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Lecture 26. Qualitative MO Theory


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Title Lecture 26. Qualitative MO Theory
Alternative Title Lecture 26. Quantum Principles: Qualitative MO Theory
Title of Series Chemistry 131A: Quantum Principles
Part Number 26
Number of Parts 28
Author Shaka, Athan J.
License CC Attribution - ShareAlike 4.0 International:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal 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 10.5446/18898
Publisher University of California Irvine (UCI)
Release Date 2014
Language English

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Subject Area Chemistry
Abstract 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: 0:00:29 MO Diagrams 0:03:36 Qualitative Guidelines 0:10:08 Homonuclear Diatomics 0:18:13 Bond Order Matches Intuition 0:29:42 Photoelectron Spectroscopy 0:35:53 Hybrid Orbitals 0:45:13 Making Bonds 0:48:24 Normalizing the Hybrids 0:50:09 Other Hyrbid Combinations
right we're back again and this time what we're going to talk about is more
qualitative molecular orbital theory we're still going to do a little bit a calculation that's for sure but we're going to tone it down a bit from of these detailed calculations and try to understand a bit more about molecular orbital diagrams as well the 1st question
is please which atomic orbitals can be combined to form a molecular In principle if we have a lot of Adams around and they all have they learned so electronic orbitals we could have a big big computational problem because we would have to take as molecular orbital arc trial a mixture of all these things and then we would have to do a ton of them girls like we've been doing on some of these problems and then we'd have to figure out what the coefficients are installed the secular determinant and then and then we might find that a lot of Members 0 so we spent a lot of time calculating an integral and doing something that that amounts to 0 at the end of less nothing new that sell a lot of science in fact pans out most most of experiments don't actually work in the few that do get published and that 1 of the best majority that don't come out either is very interesting were very important I get mothballed well suppose rather than mixing in everything we wanted to cut out a lot of the war and were willing to accept a less accurate answer because what we're trying to do His understand qualitatively that the reactivity and structure of the molecule and not so much about 2 3 4 5 digits things like the ionization energy the In that case we can dispense with a lot of the possible combinations and we can just outright said they are not going to contribute and we have 3 qualitative rules there were gonna use the atomic orbitals can come together the former molecular orbital which is in principle the localized overall the nuclei in the molecule yes number 1 the energies of the atomic orbitals are similar number 2 the cemetery is the same that has a precise meaning but for now we're going to take that and qualitative saying and you understand later on what that exactly means and number 3 the atomic orbitals overlapped at least pairwise in space if at least 8 of overlaps with B & B overlaps with C a doesn't need overlap with C & a B and C can combine to form a molecular orbital as long as the information can get from see somehow through some minerals were fine we can combine them altogether
OK let's do practice problem 30 here and look at these qualitative guidelines let's see if they make sense so here's the here's the assignment rationalize the 3 rules for atomic orbitals to combine into molecular orbitals In other words explain why they make sense without doing a lot of calculation OK rule 1 as we saw with hydrogen molecular hydrogen for example the LCA and most often involve comes constructive or destructive interference if the faces are right there is a build of electronic density if the faces the wrong there's a no-load the electron is not found there but if the interference is going to be meaningful then the wavelength and particularly that the broiling wavelength of b orbitals must be the same and that means that the energies must be the same in other words we can't really talk meaningfully of an overlap between us Leahy elephant there 2 different size scales and the atomic orbitals can have vastly different energy and vastly different size scales in the same way and only once did a similar can talk to each other and so that isn't a rationale than for why the atomic orbitals I should have similar energy doesn't have to be exactly the same but they shouldn't be too disparate or will we do the calculation of what will find is that if we include them that they come like the 2 West with a tiny tiny coefficient and we are any better off
OK How about number 2 well by the same argument they have to have the same symmetry as I said What this means will be made a little bit clearer later on in this 131 series for example this if I have a S & M P E and the peace and on and then as a ministry on the next slide you're gonna end up with an overlap of 0 because you build up positive here in negative here and by symmetry the overlap is 0 and so there won't be any combining because you're going to get equal amounts of positive and negative tone interference by symmetry so on this
