Merken
Lecture 05. Rotational Spectroscopy Pt. I.
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I think we have various things said that we need to take care of finishing of our discussion of symmetry and bonding were mostly done talking about it but we do need to talk about how we figure out if various intervals of his era in a particular space and ridiculous .period group and then we're going to talk about some the terminology that we need to get into rotational spectroscopy and need will get to talking about conservation of angular momentum so I hope to be done with rotational spectroscopy by the end of Friday's lectures that we can start vibrational spectroscopy next week let's see how that goes so
00:56
just follow ,comma discussions last time they're looking at is finding examples and seeing which orbitals conform Sigma bonds and buy bonds and I ask you to you go through and reviews are reducible representations that we came up with in class and make sure that you can branch and ,comma on that to make sure everyone gets OK so here is what we got so we had our representation of the pylons we know that they have to be perpendicular to the Sigma bonds which is the only condition that that we started reference so we had to consider the inflamed sent me out of said and by making a reducible representations based on the symmetry of those objects and reducing and we came up with the following combinations of the irreducible representations so freely out of planes said we came up with the double crime and you don't crimes and further inflamed set and we came up with the 2 prime and the and if we don't look at the character table and look at what objects belong to these particular irreducible representations we see that we got PC or old belonging to the kind of said the implants that has 1 symmetry species that doesn't correspond to any or all and then the other 1 contains the X and Y orbitals and also some durables so what we know from this is that PX and few I wouldn't make any sense because there are already involved in the signal 1 we know that the pipeline has to be perpendicular and we also know that d orbitals are not realistically going to be involved in in nitrogen compound that's what we're talking about so the energetically not available and so we know that the PC on that find that central nitrogen also the the oxygen is what's involved in the which again is something that we in new so it's useful to do these bonding examples were learning these things for a couple reasons why is because you don't need me to make a practice examples you can go through serve all the trend of Lewis structure examples from General Chemistry and due to problems like this there's really a limited number of .period groups that have few not symmetry species that you can realistically be expected using classes he do a few of those if you the ones that are harder you can really get a good handle on us and you can check your answer yourself because you know in the case of these bonding examples where should get and it should be consistent with with the year chemical knowledge
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OK so we also have a binding example in the homework word you think I'm analysis for oxalate and I'm not going to go through the whole thing just wondered if you couple hinting case you're having trouble getting started so 1st of all you hear is your basis you can draw little arrows representing the carbonoxygen bonds and why did I not represent any single and double bonds here there is an but I know news people talked about an office hours but they also yes rating has risen structures so we need to make sure you take that into account so we signed it to point group we know our basis there 4 things in a racist so we know that the the character of the identity matrix is going to be 0 and then if we do the I'm closest do 1 example of setting up a matrix so if we do see automation the wider auction service so remember the way this is set up the molecules in the exwife plane and z is coming out at you so if we retain about the Y axis here's what we get were just flipping over this way and we need to come up with the matrix that gives us that what we multiplied by the original vector so anyone switches places with 8 2 N A 3 switches places with a 4 so there's a matrix that we get for that and the character for that operation 0 so this is the kind of stuff that you should be able to do it and it's so it's useful practice on you when you come to office hours we can do more examples like this again you can make Microsoft and and do can make sure that you get it OK so that concludes our discussion of bonding and nothing but the rest of the way through this is 1 of the mutant let's
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talk about it a little bit more general way because we're going to need these sort of symmetry arguments when we start talking about spectroscopy so spectroscopy is all about the interaction of of light and matter wouldn't have different kinds of states that the molecule can be enforced talk about rotational states but then by regional states electronic states nuclear spin states and were going to have selection rules were really warrants will see that only certain transitions are allowed and the reason that happens is because of the cemetery arguments so we need to to be able to to do 1 more thing with these symmetry sorts of things so 1 thing that I'm sure you're truly record levees have seen before and in calculus some of out business just the not all so far we haven't even functions the symmetric Over 80 s symmetric on functions are antisymmetric if integrate and even functions Over symmetrical