 molecules are dynamic and organometallic compounds are quite dynamic and that is the meaning of the term fluxionality. In fact, there are several instances where the molecules behave almost like gymnast and so today we are going to talk about some molecular gymnastics. We are very often accustomed to looking at static crystal structures, but molecules are not static and they keep walking. They can sometimes talk and many times they are dancing all the time. So, if you want to think of a molecule as a static picture you are missing out on what it can really do and what it is really doing. Let us look at the overall picture of reactivity in organometallic chemistry before we look at fluxionality in particular. The first section that we have in the list of organometallic reactions is rearrangements and isomerizations and fluxionality falls in this particular group of reactions. It is in this group of reactions that we can talk about the fluxional behavior. Both rearrangements and fluxionality come into this group and by rearrangement I wish to talk about systems where there are rearrangements of the size of the ring. For example, here there is a methylene cyclopropane that is rearranged to a butadiene complex or you have a 1-5 cycloctadiene which is rearranged to a 1-3 cycloctadiene. Similarly, a 1-3 cycloctadiene which is rearranged to a 1-5 system. So, these are rearrangements whereas, fluxional behavior is distinguished from rearrangements by the fact that the ring system or the carbon framework that is attached to the metal is not changed. It is only the arrangement of the ring with respect to the metal or with respect to another part of the organometallic molecule which is changing. So, here for example, I have shown for you ferrocene which is eclipsed and one ring is substituted with a methyl group. This position of the methyl group if the ferrocene is in an eclipsed form would be looking like this where the hydrogens of one ring are on top of the other. So, one methyl group will be on top of another hydrogen atom here and this would be a energetically unfavorable situation. It would like to move over to a system where you have the methyl staggered with respect to the other hydrogens. However, the energy difference between these two forms is very small. So, you have rapid exchange between these two structural forms and that is what we are talking about as fluxional behavior. The first example that I want to talk about is an example of molecular breathing. So, here I have shown for you a mononuclear metal carbonyl and pentacarbonyl and you will notice that I have marked one of the carbon monoxide molecules in red color and that is present in the equatorial position of the iron pentacarbonyl and this rapidly exchanges with another form where the carbon monoxide is in an apical position in the same FeCO5 molecule. Now, this type of an isomerization cannot be noticed unless we have let us say 13 C labeled carbon monoxide. In which case the carbon monoxide stretching frequency in the two positions will be different and this interconversion can be measured or quantified or noticed. Unfortunately, in the case of iron pentacarbonyl this rate is extremely fast and it is so fast that it is difficult to observe this type of an interconversion very easily. One often measures these using NMR spectroscopy carbon 13 NMR spectroscopy and it is not possible to arrest the interconversions easily and that is because just like any living system that breathes the breathing is essential for the molecule and it is done at a very fast rate. So, fast that you cannot notice it by normal spectroscopic means. So, how exactly does it do it? In the case you have learnt very pseudo rotation which is quite popular and known in inorganic systems then you already know how this equatorial carbon monoxide can move to the axial position very rapidly. So, here I have pictured for you a trigonal bipyramidal molecule where the five where there are five ligands in the in the molecule in which the center is the metal atom. Now, the groups that are labeled can move in a particular direction. So, if the equatorial ligands which are labeled here can move here as E and one is labeled as a P and that will become obvious why I have done that in a few minutes. If these equatorial ligands are moved in the direction in which it is shown here. So, that the angle between the two increase beyond 120 degrees then you would move over to a system where the angle is widened and at the same time let us move the axial ligands simultaneously in such a fashion that you have this geometry which I have indicated here. So, this geometry is in fact the result of two movements one is a widening of this equatorial metal atom equatorial angle, equatorial ligand metal atom equatorial ligand angle and at the same time decrease of this axial metal axial ligand angle. So, if one is decreased and the other is increased then you end up with a molecule which is distorted and it is almost like a square pyramid in which these four ligands which I am marking here with an arrow form the basal plane. What is marked as P is in fact in the apical position of the square pyramid. Now, let us continue this motion further and then you end up with a molecule in which these two axial ligands have