Merken
Lecture 19. The Hydride Ion (Try #3!)
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well we're back and today we are going to make a 3rd try and calculating the stability of the hydride and iron and will the 3rd time this lucky and we're also going to talk a little bit today about the orbital philosophy and exactly what that means when it comes to atoms and molecules chemists love orbitals much more than they love way functions for the reasons that will see Bob OK we are 1st had the calculation with a perturbation theory we found that the hydride and iron was unstable energy was minus 3 8 and that's not favorable compared a hydrogen atom and an electron infinity and then we said What if we go ahead and optimize the radius by changing the exponent and we could do that we could get a formula for that we didn't unfortunately it's still not state that means that the true way function as has a different form and then that's all that means or it might mean if we didn't have experimented might mean that hydrogen and iron is unstable that could be true some and I was like neon unstable How can we improve our guests that's the thing that so here's the thing we had the same value of the exponent whether we picked the just the border radius or whether we picked up some atomic units is just 1 or whether we picked this data we have the saying value for both electrons and on average that's got to be true because the 2 electrons are indistinguishable but at any instant that might not be true because suppose 1 electron is near To the nucleus than the other ones than this electron is more like a hydrogen atom electron and this electron is this kind of funny 1 because most of the attractive forces temporarily shielded and so it could in principle have a widely different exponent than the first one therefore what we might try to do is we might try instead of having the same exponent needed the say are 1 a R 2 we could have beaten the minus 1 1 even the minor to art and they want to try that but unfortunately we can't do that alone because if we did that then we'll be saying that the electrons are distinguishable because 1 would always be nearer than the other 1 infected with the same and so what we have to do so we have to pick up a now underway function but on slides 470 here is symmetrical I a normalization constant out in front just called and then I have either a 1 year the Minnesota said when I want you to the stated to are 2 plus the other way around you minus stated 2 or 1 you the miner said 1 2 and then divide by 2 just so that Wednesday to 1 is equal to say that to it's equal to the 1 we tried before and that way we can now check our previous answer now then we have to have the normalization right because if we don't if we don't normalize the wave function than the energies come out haywire because we have this factor event square that shouldn't be there there for the 1st thing we have to do it figure out what that value and should be the end girls here becomes epically messy and they take a long time to do and you have to be extremely careful when you do them because if you make any kind of goofy even a minor once everything is ready you have to be very meticulous to keep track of everything and
04:25
I can get to be extremely tedious if you've got a lot of terms but I will have gone through and I think I've been very careful and I've written out in full but the answer should be at each stage and given you the rationale I don't want to go through integrating by parts over and over and over again but you should be able to look up and derivatives for many of these want you see how to do OK here's are a sign that we have to obtain an expectation value expression for the energy of the hydride and it should be an energy functional which depends on said 1 and say that to and that could be a very messy formula we don't know exactly how that's going to come out then what we have to do it is we have to find the optimal energy by choosing the correct value of Zeta 1 and say that too and they should be different and of course because either 1 of them could be the inside 1 but the 2 equal solutions there is 1 where Zeta 1 a small and Tuesday and there's isn't identical solution were stated to a small said 1 as big and that means that the surface twodimensional surface of energy versus said it wanted to has to equal minimum and that can be a little bit tricky sometimes I to find the correct value so you may want to if you're trying to search for example always make 1 of only like to bigger than 1 so that you don't actually fumble around and and fall into more than 1 hour minimum in doing this is what we have is an intuitive physical picture that suggests that this might be the better type of guest than just picking the same value having the same kind of orbital at all times so far Of course this is more flexible than the other 1 because when we fixate 1 equal status to we get the other 1 so we cannot possibly do worse than we got up before and we know what the answer was before crusader so we have a good guess of where to start when we start looking around on the energy landscape but let's go ahead and see if we strike out Earth we can at least get on base 1st let's calculate the normalization constant analyst Stuart in 2 stages when I 1st got here is the integral
