 Hello everyone, in our day-to-day life we get an opportunity to learn many things from both living and non-living objects and if we have keen observation we can learn lot of things and also if we learn something good that we can pass it on to others. That means irrespective of our age, irrespective of our profession we have lot to learn every day and hence I say learning never ends. So with this let us continue learning chemistry, especially chemistry of transfer elements. So today's focus would be on Ligand field theory and until last lecture I was discussing about the crystal field theory and its utility in understanding coordination chemistry and why people switched to Ligand field theory. Let us try to understand to accommodate and account for both ionic and covalent characters in metal ligand bonds. Ligand field theory was introduced and it is a combination of best part of valence bond theory, crystal field theory and Mulliken's molecular orbital theory. So let us try to conclude crystal field theory and its advantages and considering. Let us try to understand crystal field theory's simplicity and how it differs from Ligand field theory and what is Ligand field theory. Crystal field theory of course is a simplest model for explaining the structures and properties of transform metal complexes. The theory emphasizes mainly on simple electrostatic interaction between the metal ion and the Ligands and considering Ligands as point charges. Although some of assumptions made or inaccurate it is still very simple to understand and also useful because of its effectiveness in using molecular symmetry. It describes the properties of metal complexes such as color, magnetism, geometry and relative stability of complexes having different type of Ligands quite accurately. However, Ligand field theory is more advanced and it is originated from molecular orbital theory. It is more complex compared to crystal field theory but it is more accurate and Ligand field theory will explain many questions accurately that crystal field theory may not from this context and it is very appropriate to bring in Ligand field theory concept instead of crystal field theory to understand or to for better understanding of coordination compounds and their properties. Ligand field theory very effectively uses molecular orbital theory in coordination chemistry by giving importance to the effect of donor atoms that is the Ligands and the energy of d orbitals in the metal complexes. Same thing we observed in case of crystal field theory also the direction of approach of Ligands how they influence the energy of d orbitals. The influence of Ligands on the d electrons on a metal can be analyzed from Ligand field theory of point of view in two ways electron electron repulsion and of course this is due to the lone pairs from Ligands when they start approaching the metal ion and bonding interactions between the metal and donor atoms. The combined effect increases the energy of the d electrons which in turn depend on the nature of Ligand field and the geometry is conferred by them at the metal center. From crystal field theory we know that in an octahedral field eg orbitals that is dz square and dx square my y square interact strongly whereas t2g orbitals does not interact so strongly but rather weakly. Therefore these two orbitals along with Ligand orbitals from new bonding therefore these two orbitals that is dz square and dx square my y square along with Ligand orbitals form new bonding and anti bonding orbitals. The other three orbitals that are present on metal center that are dxy dyz and dxz that is t2g will remain as non-bonding with almost unchanged energy. Of course these assumptions we made in crystal field theory as well and then let us consider octahedral complexes. In octahedral complexes the electrons of the Ligand occupy all 6 bonding molecular orbitals whereas any electron from the metal cation occupy the non-bonding or anti-bonding orbitals. Non-bonding means it is t2g or sometime anti-bonding means it is eg especially when the metal ions have more than 6 electrons in their d orbitals. The separation between t2g and eg orbital is designated as the orbital Ligand field parameter delta O similar to what we call it as crystal field stabilization energy. So Ligands whose orbitals interact strongly with the metal orbitals are called strong field Ligands for such Ligands the orbital splitting is little larger. In contrast Ligands whose orbitals interact only weakly within the metal orbitals are called weak field Ligands for such Ligands the orbital splitting is very small. So that means still the concept of weak field Ligands strong field Ligand is continued in Ligand field theory. The other comparisons between various d configurations and strong and weak Ligands are very similar to what we come across in crystal field theory. When we talk about Ligand field theory it proposes two types of bonds known as sigma bonds and pi bonds for coordination compounds similar to what we see in organic chemistry or main group chemistry with the aid of valence bond theory. The sigma bonds are symmetrical about the axis of the bond whereas pi bonds are unsymmetrical with regard to the bond axis that we should remember and of