 Hello everyone once again I welcome you all to MSB lecture series on transformative chemistry and let us begin 54th lecture continuing discussion on UV visible spectroscopy from where I had stopped in my previous lecture. So in my previous lecture I was discussing about metal to ligand charge transfer transitions. In order to see metal to ligand charge transfer transition metal should be in lower access state and also it should be electron rich and then the ligand should be having suitable empty orbitals to accommodate electrons that are coming from metal to their through back donation I would say. So wherever the ligands are capable of pi acceptor properties capable of taking electrons to their suitable empty orbitals such as pi star or sigma star in those cases one can anticipate metal to ligand charge transfer transition. Then what is ligand to metal charge transfer transition that means as names says transfer of electrons occurs from ligand to metal this type of transition or transfer is predominant if complexes have ligands with relatively high energy lone pairs. Example sulfur or selenium or if the metals has low laying empty orbitals many such complexes have metals in highest access state you should remember. In case of MLCT metals should be in lower access state so that their electron rich in case of LMCT ligand to metal what happens metal exists in higher access states and also they have less or very fewer electrons in their d orbitals. For example KMNO4 potassium permanganate or potassium dichromate if you see they have 0 electrons in their d orbital and hence you can anticipate ligand to metal charge transfer transition and that is that LMCT is responsible for intense color of potassium permanganate or potassium dichromate in case of ligand to metal one can see in case of KMNO4 and potassium dichromate. If we consider hexabromoiridate 3 minus it has d6 electronic configuration and here it is T2g6 here octahedral complex and intense absorption is observed around 250 nanometer corresponding to a transition from ligand sigma molecular orbital to the MTEG of molecular orbital. However, in case of iridium hexabromide or you can say iridate we should call because you know hexabromoiridate 2 minus this is a d5 complex because iridium is in plus 4 state two absorptions are seen one near 600 nanometer and another near 270 nanometer. This is because two transitions are possible in this case one to T2g that can now accommodate one more electron and another one to EG though so the 600 nanometer band corresponds to transition to T2g molecular orbital and the 270 nanometer band corresponds to the same transition to EG molecular orbital. So that electronic configuration can tell you about possible transitions. Let us try to understand what is microstate. Microstate is very important when we talk about electronic spectroscopy of metal complexes and here we should recall our understanding of ABO principle that would give you information about electronic arrangement in ground state. Of course, when we arrange electrons in ground state we have to follow ABO principle, Hund's rule and all those things but when an electron is excited it need not have to follow these principles so in that case for an excited electron how to describe ground state and the exact state of the autumn so in that case microstates comes very handy. The term used is microstates which indicates the arrangement so that means all possible arrangements when we excite electrons so that means when we write all possible excite states starting from ground state they need not have to follow Hund's rule or ABO principle. So the general formula for finding out microstates is n factorial over r factorial into n minus r factorial so what is n it is the number of orbitals are total electron capacity that means it is a twice the number of orbitals or total electron capacity if we are talking about p orbital so n equals 6 if you talk about f orbital it is 14 electrons if you talk about d orbital it is 10 electrons if you talk about s orbital it is 2 electrons so that is what it refers to the total capacity of a particular orbital okay and then r is number of electrons for example here I have taken d 2 system d 2 system d 2 means it is a d orbital so total capacity of d is 10 it is 10 factorial and now 2 factorial r is the electrons here so 2 factorial and then n minus r is 8 10 minus 2 factorial means 8 factorial so this can be written as so 8 factorial into 9 into 10 we can write and now what happens this is 2 factorial you can write 1 into 2 and then 1 can write directly 8 factorial so this this goes and this so what we have is 45 arrangements so this is microstate that means 2 electrons can be arranged it apart from ground static electronic configuration in another 44 different ways so that is what the microstate gives that means it gives about all possible arrangements of excited states so 1 you leave it for ground state remaining 44 and exact test arrangements it depicts for d 2 electronic configuration so now let us look into p 2 electronic