07:02
book just over R 1 and then I put in the design data 1 the 5 1 and all that stuff square and then we have to put in and that messy thing times itself which gives 4 terms and then we have to integrate them all up and will we get here is for Bayern squared over 16 and then 3 terms and stated that all have exponential some top and Cuba terms 1 cute stated to Putin's 8 1 plus stated to quantities Q In the bottom and that comes from just doing the integral part parts there's no magic this is pretty messy and that is not too bad but now what we have to do is we have to integrate this thing over are too In order to get the normalization constant and so I've shown that Huron slides for 73 we're integrating I of R 1 which is the integral with respect our won over are too we have to put in the yard square the fate of the fire and so on we end up now is for chisquared and squared times won over 32 it's 801 to and say that take you class 2 Over quantities 81 was stated to the to the 6
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and therefore we can solve that for and we want that integral to be what because that's what normalization means and therefore it has to be won over all that other stuff but check let's put again say 1 equal say that we know from before when we did the integral just with a single value of parameters data that the normalization was a cute over and course Wednesday this 1 the normalization is just 1 over par for a 2 electron wave let's put that in end it we put it in and then we have to do a little bit of math we have won over 4 pi squared off 32 Satan To the 6 plus 2 over Tuesday added to the system that's 1 over 30 to close to over 64 that's 1 over 16 magically the square 16 and 4 that gets rid of the form and a sensors in the denominator and we take the square root of state of the 6th comes up to the top and we get say queue that's a good thing to be able to do when you're trying to generalize something he previously done in fact that's what scientists always do when they're proposing something new some extension of a theory some extension to an experiment or whatever it might be they always want to have 1 foot on land and you don't want to just jump into some kind of unknown sea of knowledge where you don't have any kind of compass for where you're going you won't always be able to check that what you've done this is wrong and that makes sense and it reduces to the previous cases whenever you can and we're going to do that throughout this calculation because although these intervals to calculate on a little bit too but tedious and and maybe seem extremely hard if you are used to doing that type of thing they're nothing compared to what's coming up 1st simplicity and so I consider the .period formulas on the slides under lead out until the very end when I actually needed to calculate the energy I'm just gonna leave it out and calculate things without the 2 0 1 electron so that the electron 1 an electron to kinetic and potential energy terms are just as they were before and we're going to calculate them just like we did before we're going to have to take the derivative ends and so forth and so on and we can take the derivative and exponentially the deal and the factor of 1 4 in this integral that I've written here on slides 475 the factor 1 4 comes from the fact that we defined the way function to be the combination divided by 2 and then the factor of 4 4 Part comes from doing the angular parts of world the integral which just is to pi times too for the fire for the faint of heart and then the rest of it is what we have to do which is the integral now over are 1 1 squared so I without the too because we took that out H 1 side and we're just going to do the 1st the electron because the 2nd electron has exactly the same kinetic and potential energy and therefore has exactly the same total energy it would just be switching the indices and does so we don't do it over why bother with now we integrate by parts and we debate by part's over and over because we've got these 4 terms and then we've got 1 squared and when we integrate by parts and we have to do it a couple of times to get rid of the R 1 square and boy do we end up with this mess here on Inside 476 the integral With respect to are 1 of this sandwich with the Hambletonian is this very messy thing with 8 8 0 1 8 State 1 squared Zeta 2 squared times State A 1 +plus say that to quality to it and then a bunch of other terms with polynomials and Zeta 1 and say that too and so great it is this big stack of things and you have to keep track of the minus signs and so forth and be quite careful here I'm in a very quiet rooms With a piece of butcher paper you now take this formula and you have to integrate it carefully over are 2 without making any mistakes and the most important thing to do when you're doing this type of work is done right out the whole thing just saying Let Y equals this whole thing and then carried along don't keep rewriting out the whole formula you go crazy always use shorthand but then when you have to put everything back in the end you have to be extremely careful