an angle of 120 degrees and the equatorial ligands have an angle of 180 degrees. This brings us to another trigonal bipyramidal geometry and this trigonal bipyramidal geometry can be rotated along along this P and P metal bond in an anti clockwise fashion to achieve this geometry which I have labeled on the right side. Now, let us see what has happened you started with two ligands which are labeled as A because they were in the axial position. But, after this pseudo rotation the A ligands are in the equatorial position. So, this particular motion which is called the very pseudo rotation transforms an axial to an equatorial bond and this rapid inter conversion is at the rate of femtoseconds occurs at very fast rate in terms of femtoseconds and as a result it is possible to have very pseudo rotations in iron pentacarbonyl such that all the carbon monoxides can be interchanged can be moved from the axial to the equatorial and back to the axial positions. Notice that one atom was labeled as P because that was a pivot around which the axial and equatorial ligands interchanged. Now, this apical P could be any one of the equatorial atoms this P could be in any one of the three equatorial positions and so it is possible to interchange all the carbonyls with one another. So, let us label them as 1, 2, 3, 4 and 5 and you will notice that atom carbonyls 3 and 4 were interchanged with carbonyls 1 and 5. So, it is possible as long as you have trigonal bipyramidal geometry to have this very pseudo rotation happening at an extremely fast rate. So, iron pentacarbonyl has got no axial or equatorial carbonyls in a distinct fashion. So, that is the reason why you have been able to interchange these carbon monoxides which were labeled in the first place. This carbonyl hopping becomes even faster and more facile when you move from mono nuclear systems to poly nuclear systems. Here I have shown for you iron pentacarbonyl and in iron pentacarbonyl there are three bridging carbonyls and six terminal carbonyls and these carbonyls keep interchanging at a very fast rate. I have shown again for the sake of convenience one carbon monoxide which is labeled in the red color. You will notice that it first goes on to the bridging position and from the bridging position it moves on to iron atom number 2. If this was the first position where the carbon monoxide was on atom number 1, it moves over to the bridging position between atom numbers 1 and 2 and then finally, it moves over to atom number 2 and again to the terminal position. So, this kind of carbonyl hopping happens because the molecule again has a breathing motion and this breathing motion is involved with opening up of the bridge to form a terminal carbonyl and then again to form a bridging position if it is possible. So, it is easy to move from a terminal to bridging and then again from a bridging to a terminal position and in the case of clusters it happens at a extremely fast rate. In fact, even in the solid state it has been shown that trinuclear carbonyls, metal carbonyls have the capacity to move from one position from one metal atom to the other. This is the reason why people have even supposed that there is in the case of metal clusters with carbonyls on the surface. It has been supposed that there is a sphere on which the carbonyls are moving and the metal cluster is in fact embedded inside the sphere and is able to freely rotate. So, this type of a dynamic behavior is extremely well known in metal clusters especially with carbonyls. So, it is also possible for metal carbonyls to move from one position to the other position in a ligand system where more than the necessary number of pi bonds are available. A typical example is metal hopping which happens in cyclo octatetraene complexes where only 2 pi systems can be coordinated to the metal system. So, here I have an iron tricarbonyl which requires another 4 electrons in order to achieve the 18 electron magic number and you can see that it is moving from position number. If you label this as 1, 2, 3 and 4 if the first pi bond and the second pi bond are interacting with the ion atom. In the second step the second and the third pi bonds are interacting with the metal atom. In another movement you can move the metal from position number 1 to position number 3 so that you have 2 and 3. Now, this could happen by a rotational come sliding movement and this type of interesting fluxional behaviors in the metal carbonyl systems have fascinated organometallic chemists for a long time. So you can move from 1 to 2 to 2 to 3 and 3 to 4 and this can go on endlessly in a very easy fashion and leading to the same type of structures. So, we can distinguish the carbonyl hopping from the metal hopping because here it is very obvious that the ligand system appears to be stationary and the metal is the one which is moving from 1 pi system to the other. In the case of some metal carbonyls like the molecule that shown here it is possible to have cis trans isomerization where the cis and the trans are distinguished by the position of the cyclopentadienyl groups. So, here is an example where a cyclopentadienyl group is trans to the other cyclopentadienyl group and the number of carbonyl molecules one is bridging and the other is terminal in each metal