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Lecture 01. Symmetry and Spectroscopy Pt. 1.
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Title  Lecture 01. Symmetry and Spectroscopy Pt. 1. 
Title of Series  Chem 131B: Molecular Structure & Statistical Mechanics 
Part Number  1 
Number of Parts  26 
Author 
Martin, Rachel

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CC Attribution  ShareAlike 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and noncommercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license. 
DOI  10.5446/18909 
Publisher  University of California Irvine (UCI) 
Release Date  2013 
Language  English 
Content Metadata
Subject Area  Chemistry 
Abstract  UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 01. Molecular Structure & Statistical Mechanics  Symmetry and Spectroscopy  Part 1 Instructor: Rachel Martin, Ph.D. Description: Principles of quantum mechanics with application to the elements of atomic structure and energy levels, diatomic molecular spectroscopy and structure determination, and chemical bonding in simple molecules. Index of Topics: 0:11:28 Dipole Moment: E Field 0:15:14 Symmetry Elements 0:26:34 Chirality 0:27:46 Symmetry Operations: Translation 0:28:53 Group Theory: Introduction 0:34:12 Point Groups: Flow Chart 
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00:06
ignoring everyone welcomes you as secondquarter peak I'm I'm professor Rachael Martin and I am going to be teaching this 2nd quarter that has to do with spectroscopy which is broadly defined to the interaction of light with matters we're going to talk about a lot of things that really get to the heart of how do we know that molecules will look like look the way they do so I want the beginning of this class is going to look like a repeat of General Chemistry and I hope that'll be really fun because we get to see a lot of these molecular shapes and structures that we know about from General Chemistry it's presented as here's a bunch of stuff to memorize and were aware they understand why they look the way they do and how we know so well modern way this quarter if you can get sad is taking the knowledge that you've learned last quarter in quantum mechanics and applying it to practical problems in molecular structure of molecular motion and things like that another really important part of secondquarter peace camp is really learning how to use mathematical tools and and mathematical formalism to describe nature so we're going to be learning a lot of problemsolving methods that might be different from things that you've done before and that's going to require a lot of practice but hopefully you'll find it worthwhile I do I think it's a lot of fun so this is this is what I do and then were spectroscopy as so you've probably all seen Annamari in the context of organic chemistry learning how molecules look the way they do on in my group we work on a more methods development so being able to use the Nword experiment in new ways to learn different things about molecules and I'll get to you to share a little bit of that with you later on when we get to the end part of the class OK so basically I'm handing out the at all a packet for you there is there are a few things in there so 1 is the sole and that has a schedule with reading assignments from the chapter the but the book is the same book as a as last quarter and if you have slightly different editions that isn't going to matter the close enough just some of the page numbers might be a little bit off parliament some notes about the scandal it's all subject to change except the exam dates exam dates are set in stone that's definitely what it will be if we get a little bit ahead a little bit behind on the topics that might change what's on the exam but the exam dates are when they are on my office hours I understand mediation change because I understand that the chemical engineers have classes that conflict with those times that the correct OK so I would give this a try of if there's not a consensus right away opted to regroup and and I look at my scandal so what if we moved there Tuesday 1 2 an hour earlier freed you wanted to come many people could make that right let's try this a different way how many people absolutely couldn't make it if it's 1 2 on Tuesday OK that's that's not very many so wanted to on Tuesday all right and then on if we move the Wednesday 1 an hour later and do it 3 to 4 how's that for people who couldn't make it if it's 3 or 4 OK who can't you absolutely can't make it to either of those times that's few enough people that workers just have to work something out so that's that's what it'll be 1 to 2 on Tuesday and 3 4 on Wednesday and I will update the folders and put that on the website of a so there are a number of resources online arm for this class so 1 is the course website which a lot of you have discovered it's pretty basic it's not fancy but all the information will be there I will hand out things like this in class once in a while but for the most part of course materials that I want you to have supplemental readings and things like that will just be uploaded on the website and you can download it and look at it in whatever form you prefer but there's also a group Facebook page which encourage you to use the group ID is listed on the club's website and that is it's I found it to be a really need supplemental tool for interacting with the class and you don't have to use it if you hate Facebook that's fine and as a matter of time but I found that it's actually a pretty useful tools so you can get on their ask questions the TA and I will check it really regularly another advantage that it has as you can discuss things with your classmates and a lot of times people can enter each other's questions you before we have a chance to to get on there so it's a lot more efficient than 50 people all emailing me the same question and waiting a long time for me to answer so do try to answer email you can email me on I get a lot of emails so that the Facebook page is definitely more efficient and other resources that are available you might notice that this class is being videotaped that means that the videos will be available online and