 will go forward to say that we have basis sets with only valence up to valence is not good enough today you cannot publish any paper with this actually alright so it is very important to realize this you must use what are called polarization functions so that is very important polarization function so what is polarization this is adding basis functions first of course to the contracted functions when I say basis functions it means it is slater or cgf please please read slater for cgf because they are identical it is just that we are not actually using slater so I do not want to write slater it is a contracted Gaussian so adding more basis functions beyond the valence angular momentum so that is important so for example for carbon that would mean adding d functions 3d I am calling it 3d but it does not matter 3 is not important d functions so adding 3d functions is important for carbon because the valence angular momentum is p it stops at p you have to add one more at least one more you can even have two more there is no reason to have one more people use one 3d functions typically one 3d function but you can use two 3d functions people are using f for f and so on many many functions today they are using so they become highly highly accurate basis set even though carbon does not have d and f they use basis functions simply because these are functions to expand the molecular orbitals it is nothing to do with actual carbon remember this contracted Gaussian or a mu these are the a mu's okay my basis set was only to expand the molecular orbitals and the philosophy was more the merrier anyway so there is no reason to stop at p okay then each of these are now again going to be expanded in terms of primitive Gaussian so again expand then come so philosophy is same I hope you understand so all again these are going to be d type primitive Gaussian f type primitive Gaussian so exactly the same philosophy and you keep doing the integral calculations and so on so for hydrogen for example I am going to use 2p maybe only one of them or maybe two doesn't matter I can also use d 3d f and so on even for hydrogen note again the total energy is not important I had said this in one day the total energy may change in only 10th digit that's not important is the difference energy what is the difference energy change that is important so that is why this large basis sets are required when you when you do a ground minus excited state let's say I have not told you how to calculate excited state yet but let's say that you know that difference even if the total energy is only in 8 9 digit that difference can be significantly important for a spectroscopic accuracy so if you have if you have missing something in the 6th digit then there can be an error which is of this spectroscopic accuracy so percentage error by itself in total energy is not important so typical example is that if I have one percent error in let's say e excited minus e ground that each of them has only one percent error then you don't know which way the error is the error is not systematic so when I take the difference the error will multiply okay so that is the the real problem and very often it happens let's say I have a thousand kilo joules some number I am subtracting that with a 998 kilo joules and my result is 2 kilo joules and that is what I am saying hydrogen bond interaction right this thousand has a one percent error this is also one percent error so the error is 10 kilo joules right this is 9 or 10 kilo joules how can we explain 2 kilo joules with the error bar of 10 kilo joules right it is ridiculous so that is essentially the problem that people want to reduce that error bar from 1 percent to 0.1 percent and if you want to do that then you need this large number of basis function and actually that will directly take us to the beyond Hartree-Fock this is the particular discussion so I want to tell that the basis set has the same feeling why I want to go beyond Hartree-Fock with Hartree-Fock is good actually otherwise so these basis sets are good but people have to use larger and larger basis sets these are called the polarized basis set for Huzinaga Dunning there is a name for this they would call originally they would call DZVP just P will be used so Huzinaga Dunning this is plus polarization they will say DZV2P 2 polarization 2D functions then you can have D af G and so on they will have different nomenclature I think it is not important in the case of the Popol's basis they call it 631G D, P and D, P is very clear for carbon first atom D for hydrogen P that is what is mean okay so this is very often also called as 631G star star many many different nomenclatures exist if I have a star star it means polarization on carbon polarization on hydrogen both if I only star it means only polarization on carbon or first atom not on hydrogen so hydrogen is includes you might have seen 61G star so this is polarization and usually there only one polarization only on first atom so these are typically a single polarization functions this basis are typically single polarization function but today there are basis which are more polarization function each of them has more D af P D everything has come so you can imagine I mean you can your imagination is your limit okay I mean in this case basis said your imagination is a limit so for everything I cannot give even nomenclature yes yeah higher and more number anyway so your results will be better more s orbital that is also done that is also done more flexibility so the point is point is what he is asking a good question is there at this point I have two choices I can have double zeta valence or triple zeta valence or I can have double zeta valence polarization so let's say you have only two choices I want to make this triple zeta valence of course you understand what is triple zeta valence I have one more s function one more p function or should I add a polarization if you have if you do both that's ideal but if you can't do both then there is a question of balance so many feel that instead of just going on this direction you should first go in this direction then go in this direction so obviously T g v p will be very good again Popol will call it differently but you understand the T g v p will be very good so