atom and this becomes now a cis molecule because the cyclopentadienyl groups are separated well separated they do not bump into each other and do not cause steric congestion. So, as a result the energy of these two forms are quite close and the energy required for moving from one to the other is also not very high notice that at the same time you can also have carbonyl hopping. So, I have labeled for you the bridging carbonyls in blue and these carbonyls can shift from the bridging position to a bridging and the terminal position. So, here I have blue carbonyls in bridging and terminal positions and here I have blue carbonyls in two terminal positions. So, I can do both carbonyl hopping or carbonyl shifting as well as cis trans isomerization. So, this type of a dynamic behavior can be explained very easily if the ion cyclopentadienyl complex moves in such a way that it generates a single ion-ion bonded system which have pictured for you here without any bridges and rotation around this ion-ion axis can lead to isomerization the cis trans isomerization and it can also equivalence the two carbon monoxides which are attached to the ion. So, the bridging and the terminal carbon monoxides can be interchanged when the molecule is in this transition state which is pictured here. So, this type of cis trans isomerization and co-hopping can lead to a fairly interesting NMR patterns in the proton and the carbon 13 NMR spectroscopy. Now, before after we can have considered the carbonyl isomerizations let us move on to simple double bonded systems and two cyclopentadienyl systems. Simple double bonded systems can undergo a variety of interesting fluxional behavior because you can have rotation of the metal with respect to the olefin and in a square planar system like the Zeiss complex where the olefin is perpendicular to the plane of the metal ligand system you can have isomerization. So, that all atoms come into the same plane. So, you can have that as a high energy intermediate and then it can go back it can go back on to the ground state which is the olefin in the perpendicular direction to the rest of the ligand systems. So, you can have olefin rotation you can also have cyclopentadienyl rotation which I explained to you a while ago and you can have rotation of one ring with respect to the other. Notice that this type of isomerization or fluxional behavior requires very little energy and so there can be slight changes in the size of the metal atom for example, which can favor one form over the other. Typical example is a case of ferrocene and ruthenocene ruthenium prefers the D 5 H structure which means the two cyclopentadienyls are eclipsed. Whereas, ferrocene prefers the D 5 D form D 5 D form and that is the staggered form of the complex and this is explained by the larger size of ruthenium which allows for the complete eclipsing of the two cyclopentadienyl rings. Let us move on a little further and combine cyclopentadienyls and olefins in this slide and here is an example of a rhodium complex rhodium olefin complex where two ethylenes are coordinated to a rhodium cyclopentadienyl unit. This turns out to be an extremely interesting system because the two olefins if they are rigid you would end up with protons which are facing each other and we will call them the inner protons. So, there are four inner protons and there are four outer protons. So, these outer protons are away from each other and they are pointing outside and if the molecule can allow for rotation of the olefin with respect to the rhodium you will notice that this will almost look like a propeller. So, end on view of this molecule would look somewhat like this where I have two propellers going round and round on either side of the rhodium. If these olefins can rotate very fast and indeed they can and this has been observed in proton NMR spectroscopy and this has been studied in detail. In fact, the exchange of the inner and outer protons can take place by an alternate mechanism without rotation and that can happen if the molecule rapidly dissociates an olefin and then the inner and the outer protons do not have any meaning and they can recombine and when they recombine the outer can become the inner and the inner can become the outer. So, a dissociation mechanism has to be distinguished from a simple rotation mechanism and this was done fairly easily because rhodium as an NMR active nucleus rhodium 105 is NMR active and as a result you can observe rhodium hydrogen coupling and this rhodium hydrogen coupling for the inner protons is 1.8 hertz and for the outer protons it is 2.5 hertz and at minus 25 degrees if you cool the reaction or the solution containing this complex and you can do that very easily in C D 2 C L 2 deuterated dichloromethane and then the rotation stops and you can observe these two distinct coupling constants. What is interesting is that at room temperature when you warm the solution you have a system where there is only one coupling constant and that is 2.1 hertz which is the average of the two coupling constants. Now, if the molecule were to dissociate then the connection between the rhodium nucleus and the hydrogen nucleus would be lost and if the mechanism of interchange of the inner protons and the outer protons was happening through