 Many of the organometallic reactions that we have looked at have some additional ligands that go along with the metal. So, when the reaction is studied, people have also found that the supporting ligand which is present on the metal plays an important role. One can notionally divide the effect a ligand has into a steric effect and an electronic effect. Though as we shall see in later slides that this division is partially artificial. So, let us take a look at what ligands or which ligands would have any significant steric effect. If you recollect some of the initial ligands that we have looked at have got carbon monoxide or a cyanide or a nitric oxide on the metal atom and these exert a very significant electronic effect. They are pi accepting electron withdrawing and deplete the metal of electron density, but on the steric side they do not appear to have any significant influence. So, I would group the ligands into three major categories. One is a group where you have a single atom like an oxo group M double bond O. So, this would also belong to this particular category nitrosyls, cyanides and carbon monoxide. The next group of ligands are those like phosphines, carbines and nitrocyclic carbines which can exert a significant amount of steric influence through the presence of bulky R groups which are located either on the phosphorous as in the case of phosphines or on the nitrogen atom as in the case of N heterocyclic carbines. So, the third group which really is consisting of only one ligand which is the hydride is interesting because it has some unique steric properties which we shall discuss towards the end of this lecture. So, now let us try and see how we can understand or quantify this steric effect. It seems to be fairly easy. In many cases in inorganic chemistry we approximate anion to a sphere and get a radius for that anion and use that as a measure of the steric influence of the anion. So, we might say P f 6 minus is a large anion whereas, chloride C l minus is a small anion and so on. So, can we use a radius for ligands or do we have to take a two dimensional projection like an angle or do we have to use a three dimensional property like a volume. These are as you can see each one of these has got some difficulties and so they are nebulous parameters in chemistry. So, they introduce some amount of difficulty in this whole subject of quantification. But the initial work that was done was done with angle parameter. So, that was developed by Tolman. So, it is called Tolman's cone angle. Popularly it is referred to as Tolman's cone angle and later on a buried volume has been estimated which is basically a three dimensional solid cone that has been used to model the ligand. Now, one should not think that this particular difficulty is unique to organometallic chemistry. In fact, this is a problem in organic chemistry in general. Even if you take the van der Waals radius which apparently is a simple concept or should be easy to obtain for most of the elements it is in fact not available for many elements. The covalent radius and the ionic radius have all got some problems associated with the type of measurements that we do in order to obtain them. Very often there are non spherical distributions of the electron cloud and in the presence of a second anion or a second atom in the presence in the close vicinity. Ion might change its shape and assume a very different distribution of the electron density around it. So, these are problems which are associated in general chemistry which make it both exciting, challenging and also complex. So, let us take a look at Tolman's cone angle and this is primarily developed for phosphines. So, we noted in the initial lectures when we talked about tri-aryl or alkyl phosphines that the steric property of the phosphine and its electronic property can be varied because of the presence of different R groups on the phosphorous. Although it is not as good as carbon monoxide the variability of the steric parameter gives it a significant advantage in chemistry. So, the steric influence is something that we need to quantify if we have to use it with some predictive power. So, Tolman initially approximated it to this two dimensional cone angle and the way he did it was as follows. He projected the ligand on to a flat surface and looked at the angle that would be subtended at the metal atom. So, this angle theta at the metal atom is a measure of the steric influence of the ligand and this is very clear that you can in fact take the outermost points of the ligand and draw a line to the metal and measure this angle using a simple protractor. In fact, he did it in a very simple way. He took he made molecular models and measured it using a protractor. Now, what is the rational behind this type of an approximation? In fact, it is difficult to estimate in a very good fashion the volume that is occupied by the ligand. That is because some of the ligands are flat like a tri arel phosphine has got three phenyl groups or three arean groups which are reasonably flat. So, the way you orient it could mean a big could change the volume that it is occupying. So, an approximation would be to project