goal you get some number if you integrate in autumn function over cemented enable you always get 0 and this is a nice thing to remember because it means that there intervals but can look pretty nasty and you could just say they go to 0 by inspection of course if they don't then you have to work it out but I that's a trick that mean professors like to pull to steer that into your frontal lobes put some really horrible looking thing on and examine content if you remember this this rule you can see that justice is 0 were going to look at how to use this in a little bit more general way with Central Europe suggest you some more examples if we wanna multiplied its functions together if you multiply to even a twohour functions you get even function if you multiply and even times and I Uganda nonfunctional we can also look at how the derivatives were quick take the 1st derivative of even function you cannot function viceversa and again if we go back to our general chemistry intuition this is something that we all understand that really intuitive level so we talk about molecular orbitals was just really simple case H if we have our 2 s orbitals in phase they add constructively and we get a bonding molecular orbital and if the other phase they interfere destructively there's a note in the middle and we get an anti binding molecular orbital and again this is this is something that we all remember so we can look at this in
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a little bit more systematic way we can talk about if we have an ass orbital and a PX or role in assuming that we get oriented the right way there's nonzero but if we look at something like Nassau orbital where the PC or old illegally in this coordinate system this orientation we have a certain situation loads of opposite signs canceled N if we have an integral like this where we have the product of 2 functions over integrating it over some symmetrical here all space we can find the symmetry species in each function In whatever quite your brand then 1 a multiply them together and that will give us a reducible representation and when we reduce it we have to look at it and see if it contains an 81 and if it doesn't then there is no overlap so let's think about what that means anyone remember is the symmetry species that is invariant with respect all transformations that have the character of 1 under every operation and what that means is that if I have to say chemical bonds and my orbitals overlap that has to be invariant tall operations if that wasn't true my chemical bond would appear and disappear when I rotate the molecule for example and that would make any sense so that's that's how you can understand how this works so let's look at some pretty simple examples so if we look at a molecule like ammonia and if we want to know whether there is overlap Of the S orbital on the nitrogen with this particularly linear combination of as rules on the 3 hydrogen so we can do that the same way so again this doesn't tell you that whether that's the only thing going on obviously we know it's not the appear orbitals involved also we just want a yesorno answer do these things are lot another thing I want to point out is that just because you can make particularly combinations of orbitals doesn't mean that that's the ground state or that that's necessarily what's going on in a given systems this is important because particularly when we look at electronic spectroscopy we are going to see excited states and things look pretty weird but we have to worry about them because we're putting in energy and kicking the electrons up there so again this is just telling us it's it's a it's powerful but it's limited in what it can give us we get a yesorno answer as to whether these things have any overlap and that's that's about it but it is useful OK so we just go through the this by inspection so if 1 is ah as orbital nitrogen and it's a sphere so it's going to have it's going to be invariant under all these transformations then if we look at the on the linear combination that we have of the 3 hydrogen orbitals all in phase with each other we have to actually look at that and see what it does of course we know it's a variant of identity because everything else 3 we do get something that looks the same it doesn't change sign and for secondly we get something that looks the same and then if we multiply all these characters together we do get something that looks like a 1 and so it has overlap so we know that there can be some interaction between used this as orbital nitrogen and this particular linear combination so now let's look at another 1 that that has a different sort of symmetry so we've got to see this as a real nitrogen again and now we have a linear combination that consists of 2 of the 3 as for rules of the hydrogen so out of phase with each other so young then does this look like a realistic orbital that really talk about terms of bonding not really but we can make linear combinations like this and see what we get into excited states we will see some things that that that kind weird OK so again we know what happens with the s orbitals invariant transformations the 2nd linear combination this could be it said it has a character to for the identity and then for c 3 we get an overall character of minus 1 and forcing movie begin about character 0 and if we multiply these together and reduce said we get the cemetery species of the and there's no way 1 and that so there's no overlap and I think I'm sure we're going to come back and talk about this later I just want to introduce it so that we get a feel for how it works and when we start talking about selection rules were and talk about it all the more so for now the most important thing to remember is the even on rule and also you have to go through this general procedure questions from readers but in the view of the world on the part of that is work to be at the heart of the people on the I took a shortcut and ended up reducing that's but I write up a little and description of others with more steps in it and posted 3 guys that might be that there might be useful thing to do you're right
