 I once again welcome you all to MSP lecture series on interpretive spectroscopy. In my last couple of lectures, I started discussion on UV visible spectroscopy and also I started discussion on DD transitions. In case of organic molecules, invariably we come across N to pi star, N to sigma star and pi to pi star transitions and also rarely sigma to sigma star high energy transitions. But along with these transitions, you can see one more transition that is called DD transition because of the arrival of D orbitals in compounds, they are called transition elements 3D, 4D, 5D, where we start with D1, whether it is 3D, 1 4D or 5D, 1 we starts with D1 up to D10. So, this is about 10 different type of electronic configuration we come across among 3D, 4D, 5D up for 30 elements. So, they show this DD transition and mainly the color of these complexes are responsible often due to DD transitions and sometime there may be some other transition. Let us look into all those things in D type. So, now let us look into the DD transition I had mentioned DD transition arises because of filling of electrons to the D orbital and then if you consider octahedral complex in a octahedral complex in a crystal field, the D orbitals remove their degeneracy and split into T2G and EG level, T2G is lower in energy, EG is in higher energy, T2G consists of DXY, DXZ and DYZ whereas, EG consists of DXY square and DZ square is a typical octahedral field. And in case of tetrahedral opposite of that happens, T2 will be higher in energy and E will be lower in energy that enough information is given in my advanced transmittal chemistry for these geometries by considering the orientation of the orbitals and also approach of the ligands towards the metal. So, based on that one crystal field splitting will occur and the energy of degeneracy of DRC is destroyed and then they will be aligned into different energy levels. So, in case of tetrahedral we have DXY square and DZ square will be lower in energy whereas DXZ, YZ and DXZ will be higher in energy that transition takes place between them. A typical example is shown here if you look into hexa aqua titanium 3 plus a D1 system here, initially it is 3D2 4S2, we have removed the 3 electrons because titanium is in 3 plus so it would be 3D1 system. So, in this one one electron is placed in T2G so this electron would be promoted here this we call it as electronic transition and you should remember it is simply it is going like this here and then if you consider tetrachlorocobaltate a 4 coordinated tetrahedral complex high spin complex. So, in high spin complex we have 4 electrons in the ground state and E state and 3 electrons in the T2 state and now either this electron or this electron can be promoted here you can see this electron is sitting here in this fashion. So, these two are typical examples of DD transitions. Now, we come across another interesting transition that is called charge transfer transition. Charge transfer transitions are of two types charge can be transferred from the metal to the ligand or ligand to the metal for example, if you consider potassium permanganate or potassium dichromate they are intensely colored and if you look into the manganese arcane state it is plus 7. So, that means now it has 0 electrons it has no electrons in the valence shell because it has 3D5 4S2 all the 7 electrons have been removed to generate Mn plus 7 so 3D0 and 4 0. So, that means, if this compound potassium permanganate is intensely colored that is you can over rule DD transition because we do not have any electrons in the DD transition that means intense violet color maybe due to something. Some electron transition how electron transition can happen probably oxygen is lone pairs are there. So, it will give electrons to the metal empty orbitals that means you can say here due to the charge transfer and without any hesitation you can tell that this is ligand to metal charge transfer transition for example, if something like this you have oxygen and then on subject UV light or visible light electron is promoted from 2P to 3D. This is the typical ligand to metal charge transfer transition and in cluster compounds they have one or more metal metal bonds color is due to either sigma sigma star pi to pi star or delta to delta star. You recall the bonding concepts I explained for metal metal bonds where we came across one bond two bonds three bonds or four bonds when you have four bonds we call it as delta bond and we can also have five bonds it is called quintuple bond if you just recollect your understanding if dz square for example, we have a situation something like this. So, here dz square dxy dxz and dyz same thing is here dyz dxz dxy and dz square it happens when two square panel complexes are interacting with respect to the principal axis they are aligned in this way in a eclipsed manner. In this case something like this so typically so now this is interaction so now if you consider this the orbits are like this so that means basically head on is there this is a dz square is sigma and then we have dxz and dyz 2 pi and then we have dxy is called delta we call it as and then similarly we have delta star for the same pi pi star and sigma star often we come across in this case sigma sigma