it on the surface using the best orientation that it would like to have. So, a second difficulty that told me encountered was the following. The angle that is subtended by the ligand at the metal can change and how can it change? Imagine the same ligand approaching the metal to in a closer fashion. If M and M dashed, if there are two different metals and if one metal is a better pi donor, then the phosphine might approach the metal atom to a greater degree. When it comes closer, this distance is shorter and this angle theta 2 becomes greater. So, this variability makes a big difference to the cone angle. Theta, the cone angle is dependent on the metal and that is because it is dependent on the metal ligand distance. So, this geometric dependence is quite obvious and it is easy to see. Tolman decided that the simple solution was to fix the distance for all for measuring the Tolman's cone angle, he would fix the distance at 2.28 angstroms. So, this was a when he made a model, he would keep it at a distance of 2.28 angstroms or the appropriate distance and then he would measure the angle that is subtended at the metal atom. So, using this type of a model, he measured various cone angles and these are listed here for you to see. It is obvious that the hydrogen, if you have p p h p h 3 that is the p h 3, which has 3 hydrogens on the phosphorous will have the least cone, smallest cone angle and that is indeed the least in this list. You can see that as you increase the bulk of the R group, the angle that you subtend at the metal becomes larger and larger. So, the largest in fact is an angle of 182 degrees that is that is a angle Tolman's cone angle measured for tris tertiary butyl phosphene. So, what does that mean 182 degrees? It really means that on one side of the metal, if you have the phosphorous atom, one side of the metal is completely blocked by this large ligand that is present. So, even though the phosphorous is having 3 ligands, which are apparently pointed away from the metal, the area that is occupied by this ligand when it is projected on the on a flat surface would indicate that about 182 degrees would be the cone angle of this particular ligand. So, this is in fact an interesting observation. You can see that many times it would be impossible to put more than 2 ligands around the metal. So, how does it matter? It is exactly the dissociation constants of the metal complexes that one is talking about. Here is a system where you have a series of series of 4 ligands connected to a nickel atom, nickel 0. So, nickel would like to have 4 ligands in order to have an 18 electron configuration but because of the large cone angles that are present at the phosphorous it is not possible to pack 4 of them. So, as you increase the size of the ligand, one tends to dissociate this dissociate one of the ligands easily. So, you end up dissociating 1 L and this is shown here in this slide as a dissociation constant is marked here. So, this increases as you increase the size the dissociation constant keeps increasing in this direction. So, as the bulk increases the dissociation constant also increases. So, let us take a look at a larger metal. Does it make a difference? Surprisingly in the case of nickel we noted that the dissociation constant increases. In the case of palladium where the metal is much larger the effect is still retained. So, in other words as you increase the size of the ligand which is attached to the metal atom you tend to form more and more of the dissociated complexes. In fact, for this ligand the metal complex that is present in solution is a P D L 2 system. So, although they are in equilibrium the amount of the dissociated complex turns out to be more and more as you increase the size of the ligand. So, it makes a difference in chemistry. If you want to do chemistry with the P D L 2 complex then you would like to have more of the large ligands in solution. And this turns out to be very crucial or very critical in the case of this cobalt complex which is an extreme example where you have 4 isopropoxy groups, 4 isopropoxy groups ligands where phosphorus has 3 isopropoxy groups around it. And the bulk of this isopropoxy group is so much that the cobalt would like to have which would like to have a square planar geometry tends to be tetrahedral in this case. So, why is this so? First of all let us take a look at the D 8 complex which is cobalt 1 is a D 8 system. And why does it prefer to have a square planar geometry and not an octahedral complex? And that refers to the difficulty of hybridizing the central metal atom to have D 2 S P 3. If you want to have an octahedral geometry you would have to mix 2 D's and 3 P orbitals and 1 S orbital. And that will give you the octahedral complex. Whereas, if you only want 4 ligands you can manage with D S P 2 that releases 1 of the P orbitals from being involved in bonding. And when you involve a high energy P orbital in these cases it is usually 3 D 4 S and 4 P which we are talking about. So, if you leave out 1 P orbital then you do not have to include the energy that is required for utilizing that high energy orbital in bond formation. So, it is better for the