later on you can watch them but if I make mistakes in class you can laugh at them that's that's fine but hopefully that will be a resource for when I talk really fascinates her great everything down which does occasionally happen another good strategy for dealing with that is to ask lots of questions that's a good thing to do anyway it's good to have a lot of class participation it makes things more interesting me and I really like to hear myself talk and that's why I became a professor but you know it's better if we get everybody participating on In the end also that that does help slow things down so anyway I never mind answering questions of stuff isn't clear I would rather be cleared up right away yes course of shore "quotation mark right 1st time in this room will see how about how this goes OK how's that sorry that OK other logistical things and while that's annoying OK maybe that is the Is that a better balance between too much feedback and being able yearly OK to anybody have any more questions about logistical stuff and how the course is going to go things like that I have 1 more thing they need to say before I forget and that is discussion sections are canceled for the 1st week just to give everybody a chance to settle into the new order on if you need help you can use a Facebook page you can email me stop by after class every Monday Wednesday Friday after class you must have some specific thing that I have to run off to I will try to hang out outside the lecture hall we can't all hang out the front room because the next class to come in and get ready but will step right outside and I always have questions for a while after each class OK so no more questions about logistical staff there's 1 the 1st homework assignments alleging asked unmitigated you today so here's homework is done work in this course you're going to have a lot of homework but I'm not integrated so there's going to be the homework problems there things that you really need to do to understand the material but I'm going to measure what you actually know rather than whether you did all the homework so that means wouldn't have quizzes sometimes ungainly lecture sometimes going in discussion if they're in discussions don't worry there will be a different 1 for every day of the week so that there's no unfairness there but you don't have to go to a particular discussion so if you can't make it to the oneyear registered for the UN don't drop the classic reregister it'll make your life difficult is go to a different 1 yeah nobody's going to keep track of it just as long as you go to 1 every week that's fine you can go to more than 1 if you like it so much you just can't resist and so anyway where we're going to do it is there will be a lot of practice problems along the way and the things that I think you should know how to do and it's just really for your benefit and these are things that are going to come back and show up on the exams and it'll be on the quizzes and in general the quizzes will be very similar to the homework problems and then the things on the exam might have a little
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twist it'll be a little bit beyond what we did in Class AAA or we looked at and homework but there will be basically related and so that will serve a couple of purposes 1 is it helps me and the team is to know what people are getting what they're not getting maybe what we need to spend a little bit more time on and it's also useful for you because you know what you needed to understand better OK so now that we're a yes no questions we I haven't decided yet what think about it so on these looks at let's see how it goes so my inclination is to just let people get help and discussion and working out you do things in an office hours and things like that but if it turns out that we just have to much then I might get in to posting solutions on the on the website maybe I'll do it for selected sports what the goes I'm not against doing it in general but I I don't want people to get into a mode where you just don't do it and wait for this solutions to be posted because it is seductive to do that then you don't know what you don't understand 1 thing about the camp is that the war for a lot of people there is also as a way of doing well in classes that involves learning a lot of information and memorizing specific things and that doesn't really work with these kind of problems you really have to learn a new way of working things out for some of you know maybe you've already learned that some of the other classes but for some people it's going to be new so it's a it's really important to spend time working them out OK so let's go ahead and then move on to the actual good stuff we are going to start
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with our review of general chemistry so we're going back to the the timing Khamenei when we talk about molecular geometry is and what different shapes molecules are and the consequences that this has really learned more quantitative ways to describe that so 1 of the 1st things that we learn about uh molecular shapes is that if you have a covalent bonds in particularly depending on the geometry of the molecule this could make your molecule have a dipole moment you have an unequal distribution of electron density yes it was ,comma I will eventually so so probably at the end of every week but the whole lecturers being videotaped so there's going to be a video of the whole thing so I'm not saying I don't think the slides going themselves are going and very much to to that OK so we have an unequal electron density in this molecule so we know that flooring is really like a negative so in this case a major there's going to be more electron density around the fluorine that's going to give it a partial negative charge there's a partial positive charge and side with the proton and that's going to make this molecules tend to have some alignment and electric field and of course this is drawn in a really exaggerated way but you get the idea that these things are going to be a line electric field then Of course we know that many molecules that have bonds have this property if we look at water same kind of thing