course the same concept we use in valence bond theory also while explaining organic molecules. Again in coordination compounds pi bonding may result from donation of electrons from Ligands. For example halogens or oxygen atoms to empty d orbitals of the metal atoms especially in case of early metals in their high oxygen states where all the d orbitals are empty and they are halophilic and oxophilic in nature are electrons from d orbitals of the metal to appropriate empty orbitals of the Ligand as in the case of metal carbonyls such as chromium carbonyl, chromium hexacarbonyl, iron pentacarbonyl or nickel tetracarbonyl and other carbonyl compounds or carbonyl clusters. In the chromate ion if you consider CRO 4 2 minus the oxygen atoms donate electrons to the chromium ion which is in plus 6 oxygen state having no electrons at all in the d orbitals. In case of carbonyl and phosphine complexes electrons from the metal orbitals especially T2g may be donated to empty pi star orbitals in case of carbon monoxide or sigma star orbitals in case of phosphines. This is also known as back bonding and such Ligands are called back bonding Ligands, pi donor or pi acceptor Ligands. So now with this information about Ligand feed theory and how it was slightly modified concept it uses from crystal feed theory can be understood and using this theme let us try to do the classification of Ligands. I shall tell you of course I will be discussing the classification of Ligands by donor atoms after couple of lectures but now for convenience with the help of Ligand feed theory let us try to understand how whatever the Ligands we have at our disposal can be classified for simplicity and for better understanding to make a coordination chemistry much simpler than what it looks like. And I was telling you the main drawback of crystal feed theory is it does not identify the system where metal is neutral and Ligands are neutral. In that case what happens metal if it is neutral it can also generate a dipole and of course Ligand neutral Ligands can always generate a dipole because of electronic humidity difference between the donor atom and the peripheral atoms. In that case what happens when the metal Ligand bond takes place that would be like dipole-dipole interaction according to crystal feed theory if you give emphasis for electrostatic attraction. In that case it would be dipole or dipole interaction as we see in case of nickel tetra carbonyl or chromium hexa carbonyl or other carbonyl complexes. But crystal feed theory does not explain about the nature of the bond having fully covalent property. So that means in order to introduce both covalent and ionic character Ligand feed theory came into existence and based on this theme let us try to classify whatever the Ligands we come across into broadly three categories. So that I shall show you of this slide. The most common one is Ligands comes with a pair of electrons that can be readily donated to the metal. So here Ligand is a two electron donor and all Lewis bases are considered as this type of Ligands ammonia, water, carbon monoxide and triphenyl phosphine. And then what happens here you can see Ligand is one electron donor both metal and X is a Ligand here contribute one electron each. So that means radical such as H, Cl and CH3 are considered as this type of Ligands. And in the last one metal has sufficient electrons and acts as a Lewis base and that interacts with the Ligand which is not Lewis base but Lewis acid. In that case Ligand Y is zero electron donor both the electrons are from metal they are called Lewis acids and examples are BF3 and ALME3. And again this type of system we can further classified into three categories and by considering both donor and acceptor properties of Ligands as I mentioned in case of chromate or carbonyl complexes and how this donor and acceptor properties of Ligands fluently crystal field stabilization energy let us look into it from these diagrams. You can see here we have the metal the metal orbital energy somewhere here and the Ligand is a pure sigma donor here and the energy is relatively lower compared to this one and when they interact this is the magnitude of crystal field stabilization energy here. That means we are interacting metal with low energy sigma orbitals low energy sigma orbitals that are filled to be precise the metal is interacting with filled low energy sigma orbitals of the Ligands in this case this is the magnitude here. Example you can consider pure sigma donors ammonia and water let us look into the second case here. So in this case we have these Ligands which have low energy field sigma orbitals and low energy field pi orbitals if you consider halides such as chloride bromide iodide they have S2 P6 electronic configuration and eight electrons are there and that means completely filled wear and shell when they interact with metal they come up with low energy filled sigma orbitals and low energy filled pi orbitals in this case what happens because of their interaction what happens CFSC decreases relatively compared to what we see in the first case. You can see drop in the magnitude of CFSC that means we can know between them which one is relatively stable and which one is relatively less