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I did get some steps OK
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so now we're moving on and so on were getting were going to get to direct notation have seen recognition before it's is something that they cannot prosper OK it's something that's really important to be able to read the literature in quantum mechanics a lot of things written down this way and it takes a little bit of getting used to at 1st but it's just a shorthand notation for writing down wave functions and writing down intervals and it just saves a lot of time so we're going to see a lot of cases where we have a lot of complex integral we're integrating wave functions together and everybody knows what the function is we don't need to keep writing it down over and over again this is just an easy way to write it it is a very compact notation and it contains a lot of information and you need to know what hot what's going on in order to be able to use it so we have to be careful not to make mistakes and and make sure that that everybody knows what's up what's in there but once you get the hang of it it's really useful and saves a lot of time OK so if we have a normalization and I know that you have seen as an Inuit that's about that's just an integral of the complex conjugate of of oneway function with some other way function overall space and we know when you get here so that equals 1 if and prime meatballs and secured to the functions of the same and equals 0 otherwise and that's just a consequence of the fact that these things were worse than normal sets OK so indirect rotation this is how we write identical it's just a surer way to do it so this funny little front half of the bracket thing is called abroad and the other one's color cat and so direct also called bracket notation and if you just have a cat yes looked all have a school moments and giggle at the Brock that's fine I can see people trying to hold back because there's no point in men's is given of there so when you see abroad by itself that's just the complex conjugate wave function that's that's all it means the cat by itself is a wave function when you see them together like this that means taking in a role that overall space so there is an immigration implied in that operation and then we can also write down this condition for what you get in a different way as the chronic adult function did you see this last quarter not really you didn't use it because everybody looked happy and looked like it was familiar when I talk about the normalization conditions where it equals 1 of a wave functions of the same and 0 if the difference that's all this it's the chronically delta functions just to a compact way of writing that down so when you see Delta sub Indian Prime that's that's a function it's it's a function kind of it's just you know just telling you that but it was 1 of the the same 0 forgot OK so now we can go through and talk about how to do some other things so here's here's how we're right on our normalization and you know I'm saying it's a shorthand notation and saves space it doesn't look like it's that much space right now but imagine that we have to put in what the actual wave functions are and so it's a big mass whereas if we can just if we use of rock annotation as long as we were in a specified system we know what the I've been functions are we can just specified them with the quantum numbers for example OK so let's look at a matrix element so I want to write down a matrix element of some operators which I'm calling America so we know that quantummechanical operators are there operators we can represent them with matrices and the matrix element in and for America is just the integral and here's how we go about writing that down and so if we wanted to make a whole matrix for Our representation of America we would just have to go through and at the set up of a matrix elements but he doesn't have any questions about this it's really important and it's going to keep coming up over and over again and I'm not gonna right way flashes over times you definitely Naseer yes several OK so if you just have like so so in Prime in b the bracket that it's an etiquette that's just the way function the other 1 that Roberts complex conjugate and so there's a lot in here so the the engine and crime are the quantum numbers that represent that particular way function C have to know what system parents if you say it's a particle in the box and we're talking about the particle in the box wave functions and you have to know what the 1 for any equals 0 Rentokil's equals wondering equals 2 years and you have to argue no that the system that you're working and what the wave functions are have to be specified but once you know that this is a shorthand way writing them down then when you get to broaden the kept together like that that's what it is that's what it implies an integration of prospects I this fundamental mean there's so there is it OK so if you look at it the the picture the end of the in the bottom right of the matrix elements so the the atom you know bracket is a cat and then the other thing is of rock and so imagine you take you may out of the middle you're putting them together indeed you know line that's on 1 part of the bride and the 1 that some interpreted cat superimposed on top of each other that solid as you just you just sandwiching next to each other and then we put the operator in between that means that we operate Omega on and 1st Robert Rivard the order operations for these things will operate the Omega on em and then we take the integral of whatever the result of ideas with the complex conjugate and overall space that helped him any more questions if if you don't understand please do ask now because it's going to it's going to come up a