flight 624 fear here it is for example if I take 2 s orbitals to not combine them in face then I get a so there's no overlap there and they can interact and former molecular orbital of symmetry Sigma likewise if I have a lesson I have PC like I might have been hydrogen fluoride for example the because the PC has the same cemetery along the Incheon nuclear accidents assess the both around a cylindrical they can combine but if I have it and on and like in the 2nd line like PY for example then there is an equal amount of positive and negative interference which I've tried to show by shading where the orbitals overlap and so then it's 0 and so that that explains that and for the
3rd 1 we said well they have to overlap at least pairwise in space that's best demonstrated by this to lower electron contour for lithium the diner using the 1 guests orbitals so the 1 asked by the time we get to live the American Center core electrons because they aren't in the valence shell were starting to occupy the 2 shelties 1 electron 1 has shelved the case shell and let him have a lost 3 charge which is much bigger than hydrogen so this 1 as it pulled away and it's like being on Jupiter rather than being on earth the polled very tightly closed to the nucleus and you can see that if I try to take a linear combination of Plus Plus which are done on the left hand the Sigma G 1 as amended plus minus the same you want as their virtually the same because if they don't actually overlap in space if they don't interfere then whether I take plus-minus minus plus 1 I square I did the same thing because they don't they're they're completely separate so there's a little bit of a little bit of a contour on the left showing is a little bit of something there but that's not going to be enough to hold lithium together that would be not completely insufficient to say that that's going to do anything to the bonding and so for that reason we just discount all the core electrons we just assume if their core electrons they don't overlap in space we throw them out and across chemists have always understood that it's the valence electrons the ones in the in the shell you're filling up the dictate everything about the chemistry and that's of course why the periodic table is periodic by
contrast here on-site 626 I have taken from a quarries excellent book on quantum chemistry and to contours but for the 2 of us and the 2 s do overlap and then the total some on the right shows you the overlapping of the 2 s orbitals building up and then the 1 s is a tight like a ball of yarn and to us that holding things together and lithium dimer does form of course but it's not what I would consider to be a strong bond now
are qualitatively and molecular orbital approach can predict and qualitatively whether simple home on nuclear diet Thomas will be stable by stable we mean they're going to have a bond order that's bigger than 0 and by this rationale for example if we take our simple and more diagram with the 2 West it's very similar to hydrogen with the 1 as we have the same bonding and on-site bonding we predict that lithium to at light to its stable but beryllium 2 would not be because brilliant too would be like helium and would have to win the bonding to him Yantai bonding and so brilliant but should not be brilliant too should not form or at least not strongly we could probably produce it under special circumstances if we wanted to but we don't predict that that's going to be an energetic bond to break however but we can't predict just aren't taking 2 at once we can predict whether the 2 stable compared to being Adams or not but unfortunately for the study of condensed phases and materials which is much more interesting from a chemistry and electronics and photo physics viewpoint we can't predict anything at all about condensed phases from this kind of analysis because the problem is that when you have a bunch of Adams they don't have to just form dimers they conform to some other structure which you did never bother to calculate and which has a much better molecular orbital diagram much better stability than whatever you did calculated so you can predict for example that can't see 2 carbon carbon it should be "quotation mark stable compared to see Adams should have about a non-zero along the water and so forth however neither graphite nor diamond nor buckyballs nor graphene is organized In that way and that's just because if you have more Adams around and you make a bigger molecular orbital diagram with those structures what you'll find is that they're much more stable than C 2 and that's why you get them instead on the other hand and which you can figure out quite easily from the ammo diagram is in fact the form we find in the atmosphere it is a dimer it doesn't for many condensed phases and it's interesting but just moving 1 electron and 1 proton 1 way or another makes such a huge difference in what you actually find in nature so let's include
