity matrix here we have to put an X Y and Z coordinate system on each item there were 6 Adams so the character is 18 most people got that right so if you got be you know the figured out with the bases was that this right the people who fell down on this 1 I forgot to put coordinate system on the central island and that that doesn't work because we're talking about the displacement of the whole thing easier to to count all the adults OK so non-expert part of this was done for you just because the test is already long and on the previous page you already showed me that you know how to write irreducible representations and use them to solve problems so we don't do that again so I gave you the answer to what you'd get if you write this whole thing out reduce it and so some people asked me during the exam Hey wait a minute does this belong to the same molecule as the previous 1 because it's different symmetry species that the pointer that I hadn't and that should be a clue that maybe something was not right here .period grew just you know for future reference OK so and sister was done for you and the question here is which symmetry species belonging to translations creations and vibrations and so then you have to go look at the character table and we want to subtract the ones that belong to just translations and rotations because of those don't come into our I Roberts spectra and then whatever is left over is for vibrations and so what we get is the translations and X and Y belonged to the and he is a degenerate representations so X and Y both belong to it it's not to me it's just 1 it was a 1 similarly RX and or I heard a generous and that's the easy to OK so whatever is left is my vibration so I can write those down so I have 3 A 1 and 2 the 1 and 3 and again if you did this basically right forgot about the coefficients wrong he lost a couple points but but mostly it was OK OK so now the next question is which ones are higher on active so again we look at the character table and we say 81 has a component of the dipole moment and it has a component of the plausibility so exposed the 1 does not have a component entitlement but it does have a component of the polarize ability the same thing for details and we look at me it has a component of the article moment and polarize abilities of its both yet carried so then last heard the question which you had the answer to get full credit was how do you know of all look at the character table was not specific enough :colon he needed to say something like you know mentioning of the components of the polarize ability of the dipole moment people who just wrote x y and z next to the ones the IRA active and X Y or whatever annexed the ones that are on an active got all points basically anything that let me know that you saw you know where to look and the character table to get the answer got full credit just now look at the character table wasn't quite specific enough OK so now let's move on to the last 1 they were going around that time that authorities were almost there OK so part the question is explained in words how the principle of IRA spectral spectroscopy differs from vibrational Rollinsford crossed the ball I want here is that and I it absorbs a photon and Rollins the photon scattered so so that's it like any any variation of that you know which was taken in beauty in writing it down was not released countered I Nova reason operate so it was not the explanation did need to be particularly profound anything that that had absorption versus scattering was that OK so now in the next problem we're looking at the specter that you would see if we measured by our spectra yes questioned the role of new media yeah that's true the difference is not all war that's that's true but it's not the that's the gross lecture it's not the physical principle held the spectroscopy operates yes I don't remember I think we gave some partial pressure but it's true it just doesn't it just doesn't question something that's you know that's the selection role and I know it is correct it's just that when I was asking about his offense the physical principle as to how the photon is interacting with the molecule but young pretty sure we gave some personal profit the because it is approved by OMB that you know that was inserted sort of many other places on the exam OK so now the next question we want to sketched the spectrum that are involved in the IRA specter of HCl and C O 2 so again the sketches I wasn't looking for artistic merit here just a few that are basically the idea in his work here is what I was looking for so you want label your access on so intensity arbitrary units basically anything the x-axis could be waived numbers could be in units of being could be Lander it could be basically any of those things along as you did it consistently and play with it and then for the spectrum of C O 2 and the EIA I am done because sealed 2 doesn't have a dipole woman so as pointed out the selection rules are such that you have to have a dipole moment for molecule together and I expect a lot of it so sealed his nominee yes all the questions if you don't drive he just said it doesn't have a spectrum yeah that's fine that's fine OK now HCL so again when I was looking for in the access should be labeled the same way and I wanted some kind of reasonable distribution of the heights of peaks you know like they're not all the same height and the spacing is to be here and for me here and that is all I wanted so what I was looking for is some understanding that the population there are differences between the different states as it the lowest energy 1 is not the most populated we haven't talked about that a great amount yet we have and mentioned it and we would've specter 1 ideally labeling the spacings here and you know basically explaining the reason why you don't respect for each sale OK we are about at a time but I think that's OK because the last 1 is straightforward anyway this just captive want something calculate next summer and start talking about electronic spectroscopy later