 Until now we have come a long way but in molecular orbital theory we have learned how to handle only homonuclear diatomics H2 plus H2 F2 so on and so forth. But we do not want to stop there right we do not want to talk only about homonuclear diatomic molecules. We want to talk about molecules like these which are neither homonuclear nor diatomic. This by the way is calphosin C and what you see here is the output of an energy minimized structure calculated using the quantum chemistry calculation software computation software GAMES it is pretty old now this is from our paper that was published I think in 2000 the work was done in 99. The calculation was done to rationalize an experiment that I had performed the experiment took a day the calculation took a year using state of the art supercomputer of that time and that is because the molecule is so large. But you can do quantum chemical calculations of molecules that are this large molecules there are neither homonuclear nor diatomic and you can get useful results like in this one you can see this red one as usual is oxygen the small white ball is hydrogen so we see that this OH hydrogen comes very loosely close to another oxygen there is a hydrogen bond and then that affects this property of this huge molecule in a very very significant manner. So of course we will not be able to go all the way where we will know how to calculate how to do quantum chemical calculations for a molecule like this. But let us see first how do we handle diatomic molecules that are not homonuclear heteronuclear diatomic molecules and then let us see how do we handle molecules that are not diatomic how do we handle polyatomic molecules using molecular orbital theory. So the first heteronuclear diatomic molecule we want to talk about is hydrogen fluoride and here I will take help of some experimental result the experimental result that I am showing you here is from photo ionization spectroscopy and we will have reason to refer to photo ionization spectroscopy later on in this discussion what it does essentially is that it measures ionization energy. So what photo ionization spectroscopy tells us is that ionization potential ionization energy of hydrogen is 13.6 electron volt we already know this number for fluorine the smallest ionization energy we get is 18.6 electron volt so that would be from the 2p orbital. For Hf we get an ionization energy of 13.4 electron volt which is very very close to the value of 13.6 electron volt for hydrogen and we get another one for 18.8 electron volt which is very very close to the ionization energy of fluorine 2p. So what we understand from this experimental result is that there is one molecule orbital in Hf whose energy is very close to that of 1s orbital of hydrogen and we have another orbital whose energy is very close to that of 2p orbital of fluorine. So when we go ahead and when we do the quantum chemical treatment we get this expression the higher energy orbital expression is 0.98 into wave function of 1s orbital of hydrogen atom plus minus 0.19 psi f and for the lower energy one it is 0.19 psi h plus 0.98 psi f these are not normalized so that the sum of coefficients will be 1. So we have an orbital lower energy that is close to that which is very close in energy and in nature to an orbital of fluorine there is another one that is very close in behavior with an orbital of hydrogen. So what we see is that unlike homonuclear diatomics we can have molecular orbitals which have greater contribution from one atom or lesser contribution from one atom. So we can have unequal contribution from the two atoms which leads to as we are going to discuss polar covalent bonds. Again from your high school you would have studied about polar covalent bonds and we know many many examples Hf OH in water all these are polar covalent bonds this is how polar covalent bonds show up in an MOT treatment. And now let me show you the full energy diagram as constructed from molecular orbital theory these energies relative energies are more or less okay they are more or less drawn to scale. So this is the orbital which has energy close to that of hydrogen atom so this is mainly like hydrogen 1s orbital point to note here is that energy of fluorine is much much lesser than energy of hydrogen fluorine orbitals is much much lesser than the 1s orbital of hydrogen as we have discussed when we talked about homonuclear diatomic molecules of second row. So the lowest energy one is mainly fluorine okay let me go a little further see what we see here is that we have sigma orbitals that are made up of a linear combination of hydrogen 1s orbital fluorine 2pz orbital fluorine 2s orbital right 2pz has the right symmetry in which it can show overlap as we have discussed earlier. So all these 3 should contribute to the linear combination but what happens is that the contribution contribution comes from square of coefficients contribution of the fluorine 2s and 2p orbital for these 2 sigma