Lecture 27. CH4 Molecular Orbitals and Delocalized Bonding


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Lecture 27. CH4 Molecular Orbitals and Delocalized Bonding
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Lecture 27. Quantum Principles: CH4 Molecular Orbitals and Delocalized Bonding
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Shaka, Athan J.
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UCI Chem 131A Quantum Principles (Winter 2014) Instructor: A.J. Shaka, Ph.D Description: This course provides an introduction to quantum mechanics and principles of quantum chemistry with applications to nuclear motions and the electronic structure of the hydrogen atom. It also examines the Schrödinger equation and study how it describes the behavior of very light particles, the quantum description of rotating and vibrating molecules is compared to the classical description, and the quantum description of the electronic structure of atoms is studied. Index of Topics: 0:01:38 MO Picture for CH4 0:13:53 CH4 PES 0:18:52 Delocalization 0:21:45 Ethylene 0:34:02 Benzene 0:43:44 Aromaticity
Chemical bond Atomic orbital Solution Chemical bond Hybridisierung <Chemie> Man page Pauling, Linus Chemistry Reactivity (chemistry) Chemical reaction PH indicator Electron Atomic orbital Chemical structure Delocalized electron
Diethylstilbestrol Atomic orbital Hydrierung Carbon (fiber) Chemical bond Linear combination of atomic orbitals Electronic cigarette Molecule Functional group Atomic orbital Valence (chemistry) Chemical structure Methane Atom Calculus (medicine) Nucleolus
Bearing (mechanical) Carbon (fiber) Atomic orbital Solution Molecule Functional group Electron Periodate Carbon Ionenbindung Ene reaction Hydrierung Carbon (fiber) Copper Topicity Chemical bond Wine tasting descriptors Combine harvester Computer animation Match Functional group Blue cheese Atomic orbital Molecule Chemical structure Tetraederstruktur Base (chemistry) Nucleolus Isotopenmarkierung
Combine harvester Bearing (mechanical) Ionisationsenergie Sunscreen Hydrierung Atomic orbital Carbon (fiber) Chemical bond Lithium Atomic number Calculus (medicine)
Phase (waves) Surface science Trauma (medicine) Carbon (fiber) Ionenbindung Density Hydrierung Atomic orbital Atomic number Carbon (fiber) Chemical bond Hydro Tasmania Hydrogen Electron Atomic nucleus Blue cheese Atomic orbital Colourant Tetraederstruktur Methane Nucleolus
Carbon (fiber) Atomic orbital Atomic number Chemical bond Methane Atom Carbon
Bearing (mechanical) Cross section (geometry) Sunscreen Atomic orbital Valence (chemistry) Katalase Binding energy Organische Verbindungen Hybridisierung <Chemie> Molecule Electron Methanisierung Emission spectrum Ocean Stratotyp Library (computing) Ausgangsgestein Natural gas Photoelectric effect Periodate Hydrophobic effect Area Golgi apparatus Ionenbindung Hydrierung Carbon (fiber) Chemical bond Hybridisierung <Chemie> Man page Erdrutsch Electronic cigarette Emission spectrum MO-Theorie Systemic therapy Tiermodell Magnetism Coordination complex Tetrahydrofuran Chemical structure Electron Medical history
Butcher Physical chemistry Ethylene Carbon (fiber) Meat Atomic orbital Aromaticity Hydrogen Molecule Hydrocarbon Electron Methanisierung Feinchemikalie Naphthalin Benzene Potenz <Homöopathie> Pond Doppelbindung Hydrierung Carbon (fiber) Chemical bond Protonation Food additive Amrinone Systemic therapy Alcohol by volume Computer animation Atomic orbital Water level Can (band) Naphthalin Carbohydrate Nucleolus Chemist Hydrocarbon Isotopenmarkierung Ethylene
Homocysteine Chemical bond Atomic orbital Reactivity (chemistry) Molecule Chemical reaction Electron Cupcake Lactitol Emission spectrum Golgi apparatus Homocysteine Doppelbindung Chemical engineering Carbon (fiber) Chemical reaction Chemistry Adenosine Emission spectrum Functional group Atomic orbital Molecule Chemical structure Isotopenmarkierung Ethylene
Ageing Chemical bond Atomic orbital Hybridisierung <Chemie> Wursthülle Atomic number Optical coherence tomography Amrinone Hydrogen Systemic therapy Computer animation Tiermodell Functional group Atomic orbital Chemical structure Electron Medical prescription Hydrophobic effect Carbon Atom Carbon Ethylene
Semiotics Golgi apparatus Hydride Resonance (chemistry) Solution Wursthülle Alpha particle Combine harvester Computer animation Electron Atomic orbital Azo coupling Beta sheet Organic food Stuffing Calculus (medicine) Ethylene
Ham Drainage divide Atomic orbital Erdrutsch Man page Alpha particle Amrinone Systemic therapy Atomic orbital PICT Benzene Chemical structure Helium Benzene
Alpha particle Potenz <Homöopathie> Sunscreen Yield (engineering) Atomic orbital Chemical structure Benzene Electronic cigarette
Whitewater Doppelbindung Density Atomic orbital Chemical bond Food additive Molecule Combine harvester Drop (liquid) Electron Methanisierung Functional group Chemical structure Benzene Active site Chemical structure Hexagonal crystal system Benzene RWE Dea AG
Carcinogenität Cyclobutadien Carbon (fiber) Chemist Wursthülle Cyclooctatetraen Wine tasting descriptors Food additive Aromaticity Systemic therapy Water Chemical reaction Molecule Electron Molecule Chemical structure Benzene Electron Naphthalin Azulene Chemist Calculus (medicine)
