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Lecture 13. Electronic Spectroscopy (Pt. II)


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Title Lecture 13. Electronic Spectroscopy (Pt. II)
Title of Series Chem 131B: Molecular Structure & Statistical Mechanics
Part Number 13
Number of Parts 26
Author Martin, Rachel
License 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 non-commercial 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 10.5446/18921
Publisher University of California Irvine (UCI)
Release Date 2013
Language English

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Subject Area Chemistry
Abstract UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 13. Molecular Structure & Statistical Mechanics -- Electronic Spectroscopy -- Part 2. 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: 0:00:48 Resonance Raman 0:05:41 Fluorescent Bacteria 0:12:11 GFP Fluorophore 0:14:27 Jablonski Diagram 0:19:19 Fluorescence and Phosphorescence 0:20:47 Aufbau Rules 0:37:56 Find J(subscript) 0:39:53 Hund's Rule 0:41:19 Term Symbols for Linear Molecules
a place of continue our discussion of electronic spectroscopy so last time we talked about the basics what it is what happens to electronic states most of which do not for Service or do anything interesting on the way back down to the ground state I also want to talk a little bit about some some applications and things that things that are interesting 1 of the things that that's fine about the cameras that there's really a lot that we can go into that's beyond what's in your book Beyond the things we can do in class as
1 mention of you these things so we can take advantage of the offer the interaction between electronic and vibrational states in resonance Roman so relieved talked multiple times about the idea that it is using different kinds of spectroscopy we get a lot of interplay between different kinds of excited states of for example in vibrational spectroscopy see occasional students were exciting something to make you know to an upper operational state rotations get excited similarly in electronic spectroscopy a lot of times we see the vibrational states and sometimes the rotational states do we have enough resolution we can also use electronic states to enhance the the intensity of particular Roman knows something we talked about how Roman spectroscopy is useful in terms of of looking at vibrational modes in molecules that 1 disadvantage that it has is that the signal is very weak compared to I ask the cost so we're looking at scattered light in the most of the lightest scatters straight off the rail line it doesn't gain lose energy and you just see the same wavelength of light that you put in resonance from deals with that problem it's enhanced and also deals with the problem of having a very complex molecule it has a lot of vibrational modes so if we think about instead of having these simple molecules that we've been looking at in 1 of the other protein so imagine you have this huge molecule there are all kinds of vibrational modes going on it's going to be much too hard to understand the spectrum of Algerian have all these peaks on top of each other and there's not really a good way to interpret so resonance Rahman deals with both of these problems at once and it we do not putting in you words is so were exciting by regional states that are associated with a particular electronic state so if war on resonance with a particular electronically excited state and vibrational modes that are associated with that particular state were going to be enhanced by a lot and so that means that not only do we see a larger signal for the vibrational modes that were interested in in the protein it also means that these modes are amped up enough such that all the ones for the rest of the protein and not interested in are not visible at the latest fade into the background so here's an application that this is something that's from Judy Kim's lab at UC San Diego says she's interested in looking at ,comma electrostatic potentials Alderon has risen enzyme that that deals with electron transfer and 1 of the things that Professor Kim has done is she's looked at attractive fan in that the other side chain of tryptophan is involved in the reaction this case should make radicals on this particular side chain and look at the difference between tryptophan an environment where exposed to the solvent and works not and it turns out that these look very different in that has some implications for how the enzyme functions and you can see the difference between these 2 things in looking at the residence from Inspector so being able to have that these vibrational modes enhanced only knew this particular electronic state in this case in a rare amino acid reflux covering many of them in the protein in fact gathering has to 1 that's insolvent 1 that's not that enables you to to learn some very specific information about this molecule in work otherwise it would be very complicated but probably water so it's a well definitely water in this in this case so the protein is insoluble but of course the inside of it is a hydrophobic environment so the trip defendants that's just surrounded by the rest of the protein is going to have a different dielectric constant in different local environment and 1 that's closer to surface that can interact with the water OK so that's just a hint as to to where we can go with with some of the stuff and power of electronic spectroscopy Iraq vibrational spectroscopy let's talk about fluorescent so