star is very high energy and pi pi star is little lower in energy and the least energetic is delta delta star this is the charge transfer between metal to metal all these transitions if you come across they are called metal to metal charge transfer transition. And then in diatomic molecules of non-metal such as F2Cl2Br2 and I2 color is due to pi is to sigma star transition in O2 color is due to pi to pi star transition in ionic crystals if we see color NaCl, LiCl, KCl color is due to F centers solid state defect many times rock salt is slightly pink in color so here what happens it is due to some solid state effects or some voids they are occupied by other different hetero anions or cations mostly it is here cations or it can be anions as well this is called ionic crystals in ionic crystals the color is due to solid defects and of course always the energy difference can be correlated to Hc by lambda or delta is directly proportional to wave number or you can write in this fashion so now it is very easy to understand that what kind of color a substance shows and then that is due to what by just looking into artist's wheel here each color has a complementary color the one opposite to it on the artist's wheel on opposite side the color in object exhibits depends on the wavelength of the light that it absorbs for example if a substance is absorbing red color that means it emits a green color and it appears as green if the substance is absorbing red color it appears as green and if it is appearing as orange means it is absorbing blue color or if it is observing blue color it appears as orange or if it is observing violet color it appears as yellow or if it is observing yellow color it appears as violet this one should remember the complementary color is shown by the substance when it absorbs the other color for electronic transition so now I have given here the wavelength range observed by the substance and also the color and also color seen by us for example if a substance absorbs in the range of 380 to 430 that's violet the color appears is yellow to green on the other hand if the absorbance is in the region of 430 to 480 that means color absorbed is in the blue region and compound or substance appears yellow in color and then again if it is observing between 480 to 490 color absorbed is green to blue and color appears is orange complementary color and if it is observing in the range of 490 to 500 nanometer it is essentially absorbing blue green color and it appears red here and then between 500 to 560 a green is absorbed and it appears purple and then 560 to 580 color absorbed is yellow to green of the light and then we see violet and 580 to 590 yellow color is absorbed and it appears blue and 590 to 610 orange is absorbed we see it as green to blue in color but if it is absorbing between 610 to 750 so red color is absorbed and the substance appears blue to green in color so this gives some idea about the wavelength range absorbed and the color corresponding to that one and as a result the complementary color it displays for us now let's go to some technical things here little bit of theory not worrying too much about complicated theoretical equations or anything we should try to understand this all due to the electrons then how the electrons are there in the orbitals and what they do so little bit of information is needed in that context so this slide is prepared so angular moment of a single electron and atom when we consider we have to consider two things one is orbital motion of the electron and also it's a spin so that means orbital motion is movement of an electron in orbit around the nucleus and then the spin is movement of an electron about its own axis you can simply correlate this one with the sun and the earth moving in the orbit so earth rotating about its own axis and also it is coming around sun so one is orbital motion and the other is spin motion rotating about its own axis taking 24 hours is spin you can consider for a typical electron and orbital motion is surrounding the moving around the sun by earth so it is something like that so that means momentum m into v we know from physics angular momentum is mass into angular velocity and n omega so now orbital angular momentum L is nothing but it arises due to the orbital motion of electron around the nucleus so L equals square root of small L into L plus 1 into h over 2 pi or it can be L equals square root of L into L L into L plus 1 here well we all know that h h equals h over 2 pi where L capital L is total orbital angular momentum it can be 0 or positive and L is small L is orbital angular quantum number or it's also called as azimuthal quantum number so typically you can show like this okay electron revolving around the nucleus now spin angular momentum it arises due to spin motion of electron about its own axis so this is given by term s equals square root of s into s plus 1 into h over 2 pi the way we gave orbital angular momentum so s equals you can also simplify it like this where s equals spin angular momentum that means ms equals plus or minus half and s equals spin angular quantum number that is half so that means s can be plus half or s can be minus half so plus half is shown in a clockwise and this is shown in anti-clockwise