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lot yes the well it depends on the context of what you're doing right so again we have to know we have to know what the system is so if you have a harmonic oscillator that sent a picture of particular potential it's over the space of 4 of that system and that's what this is really powerful because it's very general way we start to talk about and more spectroscopy which we're going to finish the talking about things and spin space it's not even in space it's not even a real physical space it'll be in the instant space which which will learn about later so it's extremely general this is used for writing down all kinds of things in physics and chemistry and yeah that it's it's not it's it's just notation but you will see it all over the place if you want to read literature in quantum chemistry or physics and it is going to come up a lot so your book mostly doesn't use it there's a little section on somewhere in the early chapters on how to do it as kind of an aside it's it's probably useful to go look it up and and read it if if you want some extra clarification on at the Wikipedia page on this is really and I also recommend looking at that but for the most part your book doesn't use it they destroy not only intervals so there will have to be some translating backandforth because I'm going use in class you'll see in the literature and your book mostly does not do it OK so let's move on 0 sorry if you requested you don't think so In enact case there's so there was no Omega that was just ii integrated the complex conjugate and with and Prime overall space and the answer that I got is the proper Delta which just means 1 of the the same 0 4 different and in 2 different things with the notation the 1st thing I did was I just set up a normalization conditions then the 2nd thing was an example of the matrix element for a America the the separate issues makes sense because will see lots more messages had introduced at the beginning OK so now we're ready to really start talking about spectroscopy and what what we're going to do here is we're just going to go through the different types of spectroscopy that that there are can use to solve chemical and physical problems and I want to put up this kind of thing picture in view of what spectroscopy is all about so In the most general sense it's about the interaction of electromagnetic radiation with atoms and molecules and we can use this interaction too probe all sorts of properties that we want to learn about the molecules and we're going to go roughly in general and in order of things that go from lowest energy highest energy and so this is an energy level diagram showing no not really to scale but hopefully it gives you the idea how much energy it takes to do different things with a molecule so we have the on electronic transitions so we have these 2 top potentials here for the electronic transitions and of course that the ground state is the bottom 1 and this Blue Arrow is showing the system observing a photon and jumping up to the next excited state so that's what we're talking about any talk about fluorescence the absorption spectroscopy when you do that in the lab and measure the optical density of something new we're talking about kids absorption here although it takes a lot of energy to perform these electronic transitions so this usually happens in either be visible region or in the UB and if we don't have enough energy to excited that we can excite vibrational or rotational transitions and all these things tell us different things about the molecule so I should back up a little bit and point out that I'm going to tell you that the quantum numbers that belonged to the stupid things so electronic states the quantum number really uses at 1 end and if we look at vibrational transitions so now were confined to the ground state of the electronic transition because now we're just putting infrared radiation we don't have enough energy to excite those electronic transitions and that little red From the ground state to the next excited state within that well a vibrational transitions and that happens in the infrared and the quantum number that we use for that is new so don't get confused it's not the it's not the frequency near new gets used for a lot of things but we have to pay attention to context for rotational transitions which these little tiny ones in between the vibrational transitions that's those happened in the microwave and we use the quantum number J so again this is a mixture of just terminology you know where we can call these things and also looking at the big picture on a single energy scale chewing and this will give give us a field hopefully for why we see certain things and certain kinds of spectra so for instance when we do vibrational spectroscopy we're going to see a whole bunch of fine structure that comes about from the rotation because vibrations take a lot more energy to excite invitation so we excite something to an excited vibrational state we get a bunch of rotational excitation for free same thing excite electronic transitions were in the fine structure due to the vibrational transitions but it doesn't go the other way you're just putting in microwaves you don't have enough energy to excited vibrational transitions and so you don't see it and so on 1 aside here is that you know you're friends and relatives to tell you that a microwave oven works by exciting in the vibrational frequencies of water when you think about that at this point of 1 of energy right so microwaves just excited rotational transitions in need by 2 to excite those vibrational transitions and so your microwave works by having an electric field that's oscillating in moving on the pulled around OK so as a general matter before we go to record spectrum