stable. Now the second third case is we have filled low energy sigma orbitals and MT high energy pi orbitals when such Ligands are coming to establish a bond with metal this is what happens here the magnitude of CFSC increases that means any Ligand that is sigma donor and pi acceptor having low energy field sigma orbitals and high energy MT pi orbitals. So they stabilize complex to a greater extent and hence they are called as stronger Ligands because CFSC is larger. So this is how you can classify the Ligands and this is how you can tell why a particular Ligand is called as weak Ligand why a particular Ligand is called as strong Ligand. Christofield theory says classifies Ligands according to spectrochemical series and also gives authenticity through electronic spectra showing the relative Christofield stability energy and shows why one Ligand is weaker one another Ligand is stronger but the explanation lies here. If I say why chloride is a weaker Ligand compared to water we should not say CFSC. CFSC is a authenticity it gives a evidence but it does not explain why in order to explain why a Ligand is weaker compared to other one we have to classify according to these three categories and we have to see where exactly the given Ligand falls. It has to fall into one of these categories if it falls here we can explain yes it has a low energy field sigma orbitals and high energy MT pi orbitals as a result what happens this is what happens to the CFSC in the same way we can explain. So this explanation gives precise meaning to the position of Ligands in the spectrochemical series. So this is pure sigma donors and they are pure sigma donor and pi donors and they are called sigma donor and pi acceptors and examples I have already given here now in case of all Ligand system will come under one of these classes their positions in the spectrochemical series is based on these properties and if somebody asks why a Ligand is weaker you should not tell because CFSC because CFSC is an evidence through electronic spectra means but it does not tell you why. So this will give you satisfactory answer for why these Ligands have this kind of different properties and of course on a later note we can also compare into something that we are observing day to day life for example here is a person who earns enough money to take care of his family when he has a student school going student what happens he takes care and he gives enough money for his school and all those things without any problem and the student becomes good and he learns properly and he achieves what he wants this is in case of pure sigma donor Ligands and then here father is business minded he earns lot of money you can see it is almost like minting money and then what happens he does not have much time to worry about his son or daughter and when he goes to school he will be giving whatever the money he has double so that he should not bother him on the other hand since he has lot of money mother also gives lot of gifts in that case what happens he does not show any interest because he has lot of money to spend and as a result he becomes something like this this is what happens to metal complexes having sigma donor and pi donor they are very very reactive and labile that is the reason when you take unhydrous metal halide and keep it tomorrow what happens it appears like wet because what happens the atmospheric moisture steadily replaces and it forms hex aqua compound that means very unstable and the other hand he is very intelligent person and he knows how much money has to be given including his fees and pocket money whatever and he gives but mother is even more clever she thinks that father has given more money to the student and she takes little money from him for future and as a result what happens this student understands value of money and and he puts all his time for studies and the student becomes a plus that means very stable so everyone should be like sigma donor and pi acceptor ligands so that they can achieve whatever they want without any problem and examples in this case are all kind of tertiary phosphine carbon monoxide olefins and heterocyclic carbons and all those things of course I shall discuss and give relative comparison of all sigma donor and pi acceptor ligands at later stage. Now let us come to molecular orbital theory as I mentioned ligand field theory has embedded best parts of valence bond theory crystal field theory and mullicans molecular orbital theory so before I introduce the ligand field theory I want to make you familiar with molecular orbital theory so that understanding ligand field theory would be very easy and for that one I have given some points here molecular orbital theory is based on delocalized bonding model unlike valence bond theory and similar to isolated atoms a quantum mechanical treatment is adopted for molecules and uses the concept of molecular orbitals considers the wave like properties of matter. A molecule is considered on a quantum mechanical level as a collection of two or more nuclei surrounded by delocalized molecular orbitals over the surface of two nuclei atomic wave functions are some to obtain molecular wave functions if wave functions reinforce each other a bonding molecular