molecule to remain in a square planar geometry rather than assume this octahedral geometry. So, that is the reason why you would like to have many of the D 8 complexes preferring a square planar geometry rather than an octahedral geometry. Now, in this particular case the major difference that we are talking about is really not octahedral versus tetrahedral or square planar, but it is tetrahedral versus square planar. It is this difference that is very striking. We know that the complex would like to have a square planar geometry but in this case it assumes a tetrahedral geometry because the angle between the ligands when you have a tetrahedral geometry is 109 degrees. Whereas, if you have a square planar geometry it would be 90 degrees. So, this difference in the square planar geometry it is the square planar geometry the angle is 90 degrees in the tetrahedral geometry it is 109 degrees and this larger angle is preferred by this cobalt tetrakis phosphine complex. That is because of the large size of the ligand it would rather have a tetrahedral geometry with poor pi bonding rather than a square planar geometry. It is well known that the square planar geometry has got very good pi interactions. Whereas, the tetrahedral geometry has got weaker pi interactions. So, if you have a ligand like cyanide which would not require large area that it needs to occupy then it would rather go for a square planar geometry. In fact, the large size of the ligand is what is forcing the complex to have the tetrahedral geometry in this case. So, tollman's cone angle is something that is very important. But very often it is important for us to realize that it has a stereo electronic influence. There are two ways in which we can call it have something that has a subtle electronic influence. First of all if you have four small ligands around the metal then they can approach the metal much closer. So, the metal ligand bond distance would be much better if you have smaller ligands. So, the cone angle at the same time this also has another effect and that is the fact that the cone angle would automatically increase. So, if you have a small ligand then you can have a larger cone angle surprisingly because the ligand approaches the metal to greater degree. So, this is something which is quite obvious if you know the chemistry behind the ligands you know that there is pi bonding you know that there is going to be a difference. But because of the complexity of the situation one has to approximate to a fixed distance. So, the distance between the metal and ligand is always fixed at 2.28 angstroms and the cone angle is measured using a protractor. So, unfortunately this was done with models to start with, but soon many crystallographic many crystal structures were available. And it was possible to derive the angle from crystallographic data. And a very important and a comprehensive paper mingo showed that the distribution of various phosphorous ligands around the metal atom can be studied using crystallography. You can derive the cone angle using crystallography. And when you plotted the complexes the cone angle of the complexes as a histogram he found that there was a distribution of the cone angles. And the mean was approximately the same place at in this particular instance it is close to 145 degrees which is what is assigned as a cone angle for triphenyl phosphene. So, it is exactly what one would have estimated using a simple protractor as a simple model. And what you get from crystallography is approximately this same. So, this tells you that the methodology used by Tolman was more or less correct. And this gives you a more accurate way of determining the cone angle. But this also brought to light the fact that there can be complications. The complications came when Koval studied the cone angles of tri alkyl phosphides. In this particular instance you have some variability in the R groups in the way in which the R groups are oriented. So, if you have two R groups which are oriented towards the metal ligand axis. If this is the metal ligand axis and this is marked with a different color. So, that is obvious. So, this is the metal ligand axis. And if the R groups are pointed towards the metal ligand axis then the angle would be smaller. If the R groups are pointing away from the metal ligand axis then the angle would be larger. So, what he found was that if you use a ligand like P O M E 3 this is particularly for P O M E 3. So, when you measure it for P O M E 3 you find that there are two distributions which are quite obvious in this particular figure. So, in other words you will end up with two cone angles for these ligands. One which is approximately 116 degrees and other which is approximately 130 degrees. So, this depends on the environment in which the ligand is present. So, it is possible to have two different angles for a single ligand. So, this is not possible when you have a measurement done using models. You would assume the most favorable geometry or the maximum possible angle that the ligand can occupy. Now, I want to move on to another topic and that is the utilization of not cone angles but what was introduced by Nolan as a buried