Resonance (chemistry) Chemical plant Aromaticity Drink Chemistry Molecule Electron Lactitol Konstitutionsisomerie Blue cheese Naphthalin Orange juice Benzene Helium Azulene River mouth Doppelbindung Hydrierung Carbon (fiber) Stockfish Derivative (chemistry) Fumigation Systemic therapy Blue cheese Chemical structure Electron Naphthalin Chemist Pipette
Stop codon Sense District Systemic therapy Electron Doppelbindung Chemical structure Electron Cyclooctatetraen
right let's pick up where we left off
we had just gone through the Linus Pauling is brilliant exposition on hybrid orbitals which is still used to this very day to rationalize a lot of things to do with structure and reactivity but let's take a closer look let's compare the hybrid orbital approach which releases from let's make pairs of electrons make bonds with the molecular orbital approach which says the way you have to do it is the way he did it with an man you have to put all positive charges where they're supposed to be and then you have to solve it and then you have to get the solution and then you can put in a year electrons into the oracles and they go into the lowest energy it once and this is a more the local artists approach to bonding because that if you're including all the nuclear but once then there's no reason why he should be drawn lines that makes a little harder for to understand that when you're drawing structures and you're pushing the lines around tennis love of those lines because it allows them to write and rationalize reactions but occasionally reaction goes it doesn't seem to behave and that could be an indication that maybe the theory of the lines is falling apart a little bit a let's talk and that about Morty localized bonding In the demo
picture we don't make hybrid orbitals so the it is used but it's completely different we must not confuse the 2 in the molecular orbital picture what we had said we had to do was we could combine together atomic orbitals that had the same Syngman Rhee similar energy it and overlapped in space for Tagesspiegel molecule with essential and like nothing we've got 4 carbon valence atomic orbitals the U.S. and 3 keys we have to know the structure why well otherwise we have to move things around and calculate the energy as a function of R & R 2 and R 3 and we already know the structure etc. draw what we want to understand it's not the structure so much we want to understand the bonding How is it working what's going on so we assume we know the structure is the same structures policy but the description of the bonding is going to be different and that's the thing that we're going to focus on those in the ammo approach you have to know the structure 1st if you don't you have to search through all possible structures if you're doing that that is a very very very long-winded and intensive calculation although sometimes people do do it just to see what might be the most stable structure if there's no experimented there it has hasn't been made let's put
our hydrogen atoms at the corners of the same you that we had before it experienced C & H D and let's see what we're going to do with these for the carbon is at the center and with our floor hydrogen orbitals and for carbon orbitals we get a molecular orbitals because recalled the linear combination of atomic orbitals rubric weak I have the same number of Oracle's that if at the end in terms of molecular orbitals what we started with OK now question is
which orbitals can we combined and the answer is ruled Tuesday but they have to have the same cemetery for this molecule and what that means is that we cannot do what appalling dead because we cannot combine the carbon to us in the car to please the aura of the other 2 peas because those have different cemetery therefore if we want to consider the 2 on cotton we can combine it with any of other atomic orbitals on copper we have to said combine it with combinations of the the hydrogen or orbitals at the 4 positions of the that completely different than because now we won't necessarily end up with 4 identical lines in terms of 4 localized bonds we will end up with the territory legal structure that's for sure because we started with them but our description of the bonding will be different now the game is that we have the carbon orbital each of the 4 of them has different cemeteries we have to combine the 4 hydrogen so that they have the same symmetry as the carbon orbital and that's pretty easy to do because is the carbon orbitals a big fat around the match means that these guys have to be as round as possible so they should just all year and that should be 1 and if the carbon orbital changes signed by plus here and minus here always going to have regions on the topic they should be class 2 hires is on about the they should be mine and so forth and so there is a combination of hydrogen but goes perfectly with each of the 4 combinations on the card and that's how that's how we're going to do so for 2 us we use 1 essay what plus 1 and plus 1 a C plus 1 st although as round as can be and this if they're already the 2 as Israel and all these guys rare this makes a gigantic orbital with no notes that goes around all the nuclei and has roughly spherical symmetry and it's called a 1 which is a cemetery label that lets suspect crossed the snow at the symmetry of the molecular orbital areas and that name anyone has to do with its cemetery under the territory he wrote .period group TD that you'll learn about later in the courts for now just treat anyone as as a label that tells us which which orbital were talking about remember