when you substitute things back in but you don't make it good let's integrated over are 2 and then we end up with us for pie for the Yankees part because there's no angular dependence to this function that we had after integrating over R 1 we just said the variable are to the parts for power and we end up with pi squared over 8 and then dysfunctional In Zadar 1 stated 2 in course there's no are left no R 1 0 are too because we integrated them out Gray finally we have to them now but in our normalization constant and we end up with is very messy things at the bottom of slight 477 so messy it'll it'll barely fit on the slide and it may actually be hard but to read for all I know you may have to stare at a quite a while even if you have a big monitor but we have this formula but that now tells us what the energy of electron 1 separately with this particular form of the wave function interacting with the nuclear years at 1 12 times 3 minus than this huge polynomial in Zadar and then there some rational functions and a rational function is use data provided by queue of Zadar and
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you can see the last 2 terms that form so if some regular polynomials some rational functions here instead 1 and 2 electrons to then has the same formula as electron 1 woods just what all the indices where we see to but what wherever you see what put to me and you get you better get the same answer if you don't get the same answer when you did that that means you made a mistake in the interim and if we put in Sayda 1 equals 8 2 equals 1 I was the very 1st thing we did then would we should have a hydrogen atom orbital and we should have the energy is minus onehalf oratory and in fact you can check them if
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you take this very messy formula and he put in 1 great because 1 of the 6 there's still 1 so it's pretty easy to do and you can watch everything come out of the water and you get minus onehalf good as a very good check because that me that doesn't mean that were correct it just means that we are wrong but we haven't made a mistake for sure but it doesn't mean that we're fresher correctly there we might still be wrong have wrong formula that reduces to the right case but usually not usually reduces to the right case you're on the right track now to complete the energy function all we have to take the to elect to 1 electron terms good we commandos and then we need the repulsion turn we need the Annagrove 1 over are 1 2 With this they expanded wave function and remember the 1 over are 1 2 in order to do that at all he knew law of cosigns as have that again In recalled what happened there we had the integral separated into 2 cases depending whether are 1 was bigger than are too or are 1 was less than are to again to over 1 or 2 over our 2 and then we had to separate the final integral into the separate cases I'm so sorry have to do that again here and everything's gonna follow through exactly as it did before the only difference is it's going to take a lot more effort because just having these 2 terms and we get all these cross terms and then we have to deal with each 1 of them separately if for clever Though we can save some work because we didn't do this before with our 1 to wear the same things on either side so that part's not too bad we could cut copy created are work we have Cliffs Notes for that and then we've got these asymmetrical ones that we haven't done before
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and might be come out to be a different thing here's the repulsion integral written out Over are too fated to and fighting here and I recall that the they apart is the only part that has dependence but that's different from before and that came from the loft cosigned says just figuring out the distance between the 2 electrons as we integrate data and I'm not going to go through changing variables for equals acts here but that's exactly what we do you want you can go back in and review that we get exactly the same thing and then we end up with these 2 terms to do to 5 times to over are 1 the 1st in a goalless Dr twohour Square site squared plus 2 and the 2nd in a row it is I D R 2 just far too because we had 1 overarching for that 1 and that 2nd goal has limits from 1 to insanity the 1st integral as the limits from 0 are white and we get 2 different cases because we had the absolute value of R 2 minus are 1 when we got the antenna derivatives it makes perfect sense that we have the the absolute value in there 4 the entire derivative because it's the absolute value of R 2 miners are 1 it's telling us how far into the Don electrons are part of course we expect that to come out when we do the calculations I'm going to have to seperate now the 2 integral and separate calculations because it's just too huge here on slides for 80 it is the 1st of the the 1st integral to over are 1 of the integral from 0 are 1 of this thing we have to expand it all out and we end up with a frightening mascot then we don't put Indiana 3 In square over aid are 1 even the minus to our 1 and say 1 policy times this huge thing rational functions instead
