 Once again I welcome you all to MSP lecture series on advanced metal chemistry. This is 18th lecture in the series and my previous lecture I had initiated discussion on ligand field theory. Let me continue from where I had stopped. As I mentioned in my previous lecture before I begin using ligand field theory to explain bonding, in bonding for coordination compounds let me make you familiar with molecular orbital theory. So that understanding of ligand field theory would be very easy. Here resolving molecular orbital description of a polyatomic molecule into a three component problem using a method known as ligand group orbital approach. For example, when we write molecular orbital diagram for simple diatomic molecules or hetero diatomic molecules it is very easy. I am sure you are all familiar with writing a more diagrams for molecules such as hydrogen, N2, O2 or even CO. But however when we want to write molecular orbital diagrams for polyatomic molecules it is very appropriate to consider a set of orbitals called ligand group orbitals. For example let us consider a triatomic molecule such as water oriented along z axis. So here consider two oneness atomic orbitals of two hydrogen atoms and each oneness atomic orbital has two possible phases and when they are taken as a group there are two possible phase combinations are there and we essentially call them as ligand group orbitals. Whether we have two, three, four or many so we can you go for this ligand group orbital concept. Now once again the number of atomic orbitals combined is equal to number of molecular orbitals produced. The energy of bonding molecular orbitals will be lower than that of isolated atoms. The energy of anti-bonding molecular orbitals will be higher than that of isolated atoms and they are almost close to the one of the atomic orbitals which is higher in energy compared to the other one in case if we are considering two atoms having different relative energies. The energy at the orientation of atomic orbitals should be similar to form molecular orbitals. For example if we take Px it has to interact with Px only Px cannot interact with Py orbital. In addition of sigma and Py bonds is similar to what we use in valence bond theory sigma bonds we use Greek symbols sigma and Py we are using Py whereas anti-bonding irrespective of whether sigma or Py we put star as a superscript at the end or on right side of that symbol. So while filling molecular orbitals similar to atomic orbitals off bow and Pauli's exclusion principles and Hund's rule should be followed and higher the bond order you should remember stronger is the bond and bond order is nothing but the number of electrons in the bonding molecular orbitals minus number of electrons in the anti-bonding molecular orbitals divided by 2. The bonding and anti-bonding molecular orbitals for core electrons cancel each other as a result there is no net contribution from core electrons towards the bond formation in a molecule as a result what happens there is no net contribution comes for bonding and then can be ignored. Only molecular orbitals diagram shows MOs created by combining atomic orbitals of valence electrons are very very important that means emphasis is given for orbitals valence orbitals and or valence electron orbitals. Now let us draw a more diagram for simple molecules such as H2 and also for other important diatomic molecules for better understanding. So now if you take you know two hydrogen atoms are coming with oneness one electron each and their energy similar so they are in the same line energy so when they combine together they generate two molecular orbitals one is bonding one is anti-bonding and two electrons are occupying the bonding here and here it is empty. So if you calculate the bond order 2 minus 0 by 2 equals 1 so bond order is 1 so thus we have a one bond between H and H that means molecular orbital theory very nicely predict the multiplicity of the bond and also once you know the bond order you can tell whether the strong bond exists between them or weak bond exists between them and how molecule is stable. So now let us consider couple of more molecules let us try to write a more diagram for helium diatomic molecule so helium molecule having H2 molecules. So now it is completely filled oneness orbital is there so two electrons are there here and two electrons are two electrons are here in this one per H2. So then if you try to form molecular orbitals we have sigma has two electrons sigma star also two electrons so net bond order is 0 so that means if the bond order is 0 then the molecule cannot exist. So simply you can say H2 cannot exist how about H2 plus when you consider H2 plus we are considering one H2 with two electrons one H2 which is positively charged cation with one electron in this case what happens two electrons are occupying the bonding orbitals and one is occupying anti-bonding so net bond order is half yes there is a possibility of existence of H2 cationic species. So this also again tell you whether a particular molecule can exist as a diatomic species or not. So now let us try to write a