here the 2 of and to the orbitals and the 2 appear higher in energy and effort talking about but a diatonic with 2 equal Adams then the energies of the same as I remarked before if the atoms are different than we have to keep in mind that the 1 that has more protons is going to have the energy levels pulled down compared to the same number and compared to the 1 with less In that therefore what I've shown here is kind of a generic diagram it might be appropriate for O 2 and S 2 and a few others there's good and bad combination of the 2 of us there is a good combination of the 2 P C that's overlapping all those have Sigma cemetery there's the P Y and the PX In that forms 2 pi orbitals and then there are 2 where there Out of face rather than having the Loeb set up there the other way round those 2 Entiat bonding prior orbitals and then there is 1 where the 1 Peters got the wrong signed compared to the other 1 there's a big note and that's the 2 PCs segment star which is usually on the top of the the diagram as the least stable molecular orbital note we have energy is on the Y axis always in these diagrams and you should understand that no matter how the diagrams drawn you can't trust unless you actually calculate the energies and if you're going to calculate the energies that you're getting into a lot of computation so if you just want to draw something that's fine but you can't trust it too much if you actually want to figure out what actually is the case because even in Adams we calculated the exact energy Eigen values for the hydrogen atom but by the time we get to cesium this success was in lower energy in the forest and they were all jumbled helter-skelter and it would take a lot a calculation that actually figure out what those energy levels were it's much worse of course with molecules because we've got many centers of positive charge pinnacles worse and there's a lot of work involved and so sometimes these things are just very qualitative guidelines but you must entrust them to literally and and be surprised if for example you change the atomic number and the whole diagram changes because that even happened with Adams and sometimes the energy differences between these things are pretty small and just change 1 thing in this goes below that MacOS below this when you 1st start out course that can be a bit daunting because you think Well I'm never going to figure out which ones below which 1 other otherwise but there are some qualitative ways will see in a 2nd that we don't have to do too much calculations the
cost in reality was so Our calculation about polarization the 2 pct always mixes with the 2 s to some extent and it just depends on what the energy differences between them how much the mixing yes the orbital energies whatever they are too is going as we did the calculation on big are the Inter nuclear distance and they got at the minimum where order the orbitals because we're interested in what is 1 that when the situation is the most stable is going to be different for example and 2 has a much smaller tighter bond than 0 2 and then have to so just the fact that they got changes will change which orbitals can overlap and in what ways and that may have a big influence on what the energy ordering it's for example and so therefore don't be dismayed if the animals and molecules appear to be jumbling around that's part for the course you would be amazed if they did not do that is sometimes a jumble around just a few pop in a few more electrons and keep everything else the same because why while they got changed than the 1 that was so favorable before but is not and so it's occupied but it now has a different energy and in any case the exact words always independent on the Mall on the molecule question but freshman
chemistry we drew Lewis structures of all these guys and we decided that in 2 has a triple bond that's why and is so dirt and why it's so difficult to fix nitrogen we spend a lot of our energy trying to take nitrogen die nitrogen out of the atmosphere and turned it into ammonia by real hammer and tongs process and it takes a lot of muscle to do that time why do we want to make ammonium because usually we wanna make fertilizer to grow crops and we don't have enough otherwise if we didn't have a fertilizer try growing things without it and if you all water rely on organic fertilizer only then you need a ton of animals and you need a way to handle all that stuff and make sure it's safe as well so let's try and the molecular orbital diagram and fill in the electrons and let's come to some conclusion about whether we would expect a single double or triple bond based on the bond order and I mean at the bond order should agree with with the simple Lewis predictions however for oxygen there is a wrangle and in fact that wrinkle is 1 of the major triumphs for the molecular orbital approach and that is that the molecular orbital approach predicts for sure that oxygen will be a diuretic with 2 unpaired parallel electrons and different orbitals and on that can't be predicted and by conventional Lewis structure the let's fill in
the oxygen and diagrams and oxygen has 6 electrons it's in Group 6 so 12 total and unifil amount to and the bottom to us to a signal to the statement then another and the to keep and then the 2 people I started to and tied bonding side by side of face you this way or that way but the electrons in molecules are just like the electrons in Adams if they don't have to pair up department is the same cast and you can have your own place then you take your own place and so since these orbitals are exactly the same energy by symmetry the electrons occupy them and then they have tend to have parallel spends time because that of the magnetic effect between them and hands rule saying that the state with the highest multiplicity life slowest in energy that Bond water comes out to be too but we definitely predict that there these electrons are going to be unimpaired in oxygen the the question is
