Molecular Structure & Statistical Mechanics 131B. Lecture 13. Electronic Spectroscopy (Pt. II)

okay so let's 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 4s or 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 one of the the things that's that's fun about P chem is that there's really a lot that we can go into that's beyond what's in your book and beyond the things that we can do in class and I just want to mention a few of these things so we can take advantage of the the interaction between electronic and vibrational states in resonance Raman so remember we've talked multiple times about the idea that in using these different kinds of spectroscopy we get a lot of interplay between different kinds of excited States so for example in vibrational spectroscopy we see all the rotational states were exciting something to annex you know to an upper vibrational state the rotations get excited similarly in electronic spectroscopy a lot of times we see the vibrational states and sometimes the rotational States too if we have enough resolution we can also use electronic states to enhance the intensity of particular Raman modes so we we talked about how Raman spectroscopy is useful in terms of looking at vibrational modes in molecules but one disadvantage that it has is that the signal is very weak compared to direct IR spectroscopy so when we're looking at scattered light you know the most of the light just scatters straight off in the Rayleigh line it doesn't gain or lose energy and you just see the same wavelength of light that you put in resonance Raman deals with that problem it's enhanced and it also deals with the problem of having a very complex small it has a lot of vibrational modes so if we think about you know instead of having these simple molecules that we've been looking at and what if you have a protein so imagine you know 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 that you're going to have all these Peaks all on top of each other and there's not really a good way to interpret it so resonance Raman deals with both of these problems at once and if we do that by putting in your so we're exciting vibrational states that are associated with a particular electronic state so if we're on resonance with a particular electronic excited state then vibrational modes that are associated with that particular state are 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 that we're not interested in are not visible there they just fade into the background so here's an application of that this is something that's from Judy Kim's lab at UC San Diego so if she's interested in looking at electronic electrostatic potentials of Ezrin Azorean is an enzyme that that deals with electron transfer and one of the things that professor kim has done is she's looked at tryptophan and the you know the sidechain of tryptophan is involved in the the reaction in this case she can make radicals on this particular side chain and look at the difference between tryptophan in an environment where it's exposed to the solvent and where it's not and it turns out that these look very different and that has some implications for how the enzyme functions and you can see the difference between these two things in looking at the resonance Raman spectrum so being able to have these vibrational modes in chanst only near this particular electronic state in this case in a rare amino acid where you don't have very many of them in the protein in fact I think everyone has to one that's in the solvent one that's not that enables you to to learn some very specific information about this molecule in where otherwise it would be very complicated but probably water so it's well definitely water in this in this case so the protein is is soluble but of course the inside of it is a hydrophobic environment so the tryptophan that's that's just surrounded by the rest of the protein is going to have a different dielectric constant in a different local environment than one that's closer to the surface that can interact with the water okay so that's just a hint as to to where we can go with with some of this stuff and how electronic spectroscopy can interact with vibrational spectroscopy let's talk about fluorescence so last time we talked about what happens to excited States a lot of them just relax back and produce heat it's not so much fun some molecules dissociate and fall apart you know then they do photochemistry but other ones undergo fluorescence and phosphorescence and this is pretty interesting so here's an example from my lab these are fluorescent bacteria that that we found at some point a couple of years ago and we still don't know what molecule makes these things fluorescent but they look neat and they illustrate what we're talking about so here the excitation wavelength has its in right on the edge of the UV like we can see some purple light and then the fluorescence is a little bit bluer and we can see that here if we look at the spectrum so the excitation wavelength is is shorter it's a closer to the UV and then here's that emission wavelength here's some other examples so these are quantum dots of various sizes that are fluorescent if you radiate them with you they shine in in the visible and depending on the size of the quantum dots we see different colors so do you guys know about quantum dots is that something that comes up in in chem II okay they're really interesting so these are these are little nanoparticles of a semiconductor material so in some cases you know cadmium telluride cadmium sulfide is another good quantum dot material and their exit ons are confined in three dimensions so it behaves as kind of an intermediate between a lot like a giant molecule and a bulk semiconductor and they're useful for all kinds of things mainly just detecting stuff I mean they're they're interesting from a fundamental physics and chemistry perspective just trying to understand how they work but they're also used in imaging applications we can irradiated UV light and then see their fluorescence and here's an interesting application of this these green quantum dots in this picture which are being used for cellular imaging we're actually biosynthesized by earthworms so this group discovered that you can feed earthworms soil contaminated with cadmium and tellurium and