so now let's look into the total angular momentum quantum number j j is a combination of both spin and spin motion and orbital motion so the total orbital angular moment of an autumn capital L is sigma L sigma azimuthal quantum number and the total spin angular momentum of an autumn s equals 2s plus 1 combined to form total angular momentum a number that is quantized by the number a term called j L and s do not necessarily have to be pointing in the same direction therefore they can range from L plus s to L minus s values so j can have L plus r minus s values it is interaction between orbital and spin angular momentum quantum numbers how they interact whether they couple L plus s well the interact L minus s this how we termed this so small j equals modulus L plus s or L minus s so that means capital J equals square root of j into j plus 1 into h over 2 pi or it can be simplified as j into j plus 1 h h so where small j is angular momentum quantum number and capital J is total angular momentum so this L and s coupling is represented nicely in this figure here and if you just look into this violet or purple conic that shows total angular momentum j that is purple and orbital is given in blue this orbital one is given in blue here and then spin is given in with respect its own axis is given and with respect to the nucleus is given in blue and together L s coupling is shown in this purple cone so this is how you can represent or illustrate L and s coupling spin orbital coupling or orbit spin coupling now let's look into the angular momentum for multi electron atoms or ions for two electrons atoms and ions we should consider what we should do is total orbital angular momentum is nothing but the orbital angular momentum for two electrons is L 1 and L so let us say L 1 and L 2 and then L equals L 1 plus L 2 L 1 plus L 2 minus 1 and until it goes to L 1 minus L 2 this is called Clebs Gordon series so where L is total orbital angular momentum quantum number it can be again 0 or positive it was defined earlier and then L also we know that square root of L into L plus 1 into H over 2 pi where L is total orbital angular momentum so now for example let's say L 1 equals 1 and L 2 equals 1 and L 1 equals 2 and L 2 equals 2 we can calculate and when you have this one if you start following this rule what we end up is we get 2 and 1 and 0 values are there and then if you go for L 1 equals 2 and L 2 equals 2 we can get values 4 3 2 1 0 like this so now let's look into spin angular momentum in the same way we look into orbital angular momentum so the spin angular momentum quantum number for two electrons say S 1 and S 2 and again we have S 1 plus S 2 and S 1 minus S 2 this is again Clebs Gordon series and where S equals total spin angular momentum quantum number that can have press R minus half and then S is we know that square root of S into S plus 1 into H over 2 pi for example S 1 equals half and S 2 equals half is there what we get is at the end using Clebs series we get 1 and 0 values for L so now let's look into together spin orbit coupling so LS coupling also it's called Russell Sanders coupling and here if you consider orbital angular quantum number for two electrons say L 1 and L 2 from again Clebs Gordon series will be having L 1 plus L 2 L 1 plus L 2 minus 1 continues and L 1 minus L 2 value and same way if you consider spin also S 1 plus S 2 S 1 plus S 2 minus 1 and then eventually we end up with S 1 minus S 2 and for lighter elements what we should do is J equals L plus S to L minus S we have that means here where J equals total angular momentum quantum number J into J plus 1 H over 2 pi this is square of so J is total angular momentum see those how you can use it but when we should use L plus S and when we use L minus S we can see for JJ coupling for heavier elements if you consider we can see L 1 plus R minus S 1 and J 2 is L 2 plus R minus S 2 if you consider J equals sigma J I so then it can go J 1 J 2 J 1 minus J 2 it comes and this is how we also get square root of J into J plus 1 into H over 2 pi and we define J as total angular momentum so now let us come to the term symbols a term symbol or a spectroscopic term represents the energy level of microstates with the same energy of a given electronic configuration so here J is the total angular momentum quantum number and 2 S plus 1 is spin multiplicity so then we have symbol like this 2 S plus 1 L J and J can have L plus R minus S term symbols we can write for either ground state or exeges state for S orbital P orbital D orbital or F orbital all the four orbits we should be able to write for example this L values depending upon L values we have to give these symbols for terms when L equals 0 S when L equals 1 P L equals 2 D L equals 3 F and L equals 4 is G and L equals 5 H L equals 6 it is I so J is excluded in term symbols because we are using J for total angular quantum number and unpaid electrons for example 0 is there 2 S plus 1 will be 1 and if 1 is there half it becomes 2 S plus 1 this becomes 2 okay and then similarly if we have unpaid are 2 are there then 2 S plus 1 value will be 3 and if you have 3 unpaid electrons the 3 spins will be there 3 half spins as a result 2 S plus 1 will be 4 and in the same way if you have 4 unpaid electrons