more diagram for water molecule it is very interesting so this is how do not worry much about mulligan symbols if you have not understood does not matter. What is important is water molecule means oxygen oxygen is coming with H2 P4 six electrons are coming and then H2 means as I said ligand group or if you consider H2 so two hydrogens are there we are getting two electrons so two electrons and six there are eight electrons are there if you place eight electrons we are placing in this fashion two electrons here and two electrons here two electrons here and two electrons here and these two electrons and these two electrons are responsible for making two OH bonds whereas these two pairs of electrons are essentially the lone pairs on oxygen. Let me show you from Lewis dot structure and also from Welles bond theory so we write like this according to Lewis dot structure what we do is so we have six plus two eight electrons are there here six plus two eight electrons are there out of eight electrons what we are using we are using here two electrons here we are using two electrons for making bond and remaining four electrons I am putting here to complete the actate and VACPR theory we have four pairs of electrons a steric number according to VACPR we call it as steric pair so we have four pairs are there out of four pairs what happens two are bonding and two are lone pairs bonding pair and two are lone pairs that means we write something like this here and then here we have two electrons so that means we have two pairs of electrons are there and these two pairs of electrons can be seen from here is this one and then if you go for a hybridization concept Welles bond theory oxygen undergoes sp3 hybridization and when it goes sp3 hybridization it has two sp3 hybridized with one electron each and two sp3 hybridized with two electrons each and this will interact with hydrogen so that water molecule is formed here again these lone pairs are there these lone pairs can be seen from this one here so the question is have you come across any example where water acts as a bidentate ligand we know that water can bind readily as aqua and then which lone pair one of the lone pairs so this lone pair is responsible for making water as a ligand and how about the second pair okay it cannot see it is little deeply buried it cannot give readily and when you make an attempt to give this one what happened the OH bond goes and it becomes hydroxo species when it becomes hydroxo species it acts as a bridging ligand and if you see in the literature or somewhere neutral water molecule is not acting as a bidentate ligand because second pair is not readily available although you can see the lone pair is there because it will lower in energy and it is not readily available for bonding when we make an attempt using base or an acid in that case what happens we are leaving one of the OH bond as result becomes hydroxo species and then that can bridge two metal centers so that means this information does not come from valence bond theory but molecular orbit theory can explain this some of these important properties now let us look into carbon monoxide carbon monoxide is very interesting molecule and when I floated my course on main group elements I did discuss about carbon monoxide and lot of students write to me asking about the stability of CO molecules when you remove an electron and all those things I must have told answer to lot of students and still continue doing it so let me you know clarify those doubts with the CO molecule of course I will be discussing more such interesting aspects as this course progresses let me write a more diagram for CO molecule here if you just look into CO molecule carbon here and oxygen is here and oxygen as once again comes with 6 electrons and carbon comes with 4 electrons we have a total of ways electrons 10 out of 10 basically what happens here 2 electrons are there here 2 electrons are there and here 2 electrons 2 electrons and 2 electrons so 2, 4, 6, 8, 10 are there if 10 are there how do you consider carbon monoxide bond order that is the question so for that one let me write again Lewis dot structure here for that one before Lewis dot structure I write let us count valence electrons we have 4 plus 6 we have 10 electrons are there and out of 10 electrons first I utilize a pair of electrons to make a bond and then 8 electrons are there first I should satisfy the update of the most electronegative atom in this case it is oxygen so I write here now 8 electrons have been utilized a pair of electrons are left I put here on carbon so if you see this electrons here so this pair of electrons are responsible for making carbon monoxide as a neutral sigma donor ligand so this is a sigma donor pair of electrons now the update of carbon is not satisfied it has only 4 electrons are there then what happens carbon monoxide pleads with oxygen whether it can donate a pair of electron and place it in between so that both of can enjoy update satisfaction in that case oxygen agrees and it puts here and another pair it puts here as a result what happens we see a triple bond