last time we talked about what happens to excited states a lot of them just relax back and produce he it's not so much fun some molecules dissociate and fall apart in the near chemistry but other ones undergo fluorescence and phosphorescence and this is pretty interesting so here is an example from my lab user fluorescent bacteria that that we found that at some point a couple of years ago and we still don't know what molecule makes these things for us and that they look neat maelstrom talking about so the excitation wavelength has it's in the right on the edge of the UV like we can see some purple light and then the fluorescence is a little bit lower and we can see that here if we look at the spectrum so the excitation wavelength this is shorter it's closer to the European shares that emission wavelength here some other examples
these are quantum dots of various sizes there for us and if you even within the they shine in indivisible and depending on the size of the quantum dots we see different colors so you guys know about boxes that something comes up and in Kenny there really interesting cities are these are little nanoparticles of a semiconductor material so and in some cases you can use Telluride cadmium sulfide is another good conduct material and the exit Honda confined in 3 dimensions so it behaves as kind of an intermediate between along like a giant molecule and of all conductor and they're useful for all kinds of things I mean just in detecting stuff and there the interesting from a fundamental physics and chemistry perspective just trying to understand how they work but there are also using imaging applications we radiate them with UV light and then see the fluorescence and here is an
interesting application of this these on green quantum dots in this picture which are being used for cellular imaging were actually buy a synthesized by off worlds so this group discovered that you can feed earthworms soil contaminated with cadmium in Torreon and they put out quantum dots the 1 of his 1st have this particular size their green in this picture the Blue is a dye that stains the nuclei and the cells and so this is just proving that they can put these Kwan dogs that were made by the reforms into actual cells and use them for imaging so why is that useful and it's funny but it's it's it's actually interesting as well because 1 of the problems with with quantum dots and biological applications is that these things really toxic show it's actually pretty amazing that earthworms can eat soil that's contaminated with cadmium Tory all not by but what they do is they they have these enzymes public health findings that bind these these toxic metals and and package them into these little quantum dots that then are coated on the surface with something that's that makes them soluble and and harmless biologically and I do not know the details of what the the coding is this has been done previously in the East but this was the 1st example of it being done with that in large quantities was something like earthworms so anyway it's useful to be able to coat the quantum dots with something that's biocompatible such that you can use them in applications like cellular imaging another fluorescence application that I'd like to talk about his green fluorescent protein so you've probably seen this in different places I it was the subject of the the Nobel Prize in chemistry in 2008 green fluorescent protein has turned out to be useful for all kinds of biological experiments because you can tagging on as a fusion protein with other proteins and how they act as a signal inside itself so fusion making a fusion protein means that you tagged the GFP onto the gene for some other protein that you're interested in and then when the target protein is expressed the GFP be expressed to an enclosed in developed and so this has been used to make all kinds of important things like glowing green mice and and has anybody seen the the glowing zebra fish the there are legal in California and fortunately but you can buy fluorescent green version of places and again the seems kind of silly you can draw little landscapes with bacteria expressing different variants of GFP that Flores in different colors but it's fantastically useful in chemistry and biology because it enables people to look to make multiplexed assays with different colors and look at where different proteins are occurring using this marker so let's talk about how it works so here's the protein it has this been a barrel structure so it's like a can that it's holding the crown before inside wiring to talk about what the crime foreigners in detail in a minute and this is important because again the GFP ,comma 4 has a specific chemical structure but it also has to have this low dielectric constant environment to work has to be stuck in sight the protein if stick it out and put it in water it doesn't forecast and so you know
where it will be used in things like fluorescence microscopy to see just a lot of detail about what's going on In cell cities there are 2 examples of official I and some squared epithelial tissue where different fluorescent dye dyes being used in the microscopy so in this case that the green is GFP in this case it's another died but fluorescent tagging of different kinds whether it's expression of a protein of its binding of a forest molecule is used all over the place to see what's happening in the vote and keep track