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once they attitude that takes up the rest of the slide here and there you can see it so much the same form as the other ones we have said want you stated to hear and then we have to say 1 was to quality Q and that again comes from integrating body parts that's what we do OK now I've
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got do the 2nd girl which is the integral from are 1 to infinity and we end up with a similar thing the infinity of course the function badges and we end up with and if we add the 2 together we get the total for the energy of repulsion of the 2 electrons with this funny symmetrical way functions and luckily for us we take to together a lot of stuff disappears cancels out and we get something a little bit more tractable we have 2 terms minus squared plus minus 1 overstated to squares and then cross terms it was closer to 2 square and then a term with 1 over 1 and some rational functions and then 1 of the 16 over are 1 and more complicated then met again as the sum of State A 1 and 6 to kill now we have we've got this done then that's the integral over are too we've now that integrate this thing over 1 just like we did before with the single electron terms and that's good because at least it doesn't get any more complicated putting this and during that time putting in the end and everything we can show that we get this formula here that is not at all obvious and that has been factorize using Mathematica to make it much easier because if we don't factorize we end up with a mile long terms that stretch across a piece of paper and it's very easy to get lost and lose terms and this very funny formula here was a 1 said it to you and then a very big polynomial and say once it too you can verify that if you put on sale 1 equals stated to equals 1 then there is the top part AD and the bottom part is 16 times a day which is 128 and 80 over 128 just happens to be 5 eights and that's what we got for the repulsion integral when we 1st did our very 1st calculations and put had just used that we didn't even have was just once so that means that again we probably are on the right track here we've probably got everything working in our favor now you gotta take this and 2 of the other ones and got out of all of us together and that turns out to be a separate things which I had to put in very very tiny print here for which I apologize and you can verify again but luckily substituting Sarah equals 1 for both of them it's not too hard to do that if you go ahead and substituted for the total energy input 1 equal status to a equals 1 you get minus3 Yates perfect just exactly what we got the 1st time so now we've got this magic formula but it seems to be right boy doesn't look complicated now what we're supposed to do is we are supposed to find the minimal Of this horrific things and the and the minimum values of Zeta 1 82 not equal that minimize this thing and then that will be our final result that is not at all easy today because what we would have to do it's we'd have to take the derivative and this thing has lots and lots and lots of terms so you can practice the chain rule here till you're blue in the face plus the quotient so if the old Cody highminded over and it's going to be a giant Mets I really matzo and therefore we are going to try to even attempt to do this analytically and you can imagine that when this kind of thing was being done back in the 19 thirties I they didn't have computers and so if you wanted to calculate things out you had to use a mechanical calculator of some type or calculate things out of hand so even as get done and you you've got this thing here but still may be extremely difficult to actually evaluated may take a long time indeed to figure out how to how to get a decent result what we're going to do that instead of differentiating this function it is we're going to plot the functions were going to apply be of Zeta onceaday too versus all possible reasonable values of say ones too we know that is a 1 and say that you can't be too small because of the 2 small than the things too big and we know that they can too big because if the 2 big than the orbitals her 2 small and we certainly don't want wooden 0 because then we may have 0 in the denominator and what we end up with something the blows up forestry for the computer to deal with so what we're going to do that is to pick some reasonable values and all the contour plot of this and just look at it where the contours are low that's where there's probably a minimum and energy and because although it's not obvious from the form of this thing just by staring at it it is in fact symmetrical ones ones it too and so we should see a symmetrical Contra apply it should have symmetry about the 45 degree axis and if it doesn't again that's a