the less notes is lower energy and so we've got this big red thing with this big fluffy thing sort of looks like a teddy bear with no notes therefore anyone has the lowest cemetery that's what we predicted above it and our 3 the general because related by symmetry orbitals and there's 1 for each of the orbitals on carbon atoms and those three-year Kulti to the 3 unnamed that has to do again with the cemetery under the territory he dropped .period group the 1 and to have meanings but I don't want to go into the exact meaning now these are the 4 bonding orbitals and they are not the same but there's 4 and they still predicting exactly 10 years legal structure not surprisingly because we started out with exactly 10 people structure the other 4 combinations I have more notes I could take the base's and I have to have some of the same symmetry but I can't become all blue now that's a disaster because now the snows in between the 2 nuclear that once and likewise I could pick the PC with red on top and blue on the bottom and I could perversely picked these 2 guys to be blue rather than red and then there's the destructive interference and again that would be a very high energy solutions therefore we can easily see that for bonding orbitals so there's going to be for bonds good and there's 4 and bonding orbitals and since only 8 electrons before bombing filled and the 4 and bonding orbitals are empty and that's almost always the way it works out when you do things correctly because not surprisingly nature finds its way into making more stable configurations here
then is an MO diagram I have for it's a little bit harder to draw the tennis tournament when you don't have just 2 players but I have for hydrogen 1 orbitals on 1 side and then I had the carbon orbitals and I have the 2 halves of the carbon lower than the 1 as the hydrogen that's good and then I have the 2 feet higher but I'd have to know that but I can certainly figure that out by looking up the ionization energy but the atoms which is well known and so I can order them like that and have 1 very good combination the teddy bear but which is down bottom the A 1 and then I have the 3 that identical the T 2 and there are slightly higher energy the key is there's no way that the A 1 and the the 2 have the same they have to have different energies and that is an experimentally testable factor that we can look at we fell out the bottom with 8 electrons for from the hydrogen for from the current and the same way we always do with molecular orbital diagrams which is once we calculate the diagram we fill it up from the bottom
In here is an actual calculation of these horrible contours from the excellent website Dr. Stefan animals here is the A 1 symmetry between the car and 1 answer remember that when we did lithium when we do those contours there was hardly any overlap way using here with the carbon 1 s is exactly the same thing the green contour of the carbon 1 as is nowhere near that those quite protons the sticking out like Tinker Toys books and so the 1 s doing no bond at all With the hydrogen on the
other hand always take the 2 as we get this spherical look can be exactly spherical because of the underlying territory tetrahedral shape but we get this big agreed contour and what's counted here the surface is strong and the 90 per cent probability that an electron and there is inside that regions and you can see that it goes around all the nuclei the carbon and all 4 hydrogen so that these 2 electrons in this horrible I had this whole big space to go around it and it's a very good overlapped with that 1 s atomic orbitals of hydrogen then on the
next 1 is that 2 key and I've shown here 1 horizontal and the 2 one-sided I apologize and and picked the same colors that Dr. will but let's say Green is positive and blues negative rather than red and blue same difference here there is a node but the important thing is is that the notice right at the carbon and so although there is a no-load it is not in between the 2 atomic nucleus what was bad with H 2 With the entire bonding is that the node was between them so that there was no possibility of the electrons being in there to glue the positive charges together here we've got 1 side building up density to hold these 2 hydrogen said and the other side of building up density to hold these 2 hydrogen and the notice right at the corner where it doesn't do any harm because it's not between the bonds if we look
at the other 2 they're exactly the same as this 1 but
they're just flipped the all the general have exactly the same energy because of symmetry but there's another 1 that's in and out again and has no right at the carbon atoms and then that the final 1 in the 3rd 1 is just up and down and it's nice that he strongly with these different perspectives because as you draw them slightly differently and look at them you get a much better idea of what these services actually look like than if you just have 1 perspective these are the 3 then that we said 32 to cemetery and these are the 3 other bonding orbitals they have a note but it's not but that was to make an intimate bonding the question is