a dissociation mechanism that is mechanism B then you would expect loss of the rhodium hydrogen coupling. So, this coupling would be lost if you have dissociation and you would have an average coupling constant if this involved only rotation of the olefin with respect to the metal olefin bond. In fact, you do observe the 2.1 hertz rotational constant coupling constant which suggests that the mechanism of interchange for the inner and outer protons is actually through a simple rotation mechanism. I will briefly discuss for you another interesting system that was discovered by Gladys and this involves a rotation of an olefin in a very strange fashion because the olefin has got a pi system and a nodal plane in the nodal plane which contains the atoms which are attached to the carbons which are bonded in a pi fashion. One normally thinks that the metal cannot move from one side of the olefin to the other. Surprisingly Gladys and coworkers synthesize this molecule which has got 2 different chiral centers. One is a rhenium center which is chiral and the other is a carbon center which is chiral. The rhenium center is marked in green and the carbon center is marked in red. So, you can either take this molecule which is r s r on the rhenium and s on the carbon. The other isomer will be equi-energitic and that will be the s r isomer. But, if you take either one of them and heat them in a chloroform or a dichloromethane solvent in a in a halocarbons solvent usually you would have to take as c d c l 2 c d c l 2 tetrachloroethane solvent. If you want to do the reaction at a high temperature and that is what these researchers did you can isomerize only the carbon the only the carbon center is isomerized. In other words it goes to the mirror image and this is equivalent to saying that the rhenium has moved from one phase of the olefin to the other phase. This is shown here in the Newman projection which is given in the lower half for you. You can see that the olefin has moved as flipped over and formed the r r isomer starting from the r s isomer. If you take the s r isomer that would become the s s isomer. So, this was an extremely interesting discovery that was made by Gladys and he showed by a series of isotopic labeling experiments that in fact it is not possible for the enantiotopic exchange to happen with olefin dissociation. So, one possibility is that the olefin comes out from the metals coordination sphere flips over and bonds to the metal again. So, he did the reaction with a labeled olefin and he also had unlabeled olefin coordinated to the metal center and then after heating it for some time he observed the diastereomerization, but the diastereomerized olefin was not the one which had the labeled olefin. So, in other words the labeled olefin which was available in solution in plenty could not exchange with the coordinated olefin. That clearly tells you that olefin dissociation requires lot more energy than what is required for the simple flipping of the olefin. So, he in fact looked at three different mechanisms and all of them very carefully and the first one involved a slipped carbocation. So, if you want to flip the olefin over you could in fact move the metal to one of the carbon centers and then you will form a carbocation which can lose the chirality at the carbon center. So, he looked at a slipped carbocation and alkylidine intermediate and also because he looked at styrene complex he investigated the possibility of moving over the metal to the aromatic ring and then moving it back again after rotating it about the vinyl aromatic ring bond. So, let me look at the slipped carbocation intermediate. The slipped carbocation intermediate requires that you move over to one of the carbon centers and then rotate the carbon carbon bond in such a way that you obtain the isomer. So, if you want to distinguish these two options the option where the metal flips over to the opposite side and the metal passing through a carbocation intermediate you need to label the two carbons and look at the stereochemistry before and after the flipping. So, if it goes through the carbocation intermediate you would expect this product to be formed where the carbon center would have undergone isomerization and the phenyl would now be cis to the deuterium whereas, in the previous instance it was trans to the deuterium. So, it is this relationship which would get affected if indeed this was an intermediate. So, they ruled out this intermediate by observing the fact by noticing that the phenyl deuterium relationship was maintained this was the only product that was observed and this product was not observed indicating clearly that it was not proceeding through a slipped carbocation intermediate. Another isomerization is the rotation of the CHR terminus and you can do that if you want to turn around only this center. If you want to turn around only this center and keep this center the second carbon intact then also you would have a different mechanism for moving from one phase of the olefin apparently moving from one phase of the olefin to the other whereas, you only flipped the carbon carbon bond. So, Gladys actually synthesized another deuterium labeled compound where the second carbon had a chirality also. So, this time he had R, R and R, R