orbitals bonding sigma orbitals is much much more than the contribution of the hydrogen atom 1s orbital and similarly for this 3 sigma orbital it is still a linear combination of h1s f2p f2s but contribution of f2p and f2s is really small compared to that of h1s so it is a mainly hydrogen atom orbital okay. Then you have this 2px and 2py orbital so f2p which do not have the right symmetry for sigma bonding so they are non-bonding orbitals on fluorine so we call them exclusively fluorine orbitals okay and then how many electrons are there we have 4 pairs we fill them in so we see that the 2 sigma electrons are mainly on fluorine they are on hydrogen also okay but mainly they behave like their property of fluorine atom. They distributed in 2s and 2p orbital of fluorine atom to a small extent in the 1s orbital of hydrogen atom and what about these 2 pairs these are the lone pairs on fluorine atom remember lone pairs if you just draw Lewis dot structure you will see that you get 2 lone pairs of fluorine 2p that is what we get in molecular orbital theory as well the only additional information is that we get to learn that in case of hf these lone pair electrons on fluorine reside in pi orbitals okay so this is a picture that we get since the electron since there is a more contribution of fluorine orbitals if you draw the electron distribution or constant probability surface you are going to get something like that dollopsided distribution in fact it is more lopsided than what it appears to be in this cartoon right so unequal contribution from the 2 atoms is nicely accounted for in heteronuclear diatomic molecules by molecular orbital theory and what you need to remember is that orbitals must have comparable energy and compatible symmetry so that they can participate in linear combination to form the molecular orbitals I will say that again atomic orbitals must have energies that are close by to each other and compatible symmetries so that they can participate in the linear combination for constructing the molecular orbital so for hf the linear combination involves h1s f2p and f2s if you go higher up in the periodic table for hcl well h we have no option it is 1s but for chlorine now the 3p and 3s orbitals have energy that is close to h1s and that is those are the valence orbitals anyway so good thing is you can form this linear combination and you can get energy diagram like this for bromine now it has become predictable we have 4p orbitals that have energy that is close to that of h1s all these are drawn roughly to scale and we have shown different things in this diagram for example unfortunately I should have cited the source but I have forgotten where we got it from but what we see is that we also get to draw the m os this is how the m os will look you see first of all this sigma bonding m o is formed by combining a 1s orbital and a pz orbital there is a node in pz orbital so this is what it will look like do not think it is an sp hybrid orbital or anything it is not it is molecular orbital it is spread over the entire molecule and for the anti bonding orbital what will it be I will just draw the atomic orbitals in case there is any difficulty in understanding in this case for the bonding interaction this is your 1s orbital of hydrogen atom and this is the 4p orbital of chlorine atom and you might remember that actually we are only showing the outermost loop inside you have shells right you have plus minus plus like that but all we are talking about is the major shell for further understanding please refer to that lecture where we had drawn these orbitals and we had explained how nodes are and how electron how wave functions are so this is the bonding combination of atomic orbitals anti bonding combination would be if you put plus sign here then it will be minus so you will have destructive interference here that is how you get a molecular orbital that looks like this you have constructive interference here that is how you get a molecular orbital that looks like this but please do not forget that your fluorine atom is here and sorry not fluorine what is this bromine bromine atom is here and hydrogen atom is here right so that is what we get from molecular orbital theory in heteronuclear dynamics we get lopsided molecular orbitals and lopsided electron distribution consequently now we want to talk about carbonyl complexes so carbonyl CO carbon monoxide is a very very important molecule from the point of view of chemistry as well as physiology it is known that carbon monoxide forms carbon monoxide uses this carbon atom as a good sigma donor in formation of coordinate bonds and also it can accept pi electrons that empty d orbitals we say right well maybe d orbitals or what is it you know sorry I goofed up a little bit there this d orbital is that of the metal from there electron density can actually come back and be accommodated in some orbital of carbon monoxide we will see which orbital so back bonding is there this is