of reactions OK so here's what the GOP for 4 years so it's got these 3 amino acid side chains tyrosine glycine and searing that undergo this reaction so this thing is covalently attached to the protein it's all inside that that giant beta barrel and when the GFP is expressed it doesn't Flores right away so that when it comes off the ribosome it's said the protein is not matured that's that's what the that's what the terminals and it takes some time for this reaction to happen these residues are arranged spatially in just the right place so that they can cycle eyes and lose water and then get oxidized and make the scramble for that then fluorescence but another thing that's really interesting about it is that you as we're you're talking about with the the a retinal inside lens proteins the wavelength at which the same interacts with light he evoked an instructor the absorption and the forces that you see can be shifted by changing the local protein environment around it and some people have been able to new shape this protein and you know partially by trial and error partially by using things like molecular-dynamics simulations to figure out which parts the protein a reporter for doing this and they've been able to generate all kinds of different colors of GFP variants and that enables people to use these multiplexed assays in different ways and so here's the arm certain what the crown for look like for slightly different variants of the GFP OK so those are some of the ways in which fluorescence is useful and you can see what some of the Carmel Forest look like again we have a lot of flat molecules were you can imagine they don't have so many degrees of freedom to move around and there near the trapped in this region protein structure and so emitting a photon is what
happens we can describe a lot of the things that happened with excited states using Jablonski program like this 1 OK so we started out in the ground state down here it's called S not angry again that were going to get into with S & T R in a minute and then we can have various things that can happen if this system absorbs the photons lessors purple line here and it goes up to 1 of these excited states in this case some S 1 then there are various pathways available to it so this dotted black line is alive non radiative decay so that's just it falls back down from that excited state without emitting a photon and we don't see that it's not so interesting so that means for measuring the absorbent slated for before using inspector for Tonga measuring absorption the observance with Beer's law will see it absorbs some light we can still observe that but if we're looking for fluorescence and that's the pathway that happens where to see anything now instead if from if electron then crosses over into this other state and falls back down from there we can also undergo radiative decay from that state again not so interesting we can we can still see that there's an absorption but the emissions doesn't look like anything and in this case the state multiplicity here matters so the ESA's Aurora singlet states and the team is tripled state and this should be bringing some bells from rating down from symbols from last quarter and if that's not don't worry too much because we're in a a review of it I think that you know it might be you might be good to go over again but so the spin multiplicity of the states is important so now we didn't fluorescence and phosphorescence these are the transitions where we fall back down from that excited state of photons emitted and we are ready said before then fluorescence that happens very quickly and phosphorescence is much slower so what's going on there is that if we have direct fluorescence that is a spontaneous emission of radiation so rubber photon following an excited state that has the same multiplicity is the ground state so we started out as an what state jumped up to a single state and photo phosphorescence is what you get if there interest system crossing service you know noticed that the potentials of these States overlap with each other and so sometimes the electron can can jump over here To the other states and that's called from crossing and then the electron falls back down from their that's phosphorescence it's usually slow and so this diagram is useful because it tells us about all these prophecies that can go on and helps us map out where the states are something we got a look at the spectra they're going to be pretty complicated because there are a lot of things going on in this diagram helps us mapped out should what they all mean let's see what else is there to say about this I also want to point out that this axis down here is intrinsically a distance and you know remember where were making the assumption that whatever the electrons do is fast relative to the nuclei so if we jump up to a particular excited state what's going to happen is you know that the nuclear I start out there you probably the equilibrium position as far as separations of their buy rating but you know an average Vladivostok from equilibrium state then we get up to some excited state and not excited state the optimal distance there may be different so you know what's happening is the electron gets excited the charge distribution is now really different other the shape of the the but or the state of the electron is has changed and so the nuclear start feeling that potential and that's going induced vibrations and start moving around and so on then you know that that's going to induce vibrations and and will see what happens there OK
so this is another version of that diagram sign like this 1 better
as far as being able see what's going on and I put this 1 in here to just because it has a lot of details as far as the timescales of what happens so you're here were killed were pointing out that the the excitation the absorption is happening really really fast so tender minus 15 seconds that's said yeah that's that's a very fast process and and we have found you know in the internal conversion vibrational relaxation compared to fluorescence so fluorescence here is on the order of their nanoseconds or so where phosphorescence happens over a much longer period of time so again this picture is all but confusing one's better but it does give you a lot of details about what actually happened OK so you know here we're talking about singled states in all the cases so I think in order to discussed this in a little bit more detail and talk about the selection rules we should do a really quick review of term symbols we think he did see the last quarter yes but maybe it's a little it didn't quite sink and perfectly clear sorry