you go from T g v to T g v p then come to T g v okay and then of course you can have a quadruple zeta valence but if you do quadruple zeta valence you must use true polarization and even more after that you may use f g for carbon slowly so there is a balance and that is why I said basis set is an art than a science because you have to balance what is the minimum number by which you can have a very good very balanced basis set should I only augment the valence should I augment polarization how many polarization functions should I augment only one angular momentum higher when I say beyond or should I go to angular momentum then for each one how many so that's why I said basis set imagination is the limit so you can keep doing whatever playing whatever you want to do but you have to understand at the at the end your computer that is the limit your imagination can have a much higher limit but your computer will limit you much earlier right so so so then what you do scale down your imagination right because imagination there is no upper bound right and you go and go on go on but then computer will give you a physical upper bound so now you scale down within the upper bound now you have lots of options in your imaginations you find out what is the place that is an art so I mean you can just think as big as possible oh I can think of thousand ten thousand so what is art about it the art is to manage this within the computer limit how do I choose a basis set which will fit my computer and yet give a satisfactory that is art that is what I said so people have found that instead of just going double zeta you know quadruple zeta is also possible you also start populating this otherwise you'll get unbalanced basis set and the results will not be good of course this result will be better than this result this result will be better than this result question is comparison between this and this and that is not a apple to apple comparison that's a problem because I'm adding not one function of the same type so that's why I'm saying apple to apple comparison is this to this not this to this this to this is an apple type comparison so obviously this will be higher better result than this so I may ask simple questions two basis said which we will give lower energy better means lower energy remember that you should be able to tell what is an apple to apple comparison you should be able to tell from the basis set this will be an apple to orange comparison so I can't tell orange is better or apple depends on your health depends on what kind of problem you have all right so that's one the second type that is also very important I must tell is yes is apart from polarization yes please tell yeah polarization is essentially because you are you are going beyond one angular momentum so it just polarizes electron density that is how the polarization k the word polarization yes so that's what I said valence well I mean at this point at no no no at this point it doesn't matter whether I call it two s or three s s is s finally so I'm saying number of s type I just said two s two s prime to give you a comfort that it is a valence split when I said triple zeta valence you don't care whether now it has gone to three s or four s but the angular momentum is more important that's why I'm giving a different name when you change your angular momentum yes one zero zero means that means you don't have I think two one will be better difference is that you're adding a more another s function that is always better than just expanding this one s function where more number of primitive that's my gut feeling again it's an apple to orange comparison but that's my gut feeling so essentially you are saying is it double zeta better or single zeta single zeta single zeta with more primitives or double zeta with little less I would say double zeta is better with the same number of total number of primitives yeah I have different double zeta you give more flexibility on the valence that is always better than single zeta in fact you will see that today we never use single zeta basis today we don't use I will tell you one single zeta basis as your pupil had but we don't use it since the discussion has come up let me discuss that that is the simplest basis set that we have STO 3G or STO NG in general this STO is later type orbiter so in STO 3G when I use I actually use single zeta 1s 2s 2p n or carbon hydrogen 1s and each of these each of these are expanded in terms of three primitive so please understand what is STO 3G so if it is STO NG n primitive Gaussian but the number of atomic orbitals use are exactly what you said single zeta so if I do a methane calculation in STO 3G then you have 1 2 actually it's good that you ask this question you have expanded my ability to ask questions in the Midsum exam I am not going to discuss STO so what is your methane number of STO 3G 1 2 5 9 right 4 hydrogen so methane has 9 in STO 3G actually STO NG 3 is immaterial total number of molecular orbital that will be generated and I will I will actually say what is the total number of molecular orbital that will be generated your dimension that is more important because if you get confused with AMU and primitive and contracted Gaussian the total number will depend on number of contracted Gaussian so that means goes into your Fock matrix diamonds right AMU number of AMU which are my so that will be methane so these are single zeta but practically today this is outdated in old days people used to STO 3G STO 2G is also used but 3G is the minimum and pretty bad basis set and nobody will publish any paper with these so minimum is double zeta minimum is double zeta with at least single polarization each of the DP you can have 2D 2P so you can have also a double polarization which will be double polarization which will be 2D 2P you can have polarization beyond DNP FG so those are what are called augmented basis I am not going to go into that there is something called augmented basis correlation consistent basis of C C P V D Z you know there are basis sets which are known as augmented correlation consistent P V D Z very very complicated basis sets which are actually augment which are actually balance double zeta no doubt but correlation consistent and augmented so what they do