that on 1 hand we have the approach where we 1st monkey with the carbon carbon orbital LT the hydrogen and that we make bond to each hydrogen and turn and that's nice because that's how we might draw on a piece of paper if we were in organic chemistry for example for just regular Lewis structures on the other we have the a similar approach and we can calculate the energy of these orbitals so I just threw them qualitatively but we can calculate them and under certain approximations and when to make the approximation better and better if we want to do more work but we don't need to do any more work to say Look Indiana there are 2 different kinds of orbitals there's there's 1 and there's a law 1 must say 1 and therefore what we do is we go to somebody who does photo electron spectroscopy and we say can you legions of natural gas and it and tell us what the binding energy of electrons are in this region and how many orbitals there are and if we do this experiment there is a difference because if there are force equivalent hybrid orbitals each with 2 electrons than they're all the same we get 1 band in the photo electron spectra pickup pick electron out of any of those and will you never ionize again it is so unlikely that you lionized period that you don't lionize twice so we don't have to worry about that and then the carbon core electrons which are the only ones left are much much higher energy so we don't have to worry about than either because we can pick the photons so that they are going come up we are going to put an extra for example and therefore if there is 1 man in the photo electron spectra polling history and the most serious washed up and if there's to dance in the end the photo electron spectrum then and all theory even a little more complicated than we don't stick like lines is more correct
and let's them and have a look at and this experiment just like the parent magnetism of 0 2 is definitive and of course it comes down in favor of animal theory otherwise we would have gone to all this trouble here on slide 666 is the photo electron spectra of methane and there are and there assigned to teach you and they want and they even have about the right ratio of size consider 1 looks like it's maybe 3 times bigger than the other there a lot of factors that go into the cross sections of photo ejections and can't just say if there's 3 orbitals you get 3 times the area of the anything as simple as that but nevertheless it does seem to make some sense and if we look at it from the vibrational progression because methane is a much more complex molecule and can't really vibrate and a lot of different ways which is of course 1 reason why the greenhouse gas because you put up the atmosphere and can absorb infrared and a lot of different ways and that radiated back down to earth we can resolve all the all the little things like we couldn't and 2 they just appear as kind of a ragged like a porcupine envelope but nevertheless we can say it's a T 2 really that's doing the lion's share of the bonding and methane and the area was the big teddy bear rather less important because a little less vibrational progression 1 we ejected electron from this then says what we have to prefer the MO theory to the theory of localized bonds even clever localized bonds with hybrid orbitals because now we have an experiment that's clearly indicating that 1 approach is better and it disagrees with the other 1 and that's what science is all about it's easy to talk but you can talk all you want is somebody doesn't experiment shows the oceans rising then it's rising and it doesn't matter whether you want say it's model if it's measure you can quibble with the measurement but you 1st have to understand how the measurement works and in fact the measurements along those lines are extremely reliable even tho the system itself is quite complicated alright
let's talk about some bigger molecules we don't want to just leave off with methane although to a physical chemist and methane is a big molecule in a lot ways and I think you can see why because they may want to know a lot of things about it that an organic chemist may not be interested and an engineers wants to burn him power so we can look at some conjugated hydrocarbons and so-called aromatic systems but I've never smelled and aromatic molecules that was aromatic to meet like a rose from the but they're called aromatic and they certainly do have smells but they usually smelling gas or or mothballs or something like that but let's look at benzene naphthalene and a few others dying so call conjugated hydrocarbons and this'll be kind of an interesting and another interesting ways simplify what could be an extremely complicated we did it from scratch it would just be terrible of calculations and make it simple and leave enough meat on the bone that we can still come to some interesting conclusions about the stability of the system 1st Leicester's consider athlete I C 2 H for ethylene is an extremely important molecules in the fine chemical Industries the feedstock for a lot of things and a lot of people are spending time and energy to figure out how to make a clean only when we run out of other ways that we have been making well we've got the 2 s orbitals on 2 cartons and the 2 pure but also and we've got the 4 1 s orbitals on the hydrogen so there are a going to the 12th molecular orbitals and because there's 12 the atomic orbitals and 12 is a lot but but we can we can still figure out what they should look like just like methane you know this is data we're going to have to start by putting the nuclei of their preferred position 120 degrees pond angles between the hydrogen and carbon and then we're going to have to solve for what the molecular orbital energies should be by putting electrons that are allowed to go over the entire nuclear framework and only if they don't want to go over here for their own reasons are they not going to it's not that we're capturing them between 2 nuclei here than on