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clue that we have about in the formula even when we typed in to do the contour plot we might in this type of 15 for a 16 or something or on some deeper result may be in fact there's something else wrong and we have to go back and make sure it's correct here in fact is the symmetrical contour plots here slide for 85 the red hearts are the parts where the energy is lower than going out to purple and blue and then going through green and yellow but gray and white where the energy is high and I think you can see that the energy is high when on the 45 degree angle the energy is high Wednesday that's too small that's because Wednesday is too small and you're on a 45 degree angle both electrons away out there and they don't have a favorable interaction with the nucleus if you're too big then both the electron answer to close and they have I a lot of electron electron repulsion and so you get this kind of saddle shape function here and what we got before is right on that purple the middle purple part that's the part we got when we only had 1 possible value of Zadar and we took the derivative we had that that simple functions and we got that values now however what you can see is that if you're willing to go off axis neither emaciated 1 very small and say too big or the other way round which is exactly the same thing when you can get a much better result because now you can see that the drop down quite a bit looks like 1 of them most about point to something and the other is about 1 something and that kind of makes sense because that 1 of them is sorta like hydrogen atoms that would be 1 and then the other 1 is really floppies way out there because quite well the 1 that's inside is pretty much shielding the nucleus charge so the other 1 is very weakly back let's go ahead and sue and I've zoomed in on the upper left here and by picking values From . 2 To About . 6 on the xaxis and from . 5 to 1 . 2 on the Y axis now we can see that the center area that red almost elliptical shape it is a little bit bigger than 1 4 1 1 and a little bit smaller probably than . 3 for the other and that we see this what we can do is we can put and values near there and with the digital computer we can do a search we can just take all possible values of Zeta wants it to on some bread and evaluate this function after all that's what the computer did "quotation mark anyway and so we can ask it to get returned the lowest value in just a double loop and that's very very quick that's like a blink of an eye to do that and if we do that we find that we have some success we find that the minimum value Of the energy functional the sale wanted to is with values of State A 1 arbitrary .period I had to wait 3 2 to 1 and for say that to 1 . 0 3 9 2 3 and while we put that into that very very messy formula these numerical values which I tried to get out quite a few digits because I'm raising them to the 6 power and doing things and adding and subtracting them and I don't want to round off to kill me and this is a pretty good thing that we kept all these digits because the energy evaluates to minors . 5 1 1 3 3 all 3 arteries this is a great success because it's finally less than an and so that means that we have a wave function perfectly good way functions and we've shown that and we know it's not the best 1 I mean that would be a miracle if it were some of the best way function we could ever find Williams to parameters and we didn't really truck go crazy or anything but at least bye supposing that 1 electron is inside the other 1 and viceversa and taking massive magical combination of the words so there was some physical insight we went from a hydrogen atom to a bigger hydrogen atoms to something more realistic and we finally got the a defendant to work so that means hydride and slightly stable but it's confined not that stable but it's slightly stable and if we compare b ionization energy of the hydride and iron which is known quite accurately sadly we find that the true hydride and iron is about twice as stable and in the sense that it has about twice the ionization energy is what we calculated the rather than minus . 5 1 it's like minus . 5 2 or something like that that's what the experiments isn't so we would have to think a long time about how to modify or wave functions In order to figure out a better value we have to introduce something else In
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well what could we do we could have blindly I would say we could take 3 exponential that gives us more flexibility but there is no physical motivation to do that the 2 the 2 exponential were chosen because we thought 1 electron was inside the other 1 now we put in 3 but it doesn't change the energy much if at all but I didn't want to do the calculations and that could be extra credit if you wanna get into that because those 9 roster are gonna be mighty mighty tedious to deal with and then who knows if we can even optimized because we can't necessarily do a Contra apply when we've got 3 variables it's very hard for us to visualize so we get after you basically ask the computer to go ahead and put in all possible