called synergistic effect in inorganic chemistry so that is why carbonyl the carbon monoxide can form very stable strong carbonyl complexes and these complexes as applications in organometallic chemistry like the one that is shown here you take a molecule like this a complex like this oxygen atom lone pair can attack say butyl lithium okay and then this R group butyl group in butyl lithium that gets attached to carbon once again carbon here is accepting electron pair and then whatever happens happens so the question is why is it that carbon can act as a very good sigma donor and then how is it that it can act as a good pi acceptor also okay to answer this question we construct a molecular orbital picture but before that let me also state that carbon monoxide is important physiological as well because you might know carbon monoxide is a highly poisonous gas as highly poisonous gas because it goes and attaches with hemoglobin hemoglobin as we know is a carrier protein it transports oxygen and CO2 and blood and the way it does it is that this here is the structure it is a tetramer and it is a metalloprotein it has Fe2 plus and there is a ligand which is sort of like porphyrin heme and then this is what happens in the heme center initially you have a low spin complex so this Fe2 plus actually hovers above the ring and the fifth position is taken up by a distal histidine now when from the other side oxygen or CO2 comes and coordinates then it transforms to a low spin complex size becomes smaller and this Fe2 plus goes and fits nicely in the cavity of porphyrin okay so that is how it takes up oxygen that is how it takes up carbon dioxide and it can give up oxygen and carbon dioxide easily wherever required that is because these oxo hemoglobin and carboxyemoglobin that is these complexes that are formed they are formed reversibly the problem is carbonyl well carbon monoxide forms carbonyl complexes that are extremely stable the formation is almost irreversible so once that complex is formed half life is of several hours so if somebody is exposed to carbon monoxide all these or a lot of these hemoglobin molecules will form this very very stable carbonyl complex with carbon monoxide which is not going to break so easily so they will not be able to participate in oxygen and carbon dioxide transport that is most important for life processes right so the question is why does carbon monoxide form such a good complex why is it that it can be a good sigma donor from carbon and why can the same carbon atom be a good pi acceptor the somewhat contentious molecular vital picture that has been constructed to explain this involves this concept of hybridization that we have discussed already and here one thing I want to remind you is that it is not necessary that all hybrid orbitals have to be equivalent they can actually have different energies it depends on what alpha beta gamma delta coefficients are now with that background this is the contentious model I was talking about these are the 2s and 2p orbitals of carbon once again more or less drawn to scale as far as energy is concerned these are the 2s and 2p orbitals of oxygen so in the model that is used remember we know the result already explain it we are constructing a model working out the energies and trying to see whether it makes sense it might make sense to a certain extent and then it might not we will see so okay so the model involves hybridization forming formation of 2 hybrid orbitals non-equivalent hybrid orbitals of 2 different energies for carbon as well as for oxygen okay so for carbon h1 is a lower energy hybrid orbital let us say h2 is a higher energy hybrid orbital now hybridization here we are talking about sigma bonds right so hybrid hybrid orbitals accommodate sigma bonds they are used for sigma bonding so the p orbital that participates in this hybridization would be pz if we take z to be the direction of approach of the 2 nuclei so px and py do not have the right symmetry as we have discussed earlier so they remain non-bonding orbitals on carbon okay right now well should not even say non-bonding right now they remain in pure unhybridized form on carbon similarly in oxygen we invoke hybridization form h3 and h4 and px and py remain as such so now this px and py are actually available for pi bonding we will come to that now here in there is an objection why do we have to use h3 and h4 for oxygen if you go back to homonuclear diatomics we said that this mixing of sp orbital does not even take place for oxygen so why would it take place here so one argument is that the CO is isoelectronic with N2 right if you compare nitrogen oxygen has one electron more carbon has one electron less so here even the oxygen atom should behave like carbon atom that is the sort of argument that is used right so now let us try and see which orbitals have comparable energy and appropriate geometry do you think h3 will participate in formation of sigma bond this is the energy of h3 