668 is is the molecular orbital diagram for ethylene we've got our for hydrogen is again but now we've got 2 carbons and we've got all the states label from the bottom of Sigmund G 280 with cemetery labels to be 1 you and so forth and so on we don't have to understand what all the means but many of them are overlap between the best orbitals on carbon and the s orbitals on protons and then there's too right in the middle there Mark and pie you there are just coming from the car and that's because those 2 are orthogonal To the plane in which the protons are so those to have different then there was the best can be and therefore they only come from the carbon they can even be this way the 2 carbons or that way and cost only 1 of them's because there's 1 double bond ineffably there's a sigma bond and then there is a pylon and so 1 of those is filled right up to where it's stable there slightly below the Tupi level we slide in all our electrons all the way up what we find His it's filled right up to that level that involves just that the P orbitals of carbon and here
is the photo electron spectrum of baffling we can also get that and now the that it's quite complicated so these peaks but that all have vibrational progressions are very very hard to resolve Amanda they may not be resolvable it all depends how carefully and how clever the experimental areas but at least they aren't so wide that they overlap with each other and we can't see them at all and they've all been assigned as you can see that 3 of the 3 you and 3 HE and so forth and there are also signs and they all correspond to injecting electrons from lower and lower in the molecular orbital diagram all the way to 280 after that maybe you need to much energy and they didn't have such energetic photons
on the cemetery labels again treat them just as labels for now don't dwell on them too much once you study group there you'll know exactly what they mean for us the the it's the highest occupied molecular orbital the so-called homo and the lowest occupied the excuse me the lowest unoccupied molecular orbital the Lumina but it's going to be the most important thing because if I'm going to be making a bomb then is the electrons right at the top of the cake that they're gonna fly off and go somewhere and make the bomb the ones that are held down further down energy we are not going to be likely to be the ones going 1st and likewise if some other coming up remain with electrons and says Hey take some electrons from me where are they going to go well they're going to go into the lowest unoccupied molecular orbital because they're going to come in and they're going to go down to the most stable state and therefore the highest occupied molecular orbital flight years and the lowest unoccupied molecular orbital what it looks like we are very very very important to understanding and chemical reactions and therefore we can focus mostly on and forget about most of the other ones and that's a key simplification the highest occupied 1 has labeled as 1 of the 3 you and the lowest unoccupied is 1 of the 2 G and they they both involve the carbon P orbitals and so on these 2 the highest occupied and the lowest unoccupied only involved high electron it's only the pie electrons that are were involved and that is a key simplification when you consider the reactivity and structure things with double bonds like carefully we
can treat all the signal just like for electrons and since they are important they're going to be participating we can rationalize whatever structure they have in any way we want and usually the the prescription and those aren't so important we just say the S P 2 hybrids doesn't matter what we call them because they're never going to do anything just going to be filled and we might as well take a simple approach like Borland's approach and just say Well they're making 120 degree and that it there's a 6 framework that's holding the atoms in place and then there's these delicate pies orbitals and for those we reserve the molecular orbital treatment because those are going to do something and so we want to treat them more accurately and because there's only 2 models this and and like that it's basically down to the same things as back to H 2 the fact that there appear rather than as a matter the matter is exactly the same and we've already done so we've we've we can leverage that now and just say we've got this perpendicular price system with 2 few orbitals and they can even be in favor of a face and we can calculate what we want to do so is just like H 2 In this case