what what what effect could that have any answers a lot because if the electrons around here that means that the material is Parra magnetic and that means that Magna magnets will interact with that they'll be magnetic forces on these Ontario electrons if all the our magnets appeared up than you can imagine there are going to be the magnetic forces so this prediction that 0 2 paramount Natick is 1 of the major triumphs of the molecular orbital approach even for these very simple systems but it we draw the Lewis structure we draw pairs of electrons the oxygen a double bond in between we find out of course the opt-out rule is satisfied everything's hunky-dory but there's no way we can look at that structure and say that is going to have a completely different magnetic property or different reactivity and then and then another molecule that has the same kind of Lewis structure with the the 3 lines like nitrogen or or Floridian and both of those of course a dime magnetic just because the orbitals happen fill up that way
so but let's have a look here I've taken on us a screenshot from an excellent video which are put on the bottom of slide 633 if you wanna watch it's really amazing and beautiful to me how people up spent time making videos of interesting things like this where you can see here it is 2 poll faces of a magnet and they're quite close and their holdings on steel but balls together to make a tighter space and then what they've done is they've poured liquid oxygen through the space in between and the magnetic force is strong enough that until the oxygen heats up and boils off as long as the liquid will stay suspended in between and you can see clearly that sticking to the Mac if you caught it's a clear liquid so that there is no other indication if you pour liquid nitrogen which is also clear liquids through then of what you find is that it costs right through there's absolutely no force on it at all that he can detect compared gravity whereas as long as you get the whole faces close enough which is why I think that put the steel balls there you can suspend liquid oxygen there watches watches boil off so oxygen is magnetic and animal approach is correct now
there is a form of oxygen you can imagine instead of having the 2 electrons paired on their keep in mind their indifferent orbitals so they're very disorganized that's really lucky for us because oxygen would be extremely reactive in fact they were paired in the same orbital and that species of oxygen so-called singlet oxygen because the term symbolizes multiplicity of the single and you can make that you can make that by decomposing various things that contain oxygen and if you make that molecule which you will find out is that it is 6 0 dreamily vicious oxidizing agent very very fast in fact that almost anything if you immersed in an atmosphere of singlet oxygen burst into flames the paper you would find itself picture starts reacting heats up in the Soweto 0 Thurmond it's also at the National Enquirer would be right there be spontaneous human combustion if we had a single of oxygen in looks and behaves much more like Florida have to which is another very vicious oxidizing agent so in a way once the electrons Parra and an oxygen can get its act together that's when it shows you its true colors is a very very strong oxidizing agent by the way are immune system is honored that trick and certain immune cells and certain immune cells certain attack cells do in fact produce singlet oxygen and created right near a bacterium and say Here small guy trial will be the 1st to brighten your day and of course it reacts with the with the molecules in the innovator and it's like a Molotov cocktail that might be all she wrote for the invading species now on-site
635 here what I have is the difference between oxygen and nitrogen sewn in nitrogen the DMO diagram looks more like this here the differences but these orbitals the bonding orbitals in the P and both of them are all filled but the bordering is different the high is lower the 2 like this are lower then the Sigma and an oxygen the Sigma was definitely lower the question is why why is that what's the rationale for that and the difference of course is they are not nitrogen very very contact tight molecule oxygen has a bigger bond distance between the atoms and of course the atomic orbitals themselves can be different so there is a qualitative rationale for this I'm not sure exactly how accurate it is but I'll tell it to you anyway and don't here it
is when the bond insurer or when the nuclei small like boron copper which seem to have a similar MO diagram to nitrogen then the overlap with high symmetry is better than the overlap with saving cemetery and that lowers the energy because when you overlap better than you put more electron density between the 2 positive charges that's a lower energy solutions the PC may actually stick out the other side so here's the idea normally I would have to record lows here and be coming in and they be overlapping and the nuclei out here and the loads like that that overlap is going to be very effective but supposing the nuclear I get too close like this then as I've shown here on the bottom of slight 636 the red states out past the other nucleus Into the Blue Of the other key orbital and vice-versa and likewise in between there's not so much chance for the red to pile up a big intensity because it's going out there has quite maximized here and so for that reason that PC orbital when the bond gets too close and maybe a higher energy solutions but the
side-by-side always gets better right so the side by side the closer you get the better it looks and finally if you're quite close that could be superior then to the signal which is sticking out the other side of this is not no substitute I would say for a proper calculation but of what's going on but it's much better than nothing at all and just saying Well the energies just move around at random and there's no rationale at all but we shouldn't take that qualitative stuff too seriously now can we can