this is you know energy increases right as you go up h3 has very low energy compared to h1 and h2 so it is going to remain non-bonding similarly h2 has a little high energy compared to h4 so it will remain non-bonding the difference is h3 remains non-bonding on oxygen h2 remains non-bonding on carbon what about h1 and h4 their energies are close enough so they form a linear combination to give you the bonding sigma orbital and and the bonding sigma star orbital what about px and py px and py like this these are x orbitals these are y orbitals they can form a pair of pi bonds right so you can generate two sets of degenerate pi orbitals and pi star orbitals also okay so when I write degenerate it is important to understand what I am really saying is this I do not think I talked about this earlier so I can write like this I will call it pi x is equal to c1 px of carbon plus c2 px of oxygen pi y will be c3 px of carbon plus c4 px of oxygen right and similarly when you take the anti-bonding combinations you will have minus instead of plus here and the coefficients are going to change so here also symmetry becomes important see px and px let us say this is x axis now they are in the right orientation they are the right symmetry to participate in a pi kind of linear combination but this px and that py do not the two py orbitals can participate in linear combination so while constructing these pi m os we do not take px c plus px o plus py c plus py we do not do that we only take x's and y's this is how the problem of formulation becomes a little simpler okay now we have to fill in the electrons how many electrons does carbon have 2 4 2 3 4 right 2 pairs and what about oxygen 2 4 6 3 pairs so now we have 6 plus 4 10 electrons we will start filling them up in pairs so sigma n b the lowest one h 3 is going to have a pair sigma from h 1 and h 4 we will have another pair and we have 4 electrons more they will reside in the pi orbitals pi molecular orbitals all right is there anything more yes one pair in sigma n b remember sigma n b is a non-bonding orbital that is a an exclusive property if you want to call it that of carbon atom right it is localized on carbon atom so what we see is that this and sigma right sigma means it is going to be highly directional now let me tell you the reason why this hybridization was done is that this is known to be used well this is what we think participates in sigma donation so if you want sigma donation to take place you want a highly directional orbital hybrid orbitals are more directional than your p orbitals right so that is why this hybridization was used in the first place so now this model nicely explains why co can act as a good sigma donor through the carbon atom because the highest occupied molecular orbital is a non-bonding orbital localized on carbon and why is it that it can accept electrons and remember the diagram I had shown you earlier when we talk about synergistic effect when we talk about back bonding then this is the diagram I had shown and I had hooked up a little bit this here is a d orbital of the metal ion we drew an orbital on the same carbon of carbon L like this this has been empty vacant orbital and we said this is how the electron cloud gets transferred so this d orbital is filled and the whatever this orbital is is vacant now remember this is the sigma bond so any orbital that is perpendicular to the sigma bonding orbital what kind of orbital would it be it has to be a pi orbital and I will show you in a minute minute what these pi star orbitals look like right so what we see here is that carbon also has this low lying vacant pi star orbitals which have the right symmetry which enables it to accept any electron cloud that comes back from the central metal atom d orbital so this is the orbital that is used in the action of carbon atom to behave like pi acceptor in carbonyl complexes now let me show you the orbitals molecular orbitals and again this is a little contentious what I would like to you to focus on is this sigma in v orbital see it is on carbon heavily on carbon and pointed towards one side it looks like a hybrid orbital and this is the pi star orbital again it is close to the carbon orbitals right carbon px orbitals look at the bonding ones the bonding ones are close to that of oxygen p x p y orbitals the anti bonding ones are actually lopsided towards carbon because they have a greater contribution from p x and p y orbitals of your carbon atom okay that is that this is the model that can nicely rationalize why carbon monoxide is such a good ligand why it forms good sigma bonds to carbon atom and why the same carbon atom can efficiently accommodate electron cloud coming back from the central metal atom that brings us to an end of our discussion of heteronuclear diatomic molecules in the next class we are going to go back to polyatomic molecules but this time we are going to learn how one can use molecular orbital theory to understand polyatomic molecules