Oct highway function then while we suppose that the molecular orbital for the pie is C 1 to PC 1 policy to 2 easy to wear 1 and 2 and referring to the 2 cartons and C 1 and C 2 were the 2 of them coefficients yet to be determined but we know they're going to come out to be Wilkins occurrences are still the same by cemetery of we have to make a secular determinant because this is molecular orbital it's got a calculate the orbital energies remember we had the cool Oman and Roland exchange in a growing so here it is H 1 1 minus the S 1 1 with overlap integral H 1 2 minus the S 1 2 with the exchange integral and so for the determinants of this times this is equal to 0 and since the 2 carbon atoms are equivalent than H 1 1 that integral and aged 2 to that integral are exactly the same so we can make those assigned an age 1 2 was already and so on if we want to
make a qualitative progress here and we wanted to proceed the way we have a lot of others that cases helium the hydride and we'd have to get our inner girls are the inside there isn't all that and go to work but we don't want to do that now that's too easy to do and were only after some qualitative description of what's going on we don't expect it to be a qualitative and be very hard to make the quantitative even if we calculate the spiral so well by just leaving out everything else and saying forget about the other stuff we could be making some big mistakes some basic errors there let's simplify things and then not do In integral all In that will be a very very good method and that's called a couple approximation an integral whatever it is it's just a number by the time you integrated a number with units but it's a number and we're going to assume that we're going just replacing rolls with the symbols numbers also and they were going to calculate things very quickly that they local approximation makes 3 assumptions and at 1st they seem laughable but in fact there there very nicely physically motivated the 1st thing in the overlap integral remember how much trouble that was to calculate that somehow we had to do all those things while here organizations that were going to say that the overlap integral is 0 0 on less you're talking about the overlap to the same place so the overlapping them between 2 neighbors is 0 that seems very counterintuitive wide because you're claiming they're making a bomb but when you look at what came out of our analysis before S was just a player in the denominator that just changed things slightly in the denominator it never dictated whether a upon formed enough it was OK so it doesn't really matter if we set it to 0 every senator 0 than were getting rid of a lot of mass because all those things go away because the multiplied by S 1 2 so those are and then 1 of the same we said to want because we're saying the it's normal and that all the cool long and rolls Ch In roles are the same for equivalent ,comma and sometimes we assume they're the same even if the comments are quite equivalent because just too lazy to figure out if they're that much difference are we are it's difficult to figure out what that would be and then the exchange or there also call resonance and roles in the business those Senegal's vanish but except for nearest neighbors and the rationale for that is that if find here and you've got a few of the more than that ghost can have some value but once again it up to here and I've got some interesting in between it's too far away so I could calculated but the small and I don't want to waste all my time calculating something that is . 1 per cent of the answer but is extremely difficult to calculate that support the use of my time so those 3 approximations of
lettuce simplify our 2nd in the tournament and get rid of all calculations conventionally you right now said for what 1 of the other girls and beta for the exchange and our secular determine just becomes alpha minus the beta alpha minus most 0 and it's I that's quite erratic equation and the solution for the energy is also plus a minor Spadea not surprisingly it's very similar to what we had with H 2 there's a good combination and that combination now in fact there's 2 electrons going in and we didn't calculate any electron electron repulsion or anything like that so induced double the energy when we say what it actually is but the advantage of this
however is we can do something that's a little bit more intimidating much more intimidating than helium for example let's try benzene benzene a C 6 8 6 we would have a 6 by 6 determined and it would have entries every quit so just expanding out as this a determinant of filed by 5 but will take forever and that's going to be a major problem to to try to calculate something like that so let's figure out how to get our our Our 6 pct orbitals in the pies system to yield 6 most without doing that
let's set up the the determined then which are done here on slides 676 some local approximation the nice thing is accepted terms right near the diagonal in Iraq each of which has beta 1 when their office they all have the same value and the 6 cartons all have the same in across for the H 1 1 each to 2 and so forth so those are all out of and then I have my energy the overlap is gone so there's no energy off the diagonal that's very convenient Everything 0 everywhere except for the top and bottom and that's because as I go around the structure 6 is next to 1 CEOs and with 1 there but all the rest is 0 so most of the thing goes away and we can even make it simpler by says we got 0 and we know that it is not 0 we can divide everything by data so that there are certain things that 1 of the offer diagonal just redefined alpha minus divided by data to be some variable so