we got those long hairs on the oxygen there's a partial negative charge in that direction there's a partial positive charge on the protons and all of this leads to hydrogen bonding in the interesting properties of water but we also know that not every molecule that has work a mail monster has a dipole moment so if we look HCL that's the case linear moment of the linear molecule that has a dipole each to us the same basic shape as water but if we look at S O 3 that's something that does have for bonds you're oxygen has a partial negative charge and sulfur has partial positive charge but it has no net dipole because of the orientations of the bonds and so in general chemistry we talk about this in kind of ahead we the way and say alright the electron density is being pulled told toward those oxygen is but they're all equivalent to each other and so the molecule overall doesn't have a dipole moment and there's nothing wrong with that it's fine but we're going to learn of more quantitative way to describe that and when you use that in our description of how chemical bonding works and also How spectroscopy can tell us about molecular motions so we're going to start with just the mathematical descriptions of symmetry that we're going to use in this course and then we're going to build up to can we use that to determine hybridization warbles which orbitals to have the right symmetry to be involved in particular bonds and if you're taking in organic chemistry this will overlap very well without how many people are in inorganic chemistry right now a few how many body taken but bank that's that's good so some of that will be familiar to you too you and you haven't don't worry we'll let people definitely cover which he did now OK so the idea here is that some say some objects have more symmetry than others and this is something that we know intuitively we can look at things in and save this object is more symmetrical and not 1 but there are ways to quantify that and what were really interested in is quantifying these things in terms of cemetery operators and then assigning each object that were interested in in our cases it's usually going to be a molecule we want to assign it to a point where and the playing group is a descriptor of symmetry that hasn't it that contains a lot of mathematical information so in general chemistry we talked about the molecular shapes here we could say something as trivial by pyramidal or a Tshaped for cease there all these names for the shapes we're not going to do that any more willing to talk about these things in a more mathematical way they signing into a point and that is more general and it gives us a lot of information OK so the symmetry elements are related to the cemetery operations so for example 8 symmetry operation could be something like a rotation so if I rotate something a rotating about an axis so the cemetery element is the axis and the operation is the rotation we could also have reflections so again you know we have a reflection access and that's the worry that the at the reflection claim is that the elements and the reflection the operation and I have a couple of links here to pages that have good examples I will go ahead and reproduce those on the class websites you can use them OK so let's just look at some abstract examples and using some of the works of MC Escher because he drew these really beautiful things that illustrate the cemetery operations very well so if we have a rotation axis that means that if you rotate the object by 360 degrees and and it looks unchanged then you haven't and folds rotation axis and that's called CNN so for this particular object it has a C 3 access because you can rotate at 120 degrees and looks the same so that's that's got a C 3 access at its highest axis of symmetry there are things that have a higher order Accies don't get fooled by this 1 because it's got these little stars in the corners so I think the highest access it has is C 4 but there are all kinds of examples in including protein structures so if we look at the protein crystal structures these are the rotation axes are really important parts of the year the symmetry that we see so To recap the definition cemetery element at the cemetery element is its convenient access it can be a plane a point about which we perform the operation and the operation is the the action that you perform to the object that leaves it looking unchanged at the end so In the case of rotations we can describe the the rotation 360 cover and OK so
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it we can also think about reflections so a reflection of the universe the cemetery stuff is really easy even golden retrievers understand it and they're not the not the most intelligent creatures but they get it on the reflection can be vertical which is defined as it contains the principal axis so if we but if we think about the Russia print with the bats that a threeaxis that's the principal axis and that's just defined as the highest order and symmetry axis that the thing has it can have all kinds of different axes will see examples of that but the highest Heisserer 1 is the principal axis and a vertical the plane contains the principal axes in a horizontal 1 is perpendicular to it Of course there are all sorts of examples here that have reflection planes this 1 is related to within sign change it's not tough you know it doesn't exactly have a reflection playing on here and so it changes sign but otherwise these are pretty familiar operations were just getting new ways to to describe them I should also point out and put on a slide this said the symbol with traditionally used for planes is Sigma so well Will will see those OK the next 1 is