volume concept. And this came about because they were studying n-heterocyclic carbines. And n-heterocyclic carbines have become extremely popular because of the various reactions which they catalyze and the unique electronic properties that they influence that they have. So, the steric properties of n-heterocyclic carbines have also captured the attention of people because the R group on the nitrogen makes a big difference. The R group on the nitrogen makes a big difference on the reaction. So, in one shot n-heterocyclic carbines are having a significant electronic effect and a steric effect. And n-hc are called superheroes in the ligand field. Now, let us take a look at the n-heterocyclic carbines. Most popular n-heterocyclic carbine as pictured here is a imidazole based n-heterocyclic carbine. You can see that much of the ligand is reasonably flat. And if one rotates the ligand around this axis, if one rotates the ligand around this axis, one would end up with a conformation which is indicated on my right side, on the right side of the screen. So, it is obvious that the angle, the Tolman's cone angle that you would obtain for this ligand would depend very much on how you orient the ligand with respect to this axis. So, this does not make a lot of sense. So, Steve Nolan who was working on many n-heterocyclic carbines devised this buried volume concept. What he did was to extend the Tolman's cone angle by assuming that you have a fixed metal carbon bond length and that is about two angstroms. He fixed this bond length as two angstroms and he took a sphere which is 3.5 angstroms. So, here is a sphere, imaginary sphere. This is an imaginary sphere around the metal atom and on this imaginary sphere you position a carbine. And you measure the volume that is occupied by this carbine. So, this is the volume that is occupied by the carbine. And that volume is actually a solid cone. And this volume, you can estimate a percentage of the volume occupied by the ligand vis-a-vis the total volume of this 3.5 angstrom cube sphere that is available around the metal. So, this percentage could be used as a measure of the size of the ligand. So, this buried volume concept was introduced by Steve Nolan is quite interesting in that it now makes the two dimensional cone angle introduced by Tolman into a three dimensional volume. Now, you can do this for phosphines. You can do it for any ligand that you can think of. You just estimate the volume that is occupied by the ligand in an imaginary sphere of 3.5 angstroms. Now, it is obvious that this 3.5 and this two angstroms are used by Nolan are two arbitrary parameters that have been introduced. And this is unavoidable because of the difficulty in quantifying the various metals that are involved and the various carbon metal distances that are present. But nevertheless, it turns out to be a useful feature and you can see you can read this communication in order to get a greater insight into this particular concept. So, let us take a look at a real life molecule. Here is a real life molecule where you have two large arial groups which are attached to the nitrogen. If you look at a two dimensional picture of this molecule, you might think that this is in fact a flat structure. And this is a nickel two complex, nickel two plus complex in which you have two carbines in a square planar geometry. And you notice that this is a system which might have a planar structure. Let us take a look at this molecule in three dimensions. Here is the molecule and you can see the two chlorine atoms are present and the chlorine atoms are green. I have oriented the molecule in such a way that you are looking at the molecule through the nickel chlorine axis. And you will notice that although this molecule is perfectly square planar, the volume that is occupied by the ligand is significantly large. And in fact, in a ball and stick model, you are able to see the nickel and the chlorine atoms very clearly. But if you use a different way of looking at it, here is a space filling model of the same molecule. And you will notice that you can hardly see the nickel atom inside this big blob of a molecule which is mostly showing only the two carbines which are present. And you can see the chlorines at one particular point where you see it through the nickel chlorine bond. Let us go back to the two dimensional representation now. This is the molecule that we have just looked at in 3D a few seconds ago. And this is the picture that we looked at. And you can see that the bulk of the ligand is extremely, the volume that is occupied by the ligand is extremely large. And this is not conveyed by the two dimensional structure. So, it is not possible to use a two dimensional projection as the cone angle to get a proper idea of the volume that is used up by the ligand. So, the solid cone and the volume that is occupied by the ligand is a better representation. And in fact, here we have a few representative examples measured for copper and silver. I have shown you two different metals purely to indicate the fact that once again in the crystal structure, if you measure the actual buried volumes, they do differ from metal to metal. But