let's let x equals 2 alpha minus divided by data and then all the other terms are 1 then we end up with the following polynomial to route if you expand out the secular determined you end up with a six-story polynomial is access to the 6 minus 6 X to the 4th plus 9 EC squared minus 4 equals 0 0 that's why it took a course in algebra in high school because now there should be a Duck Soup problem that fact that it may not be so easy if you just stare at it but there's a trick I'm going let you explore the trick on homework because it's only even powers we can redefine wires equaled EC squared and then we've only got a and if we're lucky we might be able satirize CU and figure out how to actually get get the answer or we can spot it even for a lazy in mathematical and we can see where crosses 0 and if that crosses 0 at some convenient place that is easy to tell as manager then we can try factorizing with X minus that major X not for an and see if factor of it he do that and you persistent and you find that you have repeated routes because of the Weichel sex work and then some of them are repeated again just because of the structure of what you end up with at the end the Cuban and you end up with axes equal plus or minus 1 or plus or minus 1 or plus or minus to those of the 6 routes of that equation was excellent alpha minus the overbearing and therefore
there are the corresponding energies he won which is the best best 1 Alpha plus 2 beta recall these are usually negative the 2 is equally the 3 is also plus paid you for a sequel to the 5 that's alpha minus space and then 6 itself stupid so there's nice symmetry about having energies come out now how do we get what the molecular orbitals are recall what we had to do before we go back we actually put in the energy To the original equation that we have and then we find the orbital but we get that corresponds to that energy that the general ones that have the any 3 the same and 45 % require a little bit of thought to have a sort those 2 out but whatever orbitals we get recall that they have to be off the normal the molecular orbitals have to be off the normal as well so that light that's an important thing that less simplified but I'll let you do that and here
I given you the answer the first one not surprisingly the lowest energy molecular orbital for benzene is when all the 6 recalled benzene is a Texaco playing is when all the 6 pure but also have the same fate so I can range of positive electron density around the top holding all the cards together and I get a ring around the bottom of the opposite sign but when I swear I find building density in between the car and is another axis on and that holds them all together and then the next to have some notes and but the notes are bad the most between at certain cardigans and the orbitals just like methane they hold the other parts together so there's 1 that has no this way holes these parts together and there's 1 the other with the hole these parts together and then there's the bad 3 that heavily armed officers combinations basically and the highest 1 it's 1 of the this ones this one's down and this went up in this once down so for and that has and those in between everything and tons of notes and can see it's a very critical function is going very high-energy and that's the least favorable 1 that's so strongly on tight bond orbital In
fact I by drawing simple figures just based on the site Flickr structure you can arrive at some simple rules to prevent aromatic stability you drive structure .period down and efforts over hexagon drop .period down and then at each vertex you put a line which is an animal and no 1 on the bottom then you have to to do that the 283 then have these 2 the 45 million 1 of the top the 6 and you've only got 6 electrons because you only have 1 electron and P orbital start with Saiful the bottom 2 2 this will to this woman to be game over the pace of 3 good ones and 3 winners and you left all the onto bonding once unoccupied and Ollie electrons repaired and all these orbitals party localized so we don't predict any difference at all in the Lewis structure of course advancing we single Bonderman double bond because we have to because the Lewis structure and then we say there's residents we move this year move them around like a monster in the molecular orbital we don't have to do that there are set up To beating localized
on the other hand if we pick cycle view dying and we stand the square on it .period then we have a low ones he was unaware the 203 and with the 4 but we have 4 carbons encyclopedia dying and therefore we've only got 4 electrons so we put 2 in the body there we've got to once here what that's like 0 2 again so 1 goes here and 1 goes there well that's that's not aromatic stability predicting a dire radical but I wouldn't take this kind of very qualitative things too seriously I do some spectroscopy to figure out which actually get but whenever it comes out like that where the 2 Mark pair and then there's some left the conclusion is it's not aromatic and what happens then is the ones that have foreign plus 2 pie electrons become stable and the ones with foreign like 4 rather than 6 are not especially stable and not stable at all in some cases so only the 4th 1 was to systems are predicted to have aromatic stability and that comes out of a more detailed calculation to not just playing games which shapes but it's interesting to just play games which shapes because it's very quickly and often it's good enough all still