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inversion that's a little bit harder because you can't physically do it to a model but if you have an inversion center that means you can basically turn your molecule inside out see you take every point and it's like you're pulling it through the center and having it come out the other side so everything everything all the coordinates of the physicians go from X to minus X Y miners y z minus the so things like this cubic lattice this organic molecule if you look at it really carefully that has an inversion center through the virus Capps said all these things having version centers and the the inversion operation is usually called I yes on the other "quotation mark on this would think state so it has come so it has a Cairo Center yet and it can have inversion cemetery right because it's always going to be different when you when you take the mirror image of it so apparel molecule doesn't doesn't have an aversion symmetry and that's so you know it's it's it's really it's going to make that connection that's 1 of the really important practical consequences of of molecular cemetery will see some other ones later on OK so now we get to the hardest 1 of these things to visualize which is an improper rotation so these things are called s Accies improper rotation and for all of the cemetery things I really recommend if you still have euro models from organic chemistry get the out and and look at at some of these things and convince yourself how the cemetery operations work if you don't have them come office hours you can play with mine it it really helps clear 1st learning to visualize these things OK so if we take something like methane it has a fourfold proper rotation axis and that's so that seems a little bit counterintuitive at 1st because nothing definitely does not have a fourfold rotation axis of doesn't have a C but it does have an S for the question in middle here I think the best it is supposed to be 360 sorry about that OK so not to perform the improper rotation we need to rotate by 360 overran and reflect perpendicular to the rotation axis so methane imagine my fingers are 3 of the hydrogen and the other 1 is sticking out so that means we have to rotate it 90 degrees and reflected this way perpendicular to that access and if you play around with the models you can hopefully convince yourself of that actually does work it gives you the same type of thing will see more examples of this later probably next time in class or bring in some models and use them on the document camera and we can see how these things work I guess what I'm saying is if that once hard to visualize it made it might take a little practice yes I mean How do you know and that's a good question you just have to get started looking at these things so the improper rotation is the hardest 1 visualize and so fortunately there is a really easy way to to cheat and that you have all these things listed in the .period group table so there's a point the table in the back of the book it's not as complete as I would like so I'm going to be giving you a better 1 that that you can use in you know you'll get these things on the exam and hopefully next time I'll have that printed out for you but the playing group table contains all kinds of information about molecule and 1 thing it has is that lists all the cemetery elements that that molecule hats and so 1 of the things that happen I gave you as a flow chart that's useful for assigning molecules to appoint so what I would recommend if you have trouble visualizing some the symmetry elements is when you have a problem that it has to do with molecular symmetry the 1st thing you should do is just go down the flow chart and assigned it to appoint and then that will tell you all the operations that there are after you know that you can go back and try to visualize and it's a little bit easier OK so as we signed the methane example you can have an improper rotation axis that you can have an end fold proper rotation access even if you don't have the enfold rotation axis another example is if you have staggered ethane that has an S 6 access so standard ethane is like I take mine at the molecule have the hydrogen set up in a staggered confirmation and cool it down to 0 Calvin so that it can freely workaround that that single bond and then that has an Essex inside a tiny drew this out for you so you can see how it works so we rotate by 360 over 6 and and reflect and you you end up with the same thing OK so now we get to some some consequences of symmetry so kind reality has to do with as you know whether molecules there are lefthanded and righthanded and it turns out that only molecules from some specific .period groups can be Kiraly and will talk about this more later as we didn't you talking about specific molecules so basically only molecules that don't have an AT & & S axis can be Cairo and that's also implied by having emergency center so as weary talked about if you converted it's not Tyrol and if it has both at sea and and of horizontal plane that also means it can be Carol and again this is just a different way of saying things that you were going out so can chemists and chemical engineers and biochemists here at this stage you definitely know how to tell which molecules or archival this is just a different formalism for for talking about it OK so we have 1 cemetery operations left that's not going to be important for talking about individual molecules but it will come up we get into looking at crystal structures which will do briefly and that's translation so that means that we can move things up and down side to side in space and maintaining the overall structure and again this is really important for sending crystals a lot of what we're going to talk about during the 1st part of the course is going to be isolated molecules so we were were imagining that we just have 1 molecule in the gas phase and that sold foreign in liquid phase for that matter and that's all we're thinking about but in crystals we can see translational symmetry as well OK so that's the introduction to what the the cemetery elements and cemetery operations are those are all of them that we need to worry about now let's start getting into how to use them and haven't had a deal with the the formal representation of these things for we do that anybody have any more questions but they did fucking sorry for