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values of State A 1 0 203 within reason and then see if we got anything and my feeling is we won't get so I don't want to do that we could instead of using the orbitals that we used we use 1 s orbitals and then we made 1 stretched out and the other 1 not so stretched what if we instead we took a linear combination of 1 s and 2 we can do that but that could have some advantages when it comes to doing a single electron terms because both the Eigen functions Of the single electron characters so we can just write down the energy there we don't actually have to do but unfortunately the repulsion terms gets pretty messy because we have for the 2 of us we have to minus are in the integral and so we we can end up with integration by parts 3 times more than twice and so that might not be so easy that's plenty of work as well but that could improve things and I have a very good way here I've given you the reference here on the bottom slots for 48 believe it or not Belarus in 1930 With a mechanical calculator went through this exact thing we've been doing with a much more involved wave function but I would choose a much more involved but with a different kind of wave functions he said sigh of R 1 hour to some normalization constant many good even minus Z R 1 even minor said are too OK that part that was the 1st when we did we know that this war but then what he did as he included determined the wave function that has ah 1 so we took 1 plus some constant see times are 1 2 what is that do while Ireland too members the distance between the 2 electrons that's just the scalar distance between them what this does stand is 1 are 1 2 this small it depends what CDs but when I run into a small the wave function Shrek but this is kind of an automatic if you include terms in the actual difference distance between the electrons in the wave function so it's no longer a function of just R 1 are 2 separate separate things but as R 1 hour to just a complicated formula then you can control the wave function then so that when R 1 and R 2 a year to each other that term gets small and 1 hour 1 hour to hour far away from each other that term gets bigger and then effective July the flexibility To do that and I think if you do that on at least for helium which is what the paper was about not hide right you can get within half a per cent Of the correct ionization energy so you can do extremely well by doing and and that's the basis for that argument is that you want and you know the electrons don't like to have the same coordinate where are 1 minus are too small and so putting that in there you can control and you could argue well put an R 1 2 square and so forth and so you can get into a polynomial another 1 2 if you want to this gives the energy for helium to have a percentage that Bob there is a hidden cost here which is almost unbelievable when you think that he did this with a mechanical calculator and very sharp pencil and the hidden costs of doing this is that now all of our integral but before so clean with just exponential some stuff out there now clouded with our 1 2 in their and won over our 1 to wasn't so easy and I 1 2 isn't so easy so we end up with all this complication and so as usual if you want to adjust the wave function to make a more realistic in need of multi electron systems unfortunately it gets much much much harder the other thing that can stop life by putting an arm 2 is that now they don't know what's going on so now I have this thing the way functions but I can't think of it in terms of an orbital for the 1st electron and orbital for the 2nd time in fact even in the function that I did that was the symmetric combinations that can't be written as a product of 1 electron wave functions even if if it could weaken divide through by 1 moment we get the other but we've got to different exponential so that doesn't that that's already a more complicated way function that the chemists would like to do To look at cavernous really like the idea of orbitals work each electron has its own 1 electron wave functions and then the total functions is the problem and they like that even if it's not the most accurate because it allows them to think and predict what's going to happen and think of which electron which orbital has a higher energy than another 1 or something like that and have some intuition about what's going on and it doesn't help to calculate and a very accurate energy if you then are completely lost when you look at the way function you can actually figure out what it means United that the answer you look at the way function that tells you everything that you want to know but it's not telling you what you want to know because you want handsome intuition about each electron where it is and not just the total aggregate then therefore what we are going to do now is go back to the orbital approximation and we're going to take a closer look at it and how we can systematically do things would be more than 2 electrons if we have to do with the orbital approximation because if if we have 3 electrons liberty and good luck in including are 1 2 and R 2 3 and are 1 3 and so on into the functional and then trying to figure out what's going on that's going to be a very long road to the hole instead then let's try that so I R 1 and R 2 is equal to some function of our 1 and some function of 2 and the functions themselves can be anything that could be hydrogen like raw but also they could be anything we dream up are there can be no more battles with different values of that the key is that you have 1 and you have the other 1 and you have to multiply them together to to get the told you can't just have something else if you are 1 2 and there then but it won't separating and basically why the whole problem was mess in the 1st place is because I want to win wouldn't separately the question is what what what sort of orbital should we use an American physicist by the name of John Slater suggested that what you want to use should be more battles that are easy to integrate this is like looking around a lamp post to find your keys it's the only place there's any light and you look for things that are easy to integrate because you're going to be doing a lot of minerals and so if you have something