they poop out quantum dots that are mono dispersed and have this particular size that are green in this picture the blue is a dye that stains the nuclei of the cells and so this is just proving that they can put these quantum dots that were made by the earthworms into actual cells and use them for imaging so why is that useful I mean it's funny but it's it's actually interesting as well because one of the problems with with quantum dots in biological applications is that these things are really toxic so it's actually pretty amazing that earthworms can eat soil that's contaminated with cadmium and tellurium at all and not die but what they do is they they have these enzymes called metallo findings that bind these these toxic metals and and packaged 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 coating is this has been done previously in yeast but this was the first example of it being done with in large quantities with something like an earthworm so anyway it's useful to be able to coat the quantum dots with something that's biocompatible such that you could use them in applications like cellular imaging another fluorescence application that I'd like to talk about is green fluorescent protein so you've probably seen this in different places 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 tag it on as a fusion protein with other proteins and have it act as a signal inside the cell so fusion making a fusion protein means that you tagged the GFP on to the gene for some other protein that you're interested in and then when the target protein is expressed the GFP will be expressed too and it glows in vivo 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 zebrafish the glow fish they're illegal in California unfortunately but you can buy fluorescent green fish in other places and again this seems kind of silly you can draw a little landscapes with bacteria expressing different variants of GFP that fluoresce 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 beta barrel structure so it's like a can that it's holding a chromophore inside and we're going to talk about what the chromophore is in detail in a minute and this is important because again the GFP chromophore has a specific chemical structure but it also has to have this low dielectric constant environment to work it has to be stuck inside the protein if you just take it out and put it in water it doesn't fluoresce and so you know we're able to use things like fluorescence microscopy to see just a lot of detail about what's going on in cells so these are our two examples of a fish eye and some squid epithelial tissue where different fluorescent dye is being used in the microscopy so in this case the green is GFP in this case it's another die but fluorescent tagging of different kinds whether it's expression of a protein or if it's binding of a fluorescent molecule is used all over the place to see what's happening in vivo and keep track of reactions okay so here's what the GFP fluorophore is so it's got these three amino acid side chains there's a tyrosine a glycine and a serine 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 fluoresce right away so it when it comes off the ribosome it's the protein is not matured that's that's what the that's what the term is and it takes some time for this reaction to happen these residues are arranged spatially in just the right place so that they can cyclize and lose water and then get oxidized and make this chromophore that then flores's but another thing that's really interesting about it is that you know as we were talking about with the the retinol inside lens proteins the wavelength at which this thing interacts with light you know both in terms of the absorption and the fluorescence that you see can be shifted by changing the local protein environment around it and so people have been able to mutate this protein and you know partially by trial and error partially by using things like molecular dynamics simulations to figure out which parts of the protein are important 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 multiplex assays in different ways and so here's the sort of what the chromophore is look like for slightly different variants of GFP okay so those are some of the ways in which fluorescence is useful and you can see what some of the chromophore is look like again we have a lot of flat molecules where you can imagine they don't have so many degrees of freedom to to move around and they're you know they're trapped in this rigid protein structure and so emitting a photon is what happens we can describe a lot of the things that happen with excited States using a drip lansky diagram like this one okay so we start out in the ground state down here it's called s naught and we're gonna we're going to get into what s and T are in a minute and then we can have various things that can happen so if this system absorbs a photon so that's this Purple Line here and it goes up to one of these excited States in this case s1 then there are various pathways available to it so this dotted black line is 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 and it's not so interesting so that means if we're measuring the absorbance like if we're if we're using a spectrophotometer and measuring the absorption the absorbance with beers law will see that it absorbs some light we can still observe that but if we're looking for fluorescence and that's the pathway that happens we're not going to see anything now instead if if the electron then crosses over into this other state and falls back down from there we can also undergo non radiative decay from that state again not so interesting we can we can still see that there's an absorption but the emission doesn't look like anything and in this case the state multiplicity here matters so the esses are singlet States and the T is a triplet state and this should be ringing some bells from writing down term symbols from last quarter and if it's not don't worry too much because we're gonna do a little review of it I think you know it might be it might be good to go over it again but so the spin multiplicity of these states is important so now when we get into fluorescence and phosphorescence these are the transitions where when we fall back down from that excited state a photon is emitted