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them but the that's right so well so it doesn't it doesn't have a C for petition access it's it's it's principal retention axis C 3 and what about well that's if I wanted to do a normal rotation so if I wanted to retain about the principal axis I would have to do with 120 degrees you're totally right but I'm talking about the improper rotation axis and so that's that's a really important point it can have an S3 access for soaring asked for access without having a C for access and that is the hardest 1 visualize it's going to take some practice OK so let's talk about group theory I really like group theory because it gives you a really simple problemsolving method In other words once we assign these molecules to point .period group table contains all sorts of useful information about everything about symmetry class and we can just read it often and learn all kinds of important things it also helps build intuition about things like how to make matrix representations of operations which were definitely gonna do so last quarter in quantum mechanics it's all you get that all about the properties of Linear Operators did you get into the matrix representation of of on mechanical operators a dollar are now reason and if you have no idea what I'm talking about OK that's fine so there are different ways of thought of introducing that in the beginning .period mechanics I ID number 1 is not better than the other it's just a matter of fact of preference for the type of us spectroscopy that I do it's really important to be able to look at these things as matrix representation and so I want to give you a flavor for that and group theory is a really good way to keep do that in a painless way because it's it's it's clear what the operations are so that's something that we spend some time on OK so Group Theory pertains to this notion of a mathematical group of operations basically that means that for something of a particular symmetry it describes all the operations that you can do to this object and each 1 is like its own little kingdom it has its own rules and defines what we think is the object right so in order to have a mathematical group it has to follow these rules so 1 of the transformations that you have is the identity operator and the identity operator is easier just means don't do anything and that is usually represented as capital E on the tables that will use you also see capital why in some other books you know who will stick with you but don't get confused if you see this and other places OK so another condition that has to be Medford for something to be group is that for every transformation which we can call are the inverse transformation it is also in the group and if you apply a transformation and its inverse that gives you the identity so that just means here if I have something and I reflected and I reflected back it's like they didn't do anything so the this is something that's very intuitive if you do something and do the inverse didn't OK so then if we have any 2 transformations Cold our prime the combination so you do 1 and then the other that is going to be equivalent to some other transformation in the group that doesn't mean it has to be the identity that doesn't mean it has to be either of them original transformations it's just that if you do 1 and then the other that has to be equivalent to some other transformation within in the group and the last property that we need to know is that these things have associated properties OK so this is sort of a highly abstract at this point and will kind do some practice problems we have to set up some principles of groups but really understanding the mathematical underpinnings of this is neat but but without getting that all right away we can still use it to solve practical problems and so the 1st thing that we need to be able to do in a practical sense is assigned molecules to appoint and so this is 1 of the things that that I have given you it's also on the site if you want to look at it on a laptop screen or tablet or something this is just a flow chart for looking at molecular cemeteries there are a million different versions of this on whether I made this 1 because it makes sense to me if you find other ones that you like to use that's absolutely fine with the caveat that this is the 1 I'm going to give you an example so
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you should dare to get to be familiar with it so you definitely don't want to memorize all these rules just you know where hundreds had user charge OK so we're going to have a bunch of practice problems involving doing this but what's just work through what the various things on the street mean a case of the 1st set of questions that you have to ask yourself about your your molecule is does it belong to various Army Special Groups so the 1st question is is it linear and if so does it hardly ends the same or different so if the ends are the same it belongs to the Infiniti age group so something like C O 2 it belongs there and if the ends are different so if it's like HCL it belongs to see Infiniti when you talk about low Symmetry Groups a little bit later because they're hard to explain but will will get their questions what is you the "quotation mark I think I'm going to defer that 1 told maybe next time yet they do they do have a meaning but and I think it'll be easier when you do some examples and you'll get a feel for it and will talk about it next time it's not that I don't answer and I just I think it'll come more naturally at the end of the future .period yes in the back of and so could you repeat your question the same as each other so like C O 2 where you have and you have a linear molecule and you have oxygen and both sides then that said the Infiniti OK so there hello Symmetry Groups are basically see 1 is it has no symmetry so like if I have a carbon atoms that has 4 different substituent sonnet and they're all different that's C 1 CIA is it just hasn't worked Centre CDS is just has an improper retention on the high symmetry groups are pretty easy to remember they are Tetra he'd roll TV opted he'd always OH and I ages I could you so that's something like a virus caps it would be I symmetry if you ignore the fact that the proteins that make enough for Cairo again if you read the the chapter and look at some of the examples that that will go through a little bit of a feel for these OK so if you look at your molecule and determined