about that but otherwise it's going to have a review before a user of a serene the back to General Chemistry for a minute or so we write electron configurations for Adams and periodic table using the off our rules which unlike going to state because I think everybody remembers these but the deal is that these only describe the ground state electron configuration they don't tell us anything about excited states and you have your talking electronic spectroscopy were really worried about what's going on with the excited states and worse than that their ambiguous there are often different ways to arrange the electrons In these configurations In terms of what the spinners yeah specifically what orbital therein and in general chemistry we didn't worry about you know if there was 1 electron a orbital we didn't worry about whether it was in the PX syrupy wire PC your role because we're assuming that the older generation and for free Adam that's true but for chemically interesting systems 1 hand it's not so we looked at what happens in different .period groups here depending on the local environment of the ad a lot of times those orbitals are not dinner with each other because of a foul the cemetery molecule
works so the problem here as far as the ambiguity in is that the stand electron configurations don't specify the values and synonymous with asked for a particular electron so if we have the ground state of war on nearly these electrons then we haven't specified which P or at last electron is going into then again if you're just talking about all right out out in a vacuum you don't care but for some of these applications it might not and so we need to be able to write down the term symbol I also want to point out that were not saying whether it's down so that the value of em and so this electron configuration is really ambiguous there a bunch of thought of different things going on so the terms state the term symbols unable us to distinguish between electron microscope so the microstate is just the specifics of exactly which orbitals again is it's been a person down and these things are characterized by the value of the orbital angular momentum which is Allah and that takes the values 0 1 2 3 4 etc. and these are labeled S P D D E F G just like In the atomic orbitals except for using capital letters here but so that's just it a way of telling the orbital angular momentum and then to get that value for the whole and we have to some or all of the electrons and then there's also an ass terminus spin angular momentum which is summed over all the electrons again and I was in increments of 1 half because electrons which been one-half and to ask plus 1 turned out to be an important quantity in the terms symbol the spin multiplicity so when we're talking about singlet and triplet states that's what we're talking about there and we also have to worry about the total angular momentum which is called Jr and that is equal to L process and so here's what where term symbol looks like so we have our value for the orbital angular momentum the multiplicity is to ask plus 1 and that's written as a site is the superscript in front of the L. and our total anglo momentum is written as a subscript again this should look familiar but you know maybe if you use it for anything right away that it's nice to have a little review OK so when we talk about the term symbols for a Adams we need to remember that we've got as the component of the the angular momentum which is a scalar and many the ANC the overall angular momentum is a vector and so we can consult both of these things over all the electrons in the attic so els e is what we get we sum up all of the and so values and S z is what we get for it summing up all the and Celeste values it's so vis-a-vis the options that that that can take so let's look at a higher rate these will start with an easy example and then we'll do our overlap OK so for helium out its electron configuration is 1 Saudi think is that 1 ambiguous is a pretty good it's good right we've got to adamantly that 2 electrons and that s orbital their parent there's nothing else they can do this one's actually really well specified so it's relatively easy to pay attention although micro-states and breaking down so what's do that for example were we know it's easy evasive and some Alpha the 1st electron and calling them 1 2 just for the sake of labeling of course we can't tell apart the electrons but we're here we're labeling them so if we have the first one it was spin you know we know and Sabella 0 because they're in an S or and if 1 of them is spin up the other 1 has to be spin down and so if we add up the total values Friends of elements investigate 0 for both and then we have To help was 1 values of begins at all but in this case the only value it's possible 0 and so we can deduce that L equals 0 and we know that ends the best goes plus system might assess increments of 1 2 1 values and the only answer best-value we have here is 0 and so as equals 0 also and then we can also some these things together To get Jr and we also get that equals 0 the what so again this isn't easy example but were going through how set up the Mike estates and then use the relevant values and so what we get out of this is the term symbol is a single address 0 so we have our spin multiplicity of Friday at the US tells us the value of the orbital angular momentum is 0 and then we have our J.