that is green at the rhenium, R red at the carbon and R blue at the second carbon and after the isomerization he found that both centers were flipped. In other words the metal was in fact going from one side to the other completely. So, he ruled out several different mechanisms. So, he actually showed that this product where you this product where you would retain the chirality at this carbon is not observed. So, this is not observed and it is not possible to flip the carbon independent of the other carbon. So, he showed that a complete rotation of the metal from one phase of the olefin to the other was happening. So, he also looked at alkali-dein intermediate to form an alkali-dein you would have to transfer one of the atoms attached to the carbon from one position to the other position. If you did that you would if you had a labeled carbon with labeled carbon you would be able to distinguish these two mechanisms. So, indeed he did the reaction again and he found that the diastereomerization could be carried out exclusively with no deuterium scrambling which suggested that there is no 1, 2 hydrogen shift and alkali-dein was not involved. So, the pi arene intermediate was ruled out in an indirect fashion and he also carried out a labeling study where he labeled the C H of the styrene and looked at the rates at which the isomerization were happening. So, the first result was an indirect result where he looked at benzene complex and showed that the benzene complex was in fact an extremely unstable complex and even at 40 degrees minus 40 degrees it was exchanging with a dichloromethane solvent molecule coordinated to the rhenium. So, he suggested that that would be a highly improbable situation to have the styrene isomerized by moving the rhenium to the benzene ring. So, what he suggest is that the carbon hydrogen sigma bond is in fact interacting with the rhenium center and then the because it is a sigma interaction the agostic interaction is a sigma interaction it is possible to move the rhenium from one phase of the olefin to the other. In this case he observed when you replace any one of these hydrogens with a deuterium you look at the rate at which the diastereomerization takes place the K H by K D turns out to be 1.6 for the hydrogen which is trans which is in the trans position. So, in other words it is a trans C H bond which is interacting with the metal center during the interconversion from one side to the other. Now, if you break a C H bond you would have a kinetic isotopic effect which is indicated here or if you have a weak interaction in the transition state which inter converts the 2 isomers then also you would expect K H by K D which is greater or lesser than 1. So, there are 2 possibilities now it is possible that it is interacting through the C H and moving over to the other phase of the olefin and it is also possible that it is interacting in a bidentate fashion through 2 hydrogens which are attached to the metal which are interacting with the metal. So, at this point I just want you to look at a movie which a short clipping of Jason Gatson who is a gymnast working on the parallel bars. You can see the facility with which he moves from one side of the parallel bar which can be considered as a olefin to the other side. If Jason Gatson is a metal center then you can see the facility with which you can move the metal center from one side of the double bond to the other. Let us now take a brief look at allene fluxionality. Allene fluxionality is another strange phenomenon because you have 2 double bonds and the 2 double bonds are in fact perpendicular to one another because you have a central carbon which is sp hybridized. You will have a double bond on between carbon atoms 1 and 2 perpendicular to the double bond which is between carbon atoms 2 and 3. Allene itself as you might want to recall has got 4 hydrogens but these 4 hydrogens have 2 hydrogens perpendicular to the other 2. So, if I draw the allene metal complex and allene forms interesting metal complexes with FeCO 4 which requires only 2 electrons. This fragment requires 2 electrons to achieve the 18 electron rule. So, FeCO 4 with an M can be considered as the M and the M is coordinated in such a fashion that if the 2 hydrogens HA and HB are in the plane of the allene molecule then the HC and HD are going in and out of the screen or in and out of the plane of the board. So, the metal atom is coordinated such that it is coming towards you away from the towards the viewer away from the screen and it just like this atom HD. So, both HD and M are coming towards the viewer. So, this is the geometry of the allene FeCO 4 molecule. Now, it turns out that this position is not unique and the metal rapidly moves over to the other double bond and since the 2 double bonds are perpendicular to one another it would be difficult to understand it is difficult to understand how the metal moves so easily from one side to the other. Now, when the metal moves from the pi bond between carbon atoms 1 and 2 to the 1 between 2 and 3 you will notice that the metal now moves in a position that is below the plane in which these 4 atoms are present C 2 C 3 HC and HD and the metal now comes down below the allene and it is in the same plane as the metal atom ion is in the