the spin will be 2 this is sigma S and then 2 S plus 1 will be 5 when we have 1 electron 2 S plus 1 is 1 we call it as singlet state when we have 2 S plus 1 value of 2 it is called doublet state when we have 2 S plus 1 value of 3 we call it as a triplet state and when we have 2 S plus 1 equals 4 it is called quadrate and then when we have 5 it is called quintet we should remember these things the 2 S plus 1 value determines the name of the state it's a singlet doublet triplet quadrate are quintet depending upon the 2 S plus 1 value of 1 2 3 4 or 5 then how to find out these term symbols so let us like a simple example of D1 so that it comes later so let me take it later so I can find out term symbols for several electronic configurations before that one let's look into how to determine the ground state term there are certain rules we should follow while determining the ground state term the terms are placed in order depending on their multiplicity values that means 2 S plus 1 value is given at most importance while determining the ground state terms the highest value of 2 S plus 1 will be the least energetic one that means our most stable one the most stable state has highest S value and stability decreases as S value decreases then ground state possesses the most unpaid electrons that gives minimum repulsion that means in order to have a larger 2 S plus 1 value so large number of unpaid electrons should be there and when large number of unpaid electrons are there it has to be essentially ground state means minimum repulsion as a result maximum stability and less energy lowest in energy for a given value of S the state with highest L is the most stable let's say have two systems both have the same multiplicity 2 S plus 1 in that case we have to give priority to highest L value the most stable and then if there's ambiguity for given value of S and L then the J value has to be considered the smallest J value is the most stable if the sub shell is less than half field for example D1 D2 D3 D4 will be L minus S is the most stable ground state or if it is D6 D7 D8 D9 L plus S value of J will be most stable one so that means if there is ambiguity for given value of S and L the smallest J value is the most stable if the sub shell is less than half field that's L minus S value has to be considered for J and if the sub shell is more than half field the largest J value is the most stable one you have to consider L plus L value for example let's consider carbon here we have P2 is there it's the ground state term and then we have 1D 3P and 1S and if you consider 3P has a triplet state maximum S2 S plus 1 value and ground state term among 1D and 1S so then 1D is the most stable because L equals to as a S is same so between them if you consider highest L value I had to consider highest L value is there among this one is for D and now 3 has 3 states 3P has 3 terms 3P0 3P1 and 3P2 and the smallest value of J is the most stable one as P2 is less than half field so 3P0 is less than 3P1 is less than 3P2 in terms of energy so that means 3P0 is the least energetic one and it's a ground term so this is how you can write and how we arrived this one through vectors I will show you in my next lecture so now I have given some ground state terms for different electronic configurations Pn and P6 minus n so that means whether we have P1 or P5 and same thing D1 D9 is something like that they have the similar or identical terms I can calculate those things and show you to make you familiar with identifying ground term or calculating the ground term from electronic configuration that I would do in my next lecture then P1 and P5 have the same ground state term called 2P and P2 and P4 have the same ground term 3P and P3 has unique 4S and P6 has 1S and D1 and D9 have 2D, D2 and D8 have 3F, D3 and D7 have 4F, D4 and D6 have 5D and D5 have 6S, D10 has 1S if some of them have very similar terms you can bring some correlation here for example if you look into D1 and D9 system D1 is one electron is there and D9 is one less than completely filled electronic configuration is there then we have 2D term but if you look into D2 and D8 they have identical ground state term that means two electrons are there in the D orbital and two less than half completely filled electronic configuration is there then they have three that means it's very easy to remember and then there is some correlation is there some logic is there then look into D3 and D7 two electrons less than half filled electronic configuration D5 D3 so two electrons less than half filled electronic configuration and then we have two electrons three electrons more than so completely filled electronic configuration so we have here that means two electrons less than half filled two electrons more than half filled we have 4F here and then if you look into D4 and D6 again one less than half filled one more than half filled we have 5D ground term and then in case of D5 it's unique 6S is there and in case of D10 we have 1S is there how we arrive at these things and I will show you for several electronic configuration how to calculate how to determine the ground term in my next lecture until then have an excellent time reading about uv's bus spectroscopy and enjoy the course thank you.