we testimony that the answer is yes we saw that light was a photon in 1 of our early lectures because why we get an experiment with a metal surface and we ejected photo electrons which now we know we're coming out of the atomic orbitals of the metal and we can likewise take again asked like Anthony and we can shine photons added and if the photons are energetic enough there is a chance that they will not an electron and make em to plus and then if we measure the with an energy analyzes the and energy of the electron that comes out of the photo electron and stand on our energy analyzer we will get a certain number of counts and at various energies and where we get a lot accounts that means that were actually putting in a photon that subjecting all on electron from an orbital and then the left is what we're seeing is so we can back calculate knowing the energy of each photon annoying the 1 photon injects 1 photo electrons in the experiment but the binding energy of the animal was and so we can stand down and we can eject the top electron the next 1 down the next 1 down the next 1 down in the Sissoko of you the PDS the UV photo electron spectroscopy we usually use an ultraviolet source because an ultraviolet source is much more effective and injecting the electrons if we don't use enough we have red light and we just don't inject any photo electrons because we don't have enough energy and of course that's the same reason why UV light from the sun some of which does filter down even after it has gone through the atmosphere and the ozone layer and this can be damaging to your skin because it comes in and starts injecting electrons from various molecules in your skin and your skin tries to repair itself but over time but there could be some damage that can be repaired and if you get too much sun and by the time he noticed the damage it's some sort of like trying to turn around an aircraft carrier by the time notice that you're steaming and important going too fast it's too late to stop and so the time to stop the damage is early on and if you live in Southern California like we do the best solution is to wear a hat and that's because as your haricots thinner and thinner and you may put sunscreen on your face but very few people put sunscreen on their scalp as long as they still have hair because it's too messy and so unbeknownst to them they get a lot of sand on the top of the head and if they have something going wrong unless you're inspecting yourself all the time you may not notice it until the doctor says what that has to come up come on if we assume Krugman's Theron is sufficient remember what Koopman Stern was that said that we could I'm just use the same orbitals we'd figured out and use the same ones for the ion as as the molecule on costs that can be quite right but it could be close enough and to analyze things if you Koopman ceremony is OK then the actual read of the photo electron spectrum is just telling you exactly what the energy of the molecular orbital in the molecule was initially and that's a cost very powerful because we calculate that compare With the experiment in fact of
course when you eject electron is if that electron was involved in bondage then but it's like cutting spray you know the thing goes wild because it was held very tightly when the electrons there now the electrons gone and it's held with the money losers sprang on its way to tighten its starts going into vibration and we can see that in the spectrum so if we see if we eject a certain electrons that there's a lot of vibration going on afterward what we can conclude is that that electron was extremely important for bonding if on the other hand there's hardly any progression then we can conclude that the electron was not that important for bonds so here it is found you the photo electron spectrum for nitrogen molecular nitrogen and I've labeled the band's there's peace said Muneer 16 electron volts of Peapod Inc which has a long vibrational progression and then there's peace Sigma stock which was down below we see clearly that the peace sick mother PC His hiring energy because it's easier to eject then the people so that establishes that the ordering that we've got 4 and to is correct if we did go to which is more complicated because the electrons around unpaired we find that the ordering was the other way and then below the people I is the peace stock which is the best combination of almost near 19 electron volts that's so I reiterated here on slide 640 the long vibrational progression is seen series of spikes I tells you for sure that it's the people high electrons that are doing the lion's share of the bonding in and 2 and not a peace now