same plane as the 3 carbon atoms and H A and H B. So, in other words all these atoms now became now become planar. So, let me draw the plane now. So, all these atoms are in the same plane and earlier earlier these 4 atoms or rather these 6 atoms were in the same plane. So, you can see that the metal has to move from one plane to the other and since the pi bonds are perpendicular to one another it is difficult to understand how this movement is taking place. However, if you do a computational study of the molecular orbitals of allene you notice that the highest occupied molecular orbital of allene is in fact a pi system which has donor which is the donor orbital for the Fe C O 4 which is wrapping around the allene in such a fashion that it moves from one side of the or from one end of the allene to the other end. So, it is very easy to understand now if you look at this molecular orbital how the metal atom is moving from one side to the other side from one side of the allene or one end of the allene to the other end of the allene because there is a smooth pi system along which it can travel. Of course, if you remember any olefin metal bond involves two components the sigma component and the pi component. The sigma component would not be disturbed when the metal moves like this, but the pi component would be disturbed. So, if the sigma component is very strong interaction and if the pi is interaction pi interaction is weak then there is no difficulty in understanding how the metal is able to move from one end of the allene to the other end. So, now let us move on to a system which is called ring whizzing ring whizzing again is very common in the case of cyclopentadienyl complexes. It is required sometimes by the electron count on the metal. So, in the case of titanium where you have titanium 4 where 4 cyclopentadienyl anions are interacting with the titanium you cannot afford to have 20 electrons around the metal. So, the metal compensates or rather corrects for this difficulty by having two cyclopentadienyl atoms as eta 1. So, these are eta 1 atoms and these ligands these are eta 1 ligands and these are eta 5 ligands. So, you can understand or you can envisage a situation where the eta 5 ligands become eta 1 and the eta 1 ligands become eta 5. So, let us mark this in a different color now and so these rings are labeled as A, B, C and D and in this molecule the A, B have interchanged with C, D in terms of hapticity. So, the hapticity of A and B were eta 5 the hapticity of A and B on the molecule on my right is actually eta 1. So, these are eta 1 and these are eta 5 now. Now, we have written it as if both A and B change simultaneously this need not be the case. You can have a flip where C becomes eta 1 also and then there is an interchange of the ring in such a fashion that no at no point in time the electron count around the titanium exceeds 16. So, here is one example where cyclopentadienyl haptotropy leads to very fast ring exchange. This was studied by Cotton and this was this was a very interesting system which was studied using carbon 13 nama spectroscopy and proton nama spectroscopy. Now, this type of a situation is very common in main group chemistry also where both due to the size of the metal atom and due to the electron count which cannot exceed 8 now the valence electrons cannot exceed 8. So, you and you tend to have systems where you have less than 1. So, 5 atoms of the carbon coordinated to the metal atom here we have shown a beryllium which is eta 5 on one end and is eta 1 on the other and because it is B e 2 plus it can support 2 cyclopentadienyls. But at the same time it cannot 2 it cannot support 2 eta 5 cyclopentadienyls and. So, it is it decides to have eta 5 and eta 1 and because it cannot distinguish between the 2 cyclopentadienyls there is a rapid exchange between a structure where the top ring is eta 5 and the bottom ring is eta 1 and on my left side I have eta 5 on the bottom and eta 1 on the top. So, this is called cyclopentadienyl haptotropy and this haptotropy was studied at various levels of theory and experiment. It can be simply understood as elegantly explained by Hoffman by a sliding of the metal along the cyclopentadienyl bisecting plane. So, if you draw a cyclopentadienyl system where the 2 double bonds are fixed then you notice that there is a plane which is dividing the 2 and if the metal moves from one end of this arrow to the other you go all the way from eta 1 to eta 3 to eta 5 and so here I have shown for you a system where the metal is bonded to only carbon atom number 1 and as it moves towards the center along this arrow as it moves along this arrow you have an ally like coordination where 3 carbons will start interacting this will be eta 3 and if it moves further then it moves to the center of the ring and then it is eta 5. It is very rare to have 4 carbon atoms interacting with the metal in an eta 4 fashion and that means the anion has to be supported only by the carbon and that rarely happens. So, ring whizzing was also studied extensively with copper complex where because of electron count you would like to have a system which is less than eta 5. So, in liquid sulphur dioxide at minus 70 degrees one obtains a structure where copper is in fact coordinated only to one