configuration here p 2 here the total capacity is 6 factorial 6 electrons 3 pr which are there and then r factorial is 2 electrons 2 factorial and now it is 6 minus 2 6 minus 2 can be written as 4 factorial and you can write here okay here you can write 4 factorial 5 into 6 and here 6 factorial 1 can write just simply 2 and then this is 4 factorial we can write here it this goes and there is 3 so number is 15 so that means in 15 possible 15 different ways 2 electrons present in 3 pr will itself can be arranged so that is what this microstates says the mean distance between the electrons may vary from one arrangement to the another average inter electron repulsion will also vary hence the 44 arrangements will split into a number of levels of different inter electronic repulsion and therefore of different energies so when we arrange these things we are looking into all possible arrangements as a result what happens there can be variation in inter electron repulsion accordingly the energy of those transitions would also vary in pr shin blue the color is due to the charge transfer between metal between the metals I mentioned you so here you can see instead of pr shin blue where we have iron 2 and iron 3 if we look into this complex here where both the iron atoms are in plus 2 state it is white in color so you can see the difference between these 2 species and how to distinguish LM CT from ML CT for example let us say we have moderate oxygen state of the metal and also ligands are capable of accepting and also donating in those cases if the color is there how to interpret or how to distinguish between metal to ligand charge transfer or ligand to metal charge transfer it is very simple by observing the variations in their energies by altering the metal iron or ligand so what we can do is we can keep the metal iron steady keep on changing the ligands and look into the transitions and same thing we can do now we can keep the ligand intact keep on changing the metal and we can see and for a then this observation should tell you about this one for a metal LM CT energy decreases as the metal becomes more and more oxidizable one should remember this one so this is how you can distinguish between LM CT and ML CT for a ligand to metal charge transfer energy decreases as the metal becomes more and more oxidizable if the more and more oxidizable means it is very rich in electron so that it can readily give electron means probably electron can be excited very easily for a given metal ML CT energy decreases as the ligand becomes more and more reducible so if you understand the nature of the ligand and also the nature of the metal distinguish or understanding or distinguishing between LM CT and ML CT should be a problem so we can distinguish these two very clearly with clarity without any problem for a given metal to ligand charge transfer energy decreases as the ligand becomes more and more reducible I mentioned let us look into that now we have pyridine N oxide is there and for this one we have 25 450 T 2 G 2 Pysart transition and now we have here in this case what we have is energy is increasing whereas here energy is decreasing so that means energy range is this one this is more easily reducible if it is more reducible you can see the impact of ligand structure on ML CT we shall try to make ourselves familiar with atomic term we use term symbols we call it okay and also the number of state we give what atomic term this is about term symbols I am telling you and also mulligan symbols how they are used for different orbits that I have already showed you earlier in the table let us look into some of those things keeping UV with spectroscopy in mind so now for example S number of states 1 A 1 G is the term given no splitting it is spherically symmetrical and then P 3 is there T 1 G no splitting and when D 5 T 2 G and E G 2 splitting fits into triple degenerate and doubly degenerate and F will split into of course 7 states 7 split into 3 triple degenerate and 1 single state and in case of G what would happen is 9 are there as a result 1 single no splitting 1 double degenerate and 1 triple another one triple that means 3 3 2 1 9 here 3 3 1 here 3 2 so like that so this is how the terms in octahedral symmetry can be seen and of course for tetrahedral symmetry remove G because it does not have center of symmetry okay now this shows all possible transitions of course by label is there for each energy level you should be able to guess what transition for example if it is going from here to here you can say ligand to metal and this is also ligand to metal and this is DD transition and then if it is going from ligand to ligand it is there ligand to ligand and then this is metal to ligand and this is metal to ligand. So this picture gives you idea about all transitions metal to ligand ligand to metal and also DD transition and also you should remember relative energies of various orbitals you can see here this is a typical sigma donor and pi donor so there you can anticipate ligand to metal charge transfer transitions and whereas