 Hello everyone, once again welcome you all to MSP lecture series on advanced transformational chemistry. In my 12th lecture I did mention about interesting aspects of valence bond theory and how there are some exceptions or how there are some you know different type of vibration we came across to explain totally different type of bondings especially in case of heavier P block elements where we have multiple bonding. Now we shall move on to another very fascinating concept which appears almost complete in explaining all properties reactivity and all applications and spectroscopic properties of transmittal complexes or coordination compounds that is crystal field theory. Before I really start digging to crystal field theory let me try to give the background to this crystal field theory. The basic idea of the crystal field theory that the metal ions in the complexes is subjected to an electric field originating from the ligands was first observed by Bacquerel in 1829. The same Bacquerel who discovered radioactivity along with Mary Curie and Peary Curie, Henry Bacquerel. The same year Bete who has contributed significantly in developing crystal field theory a physicist carried out work by correlating symmetry and crystal field strength influence on electronic levels of the gaseous metal ions and laid down an excellent foundation to crystal field theory. That means the Bete's contribution is quite remarkable in developing a complete concept of crystal field theory. During the same time Dutch physicist Cramer's reported that the electronic levels in molecules containing an odd number of electrons must remain at least 2 fold degenerate. So this is also called as Cramer's degeneracy rule in the absence of any magnetic field which is closely related to Bete's double group theory. Double group theory means when he started explaining he told that the degeneracy of gaseous metal ion will not remain intact when it enters to crystal field and it is destroyed and it forms a set of two groups that is what he mentioned that is called Bete's double group theory and this is more or less similar to what Cramer's observed and called it as Cramer's degeneracy rule and that way many physicists contributed significantly for crystal field theory. In fact the physicist who developed this theory which appears almost perfect even today to explain literally everything about transmittal complexes. The first application of new theory was made by Van Bleck in 1932 by realizing that the quenching of the orbital momentum would be a consequence of the crystalline field model. He succeeded in explaining why the paramilitarism of the complexes of the first transmission series corresponds to a spin only value, spin only value is calculated using the equation. Also the crystal field model was able to predict in which cases there would be small deviation from this empirical rule that means crystal field theory explains involving orbital momentum the small variations that observed in the magnetic properties. Here calculations of Scalp and Penney and of Jordan all are physicists showed that both the anisotropy and the variation of the magnetic susceptibility with the temperature could be exactly predicted and calculated. So that means they showed that yes using crystal field theory one can use calculations and explain all these properties related to magnetic properties. They also confirm that basic idea in the Bete Van Bleck approach that the crystal field reduces the degeneracy of the electronic levels of the gaseous metal atom. That means yes they further confirm that crystal field theory is correct and the degeneracy of DR builds are destroyed or removed. Also another Dutch experimental and theoretical physicist Gorter showed in his paper with the crystal field of a regular tetrahedron will produce the same level as those produced by a regular octahedron but with the level order inverted. Now we know that how the splitting is in octahedral field is reversely in case of tetrahedral field. For example in case of octahedral field if you have EG higher energy and T2G lower energy when you go to tetrahedral field opposite is true T2 becomes higher in energy and E becomes lower in energy. So this was predicted through experimental and theoretical work by physicist Gorter. So later attention was given to understanding and calculating the magnetic behavior of the complex ions. Eventually Van Bleck's crystal field theory become a popular and a complete theory to explain almost all aspects of coordination compounds. So later when ligand field theory and molecular orbital theory were developed there is a reason for modifying or refining crystal field theory to turn into ligand field theory and eventually come up with molecular orbital theory there is a reason I shall tell you those things later. Crystal field theory and valence bond theory almost appear to be special cases of molecular orbital theory. So that means it indicates molecular orbital theory has taken the best part of crystal field theory as well as valence bond theory and also one can call this modified molecular orbital theory is more or less same as ligand field theory and these things were shown by Van Bleck and also British physicist Penny and Penny again worked in looking into the magnetic properties of manganese ion and several other metal ions. The concept of strong and weak ligand work on potassium ferricinate manganese 2 ion and also magnetic behavior of vanadium, titanium and chromium proved the efficacy of crystal field theory and unlike the coordination theory too many conflicts came from bloom strand. So here we did not see much of rivalry but people started looking into it and critically evaluating and start appreciating and also they used it in their later