value and so this sum this single at state is what you get for anything that has a closed some shop that's when it's so that's where things like OK so now wants to harder example that 1 was very simple also get a carbon atoms so in this case we have a lot more micro-states that we have to worry about the war possibilities for the electrons to adopt different conformations and we have to fill some shells we have 1 has to to us too those are going to have a single 0 the term symbol any filled some Shell has it so we can just write that down OK so now we have to deal with the Tupi electrons and for that we have 6 possible spin orbitals so Aspin orbital is the combination of which not Is the electron and and what's its spinners it's been operation down and so on given that we have 6 possible spin orbitals that gives us 15 micro-states and somehow I got that is there our 6 places to put the 1st electron so it can be in each of the 3 fewer rules exceeded the upper down and then electrons can't occupy the same state in same manner and so when I go to put the 2nd 1 somewhere 1 of those configurations is already used up and so that gives me 5 options for the 2nd 1 but that the electrons are indistinguishable so only half of those microstate training so that's how we end up with 15 so let's figure out where what they are this means that you were going to go through and make a table of the microstate and organist see what the term similarly Geffen this we're going to get a bunch of term symbols corresponding to possible configurations of these electrodes are it's what we've got is we can have each electron in being either up a down so Alpha is spin that means and semesters plus one-half beta is spin down and semesters minus one-half and we can stick each electron any of the 3 pure rules and it can be the and so we're going to make a table of the possible micro-states that this thing can can occupy if we just have these 2 electrons and so the notation here is just you know I'm saying we've got the 1st electron I you it With its you we've got this antebellum value an EU pluses up and and minuses down let's do a couple of examples here so we've got 1 plus 1 plus of course we're going to see that that doesn't turn out to be a real the possibility because we can't have the electrons in the same state they can have the same set of quantum numbers and so forth and Savelli calls to we're going to see that the only possibility is the 1 in the middle if we go down and see and look for ways to come up with against Sevele equals 1 we can have 0 plus 1 plus 1 plus 0 minus 1 minus 0 plus there are different ways to add up to that value events at all 4 Antonelli will 0 there are even more different ways to to add this up so we've got options for and some illegals plus 1 0 at minus 1 and there are different ways to add a furor your micro-states to get that value and so we can go through make a table although the possible receipts that you can get and then what organist and if you don't get a chance to scribble this down don't worry about it it's all it's all going to be there and you know hopefully his review where is the somebody's micro-states violate the Polly exclusion principle so 1 plus 1 plus means you have and Sevele for electron 1 equals 1 and and suggested that 1 equals 1 half and so on and so for electrons to Israel's 1 and this 1 also has plus one-half and that's not a lot of violates police Clinton principles so I started by just writing down all the possibilities that you could have but this 1 doesn't work and we can see the same thing for 1 minus one-liners and so you know we can go through and all of these micro-states they're forbidden by the exclusion principle and we see that we get 15 micro-states left as we expect so he knows those are just written down for completeness you're going through all of the possible micro-states that could exist but those that who do not work out till its work with the ones that are left and so now what we're going to do is go through and find the arms the values of begin Sevele and against us so that we haven't L S & J values and so on the largest valued and Sibelle is and that happens when and so equals 0 so L equals 2 and as equals 0 for this particular term symbol so we can write that down as some kind of a single entity state so we still haven't found J but we can say that for later and so if l equals 2 then we have our own values of begins at all as 2 1 0 minus 1 and minus 2 and so now we need to account for all the maker states corresponding to those from the stable so we want to pass out which 1 microstate from each Ichiro the middle column so don't get