practice problems let's consider the following molecules and let's consider them and see which 1 it's an organic chemist would predict to be aromatic that the special stability benzene was used as a solvent for a long time quiet because it doesn't react with anything so it's a perfect solve things won't dissolve in water for the reactions flowing water dissolve and benzene and the reaction goes very quickly the problem was of course benzene is quite for carcinogens like a lot of these systems and so on if you breathing a lot of them boiling about them and bring it on a daily basis it's not the greatest and that's why they went away from but consider
them benzene we know it's aromatic let's consider naphthalene which is in mothballs that's that smell as ceiling which you probably haven't seen or smelled and then cycle architecture was take 3 and see what they are well 1st thing is the names if if you don't know what the structures are referred to the names are useless we have to know they are going to be aromatic unless in the Lewis structure they would have alternating single and double bonds and we could do resonance and moving things around so that they would all be equivalent half the time single and double if they not even like that then forget it it's not going to be an aromatic system for the part that can do that trick with residents is not be and they have to have a slightly structure as well so the snake bites its tail because that's important and how those 2 last terms come in if those don't come in a lot of things changed character and analysts structures and and count themselves for naphthalene we've got to benzene rings fused together now if we were actually going to do the animal treatment we'd have to be careful because these 2 carbons without any hydrogen could have been a different Coolum integral than the others and the others will all be the same and so we should take that into account we should have Alpha 1 announced 2 for a lazy we just say Well they're about the same call mouth and drawn the Lewis structure here 1 them and we could play a game with residents then and draw 1 the other way we cannot be electrons in the pipe system we forget about the same we forget about the hydrogen and there's 1 2 3 4 5 6 7 8 9 10 best foreign policy to for any calls to cancel it's plainer and In fact aromatic for as helium which is a structural isomers of Nathalie and there's a seven-member drink glued to a five-member drink and I can still draw the double bonds the same way it's kind of amazing that works like that and it's a beautiful blue collar and again I come system might come out of the tent high electrons and the the localized and most go over the whole thing and it's plain error and it's very nice example of an aromatic system that's not so trivial like the benzene 1 and then here
or what I shall use of mushroom that is blue it's absolutely amazing but in fact this mushroom makes an energy derivatives for some reason probably extremely interesting chemistry usually 1 plants make interesting molecules it's because they're keeping bugs off or keeping other things away because to plants they can move and if you stock and bugs are crawling all over you you need chemical warfare to keep them at bay usually than if you see a brightly colored but from like this you you admire its beauty and its beautiful blue collar but let someone else figure out if it's safe to eat there are people who do that for a living and it's very interesting to see how courageous they are usually very tiny piece and then wait and see if what happens and think you don't little their Warren and I'll let them do that but I don't eat them mushrooms that you find around the back of this beautiful blue collar or the ones with the orange peels either because that would be the last thing you do 1st I collected territory
drawn like a stop sign with 4 double bonds but it only has 8 high electron so that's not employers plus 2 and in fact the system is not aromatic and it's not playing Texas has a 3 D structure and looks much more like alternating single and double bonds that are localized so that 1 and not surprisingly that's not aromatic doesn't usually have a trivial OK we're going to leave it there and for our very last lecture what I want to do His go through where we started where we got to and all the things we covered because we've covered a lot of ground from electrons and photons to Adams 2 molecules and we've done it in a certain sense systematic way but I hope that made certain things that you wondered about much clearer and maybe caused you to want to learn more about some of the things that you never heard so leave it there and then some of them the next lecture


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