depending on how they augmented how many P V double zeta triple zeta quadruple zeta they balance the basis set so just as I told you if they are using triple zeta they would probably use minimum polarization one polarization if they use quadruple zeta they will use two polarization and one more of the other higher angular momentum so for example carbon if I am using Q Z V then this is my S and P then I will have 2D functions one F functions so when I say augmented C C Q Z P V Q Z automatically DNF will come that people now know so these are all a part of the part of the nomenclature because people have realized don't only go for valence as soon as you go for valence include one more polarization of D and one more of the higher angular momentum but obviously D number should be always more than F number so if I do carbon with a 1D function and 2F function that is bad because if you have to tell what is contributes to carbon more than D or F then of course answer is D first then F so again that is a balance so never use 1D 2F so I hope you understand so these kind of basis sets are not just the valence double zeta augmented essentially takes care and correlation consistent takes care how the D F G angular momentum will come they keep on coming so I think beyond the point it is not really interesting because you have to just know the nomenclature and you know and people have used standard nomenclature you can't change it now all right you can argue but you can't change it everybody uses that so you just have to know this is really like information more of information as long as you understand the philosophy you should be happy but if but but one more function that I must add before I complete the basis set is what are called the diffuse functions so for many many many problems I need to add apart from all these something called diffuse functions now what is a diffuse function diffuse function is a function which decays very very slowly that means let's say hydrogen I have a diffuse function the function is diffused over a large range so the the function will actually decay if I start from here it will decay very very slowly so at a larger sorry at a larger the density there will be still some density now if you look at slater function or Gaussian function what determines either r minus r a or you know doesn't matter whether one or two what will determine the diffuse nature of the function can you tell me alpha so alpha should be high or low no it should be low to have a good diffuse function alpha should be low right so all you do is to add diffuse functions typically one or two diffuse function and usually we add diffuse function which are valence that is usually good enough don't have to add for carbon you add only s and p that is good enough don't have to add d okay valence diffuse functions may be one may be one in number again they can they would be Gaussian of course with very low exponent may be even one will do but at least it is required for many problem where particularly if you want to calculate electron affinity where the the anion the electron negative the electron has a effect very large distance from the nuclei it is very important many times even excitation energies okay many times even hydrogen bond which are diffused over a long range so that's chemistry if you get a low exponent how low alpha can be typically 0.01 as low as that so let's say I use a primitive Gaussian of this kind so this alpha to be typically 0.01 0 1.0 to that low to have a so it is also important today to add diffuse function and a typical diffuse basis sets is 6 3 1 g plus plus d comma p what does this mean now you have one diffuse function for carbon and hydrogen plus one set of polarization function d comma p many times people use diffuse function only for the heavier atoms so for methane they will use only for carbon not for hydrogen but you can use the actually typically people use for both carbon and hydrogen only valence so you have a one additional s carbon one additional p carbon okay and one additional hydrogen s plus a d function for carbon p function for hydrogen so now if I ask you what is the total number of molecular orbitals for 6 3 1 g plus plus d comma p can you calculate for methane it's just fun repeat the calculation now you understand yes now I am now using in addition diffuse functions so what is the total number one one diffuse function one contracted Gaussian I mean they are actually not even contracted they are actually just primitive so contraction is also one in number but that is not important I am asking you what is the total number of atomic orbitals so add to this add to this 1 d function 1 p function right I mean you call it 3d or whatever you want to call it 2p plus one set of s and p diffuse one set of s function diffuse for hydrogen right so you have 1 2 3 4 right 7 10 13 and then you have a d function let's say typically 5 18 for carbon so I had you remember I had 9 originally I have used 1 4 13 and 1 d function 5 18 and for hydrogen I have 1 2 5 1 6 so 6 into 4 24 plus 18 42 function okay so if you do the same methane calculation you can have 9 functions for STO 3g 2 that's 42 function for 6 3 1 g plus plus d comma p the d comma p is often also called star star you know star plus star star but people had problem you can't use too many too many superscript so that is when people changed that let me write the polarization in bracket originally even diffuse of diffuse is written with plus plus if 1 plus means only carbon if it is plus plus means carbon and hydrogen okay so that's the rule I mean you can extend that ammonia whatever you know so that's a rule and I think this diffuse functions are also very important to add so that you get a chemically accurate results okay because because many of many of the problems electron density stays very very far away from the nuclear Gaussian remembers I told you decays very rapidly so it does not capture the real problem so that is the reason I use a Gaussian with a low diffuse function even even slater with the same diffuse function will go even further but it's square so at least you need in the Gaussian diffuse function so that is the basic philosophy okay yeah I don't want to I think it's I have already overstepped the time limit I