let's talk a little bit about hybrid orbitals because if you've had a course in organic chemistry spend all your time talking about sp to hybrids as the 3 hybrids this and that's where they come from we really systematically talked about them in any detail but shortly after the height of the London 1 as no 1 S B plus 1 sp 1 shortly after that paper came out Linus Pauling proposed a systematic way to rationalize Lewis structures so Lewis structures were in the nite in the team's 19 16 17 in there and then quantum mechanics comes and then they could understand bonding and now but they still like Lewis's is way of drawing things with pairs of electrons and the architect ruling that rationalize the lot of chemistry and nobody wanted to throw that completely away unless you absolutely have to because it seemed to be extremely useful to understand that but what Pollan proposed then is each bond or orbital takes a pair of electrons and that's the same as Lewis and the bonds of localized between 2 atoms firemen and year and there here I can have a bond between them but that's it that's why I draw a line between them and I don't draw the lines snaking around over here in the molecular orbital approach we can't think of things in terms of those lines holding things together like that because we have to 1st put in all the things and then although it may be that certain bonds higher molecular orbitals our formed almost entirely from the atomic orbitals of the 2 partners but it doesn't have to be that way it's not a precondition then when you draw a line you're putting a pair of electrons in there and you're saying that the pair of electrons glue the nuclei together so speak but polling was able to go much further than that and that's because he was able to also explained the shapes of simple molecules why did they have the bond angles they did why were certain molecules plainer and other ones not and the structure of of some of these were known of course but the bonding the rationale in terms of the chemistry was not very well understood methane for example is Tetra he drove C H 4 this is probably going to be a review but let's review it anyway but
here's what here's what went on :colon wondered how he had carbon and for hydrogen why you got attaches legal structure and in particular you know what the valence orbitals for the carbon atom or are you going to ask which is round and then you've got 3 2 pieces that are all at right angles to each other and in methane the bond angle the bond distances are all identical and the bond angles H C H are all 109 . 5 degrees the territory he galangal How can we but do that well let's look at the valence shell electron configuration of an isolated carbon atoms it's too S 2 2 P 2 and that the 2 electrons in the 2 are gonna spread out because the 2 in the carbon atoms have the same energy by symmetry and therefore they're going to spread out and have the same they're going to be parallel spans the US electrons the shells lower and the 2 electrons in the shell are paired and so there's no way that there's no hook their hydrogen comes up with 1 electron to that to at shelf there's nothing that can happen because it's Phil so it could just bounce off I'm not going to get a bond of form that I could get a bond with 1 electron from the hydrogen and then another 1 from 1 of these to be but I've only got 2 of them and therefore naively what you would expect is you would expect to find CH 2 and he would also expect that the 2 hydrogen is a B at right angles 1 would be to be excellent salmon would be to PAY and if we don't find CH 2 I guess you could find enough flame in a combustion reactions but certainly not done is not stable form ch forests the stable form for sure and the bond angles are not 90 here's the red
here's the way polling then explained what goes on 1st but making a molecule is like starting a business and when you start a business you have to borrow a little money usually because otherwise you can get going and so what we do to stop this molecular formation at least in our minds is we take the initial stable configuration to us too the 2 key and we grab 1 of the US electrons and we move it to the vacant to peak that's borrowing energy such borrowing money we've gotta pay that back but now after we borrow we've got 4 half-filled orbitals and that's great because we've got 4 hydrogen atoms coming in that's exactly what we want now
still although I've got no go because I've got 4 some of these orbitals but 1 among and and 3 Europe's and so self-righteous just naively combine each hydrogen with 1 orbital then they are can all be the same and because the is round and kind of at a loss as to where put that that 4th hydrogen anyway where should be and the other should be at 90 degrees still so that that's all I'm not going to work therefore what we have to do is we have to somehow combine these orbitals into I baubles they're all the same and since there's 1 s and 3 three-piece and all of our combination should be 25 per cent less and 75 per cent P and that's why they call S P 3 hybrid orbitals they point also told that the positions were refined the hydrogen atoms but it's kind of an interesting but some mathematical the point is that if you don't Orient where the hot button Adams are in a very clear way than it takes you a long time to figure out what the hybrid orbitals are so let's have a look that heretofore
starting orbitals done these are not meant to be quantitative in any way the just drawings but there is around 1 and there's 1st 3 dumbbells at right angles and I've taken it to us to have positive Phase 2 of colored red Miller's of positive and negative studies as shown and now
what I want to do is I want to put hydrogen is where I know they are because I know it's attached he and then I want to figure out how to make for orbitals 1 of which points of each hydrogen to make a bomb the key is to draw out you but I've drawn here on slides 640 setbacks and to put the hydrogen is at the corners of the cube on the top corner he picked kitty corner 1 way and on the bottom you take it the other way and that's ever so much easier than the usual but you might draw of putting 1 straight up and 3 down like this is a territory he this makes it much clearer to see color the the 1 against around the nuclei of the hydrogen red just because I'm gonna pick the positive face untreated picking the face I want now to make a bomb if the heightens red cards in the center of the key to what I need to do is take a combination of those guys so I get a rare thing pointing at the thing that's the hydrogen that I know they can constructively interfere and 2 electrons consolidation there and I can get a bomb and that's the idea than behind the hybrid orbitals