between carbon monoxide and oxygen so now the triple bond is there so these triple bonds are responsible for giving bond order of 3 here so these electrons are coming from this pair and this one and this one if you see that is because of this one now okay so this one it looks like it remains non-bonding and several books proposes several type of molecular object diagram nevertheless it is non-bonding but it is little lower in energy but still we are considering what happens these 6 electrons are responsible for making the triple bond bond order 3 and for example if you remove one electron to generate CO plus then what happens the energy of this one further drops and comes lower little lower so in that case what happens you have to consider that also as a bonded in that case what happens where bond order will be 7 minus 0 by 2 7 electrons are there bond order 3 5 so that means CO plus bond order increases and this is how you can give a correct answer for CO plus versus stability of CO molecule so there should not be any doubts about that one so this is non-bonding and this non-bonding is this is the we are talking about this is how one can understand CO and what would happen and of course here next when it acts as a you know pi acceptor metal electrons will be going to this one when the metal electrons goes more and more electrons are going to pi star then what happens the bond order would start decreasing and eventually sometime what happens this triple bond will almost become double bond as a result we have multiple bond between metal to carbon I will be discussing all those things in detail and in fact you should remember the fact that a carbon monoxide can take anywhere between 0.2 to 1.2 electron density into its pi star so accordingly you can see the strengthening of metal to carbon bond to the same extent weakening of carbon to oxygen bond of carbon monoxide so yeah this is another one I showed you so this is how the another carbon monoxide MO is shown and also I have also come across this point of things and here they predicted as anti-bonding yes if it is anti-bonding then you have to consider these things are bonding this also you should consider then 8 minus 2 it becomes 6 and after removing one electron what happens its sigma bonding becomes lower then it becomes 7.5 this also holds good but this not appropriate and because for bonding purpose it should not be considered deeply buried the oxygen lone pair that is the reason probably I believe it is not the right one and the right one is the one I wrote here this is the the most appropriate M O diagram for carbon monoxide let us look into another interesting molecule BF3 and BF3 we have 3 electrons in the valence cell of boron and then we have 3 fluoride ions are coming or 3 fluorine atoms are coming with 7 electrons that means in order to construct this one I should consider 4 valence orbitals of boron that is 1s and 3p similarly I had to consider 4 orbitals from each fluorine atoms so that we should have 12 ligand group orbitals will be there that is the reason to understand them I have given different color it does not mean anything they are all now ligand group orbitals having the similar properties but to distinguish I have just given different color so that you can counting would be very easy so 12 ligand group orbitals are there that means now what we have is so 3 electrons are coming from boron and then 7 into 3 21 are coming from so total we have 24 electrons are there so this molecular orbital diagram should account for this 24 electrons let us see how it happens so you can see here the field ones 2 electrons here and then 4 electrons and 6 electrons so this 6 electrons represent 3 BF bond formation these electrons here and this one would represent 3 BF bonds so that means we have utilized 6 electrons are there and what is this one what is this one here ok this one is essentially coming from one of the lone pairs of fluorine atom one of the lone pairs of fluorine atom let me show you using Lewis dot structure here so boron is there and I make I write something like this and utilize 6 electrons for making 3 BF bonds and then whatever the electrons left I should satisfy the octet I will start writing like this at the end you can count whether my writing is correct or not so now if you count totally we have 24 electrons are there so 24 electrons are there and then but boron has only 6 electrons it is electron deficient and also it is a Lewis acid so now the question comes if we have BF3 and we have BCL3 F is a more electronegative atom so then when we compare the Lewis acidity strictly speak according to periodic properties BF3 should be a stronger acid and BCL3 should be relatively weaker compared to BF3 it is also a stronger acid but when you look into actual properties BCL3 is a stronger Lewis acid compared to BF3 then how to explain that one here what happens you are talking about 2p orbitals and 2s orbitals again also here 2p and 2s so orbitals are of same size as a result overlapping is same and since the energy of 2p is same and then basically what happens a pair of electron