work. With the input from crystal field theory John and Teller we call John Teller theorem or John Teller distortion I am talking about the same two gentlemen here with the input from crystal field theory John and Teller had shown in 1937 that no non-linear molecule could be stable in a degenerate state and such a configuration must immediately distort that means when we have this is more or less applicable for dx square by y square and dz square because they are always lying in the direction of approach of the ligands especially in octahedral geometry and also this is more pronounced among octahedral complexes that means when they have uneven filling or uneven or odd number of electrons that is what it is referring so that means no non-linear molecule could be stable in a degenerate state and such a configuration must be immediately distort. So via nuclear displacements in the molecule in such a way that the degeneracy is removed so that means such molecules will try to remove the degeneracy and go to lower symmetry. So when we calculated the John Teller distortions for molecules of the form m l 6 that means octahedral molecules and showed how this configuration of instability affected the magnetic moment of the molecules. Crystal field theory of Bitte and Wamblik does not consider the role played by the ligands other than producing a steady crystalline field that means the role of ligand ends there after generating an electric field to influence the metaraion and its electron. So that is what crystal field theory is all about but ligand field theory indicates a hybridization of the pure crystal field theory with molecular theory of mullicon. So what ligand field theory does is it takes hybridization concept and also it takes pure crystal field theory and also considers molecular theory of mullicon. So that is the reason it is a very perfect and refined theory to explain literally everything related to ligand field theory. There are few things that could not be explained with the crystal field theory that also can be explained without any ambiguity using ligand field theory. So the ligand field theory incorporates the best features of both the pure crystal field theory and the molecular orbital theory and is a superior route for understanding the metal complexes considering all aspects. So nearly all the results of the crystal field theory are also valid in the ligand field theory. And now as precisely these people concluded crystal field theory are looks like a subsidiary branch of ligand field theory although crystal field theory contributed significantly to come up with ligand field theory. So these are the some references that are pertinent to early work on crystal field theory before Bain and Wathbeck proposed their wonderful crystal field theory. If you are interested you can look into these books and also papers. So now we know that crystal field theory is an electrostatic model and uses the ligand electrons to create an electric field around the metallocentrum. So that means the electric field that is generated with the ligands that are approaching the metal they have a greater influence on deciding what kind of geometry a metal should assume. So attraction between the central metal atom and the ligands in a complex is purely electrostatic. That means according to crystal field theory concept the attraction between the central metal atom and the ligand in a complex is purely electrostatic. That means if the metal is a cationic in nature and the ligands are anionic then it is purely the ion ion interaction. On the other hand if the metal is cationic and the ligand is neutral and ligand will generate a dipole so then it is called ion dipolar interaction. How it generate dipole when you have a ligand such as ammonia or water because of the electro negativity difference N or oxygen would carry negative charge and whereas peripheral hydrogen atom carry positive charge now this negative which has the N or O will be directed towards the metal that is the reason we call it as ion dipolar interaction. Metal is a positive ion of charge equal to its oxidation state and is surrounded by negative or neutral ligand such as ammonia or cyanate. The negative end of the dipole in the ligand is directed towards the metal ion. The electrons on the metal center are under repulsive forces from those on the ligands. That means when the ligands are approaching the metal with a pair of electrons and already electrons are present in d orbitals they would experience a repulsive force as a result of this one the electrons already present on the metal would occupy d orbital furthest away from the direction of approach of ligands. That means when the ligands are approaching the metal and the electrons already present in the d orbitals will occupy positions furthest away from the direction of approach of the ligand. And here ligands are just point charges and crystal field theory gives emphases and it states that no metal and ligand orbital interaction that means according to crystal field theory there is no orbital interaction in metal complexes. In the free metal all the d orbitals have the same energy under degenerate. You take a metal ion metal atom you atomize into metal gaseous metal ion till all the d orbitals are degenerate. Once they enter into ligand field the ligand field destroys the degeneracy of those orbitals and they possess different energies depending upon the type of ligand field we have in the vicinity of metal center. So that is depicted in this diagram electrostatic interaction between metal ion and donor atom is what crystal field theory says for example if you just look into it separated metal and ligands have high energy and coordinated metal and ligand stabilize it to here and then destabilization