nevertheless, the accepted buried volume percentage is taken as the one where you have a fixed distance of two angstroms and a fixed imaginary sphere of 3.5 angstroms. So, the percentage buried volume for copper from crystallography here, you have a list that is available for copper and silver. And you can see that there is a slight difference between the two. Now, let us take a look at the influence of this buried volume and the influence it has in chemistry. So, here I have a bond dissociation energy. And you can see that the bond dissociation energy is related to the cone angle. If you have a large buried volume, percentage buried volume, then the dissociation energy is small. When you have tertiary butyl groups on the nitrogen, the buried volume turns out to be significantly smaller. And that is given here. Whereas, if you have a mesotyl group, because the mesotyl group is flat, it occupies less space. You can see that that has got a larger bond dissociation energy indicating a better metal carbon bond strength. So, the percentage buried volume is related to the cone angle and is a good measure of the steric parameter of the ligand. So, at this point, let us just summarize what we have been talking about. Approximations are required in order to quantify the steric effects. We have seen both in the cone angle that we that Tollman measured. And in Nolan's buried volume concept, there was an approximation made. And that approximation was to fix the metal ligand bond distance in order to get some consistency in the buried volumes and the cone angles that you report in the literature. The percentage volume that is occupied by the ligand is a better estimate of the steric influence of the ligand. And in one can in fact use crystallography to if you have a large number of complexes, it would be easy to have a distribution of the cone angles or the buried volumes and make an estimate, a better estimate of the buried volume that you should use in order to calculate any property of the molecule. So, we should also remember that there is a variation in the type of the volume that a ligand occupies. And it really depends on the environment that is available for the ligand. So, in the case of tri tris methoxy phosphine, phosphite, in the case of the tris methoxy phosphite, the crystallographic data clearly showed that there are two cone angles that are possible for this particular ligand. This is very much akin to what we see with the balloon. If you want to measure it at the vernier calipers, then the size of the balloon depends on how much we squeeze the balloon with the calipers. So, one cannot have a unique size for the balloon when you measure it with the calipers. Similarly, the cone angle you can have a similar situation and you can have variations in the cone angle also, in the buried volume also. In recent times, it has been possible to estimate this cone angle or this volume using some computer programs. And these are useful when you do not have a crystal structure and when it is cumbersome to make a molecular model in order to estimate the cone angle. So, here are two references to papers where, in fact, you can use the web in order to estimate the buried volume of a ligand in this particular website. And you can also have cone angles measured automatically. So, let us take a look at the hydride which I mentioned as the other unique situation in chemistry. Hydrogen always poses a problem when you want to generalize some concepts. Hydrogen sticks out as a unique element and in this particular case, it is a unique ligand. And if you ask the question, what is its size? It is difficult to give a proper answer for this question. Here is a molecule which I have shown for you, where a ruthenium atom is, this is a ruthenium atom, which is pictured here. Let me just show you, here is a ruthenium atom, which is complex to an aromatic ring. So, this is an aromatic ring system that is available for this metal to complex. So, this is the complex that we are talking about. You have two nitrogens and that is a biperidic. And this ruthenium is coordinated to hydride. And you can see that this is a typical piano stool geometry that the ruthenium is occupying. You have a situation where you have a flat stool, which is sitting on three legs, two nitrogen and one hydrogen. And this hydrogen is occupying a reasonable amount of space next to the ruthenium. And here is another example. And this example, I am going to choose a rhodium complex. And in the rhodium complex, we have triphenyl phosphines attached to the rhodium. And because it is rhodium one, you have a ligand, which is a hydride. And in the two complexes differ in a very simple fashion. That is in one case, you have four. This is tetra case triphenyl phosphine. And this one has got three triphenyl phosphines. And the fourth ligand is in fact a carbon monoxide. So, let us take a look at the complex in 3D and see how this complex is fair. So, this is a complex, which is the carbon monoxide complex. And you can see that you can see that the complex has got a hydrogen and a carbon monoxide in an axial position in a trigonal bipyramidal geometry. And the three equatorial