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mission at something about a molecule remains sweeps through a range of frequencies and measure the signal so this is I new and this new really is the frequency and applied as a function of frequency so who here is actually taking the spectrum of a molecule yourself of any kind should be almost everybody right to do this and another in general chemistry some we have here is certainly taken an absorption spectrum raising and if you if you have the year's loss OK then ,comma IRD that we have on many more abuse than that yourself a good so it's you have some experience with all these things so 1 of the things that you probably know is that at least in NMR Aymara and fancy spectroscopy this description of usury the frequency and the sweep through and see the response isn't 100 per cent correct there's other guys you can do it that way but it's not the only way to do it and we will talk about what happens in these modern instruments but OK so here's another view of the same kind of thing what energy range does stuff happened and so here's the electromagnetic spectrum and it turns out people were pretty clever at making use of electromagnetic radiation and its interaction with molecules we can use just about every part of the spectrum to learn something about things that were interested and so we talk about radio frequency that is the resonant frequency of nuclear spends so and more spectroscopy is down here we will talk about it later they want to get into the microwave bats were really excited rotational transitions I R is a worry with good vibrations UV vis spectroscopy is or we can excite transitions of the valence electrons so this is what we're usually looking at the little Specter for polymers and molecular biology labs we and when we investigate years walk that's what's going on here were looking at transitions avails electrons if you want to look at core electrons and for instance find out what Adams were present on the surface then you need Xrays so Xray photo electron spectroscopy can be used for that so we need higher energy to excite those with more tightly bound to core electrons this starts to get a little bit exotic you need a big Xray source this is something that you would do at media synchrotron near source big national out it's not an instrument that people would typically have sitting around allowed these other things are and then the last 1 year gamma rays this also sounds pretty exotic right this is we can actually look at expectations of nuclear states it's called must power spectroscopy and that's done with gammarays so we will go through many of these types of spectroscopy not all were not going to talk about the XPS there was very spectroscopy so much but the others we will go through hearing and give you a feel for how it works some of these things are things that you're very likely using your research In order to talk about the mechanics of how spectroscopy works and started really getting into it we need you talk about the war Oppenheimer approximation and I know that you've seen this last quarter life was just reviewer quickly because you know maybe footnote a little bit more practical context so that what the Oppenheimer approximation just says that the electrons move around a lot faster than the nuclei and that means that we can separate them which is really good because we would have very ugly problems have affected work and of course it doesn't it's not a good approximation in all cases but for many of the things that that we want to do is chemists is a good approximation and so what that tells us is that the you know we have some overall wave function for the molecule and it involves the motions of the electrons in the nuclei and we can separate variables and treat them separately just because the electrons are tiny they're moving around really fast the nuclear Maidenhead takes someone would catch up but so the electronic wave function does depend on the positions of the nuclei which we know we've been talking about molecular orbitals and things like that you were the electrons are around and in Bonn so it's not that it has nothing to do with the nuclei all all the positions are important but there's motion isn't really important on the time scale electrons under this approximation which is usually pretty good so we can consider the newly hired sitting still on the time scale we're worried about the electrons and so here's shorting the equation for the electrons so we got hot Hambletonian Norway function and now notice these have a subscript of epsilon to indicate that we're talking about the electronic states that its quantum number and this is a function of the electron coordinates and the nuclear but the nuclear ordnance for retreating fixed and then we go to talk about the nuclear motion and this is rotation and vibration that just season overall smeared out potential from the motion of the electrons it sees the average of what the electrons are doing that and so here we have a Hambletonian for the nuclear transitions and it's got some scripts of new and Jaromir those are quantum numbers for vibrations invitations and those just depend on the nuclear accord because it's just seeing some overall spirit of potential from the electrons a so again this is a really useful approximation because it means that for the most part we can treat our electronic spectroscopy as separate from workstations and vibrations under any conditions OK so that is it for the kind of you know basics and Housekeeping kind of stuff and review let's move on to actually talking about quantification Asian invitation the angular momentum and things like that that we need to go rotational