in this case what happens it is metal to ligand back bonding. So now how to examine the arrangement of microstrates okay in case of P2 I wrote 15 microstates in case of D2 I wrote 45 you may be wondering how one can arrange these two electrons in five different D orbitals what are the possible ways let us examine in case of P2 of course we label Px, Py, Pz and also we put minus 1, 0 plus 1 quantum numbers. Now two electrons we put in ground state it is like this and as I said when we write excited states they need not have to follow Pauli's external principle or Auffbo principle or Hund's rule. So now one is like this one is down other one is both of them can be paid and when you both of them are can be paid they can be either in Px, Py or Pz and similarly you can keep on arranging and then one upward spin and one low spin also you can have something like that again these possibilities are there. So totally if you count it will be about 15 different states are there including this ground state that means now your job will be to see whether any other possible arrangement is left out. So then this microstate calculation would go wrong but however you can just see try to write and try to make yourself familiar in writing all possible microstates at least for smaller ones when we get 210 all those things it is very tedious nevertheless one should be able to write and also in case of D2 we have only 45 make an attempt to write all 45 arrangements of microstates. So why these arrangements have different energies that is the question as I mentioned already the mean distance between the electrons may vary from one arrangement to the another as a result average inter electronic repulsion will vary. So as a result these levels will be split into a number of levels of different inter electronic repulsions and therefore of different energy. So this can tell you satisfactory answer why these arrangements have different energies as a result you can see more transitions of course we get lot of transitions but when we apply selection rules most of them will be eliminated and further spectrum will be simplified. So that is really good so that understanding would be less complicated and much more easier. So now although p orbitals degenerate and have the same energy the electrons present in them interact with each other and result in the formation of a ground state and one or more excited states. This is again little bit stressing upon the origin of microstates besides electrostatic repulsion following factors also influence each other. So by interaction or coupling of magnetic field produced by their spins electron when they are spinning with respect to particular axis it is one axis what happens they can also you know produce a magnetic field by coupling of the magnetic fields produced by the orbital motion of the electrons. So since electrons are moving in orbital motion any circulating charge would also produce magnetic field when it is placed in a magnetic field. So that means that is called orbital angular momentum also should be accounted and when several electrons occupy a sub shell the energy states obtained depend on the result of orbital angular quantum number of the electron. So the resultant of all the L values is denoted by a new quantum number called resultant angular quantum number represented by L. L is the term L can take any value like this 0, 1, 2, 3, 4, 5, 6, 7 corresponding to and this term such as S, P, D, F, G, H, I, J, K, L we have given and if the L when L equals 2 we have to go for term D these are the terms and these are the symbols we are using. So for example if we have one electron is there say in P orbital we have one electron is there L equals 1 here and if 3 electrons are there L equals 0 and if 2 electrons are paired here L equals 2 so this is how we can arrive at this resultant angular quantum number. So now once again go back to P2 electronic configuration. So here angular momenta is quantized into packets of magnitude H over 2 pi that you must have studied in your plus 2 for P electron L equals 1 orbital angular moment 1 into H over 2 pi is shown by an arrow of unit length 1 unit length like this. For 2 P electrons the way in which the L values may interact with each other can be shown diagrammetrically in this format. For example if 2 are there so 2 will be having unit length like this and what are the possible ways these interact can be seen here. So for example if both of them are interacting in this direction the net resultant would be 2 okay value is 2 so this is since value equals 2 if you go for S P D 0 1 2 so this is D state we call it as. Here if they interact in an angle such that this is quantized okay this is unit in that case what happens L equals 1. If L equals 1 we can go for P state P state and if they interact in this opposite direction so net resultant would be L equals 0. So then it is yes state here so this is how orbital angular momentum we can see here okay orbital angular moment can be seen here not moment. So one can see this is how you can calculate orbital