and we already said before that in 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 of a photon from an excited state that has the same multiplicity as the ground state so we started out in a singlet State jumped up to a singlet state and then emitted a photon phosphorescence is what you get if there's inter system crossing so this you know notice that the potentials of these upper States overlap with each other and so sometimes the electron can can jump over here to this other state and that's called inter system crossing and then the electron falls back down from there that's phosphorescence and it's usually slow and so this diagram is useful because it tells us about all of these processes that can go on and helps us map out where the states are so when we go to look at the spectra they're gonna be pretty complicated because there are a lot of things going on and this diagram helps us map out what they all mean so let's see what else did I want to say about this I also wanted to point out that this axis down here is intranuclear distance and you know remember we're we're 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 gonna happen is you know the the nuclei start out at there you know probably the equilibrium position as far as separation so they're vibrating but you know on average they're going to start out from the equilibrium state then we get up to some excited state and in that excited state the optimal distance there might be different so you know what's happening is the electron gets excited the charge distribution is now really different you know the the the shape of the the orbital or the state that the electron is in has changed and so the nuclei are gonna start feeling that potential and then that's gonna induce vibrations they're gonna start moving around and then you know that that's going to induce vibrations and and we'll see what happens there okay so this is another version of that diagram so I like this one better as far as being able to see what's going on I put this one in here too just because it has a lot of details as far as the time scales of what happens so you know here we're we're pointing out that the the excitation or the absorption is happening really really fast so 10 to the minus 15 seconds that's you know that's that's a very fast process and then we have you know in the internal conversion and vibrational relaxation you know compared to fluorescence so fluorescence here is on the order of nanoseconds or so whereas phosphorescence happens over a much longer period of time so again this picture is a little bit confusing the other ones better but it does give you a lot of details about what actually happens okay so you know here notice we're talking about singlet States in all the cases so I think in order to discuss this in a little bit more detail and talk about the selection rules we should do a really quick review of term symbols what do you think you did see them last quarter yes yes but maybe it's a little it didn't quite sink in perfectly if it did sorry about that but otherwise it's good to have a review before we use it okay so we're gonna go back to general chemistry for a minute so we write electron configurations for atoms in the periodic table using the Alpha power rules which I'm not gonna 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 know here we're talking about electronic spectroscopy we're really worried about what's going on with the excited States and worse than that they're ambiguous there are often different ways to arrange the electrons in these configurations in terms of what their spin is you know specifically what orbital they're in and in general chemistry we didn't worry about you know if there was one electron in a p orbital we didn't worry about whether it was in a px or a py or PZ orbital because we're assuming that they're all degenerate and for a free atom that's true but for chemically interesting systems a lot of times it's not so we've looked at what happens in different point groups you know depending on the the local environment to the atom a lot of times those orbitals are not degenerate with each other because of how the symmetry of the molecule works so the problem here as far as the ambiguity is that the standard electron configurations don't specify the values in M sub L and M sub s for a particular electron so if we have the ground state of boron and we fill in these electrons then we haven't specified which p orbital that last electron is going into and again if you're just talking about a boron atom out in vacuum you don't care but for some of these applications it might matter and so we need to be able to write down the term symbol I also want to point out that we're not saying whether it's spin up or spin down so that's the value of M sub s and so this electron configuration is really ambiguous there are a bunch of of different things going on so the term state the term symbols enable us to distinguish between electron micro states so the micro state is just the specifics of exactly which orbital is it in is it spin up or spin down and these things are characterized by the value of the orbital angular momentum which is L and that takes the values 0 1 2 3 4 etc and these are labeled s P D F G just like in the atomic orbitals except we're using capital letters here but so that's just a way of telling the orbital angular momentum and then to get that value for the whole atom you have to sum over all of the electrons and then there's also an S term the spin angular momentum which is summed over all of the electrons again and that goes in increments of 1/2 because electrons are spin 1/2 and 2's plus 1 turned out to be an important quantity in the the term symbol that's 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 J and that is equal to L plus s and so here's what your term symbol looks like so we have our value for the orbital angular momentum the multiplicity is 2 s plus 1 and that's written as a superscript in front of the BL and then our total angular momentum is written as a subscript again this should look familiar but you know maybe if you didn't use it for anything right away it it's nice to have a little review okay so when we talk about the term symbols for atoms we need to remember that we've got a Z component of the the angular