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spectroscopy so I guess that's not entirely true that wouldn't review we are going to talk about some of the things that you learned last quarter but give it a little bit of a different spin if you like so please review Chapter 3 if if you don't remember really well and I really recommend reviewing all this stuff from last quarter as we talk about it just because Quantum is when these things were at least I found when I was learning and as a student it's not very intuitive and you really have to you know when you get more information about how it works you really have to go back and review the basics and make sure that you understand that and it makes more sense every time you go back and do that so please do review so 1 of the things that came out last quarter is the case of a critical race and you might wonder why you're interested in a political honoring and that's a fascinating question 1 thing about basic quantum mechanics is that you can end up with a lot of these examples that don't sound very practical see look particle box and a particle honoring the particle a sphere and harmonic oscillator as I write is that is that what she did so why do you think that we take these particular things is it because there are extremely realistic and they describe everything in chemistry and physics yeah it's because those are the only things that you can solve analytically anything anything more complicated than that you need computational methods there are lots of computational methods there's a huge field of computational chemistry were people do electronic structure calculations there is a big center for that UCI but these simple cases where you do the things that you can solve do give us an intuition about processes that we care about so if we think about particle wandering in and of itself that's not necessarily the most exciting thing you know you have some particle going around but you can also think about it as a rigid rotor so the pictured by atomic molecule that's just in the gas phase it's off by itself it's not interacting with anything so we have diatonic molecule and its rotating around if you pickup point on that molecule and follow its rotation it looks like a particle wondering right we can use the same mathematical treatment to talk about our rigid work so what do I mean by rigid work that means that the bonds between those 2 nuclei isn't flexing at all it's not changing it's not bending its it's just rotating around as see that an approximation that works pretty well at low temperature chauffeuring lowenergy states and we also depend on the molecules we have a very stiff bond that works better than a favorite floppy bond but it is a parks and approximation of weakening start out with OK so we can go through angular momentum and if we're talking about a particle honoring we have something that's in cylindrical coordinates that's that's certain natural coordinate system use here because we have a ,comma molecule we can say it's irritating about the axis In this plane so it makes sense to do this in cylindrical coordinates and another thing to go review and look up the Wikipedia page if you're not really upon it is however is how transform back and forth between Cartesian coordinates and cylindrical and spherical coordinates is not something that we need to know how to do OK so here's here's our angular momentum In the classical case so we have a regular momentum about C is plus or minus the momentum times radius Everything that idea the moment of inertia here and we can you know we can calculate the moment of inertia for diatonic molecule In the book it goes into all the different kinds of rigid rivers that you can have that have different moments of inertia and that's a useful thing to look at it's it's good to 2 go for it understand how it works it's not something we're going to spend a huge amount of money in class because it it boils down to a lot of crap to memorize lot of formulas and that's not really what we're about 1 would have himself problems so in class were mostly can focus on the diatonic case with the understanding that there's all this other stuff that you can do bring a look at the case worry console things analytically and where will you can for some of these other things too anyway it's worth going and looking at it just to make sure you understand how it works but were not willing to focus on in class so if we take care of him not to go through and insult the assuring equation for this for you I assume he did that last quarter but will just go through the the argument of for how you get this so in the quantum version of this weekend you use an analogy to the debris wavelength for the year of the momentum here and the fact that it has to be quantized comes from crude from the the fact that has periodic boundary conditions so it's a little bit strange but it makes sense when you think about it so are a function has to be single value so that means that you never have a