orbital is generated or formed and it is nothing but the region between the nuclei where high electron density exists on the other hand if wave functions cancel each other an anti-bonding molecular orbital is formed that means a node or a region where zero electron density exists between the nuclei. So this is how you can represent summing up and subtraction so here you can see the electron density resides here when the waves are reinforced on the other hand when the amplitude of waves subtracted so you can see a node between two electrons this is called anti-bonding and this is called bonding. So contours and energies of the bonding and anti-bonding molecular orbitals in H2 I am going to show here you can consider two isolated hydrogen atoms having one electron in their 1s orbitals when they interact as I mentioned two levels are generated one is due to subtracting and one is due to addition and energy of isolated atoms remains here and now the bonding molecular orbitals are generated where you can see two nuclei are there and between electron density resides this is called sigma 1s and this is anti-bonding where we call sigma star 1s all anti-bonding will be given the superscript star next to it so node is generated here this is called anti-bonding and of course this is very very important the symmetry classes of SP and d-orbit of the central atom of an ABN molecule with respect to the point group in most cases the z axis is principal axis of the molecule so whatever the molecules we are considering where in coordination chemistry or in a just always we keep z as principal axis for example if I ask you a question to write crystal field splitting diagram for a molecule okay octahedral molecule or a square panel molecule kept along x axis if a molecule is kept along x axis instead of z axis then it will be in y z plane then accordingly what happened the splitting varies so one should be able to understand these aspects if you understand these aspects you should be able to write crystal field diagrams no matter which axis we are considering as principal axis so nevertheless here we have considered z axis as principal axis and when we consider according to various point groups what are the mulligan symbols we are giving and what is the nature of bond we come across for various orbitals I have listed here this is very good very informative and there is no need to remember this one okay just whenever you get time go through this one to understand the terms we are using for different orbitals under different point group for example if you consider tetrahedral or octahedral s orbital is symmetrically spherically symmetrical and it forms sigma bonds and we say it is a 1 g so same thing is there and p orbitals p x p y p z or degenerate we call them with t 1 u that you have seen or you are going to see okay and then dz square and dx my square we call eg that is what is here and dx y dy z and dx z collectively called t 2g so these are the terms we are using and again in case of td because of lack of centrosymmetry we remove the g and that holds good here we can say of course pr build some variation will be there and if you take d 4 hat for square panel complexes you can see whatever the no mullican symbols we are using you will be coming across in ligand feed theory as well as in molecular orbit theory and then yeah this is for octahedral and this is for tetrahedral complexes geometry and this is for square panel and then I have just expanded what is that one what is mullican symbol a means singly degenerate or one dimensional symmetric with respect to rotation of the principal axis because of it is a spherically symmetrical nature it is symmetric with respect to the rotation with respect to any axis for that matter and b singly degenerate or one dimensional anti symmetric with respect to rotation of the principal axis on what basis we have given for example if you want to try to see a particular orbital and with respect to a geometry you can understand whether the statement is true or not and e means doubly degenerate or two dimensional e g we are using so t mullican symbol triply degenerate or three dimensional so that we use in case of t2g and subscript one if you use like a1g b1g or b2g one means symmetric with respect to the cn principal axis if no perpendicular axis then it is with respect to sigma v in some molecules will act a perpendicular axis in that case we have to consider this one with respect to sigma v and subscript two means anti symmetric with respect to the principal axis if no perpendicular axis then it is with respect to sigma v again and g means symmetric with respect to the inverse that means if they have center of symmetry and subscript u anti symmetric with respect to the inverse so this is the explanation for various superscript and subscript we come across for various mullican symbols. So let me stop at this juncture and continue discussing molecular orbital theory to make you familiar with understanding for simple molecules and also a couple of very interesting main group compounds and then I switch over to ligand field theory to explain the bonding in various transformational complexes for various geometries until then have an excellent time reading chemistry.