positions are occupied by the three triphenyl phosphines. So, this complex is in fact having five ligands. And the five ligands occupy the five points of a trigonal bipyramidal around the rhodium. And so, this seems to be a very reasonable complex too, just like the ruthenium complex that I just showed you. Now, if you measure the angles around the rhodium, you can let us just measure this angle. Here I have a phosphorous, a rhodium and a phosphorous. And this angle turns out to be close to 115 degrees or it should have been close to 120 degrees. And here is the second angle and this is 116 degrees. So, you can see that these angles are close to 120 degrees. So, now, let us move on to another complex, which I mentioned. And this complex has got four triphenyl phosphines. And these four triphenyl phosphines are almost occupying the vertices of a tetrahedron. So, where is the hydrogen present? The hydrogen is in fact on one of the phases of this tetrahedron. And you can see it right here. You can see the hydrogen that is sitting on the rhodium. And that is on the phase of a tetrahedral tetrahedron that is formed by the four phosphorous atoms, which are linked to the rhodium atom. So, you can see that the hydrogen is really sterically accommodating. And it is not demanding the fifth position in a five vertex geometry around the rhodium. So, it is almost as if there are only four ligands around the rhodium. And the hydrogen is occupying a small place on the surface or on the sphere of the rhodium atom. So, let us proceed with this. Let us take a look at the angles that I was talking about. Here is the case where the rhodium has got one carbon monoxide and three phosphines. And the hydrogen is occupying a unique position. That is the apical position on the TBP geometry. And in the case of the tetra crystalline phosphine complex, the hydrogen is occupying one of the phases of the tetrahedron. And the four phosphorous ligands seem to be occupying all the space around the rhodium. So, the angle around the rhodium is almost close to phosphorous rhodium. Phosphorous angle is close to 109 degrees. And if you see it closely this is both angles appear to be the two angles that are marked are close to 109 degrees. So, now in the remaining time I would like to discuss some of the electronic effects that the ligands exert. And we have already discussed in the case of both anitrocyclic carbines and in the case of phosphines the type of electronic parameterization that can be done. In fact, Tolman who devised the Tolman's cone angle was the same person who devised Tolman's electronic parameter. And this is a quantification that is based on a simple spectroscopic measurement. If you take nickel tetra carbonyl and substitute one of the carbon monoxide with a ligand the ligand of choice that you want to measure the electronic parameter for. Then the three carbon monoxide that are on the other side of the nickel change this CO stretching frequency depending on how much electron density is available on the nickel. So, if you have a large amount of electron density on the nickel then the carbon monoxide stretching frequency goes down. So, the electron density that is given to the metal is inversely proportional to the stretching frequency. Now, you will have two stretching frequencies of for the three carbon monoxide if you have a C 3 V symmetry around the metal. So, you would have to take the average of the CO stretch and this is what you have as the Tolman's electronic parameter. Now, it is also possible to use carbon 13 NMR spectroscopy and these two parameters what you measure using Tolman's spectroscopic parameter the carbon monoxide stretching frequency and the carbon 13 chemical shift appear to be related. People have correlated the two and have found for the same ligand if you plot the Tolman's electronic parameter and the carbon 13 spectral data they are correlated. Now, this carbon 13 spectral data is very much dependent on the electron density around the carbon and the carbene carbon has got this unique chemical shift around 180 p p m or parts per million and that shifts to an up field region when it is coordinated to the metal. And that the chemical shift that you observe for the carbene carbon when it is attached to palladium a palladium 2 bromide complex is what is used as a standard for this carbon 13 measure of the electronic parameter. So, here I have given for you a couple of different N-heterocyclic carbene and the electronic effect they exert and you can see that depends on the both the angle and the both the angle and the electron density that the carbon exerts. Now, the question comes up can we do a an estimate of any property for the metal complex using only electronic effects because we mention that state parameters are in fact stereo electronic can we just use the electronic parameter to get an estimate of any particular property. Now, these properties could be metal ligand bond distances it could be bond dissociation energy or it could even be a kinetic parameter as the reaction as the rate of a reaction in which these ligands are present. Now, what we what has been shown in the literature is that this property