wave function for my rotational state my molecules rotating around when it comes all the way around the circle and makes a complete circuits visit it goes to buy workstations it has to come back to the same place and that just intuitively make sense right you can't have something discontinuous happened to it as it's going around in circles and the quantification comes out of that condition because an integral member of wavelengths has to fit in that circle so here's here's how we would write that down so some integral member of the wavelengths has to to go within that circumference for the article point on the molecule rotating around the ring and so that's where we get the quantification from the case of here's the quantum a version of the angular momentum in the direction and what we get out of it is that it comes in increments of and Seville which is its quantum number times work and and Cervelo can be 0 customers want customers to etc. OK so now we described busy component of angular momentum of circuit but sold them more
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the so the natural place to put this isn't in cylindrical coordinates and of course fixed because we're talking about a diatonic molecule rotating and we Senator rigid rotor so its radius can change it can't library stuck at that particular radius so are becomes a constant that part integrates out and so were Tony and simplified and so now here's how I write down that equation in direct quotations so again if you don't remember what the wave functions for this look like go look in Chapter 3 but instead of calling them sigh I'm just going to put that ends the in the cat and that indicates that I'm talking about the wave function for that particular and Sadella value and so I ran out the assuring the equation substituting and for what the Hambletonian actually is here's what that looks like and I also want to point out that angular momentum and the angle are complementary values what we mean by complementary values in this context it you know his at that rate often last quarter yet exactly right yet the complementary in the sense of the uncertainty principle so it's like it's it's an analog to position and momentum you can't know the angular momentum and the angle so the complementary observables and I bring this up because I wanted to point out that the there is a UN 0 angular momentum state and that's that's legal and that would seem to violate the uncertainty principle right because we know the angular momentum with absolute precision there it's 0 and this is a little bit counterintuitive when we had you know for people who are used to thinking about mechanics that because if you think about vibrational energy levels like your your harmonic oscillator potential there's a 0 . energy right that you never have 0 energy for that for rotational state you can you can have 0 angular momentum the reason for that is that in that case were you know that were you know that with infinite precision you don't know anything about the angle it's just out in space you know nothing about it all so that so that's why agreeable havezero state for that OK so now we've talked about the z component of angular momentum we have something retaining honoring now what about if we have the particle free to rotate over a whole sphere did you did you do this last quarter to the talk about hydrogen notably functions again everybody has seen those from general chemistry as well so now we need to talk about the general angular much for a particle honest here and I think we're not gonna finish that this time will be to on this going is to pick it up next time does anybody have any questions about what we did today is kind of jumpy around between different topics but there were some terminology things that we need to clear out before moving on to very heavily and I will see you could find
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Schwingungsspektroskopie
Chemische Bindung
Chemische Forschung
Funktionelle Gruppe
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Konformation
Single electron transfer
Distickstoff
Oktanzahl
Oxalate
Chemische Forschung
Stickstoff
Computeranimation
Entzündung
Doppelbindung
Spezies <Chemie>
Chemische Struktur
Sense
Chemische Bindung
Operon
Molekül
Funktionelle Gruppe
Oxalate
Fülle <Speise>
Reaktionsführung
MetallmatrixVerbundwerkstoff
Mähdrescher
Azokupplung
Ionenbindung
Vektor <Genetik>
Orbital
Expressionsvektor
Molekül
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Metadaten
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Titel  Lecture 05. Rotational Spectroscopy Pt. I. 
Serientitel  Chem 131B: Molecular Structure & Statistical Mechanics 
Teil  05 
Anzahl der Teile  26 
Autor 
Martin, Rachel

Lizenz 
CCNamensnennung  Weitergabe unter gleichen Bedingungen 3.0 Unported: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen und nichtkommerziellen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen und das Werk bzw. diesen Inhalt auch in veränderter Form nur unter den Bedingungen dieser Lizenz weitergeben. 
DOI  10.5446/18913 
Herausgeber  University of California Irvine (UCI) 
Erscheinungsjahr  2013 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Chemie 
Abstract  UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 05. Molecular Structure & Statistical Mechanics  Rotational 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: 0:00:55 Which Orbitals can Form Pi Bonds 0:06:12 Symmetry Properties of Functions 0:08:33 H2 Molecular Orbitals 0:09:00 Vanishing Integrals 0:15:35 Dirac Notation 0:25:54 Big Picture: Spectroscopy 0:34:20 BornOppenheimer Approximation 0:38:21 Quantization of Rotation 0:45:39 ZComponent of Angular Momentum 