due to ligand d electron repulsion. Whereas when the metal to ligand bonds are established the energy would tend to decrease but on the other hand the electrons that are already present in the metal atom would experience repulsive forces as a result again energy is elevated and further splitting due to octahedral field is shown here. So that means one should be able to write in this order separated metal and ligands and this is electrostatic attraction and metal ion press coordinated ligands will be lower in energy and ligand d electron repulsion would increase it and then depending upon the direction of approach of the ligands and the orbitals in which electrons are there the splitting takes place in this fashion and this is a typical splitting pattern I have shown for an octahedral complex where T2g is triply degenerate and Eg is doubly degenerate Eg is nothing but dz square and dx minus y square and T2g is nothing but dx at dyz and dxy orbitals. To make it clear I have shown here so free metal and plus ligands would be having higher energy and then metal ligand electrostatic interaction establishes metal to ligand bond and as a result energy drops considerably and then the repulsive forces increases and depending upon the type of ligands we have and their relative orientation with respect to the direction of approach of the ligand they split and this splitting with vary with various ligand fields the splitting would be different for different crystal fields for example octahedral square pen or tetrahedral trigonal bipyramidal all those things now one by one we shall start looking into those things. So what is ligand field theory? Ligand field theory is one of the very useful bonding theories to explain the electronic structure of complexes it is originated from the crystal field theory of ionic crystals to metal complex system when this theory was originally developed to understand solid state chemistry. So consider a ligand field generated by 6 ligands coordinating octahedral into a central metal atom of course it is very appropriate to call crystal field theory as ligand field theory because the electric field is greatly influenced by a ligand field. So the ligands that are approaching the metal ion as a result probably it is more appropriate to call this theory as ligand field theory rather than crystal field theory. So consider a ligand field generated by 6 ligands coordinating octahedral into a central metal the electron phase of the ligand is called the ligand field to electrons air pair of electrons negative charge of ionic ligands or negative end of a neutral ligand exert repulsive force on the d orbitals on the metal d orbitals which is anisotropic depending on the direction of the orbitals these are the fundamental aspects one should remember. Now consider the metal cation at the origin from which Cartesian coordinates are considered it is very simple you write Cartesian coordinates x axis y axis and z axis and the extended so that x axis minus x y minus y z minus z is there at the origin place the metal atom and then also at the origin try to keep all 5 d orbitals and you just analyze their relative orientation so your job is done. So now when you look into their relative orientation and the direction of approach of the ligands for example after putting the metal atom at the Cartesian coordinate origin now bring 6 ligands in octahedral fashion that means now if you try to write an octahedral geometry with metal at the origin of Cartesian coordinate you can see the direction of approach of ligands towards the metal coincide with z minus z x minus x y minus y directions. So now if you look into d x square minus y square and d z square are oriented along the direction of the axis that mean d x minus y square is oriented along x and minus x and y and minus y d z square is along z axis so that means whatever the ligands that are approaching along these would experience maximum repulsion as result energy is elevated. On the other hand when the 6 ligands are approaching along the 6 directions and if you look into the orientation of other remaining d orbitals such as d x y d y z and d z x they are between these axis they are between these planes as result what happens they experience less repulsive forces from the electrons coming from the ligands as result what happens their energy is lowered with respect to the zero energy or barycentrum. If ligands are placed on the axis the repulsive interaction is larger for E g orbital that is what I mentioned then for the T 2 g orbitals and the E g orbitals are destabilizer and the T 2 g orbitals are stabilized to an equal extent. The energy difference between the T 2 g and E g orbital is important and the average energy of this orbital is taken as zero energy that is where you put barycentrum. If the energy difference between the 2 E g and the 3 T 2 g orbital is said to delta O this is called crystal filtration energy for octahedral splitting. The energy level of the E g orbitals is plus 3 by 5 delta O and that of the T 2 g orbital is minus 2 by 5 delta O. So if you put here 4 electrons and you put here 6 electrons then you will end up with zero electron at this barycentrum. So delta O may also be expressed as 10 delta Q or 10 d Q in this case the energy level of the E g orbital is plus 6 d Q and that of the T 2 g orbital is minus 4 d Q. So this is how crystal field stabilization energy is defined. I think I will stop here and I will give some time for you to read and understand. In my next lecture I will proceed with explaining more geometries through simple methods so that you should be able to write crystal field splitting diagram literally for any geometry that comes to your mind. With this have an excellent time reading chemistry.