that it doesn't belong to any of these special groups then the next thing to do is find the principal rotation axis so what you're seeing and then we go down to the next step which is does it have C to Accies so sold 180 degree rotation perpendicular to CNN and if it does that it belongs to the Indian groups so I guess this is the end of find our 1st answer to your question about what to see and mean the dean groups meaning it has C 2 axes perpendicular to the sea and axis will see a little bit more about what that implies for the shapes of these things OK so then we go through these these D group so we can look at doesn't have a horizontal reflection plane to remember that the horizontal reflection plane is defined as perpendicular to the principal axis and so if it does that it belongs to a D and H group if it doesn't then you look at whether it had a drew reflection plane which also contains the principal axis and to classify it accordingly and then if it doesn't have C 2 axes perpendicular to the principal axis then we go down the other branch of the street and I think rather than going through all of this on the chart is it's kind of abstract was just do some examples so let me switch over to this document ,comma thing yes was you you're right I do I need to fix that so he added is supposed to be the nowhere following please mark that on your paper copy the Howell fix online the 1 going down and this is why I do not persuade slides online before class because no matter how hard you try there's always at least 1 the day OK so
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here's the other the way in which we're going back to General Chemistry you have to be really good at Lewis structures so if if you need a little bit of review on that now's a good time to go do it OK so what's what's look at some examples so if we have siege and of course of which 1 it is depends on how you draw it but I'm going to go out like this and Arafat but we can also draw that's a that's a perfectly fine 1 2 so on we can decide whether these things have a right to have the same cemetery along and then of course remember that now they're threedimensional OK so do I have on grandfather volunteer to assign 1 of these things to .period group with using the flow chart sorry your income the yes and no story everyone will help you because of course when you're up here you want help break OK so what are we think suffered 1st situation to see all too does it belong to 1 of these special groups like it's not linear it's not 1 of the low symmetry 1 it's not 1 of the high symmetry once so so now right In case so that means it must have a principal axis only think it's principal accesses and that's right it's to access does it have perpendicular C axes so it's it's got this thing yeah know what he thinks and now right that's right Castaneda situated seem to be so which is it the that's right great great job thanks for being the a 1st volunteer looking out of the Romanian descent has she got that question that doesn't have a seat to access in the plane coming under the paper will also it's its principal axis is in the paper rate and so on it's got different substituent signs on these things so so now right yes that's all you can write to see When access like that was so vital that over then the chlorine is they're going to be on top and the hydrogen solely on the bottom so it's not the same so I consulted over this way I can put it over that way In the guests each looking absolutely right so 1st of all does everyone understands how we got it's not 1 of the special groups so then we went to find the principal axis so this you just going to have to look at and say alright what's the highest order rotation axis that this molecule has In this case it looks like I can foot over this way and so do a 180 degree rotation but I can't do anything like you could think about OK I could try to turn it 90 degrees but that wouldn't work right because I'd have a proponent of chlorine swapping places it wouldn't be the same and it doesn't have any C 3 symmetry so the highest order axis that I can get is that seek to give the routine income so now the next question is doesn't have a C to Axis that's perpendicular to this to axis so we've narrowed it down to you either he had the secret Service on Indian groups and so weary decided orators are seen to access this way we can flip it over like that so that looks like it puts us in the syrup straight Everybody restraint look at good OK so then we have narrowed it down to situation or to be so which is it so the question is what it comes down to do we have a horizontal reflection plane perpendicular to the principal axis so what that means is if I take this molecule and stand up like this and cut through the middle and a reflection of of what will happen if I do that the Korean's all swap swap places with the protons and won't be symmetric so it doesn't have a horizontal reflection plan and I think what people were asking about is it has to vertical planes right as you can do it this way you can do it this way and that is why it ends up being seen to be because you do have those political reflection plants and so the neat thing about this is that when we talk about all kinds of properties like chemical bonding molecular vibrations all sorts of things that you would think would be a very specific to a particular molecule it turns out that a lot of them just depend on the symmetry that we have and so this molecule and things like water at all belong see to the point group we can learn a lot of things about for example the vibrational spectra and I think we're out of time so we're going to leave it at that for right now and don't run away yet because I have always been the same and that is for those who asked about homework here who
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work to be done before next class is to assign all these molecules to appoint group which of course on this is not my screen showing that the document ,comma by their online anyway so goes so go check out the website all your examples and also Beecher bring your packet to the next class because we're going to need it to do examples like think somebody