confused between looking at you know things that violate the exclusion principle and things that were crossing out because we've accounted for in the term symbol so we're just saying this microstate is accounted for by these particular values of Ellen as they belong to the same with the state so we have 1 In this work and bring across that 1 from each row why did I picked this particular ones it's arbitrary we just want know How many of these micro-states belong to that particular the term symbol OK so that accounts for that particular term symbol we still have a bunch of estates left so the next value of sensible equals 1 is a sensible equals 1 and if that happens when we have values events about there plus 1 0 minus 1 now we need to account for those micro-states so well equals 1 spend multiplicity is now 3 sources of triplet peace state and so we need to account for the mike estates that correspond to that and again crossing at 1 from each other Place in an arbitrary manner In that gets rid of 9 of them and so now we have left is instability will 0 in Sebastopol 0 and that gives us a single state so we know which term symbols are available from this carbon atoms and we just have to find the subscript problem so we have a single the state we know that and sabbatical 0 and so here are possible values for and J. we've got from to minus-2 in increments of 1 and so that means that day has to be too In so years our final term symbol for that and we also know that the DeGeneres used to date was once so that's 5 and then we can move on to the triplet peace states that we found and we have all of these values for and some day and so we can see that J-PAL's too for that 1 also yeah so we have to use so again here we have to be careful because we have more than 1 set of J values so we have 1 set 2 1 0 minus 1 minus 2 that corresponds to staples too but then we also have a set corresponding to J. equals 1 we have 1 0 and 1 in there and then we also have an extra day 0 left over and so we get 3 of these tripled states with different values of J and then the last thing we have left over is this single state that's just sing would pass 0 and so if you have an electron configuration ending in and P 2 these are the term symbols that that we end up with format OK How do you know which 1 of these is the ground state so who owns rule tells us that the state with the largest value investors the most stable if you have states that have the same value about us then higher L value is more stable if these are the same than which 1 is more stable depends on whether the sum shall is more a less than half and so forth this particular set of terms stumble symbols the report he 0 as the ground state OK so that is just a review of term symbols and that is a different way of doing it from how it is in your book if you like how is in your book better that's completely fine if you like this by better that's good too question and PTO heirs the end of an electron configurations and here we said 1 has to 2 S 2 2 PTO you have you had any electron configuration you will get a bunch of singlet that's 0 states for the closed shells and and this would give you the details electron so 1 thing that's nice about term symbols is that you know once you figure out how to do it there's really a limited number of of options for electron configurations OK so what were really interested in for stuff that warranted due this quarter is term symbols for new molecules so you know we just 1 over the atomic once just as review so hopefully remember whatsoever what they look like butter for these types of things that were going to do in terms of talking about selection rules electronic transitions were interested in the ones related molecules so here's what they look like basically were just were using Greek letters instead of English letters for a lot of terms and in the term symbol but here S is the total spin quantum number and you know this which was l before its capital landed here that's the orbital angular momentum along the introduce clear access so that's it's a linear molecule so it's along the the bond for many here is the totaling lamented the tunneling lamented as opposed to the orbital angular momentum going into nuclear and GE or you is the parity that and that's with respect to reflection through an emergency feminine Paulson minus is the reflection symmetry along the plane that contains the Internet clear access and we probably need to look at some pictures for this to make a lot of sense so and are there from German there is that the words ElBaradei in broader and that means even and odd basically sir the available
to your memorandum I a wave
function is gene or even if it doesn't change under a version and it's all if it does so GNU just described if we inverters linear molecule its wave function change sign or not and in central symmetric environments like a linear molecule anything that hasn't version center transitions between at G 8 and G or UN-AU are forbidden and we shared which should be clear why this is from the Vinod role if we have an even times even or odd times in autumn and then we stick the odd operator in between 14 and up with and on function in an in an environment like this where there's an inversion center that's called the ports role again only works if you molecule has an inversion center so if you have the states of the same name here
to Jesus to use then that's a forbidden transitions and otherwise it's allowed and so I think that is what organization about terms symbols for right now if file if you need to review how to do atomic term symbols please do we're not going to spend a lot of time on it's not something that I really can test you on right now we distributed in order to understand what the ones for linear molecules look like and next time we talk about selection rules and actual transitions have next weekend
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