don't want to bore you with basic set I mean to a point it is interesting beyond a point it is boring as long as you understood the philosophy rest is boring if I now start to give you di and alpha i numbers it is absolutely boring those who are interested can look up the literature there is a basic set library you just go and Google basic set library you will get that basic set library from various programs and everything every expansion coefficient contraction coefficients are given you just need to know how to read them there is a format so just know how to read them but the but I think I just wanted to tell you the philosophy of the basic set before I close this part and I think now what we will do is to actually go beyond Hartree-Fock but before I do do that we still have to discuss some properties of Hartree-Fock and one of the important properties that I will start after the mid-sem exam is the Brillouin's theorem which is a very important theorem just like Kupman's which comes out of Hartree-Fock and that will simplify the later discussion so but but I think to an extent to a large extent the technical discussion of Hartree-Fock is over there will be some other discussions of Hartree-Fock which will actually highlight the deficiencies of Hartree-Fock okay to show that why should we go beyond Hartree-Fock yeah you have a problem in number count okay yeah maybe maybe I made a mistake that's possible one two three seven one diffuse function five twelve then you have eighteen eighteen for hydrogen I have one two five six so eighteen plus six into four that's 42 I mean I could make a mistake it's not a problem don't worry about it but as I mean again understanding is important number count I can make and I don't have to give exam but in exam you can't make mistake okay we do we do plus plus essentially means yes we do I mean it depends if I if I tell you don't add don't add I mean I will be very very clear in the exam in a paper I will tell you what you have to I just want you to understand capture indeed I mean I'm not I'm not going to test you what is a better basis set okay that I'm not going to test alright so what I will do after the mid-seventh exam to talk about deficiencies of Hartree-Fock and one of the two very important deficiency I'm going to talk about is of course in the calculation of difference energies and yeah and and how the the when you stretch a bond how does the Hartree-Fock behave in fact it does not behave properly even for hydrogen molecule we are talked of H2 molecule so I'm going to give an example and that is where I will start that how you get a wrong potential energy surface even for hydrogen molecule with a Hartree-Fock single close cell Hartree-Fock so that will be my starting point so good I have told good things about Hartree-Fock till now I have to start with some bad things the last good thing that I must tell about Hartree-Fock is that Hartree-Fock recovers 95 to 97 percent of total energy that's that's beautiful but as I told you it's not good enough and we have now discussed Hartree-Fock only at a geometry at a fixed geometry at an equilibrium geometry Hartree-Fock works well if you stress the geometry many times Hartree-Fock does not do well so one of the examples that I will start with is hydrogen H2 molecule how how why it is bad I'll try to explain the physics and of course the two three to five percent error is too much of an error for a difference energy and and then then I will talk of Brillouin's theorem and then eventually how to improve the Hartree-Fock Brillouin's theorem will be a part a technical theorem to improve the Hartree-Fock which will aid in improving the Hartree-Fock and that that will be the rest of the mid-sem exam after the mid-sem exam so first one or two lectures will be still on Hartree-Fock and after that post Hartree-Fock theories so we'll see post Hartree-Fock theory again sky is the limit we'll see as much as we can do all right so suddenly I want to do perturbation theory mp2 etc etc and ci these two things and probably little bit of couple clusters and DFT okay now as you know that there's a little bit of potpourri so after mid-sem you know I have to I have to tell you that I can't go very systematically in depth for each chapters because otherwise you know if I go only perturbation the one possibility I do only perturbation in ci and forget about the rest which I think is not good idea today so so I have to and we have we have another 18 to 20 lectures after mid-sem so total about 40 lectures so I finished 18 lectures but with a little bit of one and a half lectures sometimes is almost like 19 20 so it's okay so we have really reached the halfway mark today okay and and the rest half we will do as good as possible that we can do and many of the time the course actually is to end here I mean but I am pushing the frontiers a little bit more actually want to do a little bit of couple cluster to be honest that is the gold standard of quantum chemistry today okay so we'll see how we can do that I have to also introduce a technique called second quantization which I have not done all right so I will formally introduce anti-computation rules and all that so you can see there is a lot to do and I have to somehow make sure so I will collect my thoughts what are the best things to bring in this one one week break and the exam I suppose is happening on Monday since you didn't come back to me with any alternative date so it stays on Monday first thing I write that in the morning okay and somebody else somebody else will normally I I stay in the end same exam but mid-sem I try to avoid and somebody else will come and supervise of course my TAs will be there I hope I'll be available in telephone if there is any problem just call me all right because I have to go to Chennai on that day but little bit in the afternoon I'm going so morning I'll be available okay and I will tell some some faculty for formally be there so Monday 8 30 in the morning is that right 8 30 to 10 30 is it two hours two hours okay and which room here only that is not told yet you have not seen none of you have seen which room but at least you have to see you take the question papers there and I have to tell the faculty which room it is all right so yeah okay thank