angular moment for P2 electronic configuration. All these 3 interactions are possible since the angular momentum is quantized. Permissible arrangements are those where the resultant is a whole number that you should remember so we should put in an angle such that you know the resultant will be a fraction 1.5 1.7 that is not allowed one should remember the permissible arrangements are those where the resultant is a whole number it should be 1 2 3 or 0 or even more for P state the vectors L must be at an angle to each other such that the resultant is a whole number. So here resultant is a whole number here whole number it is a whole number 0 1 so this is the criteria for arrangement. Now let us look into spin orbit coupling when several electrons are present in a soft shell the overall effect of the individual orbital angular momentum L is given by the resultant angular quantum number L that I showed you. So similarly the overall effect of the individual spins MS is given by the resultant spin quantum number capital S the smalls represents this one MS whereas the larger one is essentially sigma S or sigma MS I would say in an autumn the magnetic effect of L and S may interact or couple giving a new quantum number called J this is called total angular quantum number this is very important this is essentially vectorial combination of L and S this is also called as resultant coupling or LS coupling or spin orbit coupling in an autumn the magnetic effects of L L is L is sigma L and then S is sigma MS. So this one in an autumn the magnetic effects of L and S may interact or couple giving a new quantum number that is designated as J called total angular quantum number this is also called as resultant or LS coupling. Now P2 we have 2 1 0 or there DPSC is there and S equals 1 not 0 is there and then coupling of spin angular momentum also one can see MS equals 2 electrons can be like this then S equals 1 and 1 they can be paired in that case S equals 0. Now let us try to see spin orbit interactions or LS interaction. Now we have to take this one and start interacting this one should interact with all 3 and this also should interact with all 3 and see totally how many we get. For example here L equals 2 we shall start and S equals 1 they can interact in such a way that the resultant will be some 3 this is J equals 3 and when they interact something like this L equals 2 is interacting with S1 J equals 2 and L equals 2 can interact with S equals 1 in this fashion. So 3 possible ways are there in angle 1 can be net in the same net and then other interaction will be having a whole number 2 other one whole number 1 will be there. So now we have generated 1 2 3 states and now if you take one value now take 1 and then 1 L equals 1 S equals 1 can interact in this way or it can interact J equals 2 and J equals 1 and J equals 0. Similarly L equals 2 can interact with S equals 0 S is not there. So it is J 2 is there and L can L equals 1 can also interact with this one it is not there 1. So like that we have again another 3 states are there. So this is how you can calculate each of these arrangements corresponds to an electronic arrangement spectroscopic state represented by a term symbol. This is how we can give term symbols or this is the origin of term symbol. So now how to find the term symbol for the ground term? Now to begin with let us consider a D6 electronic configuration for this one we have to write the ground term for this one what we have to do is we have to calculate L we have to calculate S we have to calculate J. So once we calculate we can apply for this one here and then that will give you the term symbol for ground term symbol for this D6 electronic configuration. We can place electrons like this and to calculate L equals sigma L we can take 4 plus 5 5 minus 3 5 minus 3 will be equals 2. So this is L equals 2. So we are taking D here and then resultant spin quantum number we have to take we have 1 2 3 4 are there 4 that means 2 when we take 2 S plus 1 2 into 2 plus 1 equals 5 this is 2 S plus 1 at next J. J equals R S or spin orbit coupling so what it says J equals L plus S if the orbital is more than half field or J equals L minus S if the orbital is less than half field that means it can be L plus or minus S. So in this case it is more than half field D6 electronic configuration we should consider L plus S so L plus S means it is 2 plus 2 this is J okay J value. So now you have to write this one is D and then 2 S plus 1 spin multiplicity is 5 and this is this is 4. So this is 4 this is the term symbol for D6 electronic configuration. Let us find out term symbols for a couple of more electronic configuration to make you familiar or now use this formula and try to write ground term symbols for all electronic configuration starting from D0 to D10 and also P1 to P6 to make yourself familiar so that you will not do any mistake. Let me stop here and continue further discussion in my next lecture until then have an excellent time reading inorganic chemistry especially and thank you for your kind attention.