momentum which is a scalar and then the overall angular momentum is a vector and so we can sum both of these things over all the electrons in the atom so LZ is what we get when we sum up all of the M sub L values and SZ is what we get for summing up all of the M sub s values so these are the the options that that that can take so let's look at how to write these we'll start with an easy example and then we'll do a harder one okay so for helium atom its electron configuration is 1s2 so what do you think is that one ambiguous or is it pretty good it's good right we've got two atom we've got two electrons and that s orbital they're paired there's nothing else they can do this one's actually really well specified so it's relatively easy to pay attention to all the microstates and write them down so let's do that for an example where we know it's easy okay so M sub L for the first electron I'm calling them one two just for the sake of labeling of course we can't tell them apart because their electrons but we're here we're labeling them so if we have the first one as spin up you know we know M sub L is zero because they're in an S orbital and if one of them is spin up the other one has to be spin down and so if we add up the total values for M sub L and M sub s we get zero for both and then we have 2l plus 1 values of Big M sub L but in this case the only value that's possible is 0 and so we can deduce that l equals 0 and we know that M sub s goes from plus s 2 minus s and increments of 1 to s plus 1 values and the only M sub s value we have here is 0 and so s equals 0 also and then we can also sum these things together to get J and we also get that J equals 0 so again this is an easy example but we're just going through how to set up the microstates and then deduce the relevant values and so what we get out of this is the term symbol is singlet s0 so we have our spin multiplicity out in front of it the s tells us the value of the orbital angular momentum is 0 and then we have our J value and so this this singlet state is what you get for anything that has a closed subshell that's what it's that's what it's going to look like ok so now let's do a harder example that one was very simple let's look at the carbon atom so in this case we have a lot more microstates that we have to worry about there are more possibilities for the electrons to adopt different confirmations and we have two filled sub shells we have one s 2 + 2 s 2 those are going to have this singlet s0 term symbol any filled sub shell has it so we can just write that down ok so now we have to deal with the 2p electrons and for that we have six possible spin orbitals so a spin orbital is the combination of which orbital is electron in and what's its spin is it spin up or spin down and so given that we have six possible spin orbitals that gives us 15 microstates and so how I got that is there are six places to put the first electron so it can be in each of the three P orbitals and it can either be up or down and then electrons can't occupy the same state in the same atom and so when I go to put the second one somewhere one of those configurations is already used up and so that gives me five options for the second one but then the electrons are indistinguishable so only half of those microstates are unique so that's how we end up with 15 so let's figure out what they are this means that you know we're going to go through and make a table of the microstates and we're gonna see what the term symbols are that we get from this we're gonna get a bunch of term symbols corresponding to possible configurations of these electrons all right so what we've got is we can have each electron in being either spin up or spin down so alpha is spin up that means M sub s is plus 1/2 beta is spin down M sub s is minus 1/2 and we can stick each electron in any of the 3 P orbitals and it can be either up or down and so we're gonna make a table of the possible microstates that this thing can can occupy if we just have these two electrons and so the notation here is just you know I'm saying we've got the first electron you know in with its you know we've got this M sub L value and you know Plus is up and and minus is down let's let's do a couple of examples here so we've got 1 plus 1 plus of course we're gonna see that that doesn't turn out to be a real possibility because we can't have the electrons in the same they can't have the same set of quantum numbers and so for M sub l equals two we're gonna see that the only possibility is the one in the middle if we go down and see and look for ways to come up with Big M sub l equals one 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 of M sub L for M sub l equals 0 there are even more different ways to to add this up so we've got options for m sub l equals +1 0 and minus 1 and there are different ways to add up your your microstates to get that value and so we can go through and make a table of all the the possible microstates that you can get and then what we're gonna see and if you don't get a chance to scribble all this down don't worry about it it's all it's all gonna be there and you know hopefully this is review we're gonna see some of these microstates violate the Pauli exclusion principle so one plus one plus means you have M sub L for electron one equals one and M sub s for that one equals one-half and M sub L for electron two equals one and this one also has plus 1/2 and that's not allowed it violates the Pauli exclusion principle so I started by just writing down all the possibilities that you could have but this one doesn't work and we can see the same thing for one minus one minus and so you know we can go through and can all of these microstates that are forbidden by the exclusion principle and we see that we get 15 microstates left as we expect so you know those those are just written down for completeness you know going through all the the possible microstates that could exist but those do not work out so let's work with the ones that are left and so now what we're gonna do is go through and find the the values of Big M sub L and Big M sub s that we have and deduce our LS and J values and so the largest value of M sub L is 2 and that happens when M sub s equals 0 so l equals two and s equals zero for this particular term symbol so we can write