just the electronic property is not sufficient to model any of the ligands influence completely. So, in the case of the E C W model that is used by Drago. Drago model the electronic influence of a ligand using the electrostatic effect and the covalent effect and he described these parameters estimated these parameters for various ligands and this does not quantitatively reproduce the property of a metal complex. Some properties are reproduced, but some are not and this is primarily because there is no parameterization for the steric property. So, in this lecture we have actually dealt with two different parameters steric parameters and electronic parameters and it is quite obvious from this particular data that I have shown you that the electronic parameter alone is not sufficient to model the property of a molecule. Any property and the model that has been successful that has received reasonable amount of acclaim is what is known as a quantitative analysis of ligand effects Q A L E. So, Q A L E is a acronym that is available for this particular method developed by Gehring and Proc. These two people have developed a simple equation which relates a property any property of the molecule to the electronic and the steric parameters chi is a electronic parameter that we need to plug in and theta is a cone angle and it is a steric parameter. You will notice that theta appears twice in this equation one is theta into b and another is the parameter c into theta minus theta s t. Theta s t refers to the limit of the angle which is like the steric limit after which there is some influence from the steric parameter. The E A R is the number of a real groups present on the ligand very often an aromatic parameter is required in order to model the ligand properly. E is of course a simple constant that is added to get a proper fit for the property and these parameters. Now, the last paper that was published in this area is in 1996 by Proc and Gehring and this gives you a good summary of the many different nuances that are involved in utilizing this quantitative analysis of ligand effects model. Now, let me just illustrate how this quail can be used here is a plot of this dissociation energy. The dissociation energy is a simple loss of carbon monoxide in this five coordinated complex and this rate is dependent on the cone angle of the ligand L. Cone angle of the ligand L is plotted in this x axis and the log k is plotted along the y axis. You can see that up to 160 degrees there is no influence of the cone angle on the rate of dissociation. But after 160 degrees the larger the cone angle the faster the dissociation. So, the dissociation becomes more easy as you have a bulkier L and this is quite obvious. But what is interesting is that the quail model incorporates a threshold cone angle. So, that you can in fact model this threshold steric parameter that is available for each reaction. Now, it is obvious that this is reaction dependent and for this particular reaction theta s t would be 160 degrees theta s t will be 160 degrees in the equation that we just showed you earlier. So, here is the equation for displacement reaction where benzene acetone which is shown for you here is replaced by two ligands. The nature of these ligands can affect this dissociation and the del H for this particular reaction has been measured. The heat liberated when you replace the benzene acetone with these two ligands. It has been shown that there is in fact an influence of the steric parameter and there is an influence of the electronic parameter and also the aryl groups. If you have aryl groups on the ligand L then it turns out that that has got a better a better a larger dissociation. If you have an aryl group it has a different heat of reaction for this particular exchange reaction. So, you can see that if you have a chi which is which is indicated here the tolman's electronic parameter then that has a significant influence on the del H and the larger the chi the larger the heat that is generated in this reaction. So, if you can measure various parameters like bond distances, bond energies and you can relate them with a steric parameter and the electronic parameter it becomes a useful exercise when you want to design a new ligand in order to have a better reaction. So, in fact in the literature it has been it has been shown that equilibrium constants p k values or electrode potentials all of them can be related to using this quail equation. In a recent paper it has been shown for the oxo transfer reaction in molybdenum 6 complex that you can quantitate the effect of the ligand using you can quantitate the effect of the ligand using this quail equation. So, let me just conclude by talking about the difficulties that we have in steric quantifying steric and electronic parameters. Steric parameters can be obtained in a reasonably good fashion using crystallographic data. This is in fact a great advantage, but you have to use it with caution. And secondly electronic effects are also measured very accurately using spectroscopic data, but if you want to have predictive value in chemistry it turns out that you have to use both steric and electronic effects.