from one of the fluorine atom will be donated here so that means now what happens octet is satisfied that pair of electron is shown here so this happens whereas why it do not happen in case of BCL3 BCL3 we are considering 3p orbitals and the because of the orbital mismatch this overlapping of 3p electrons with 2p orbital is not effective as a result what happens still boron remains electron deficient as a consequence BCL3 is much more stronger Lewis acid compared to BF3 so again this can give you very satisfactory answer about these trends or properties so that probably you may not be understand even from valence bond theory of course if you use valence bond theory also you can write if you use valence bond theory then we have to talk about sp2 and then keep the p orbital empty that empty p orbital would take electron from one of the fluorine atom so this is how you can explain in case of polyatomic molecules okay now we have utilized the 8 electrons 2 for bad donation from fluorine to boron and remaining electrons will be so 16 electrons are there those 16 electrons are 1 2 3 4 1 2 3 4 5 6 7 8 that means these 16 electrons remain as non-bonding here they are non-bonding electrons 16 electrons is accounted that means 16 18 20 22 24 all 24 electrons are accounted so this is how you can explain without any problem the bond formation and the existence of BF3 molecule and also you can also predict and tell about its Lewis acidic nature with respect to BCL3 this shows superiority of molecular orbital theory over other bonding concepts that we use so now let us look into another interesting molecule SF6 so before we shall focus our attention on this amour diagram I will show you this one with valence bond theory of course SF6 when you look into it Lewis dot structure cannot explain because we have here 12 electrons are there 12 electrons are there it shows only about octet that means beyond 8 it does not believe so that means BF3 also you cannot explain where electron rich metals more than 8 electrons are there Lewis dot structure cannot tell but partially to an extent Lewis structure is true that is proved by molecular orbital theory. If you look into valence bond theory what happens you can see clearly here we have 3s we have 2 electrons are there and 3p we have 4 electrons are there we have 3d orbitals are there which are empty yes I can utilize them very similar to outer orbital complex like sp3d2 I can make 6 sp3d2 orbitals and then put these fluorine coming with 12 pairs of electrons because once all the electrons are taken out they become F minus and each one will be given 2 electrons that means 6 electrons will be coming to yes so sp3d2 will be completed so this is how valence bond theory predicts the geometry of SF6 as an octahedral and it is a sp3d2 hybridized system but if you look into this amour diagram here the energy of 3d is too high I forgot to put here energy energy is too high that means nowhere you can see the participation of EGR T2g with F orbitals. So instead how it is explained you can see 6 fluorine atoms are coming with 12 electrons already we are here we are having here 6 electrons are there that 6 and 6 12 should be accounted and here if you see a pair of electron is there and then 6 pairs of 6 electrons are the 3 pair and then this 8 electrons we see here are fine and then we have another 2 pair of electrons are here that is coming from fluorine they do not find suitable orbitals from sulfur and as a result they remain non bonding so that means SF6 solely stabilized with only 4 pairs of electrons then what it is then it is a hypervalent molecule such molecules we call it as hypervalent molecules and 6 8 electrons are there that makes octet is satisfied octet Lewis acid and then 4 electrons are there and these 4 electrons means 2 fluorine bonds essentially keep the electrons towards itself and make weak bonds can be placed in because of the very high energy of the orbital so they are not participating in bonding they are called hypervalent molecule. Similarly if you consider sodium hexafluorosilicate Na2SiF6 that is also hypervalent molecule then how it is octahedral geometry as what happens it is highly symmetric what happens this is like almost dynamic process they keep changing as a result what happens it looks very stable and the stability comes because of kinetic. So for example if the moisture or something try to attack there is no vacant site on sulfur as a result what happens it appears SF6 appears more stable compared to SF4 nevertheless when you heat it and get rid of 2 fluorine atoms it is vulnerable for hydrolysis. So SF6 is a hypervalent molecule and they it never employs 3D orbitals in this bonding scheme. So let me stop at this stage and now with this information on molecular orbital theory let me switch over to Ligand field theory of course Ligand field theory is more or less molecular orbital theory but it has crystal field theory component also it has taken mixing of orbitals that is New Orleans bond theory is also taken so let me discuss more interesting chemistry based on Ligand field theory in my next lecture.