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that you can just go like that and get the answer by looking in a table that's going to be extremely quick to do if you are proposing functions that are very messy to integrate or take a long time but then going to be spending forever and he proposed these functions are written on the bottom tier slide for 90 there often called Slater orbitals but they're there's sort of like hydrogen like orbitals with an angular part but rather than having a polynomial arm where we had the radial knows recall for the hydrogen atom these functions don't have any radial notes like that they're just various powers and are and then even miners say they are and then some angular part if we are dealing with an Zeta here is just a parameter that we optimize isn't equal to the nuclear charge like like it should be if if we would just dealing with 1 electron systems they're convenient to integrate they don't have any radial knows we can use them they're really commonly used handcuffs Kwan chemistry and the helium I've written out here while the single electrons orbital the single electron wave function on the 1 hand orbital for helium it's pretty well approximated by a Slater the term with 2 terms so the 1st term is about 84 per cent Slater 1 orbital was said at 1 . 4 5 3 and then another 20 per cent or so where Slater orbital wizard equals 2 . 9 1 the other an electron orbital after the other particle has exactly the same form of the and the total for the 2 of them is the product of the things and that gives you the best value because the 2 different values of Zadar then in the jargon this is called a double zeta Oracle and then there are all kinds of jargon terms in quantum chemistry depending on a lot of things what kind of potential terms you included how many interacting particles you are allowed in Europe equations how basis said you chosen what kinds of functions you allowed to be admitted this candidates to get the energy and so forth and there are very important to know if you're in the business because they're going to tell you how much computational work you're going to have to do I think you can see that even by what we did by hand if we take something with more terms and that the amount of work expands very rapidly and sometimes it just gets completely unmanageable even for a 1st supercomputer to do so it may become unmanageable major take exponentially longer and we can't wait around that long because our grantees up for renewal before so how can we do with these orbitals well for the best double zeta orbital and the energy of the helium and comes out to be minus 2 . 8 6 1 7 In terms of Hartford for the symmetric the wave functions that I propose for hydride which is not just a product of 2 orbital the energy is minus 2 . 8 7 5 so that but in that when we don't have orbitals anymore we just have this symmetrical way function 4 hydride apparently based on your orbital approximations hydride just isn't stable every and so it would be kind of tedious to find that out I think and I'm not quite sure myself how that's proven but if we if we take 2 double zeta term like that with hydride and do the same thing we get an energy higher than minus a half oratory so that simple symmetric of functions this is better however we would be able to
49:12
get 4 3 4 5 electrons and so forth what's going on and hydrates have a special case because is only a single charge of 2 electrons and so on and so for other atoms were going to get pretty accurate results by looking at these orbital approximation we don't necessarily have trouble about the fact that it's not super accurate because we can make a pretty accurate the question is now How do you solve these equations if you've got to 3 4 tens of barium and close this lectured by this picture of of Douglas Hogg tree he met with meals for In his adviser was professor Rutterford and he was implied he was very good and math and he was very interested in this new theory at the at the sport come up with that was eventually superseded the former model of the explained some things by quantise an angular momentum saying it had to be In units of age bar and that explained some of the energy level dependence but ultimately was shown to be incorrect and the correct various courses the Schrödinger equation which gives us everything correct he devised a method that was then modified but the Russians Fox and together it's called the Hochtief Fok approach and it's something that you have to know about if you're going to get into anything about calculating the synergies because by far the most commonly