that down as some kind of a singlet D State so we still haven't found J but we can save that for later and so if l equals 2 then we have values of Big M sub L as 2 1 0 minus 1 and minus 2 and so now we need to account for all of the microstates corresponding to those from this table so we want to cross out which one microstate from each row of the middle column so don't get confused between looking at you know things that violate the exclusion principle and things that we're crossing out because we've accounted for it in the term symbol so we're just saying this microstate is accounted for by these particular values of L and s they belong to the singlet D State so we have one in this row and we're going to cross out one from each row why did I pick those particular ones it's arbitrary we just want to know how many of these microstates belong to that particular term symbol okay so that accounts for that particular term symbol we still have a bunch of microstates left so the next value of M sub l equals was M sub l equals 1 and that happens when we have values of M sub s that are plus 1 0 and minus 1 so now we need to account for those microstates so l equals 1 our spin multiplicity is now 3 so this is a triplet P state and so we need to account for the microstates that correspond to that and again crossing out one from each place in an arbitrary manner and that gets rid of nine of them and so now all we have left is M sub l equals 0 M sub s equals 0 and that gives us a singlet s State so we know which term symbols are available from this carbon atom and we just have to find the subscripts for all of them so we have the singlet D State we know that M sub s equals 0 and so here are our possible values for M sub J we've got you know from 2 to minus 2 in increments of 1 and so that means that J has to be 2 and so here's our final term symbol for that and we also know that the degeneracy is 2 J plus 1 so that's 5 and then we can move on to the triplet P states that we found and we have all of these values for M sub J and so we can see that J equals 2 for that one also you know so we have these so again here we have to be careful because we have more than one set of J values so we have one set of you know 2 1 0 minus 1 minus 2 that corresponds to J equals 2 but then we also have a set corresponding to J equals 1 we have 1 0 and minus 1 in there and then we also have an extra J equals 0 left over and so we get 3 of these triplet States with different values of J and then the last thing we have left over is this singlet state that's just singlet s0 and so if you have an electron configuration ending in NP – these are the term symbols that that we end up with from that okay so how do you know which one of these is the ground state so hoods role tells us that the state with the largest value of s is the most stable if you have states that have the same value of s then the higher elven if these are the same then which one is more stable depends on whether the sub shell is more or less than half-full and so for this particular set of terms two symbols the triplet p0 is the ground state okay so that is just a review of term symbols that is a different way of doing it from how it is in your book if you like how it is in your book better that's completely fine if you like this way better that's good too question NP – is the end of an electron configuration so here we said 1s2 2s2 2p2 you know if you had any electron configuration you would get a bunch of singlet s0 states for the closed shells and then this would give you the valence electron so one 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 okay so what we're really interested in for stuff that we're gonna do this quarter is term symbols for linear molecules so you know we just went over the atomic ones just as a review so hopefully you remember what what they look like but for the types of things that we're gonna do in terms of talking about selection rules and electronic transitions we're interested in the ones for linear molecules so here's what they look like basically we're just we're using Greek letters instead of English letters for a lot of the terms in the in the term symbol but here s is the total spin quantum number and you know this which Elba for its capital lambda here that's the orbital angular momentum along the internuclear axis so that's it's a linear molecule so it's along the the bond Omega here is the total angular momentum the total angular momentum as opposed to the orbital angular momentum along the inner nuclear axis and G or U is the parity that's and that's with respect to reflection through an inversion Center and then plus and minus is the reflection symmetry along a plane that contains the inter nuclear axis and we probably need to look at some pictures for this to make a lot of sense so G and you are there from German there if the the words are gerado and in grata and that means even a nod basically so maybe I don't help you remember I don't know a wave function is G or even if it doesn't change under inversion and it's odd if it does so G and you just describes if we invert this linear molecule does its wave function change sign or not and in centrosymmetric environments like a linear molecule anything that has an inversion Center transitions between a G at a G or au and au are forbidden and we should it should be clear why this is from the even-odd rule if we have an even times an even or an odd times an odd and then we stick the odd operator in between we're going to end up with an odd function in a in an environment like this where there's an inversion Center and that's called the port's rule and again it only works if your molecule has an inversion Center so if you have states have the same you know two G's or to use then that's a forbidden transition and otherwise it's allowed and I think that is what we're gonna say about term symbols for right now if if you need to review how to do atomic term symbols please do we're not gonna spend a lot of time on it it's not something that I'm really going to test you on right now we just reviewed it in order to understand what the ones for linear molecules look like and next time we're going to talk about selection rules and actual transitions have a nice weekend you

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