carbon atom and this is indicated by the structure which is given here, but in the NMR spectrum even at minus 70 degrees it is obvious that the copper atom is not stationary. It is moving from carbon atom 1 to 2 to 3 to 4 to 5 you will notice that a movement of the copper from 1 to 3 is actually like an allyl group which is shifting. If it shifts from 1 to 2 or 1 to 5 then it can also act as if it is doing a 1, 5. So, because of these shifts which are metallotropic shifts now instead of prototropy which you have observed in organic chemistry you can have very easy shifts which can be studied at low temperature. Now, when you shift from 1 to 2 and this is a result of 1, 2 shift if you have only 1, 2 shifts then you will notice that the carbon atom which if it is initially carbon atom number 1 is labeled as B then it becomes A when the copper moves from atom number 1 to atom number 2 it changes from A to B and if it moves to atom number 5 it changes again to B. Whereas, in a similar fashion when copper is at atom number 1 the B what is labeled as B becomes A and what is labeled as B becomes C when copper moves to atom number 5. Both of these are 1, 2 shifts. So, you cannot distinguish between the left and the right between moving to copper atom 2 or copper moving to atom number 5. So, what you notice is that A changes all these shifts. Over time B also changes B will also change all the time whereas, atom number C moves to atom number C moves to atom type C when you have 1, 2 shifts in this which is labeled as 4. So, what you have is a situation what you have is a situation which can distinguish between 1, 2 shifts and 1, 3 shifts because in 1, 3 shifts you have atom numbers B which is changing only half the time and C and A end up changing all the time. So, this type of a change a shift which is happening either in a 1, 2 fashion or in a 1, 3 fashion ends up changing the type of carbons in an unsymmetrical fashion. Let us take a look at what will happen if it is completely random. If it is completely random and both 1, 2 shifts and 1, 3 shifts can happen and that is pictured here on this slide for you. Then all the carbon atoms will become will the change in the line widths of all the carbon atoms will be the same. It was a simulation study that was done by George White sites and he showed that a 1, 2 shift will have a change in the type that I have shown you here whereas, a pure 1, 3 shift will have a change which is shown here and completely random shift will have a change which is the same for the two resonances which are marked by this blue arrow. So, in these two cases if you have a pure 1, 2 or a pure 1, 3 shift the line shape would be in a skewed fashion. So, you can see on the 1, 3 shift the second resonance is the 1. If this is 1, this is 2 and this is 3, resonance 3, the second resonance is decreasing faster than the first resonance. So, this kind of a skewed change will happen if you have only 1, 2 shift or only 1, 3 shift. A random shift would lead to a uniform change of these two peaks and in fact, in the experiment it was found that it was only a skewed shift that was happening and as a result he concluded that either it has to be a 1, 2 shift or a 1, 3 shift. Now, we have already looked at the fluxional behavior of alleles and here the metal moves from carbon atom 1 to carbon atom 3 if it is eta 1 bound or it can move from one phase to the other phase if it is a metal flip. So, this is something which we have looked at earlier. We can also have changes during a reaction. For example, there is this change that needs to happen when you have a nucleophilic attack on a metal center and let us say a chloride is attacked by a water molecule or rather a chloride is replaced by a water molecule and in the intermediate both chloride and water are bound and the total electron count increases and so the metal instead of increasing the electron count the metal goes from eta 6 to eta 2. So, this type of a movement is also possible in during the course of a reaction and it may not happen in a static molecule. And here I have for you pictured a transition state which has been simulated and you can see that the 6 membered arene drain which is you can see that the 6 membered arene drain which I have here which is shown here the 6 membered arene drain. The 6 membered arene drain keeps changing as the chloride comes in and goes out. So, this type of a dynamic behavior is something which can be noticed only during the course of the reaction. So, to conclude this discussion about fluxional behavior one must note that the fluxional behavior is associated with a fairly flat potential energy surface. When you have a flat potential energy surface and you have several structures having similar energy then you can have very good fluxional behavior. And one also needs to have a small energy gap for moving the metal or the moving the organic fragment from one position to the other. In other words the energy of activation for going from one of these minima to the other minima should also be small. And in general 18 electron count holds the key to fluxional behavior you have several structures which are having a maximum of 18 electrons and preferably 16 and during the movement also the number of electrons maintained at 18 or less.