used method at least to start with you when you're looking at the systems and it's an extremely clever method because it gives you some physical motivation for what you're going to do and there on top which is very important he gives you a numerical procedure with a welldefined stopping criterion for calculating that the the energy and when you should stop and I'm going to pick this up next time by taking the the probability distribution of 1 electron and rather than having the real life electron there with the first one buzzing around like to fly I'm going to take 1 electron and then smeared out and just it's all charge distribution and then I'm going to let the now it's not alive anymore it's dead it's just a static charge distribution 911 the 1st electrons interact with this static charge distributions and with the nuclear and then I'm going to try to solve the real life wave functions Of the 1st electrons and then I'm going to have to figure out I would prove my solution she sold pick it up From there With this nice picture of Douglas fir trees staring out from the past
00:00
Mineralbildung
Sonnenschutzmittel
Elektron <Legierung>
Zellkern
Hydride
Zellkern
Atomsonde
Zusatzstoff
Hydride
Orbital
Ordnungszahl
Konkrement <Innere Medizin>
Erdrutsch
Eisenherstellung
Elektron <Legierung>
Thermoformen
Pharmazie
Molekül
Funktionelle Gruppe
Orbital
04:24
Fülle <Speise>
Feuer
Hydride
Setzen <Verfahrenstechnik>
Base
Genexpression
Hydride
Orbital
Lösung
Erdrutsch
Oberflächenchemie
Chemische Formel
Physikalische Chemie
PCT
08:28
Sonnenschutzmittel
Potenz <Homöopathie>
Elektron <Legierung>
Fülle <Speise>
Feuer
Hydride
Potenz <Homöopathie>
Setzen <Verfahrenstechnik>
Mähdrescher
Orbital
Fleischerin
Erdrutsch
Teststreifen
Azokupplung
Blei208
Sense
Elektron <Legierung>
Thermoformen
Chemische Formel
Chemische Formel
Funktionelle Gruppe
Wasserwelle
Funktionelle Gruppe
Systemische Therapie <Pharmakologie>
16:34
Mineralbildung
Potenz <Homöopathie>
Elektron <Legierung>
Hydride
Wasser
Tellerseparator
Konkrement <Innere Medizin>
Erdrutsch
Derivatisierung
Herzfrequenzvariabilität
Sense
Elektron <Legierung>
Chemische Formel
Chemische Formel
Funktionelle Gruppe
Aktives Zentrum
21:13
Sonnenschutzmittel
Zetapotenzial
Fülle <Speise>
Elektron <Legierung>
Hydride
Setzen <Verfahrenstechnik>
Computational chemistry
Orbital
Disposition <Medizin>
Zelldifferenzierung
Konkrement <Innere Medizin>
Metastase
Erdrutsch
Thermoformen
Chemische Formel
Alkoholgehalt
Funktionelle Gruppe
Funktionelle Gruppe
28:10
Zellkern
Hydride
Konkrement <Innere Medizin>
Derivatisierung
Sense
Eisenherstellung
Elektron <Legierung>
Querprofil
Alkoholgehalt
Linker
Funktionelle Gruppe
Ionisationsenergie
Funktionelle Gruppe
Atom
Elektron <Legierung>
Potenz <Homöopathie>
Hydride
Querprofil
Setzen <Verfahrenstechnik>
Mähdrescher
Torsionssteifigkeit
Wassertropfen
CHARGEAssoziation
Herzfrequenzvariabilität
Bukett <Wein>
Chemische Formel
Periodate
35:38
Mineralbildung
Chemische Forschung
Zetapotenzial
Chemische Forschung
Orbital
Hydride
Konkrement <Innere Medizin>
Computeranimation
Aktionspotenzial
Quantenchemie
Elektron <Legierung>
Wildbach
Nanopartikel
Helium
Cadmiumsulfid
Funktionelle Gruppe
Ionisationsenergie
Lösung
Atom
Fülle <Speise>
Elektron <Legierung>
Hydride
Potenz <Homöopathie>
Helium
Mähdrescher
Tellerseparator
Einschluss
Torsionssteifigkeit
Erdrutsch
Komplikation
Thermoformen
Chemische Formel
Pharmazie
Zetapotenzial
Chemiestudent
Orbital
Quantenchemie
Nachwachsender Rohstoff
49:12
Tiermodell
Elektron <Legierung>
Ordnungszahl
Lösung
Altern
CHARGEAssoziation
ForkheadGen
Natriumdiethyldithiocarbamat
Paste
Orbital
Systemische Therapie <Pharmakologie>
Barium
Atom
Metadaten
Formale Metadaten
Titel  Lecture 19. The Hydride Ion (Try #3!) 
Untertitel  The Orbital Philosophy 
Alternativer Titel  Lecture 19. Quantum Principles: The Hydride Ion (Try #3!) 
Serientitel  Chemistry 131A: Quantum Principles 
Teil  19 
Anzahl der Teile  28 
Autor 
Shaka, Athan J.

Lizenz 
CCNamensnennung  Weitergabe unter gleichen Bedingungen 4.0 International: Sie dürfen das Werk bzw. den Inhalt zu jedem legalen Zweck nutzen, verändern und in unveränderter oder veränderter Form vervielfältigen, verbreiten und öffentlich zugänglich machen, sofern Sie den Namen des Autors/Rechteinhabers in der von ihm festgelegten Weise nennen und das Werk bzw. diesen Inhalt auch in veränderter Form nur unter den Bedingungen dieser Lizenz weitergeben. 
DOI  10.5446/18897 
Herausgeber  University of California Irvine (UCI) 
Erscheinungsjahr  2014 
Sprache  Englisch 
Inhaltliche Metadaten
Fachgebiet  Chemie 
Abstract  UCI Chem 131A Quantum Principles (Winter 2014) Instructor: A.J. Shaka, Ph.D Description: This course provides an introduction to quantum mechanics and principles of quantum chemistry with applications to nuclear motions and the electronic structure of the hydrogen atom. It also examines the Schrödinger equation and study how it describes the behavior of very light particles, the quantum description of rotating and vibrating molecules is compared to the classical description, and the quantum description of the electronic structure of atoms is studied. Index of Topics: 0:00:38 Hydride Try #3 0:42:20 The Orbital Approximation 0:49:42 HartreeFock Approach 