2 so what do we want for HA will HA is 1 unit and acts in a positive direction 1 unit and why in the positive direction and 1 unit in C so that's the 1st hydrogen the HA to to make up hybrid or on carbon the correct combination .period at that is to just take it seemed to us that surrounds that points no and then P X .period employer sets the Reds over here he was neither reads over their push it up easy now the roads .period right at that hydrogen Mark H. a therefore that's the correct combination to make a bomb with a check and I've got for and I can easily then take the others and make bonds so we can get the others and
for H B which has Aztecs negative and why negative I just changed the sign of the PPE orbitals so to S -minus C 2 P X minus C 2 Y plus because it's still lot of scary corn C to PC and then freight scene there's another combination the minus signs move around so that it goes to that corner and then for H T minus signs move around again and in fact to get all possible combinations wants all plus all the others have 2 minuses at least 5 In the formula exactly 2 4 and that
then gives us for combinations I start with 4 ironed out with 4 but before I end up with mathematically in our all identical and mathematically they pointed the territory he drill angles and therefore I predict that with this series that I'm going to have 4 equal bonds and they're gonna be 109 . 5 degrees now the question is what happened to the energy we borrowed what happened well we borrowed energy to unheralded to electron promoted To the 2 key but now but we get all that energy back and more OK because we started a successful business so to speak and we made for very nice strong bonds between hydrogen and carbon and that is a winner that's excellent Veronica like crazy and so Back then allows to recoup energy that we borrowed plus more and so that explains how that could in fact happen so we did C H 4 and not CH 2 and we get 109 . 5 and not 90 degrees the
carbon barbarism course whatever they are they have some complex mathematical form we haven't sold for them we just threw some qualitative shapes whatever they are there's normalized that's for sure and so they're all normalized in a Gulf to x squared to s squared is is 1 of the overall space and they're all orthogonal so the 2 PD S is orthogonal to 2 PX and I think you can see that by cemetery but those Senegal's Rawls 0 because 1 of the positive and of course if the right angles of the two-piece integral 0 that's easy to see as well that lets us
normalize our polling hybrids and we have to take it let's take our starters 20 points of HA we've got to ask us to be exposed to what was to quantity square we end up with 16 terms but 12 of them across terms between S & P and I'm not calculate those I know there's 0 and the other 4 conveniently I don't have to calculate either because the 2 squared which I assumed was 1 and so we get for that add up and they add up to 4 and that's the end of the calculations and therefore we divide each hybrid bike 2 I can make them the 1st hybrid I can call at 5 a that points toward the hydrogen it's one-half 2 2 they are supposed to be exposed to PY plus 2 PC and I can normalize wants the same way there
are a lot of the hybrid combinations they're derived in exactly the same way if I got on the S P then I can take far as the arrest minus the roughly speaking and I can get something that pushes positive Breedlove 1 way or a positive red Loeb the other way and anonymous hybridize like that will make bonds of 180 degrees that's like a settling for example if I have 2 P 7 s 2 .period it is a plane so it's going to be playing DSS no direction so S sp 2 hybridized would be at 120 degrees when you work out the 3 combinations and playing there as 3 is better he droll and then to explain transition metals if you get very enthusiastic and they can have 4 and 5 Adams stuck around the middle often they do and you run out so you say Well if I run out recipes let me throw in some deeds and that you can actually they're very hot for me anyway to see and of but you can take and you can I have a deed to the U.S. 3 and now you've got 5 and that can make a trickle by pyramidal on something with the North and South 3 sticking out equatorial playing and you can take easy to sp 3 hybrids and you can make a not usual structure that has come to the north and south pole to hear to here and there that's what I don't know how much reality I would put into those orbitals I think at that point you're playing a bit of a mathematical games but rather than a realistic description of the bonding but anyway I'm historically that's 1 way to rationalize how you can get those other stable structures and why they have the geometries that they do and all these hybrid orbitals matched the qualitative valence shell electron pair repulsion and which just basically said the electron pairs around central added are sort of like electrostatic charges let's say their pages repel each other and they try to move apart as far as possible as the qualitative CPR approach OK next time what we're going to talk about is why I approaches in fact fall short but even from method
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