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Lecture 25. Optimizing H2+ Molecular Orbital, H2, and Configuration Interaction


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Title Lecture 25. Optimizing H2+ Molecular Orbital, H2, and Configuration Interaction
Alternative Title Lecture 25. Quantum Principles: Optimizing H2+ Molecular Orbital, H2, and Configuration Interaction
Title of Series Chemistry 131A: Quantum Principles
Part Number 25
Number of Parts 28
Author Shaka, Athan J.
License CC Attribution - ShareAlike 4.0 International:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license.
DOI 10.5446/18904
Publisher University of California Irvine (UCI)
Release Date 2014
Language English

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Subject Area Chemistry
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: 0:03:28 Polarization 0:12:33 H2 0:15:50 Molecular Orbitals for H2 0:18:24 The Potential Energy Curve 0:20:19 The LCAO-MO Problem 0:31:50 The Valence Bond Approach 0:40:28 Wrapping up H2 0:45:53 Bond Order 0:47:28 Comparing H2+ Through He2
well of the quarter coming to a close and so is series of lectures
today what we're going to do is continue our exposition of H 2 plus and move on to page 2 were going to optimize our molecular orbital treatment of H 2 plus and then we're going to kind of throw in the towel because stage 2 would be at least as much work if not more work than helium and we did it from scratch so that point we're going to adopt a more qualitative view of molecular orbital theory the kind of you the people in the business often use when they talk about bonding and much much more complicated atoms and molecules that have many many electrons and nuclear all over the place will also touch on a very important idea called configuration interaction and we'll see how that can influence the energy so we calculate an improved the results that we
what we're worried that the other last lecture what we tried to do is we tried to include slated to ask little and to improve the energy for H 2 plots and what we found without going through the whole calculations about whether calculations concludes is that when we allow any amount of the 2 as someone asked and basically on decides on its own the the 2 West is not very important doesn't include very much of it and the energy doesn't prove and what that means in fact is that to us was a very bad choices I think you can kind of see White West might be a bad choice to include is a bigger and H 2 it's more like H 2 plus is more like a sausage so if we want to get something to be more like the electron density that we expect in the a molecule we don't want to include another round there and basically the calculation of concludes the same thing so whenever you include orbitals and then you get very tiny coefficients what that means is that you made a poor choice if you're making them by intuition made a poor choice and it's possible to make a bunch of poor choices even using a computer and spent a lot of computer time and then come to the conclusion that none of those orbitals contributes Sigmund none of those atomic orbitals Slater orbitals contributes significantly to the final result on and so the question is knowing that how can we make a better choices and in fact this is quite important because even if you're using the computer to help you with the program like spot Garcia you have to make an intelligent choice about the basis the the orbitals you're going to include in the calculations and if you include a lot of them that are relevant and that's like going down every day and on street and staying to the right hand side and going through a whole neighborhood rather than taking the Boulevard straight through the calculations to get to the answer well and
here's the idea supposing I'm hydrogen and I have my spherical 1 a orbital here and I bring up proton the electron is going to be attracted to the protons and so I expect that this horrible is going to stretch in that direction in other words it's going to be polarized by the presence of the other positive charge and that stretching in 1 direction on the into nuclear accidents can be represented very well biosphere because this fear moves out in every direction equally and therefore I don't want to use the spherical orbital I want use an orbital that shaped more like this with some direction and because of that but I want to use is in fact a to PC Oracle that's what I have to use there is no 1 in the easy of course so I have to use it to PC Europe at all and that would have a plus and minus and I could directed so that the electron density built up in the direction of the nuclear Of course if I include 2 PC which has co-signed data in its in its functional form and then my integral Scanlon hard to do because now I have this extra data and so forth but if I included this cheap easy and the original basis that I can improve the results along the other girls get harder they are impossible we could certainly do them all together and if we had world enough and time we could do that sort of thing but I'm afraid that we will be able to go through that and greater detail and take to lectures justice simply do all those intervals 1 after another although it as it is fairly relaxing to occasionally decided to do a problem from scratch and go through it and understand every single thing about and that's how you become an expert of course so here's what we're going to
do we're gonna try a trial function here on Flight 597 of the forms of coefficient times 1 is a plus-one 1 sp plus some other qualifications 2 times to PC a plus 2 PC B we have to keep things equal between the a and B because of the symmetry of the problem but including these 2 P orbitals lets us include polarization but in way functions but we know from experience how important this parameter funding Greek squiggle is in the expungement and so we're going to just straight away used Slater orbitals we are going to just stick to the hydrogen like wave functions because we've seen but every time we allow the various so that things can stretch out a little bit but we get much much better results so if we're trying to get better results we might as well put together and then hear the forms for the functional forms for the White House and the 2 key see that we're going to include their sale 1 1 Hassan there's said to for the 2 and of course there's the articles that we get from a to B or
when we 1st started out although it's simpler to let say 1 equals in that's more restrictive and then just optimize the coefficient C 1 and C 2 and that go back and optimize say 1 year optimizing the linear coefficients the parts of the fix things you're using that's a pretty simple calculation to do that amounts to linear algebra when you start optimizing things in the exponent it's much much trickier and usually it involves a lot more work Oh here's what we get there and after quite a very long calculations on the minimum energy it is minus . 5 9 9 0 7 but in terms of hot tree and the optimum into nuclear distant spots of the is 2 . 0 0 times a not the ball radius and this is what C 1 equals 2 1 and 2 is equal to 0 . 1 6 1 so about 16 . 1 per cent of the PC included when the Tuesday as saying it the optimum and that's quite a bit and what that means is that we made a good choice and we can see we made a good choice because the energy improved in the radius was much closer to the truth experiment radius and cost the joint values say there is not 1 that turns out to be 1 . 2 for some of us stretched out a little bit like it was before there is an overall normalization and to make sure that your whole molecular orbital is normalized but the relative amounts a R 1 6 100 per cent so speak and 16 per cent and as I said we get quite a bit of improvements by doing this now we let people although the
very then our controls are tougher and we have these 2 parameters and we end up with a very long formula at the end and then after all that we have to optimize this long formula and find that the minimum values of their 1 executive and that's an even longer calculations but we can do it and it's not too bad it can be done by hand even it's not a big deal it just takes time and patience and if you do that and then you find that the minimum energy is now minus 0 . 6 0 0 3 6 the radius is the same C 1 is 1 of C 2 is now . 1 3 8 13 . 8 per cent changed a little bit sale 1 is 1 . 2 4 5 8 which is close to the value that we had before and say that too but this for the key orbital is 1 . 4 2 2 4 the exact energy is minus 0 . a sixfold to all got up and so we are very closely -minus 0 . 6 0 0 and of course with 1 electron only the moral approximation is not really an approximation at all because there's only 1 electron so of course we would expect to be able to do very well once we get the form of the orbital down we could include more terms you can say well which ones would we include would we included to West Point in the other direction the answer is no that would do absolutely no good at all should we include 3 D that looks like clover leaf with 4 loads the answer that it is no that's not going to help us at all if we but function like that in it's coefficient comes out to be essentially 0 we could put a treaty said square which is unique 1 that looks a little bit like pure battle with that rang around the center and if we include 2 of them but as well and by that time we really do need a computer to the calculation doing it by hand it's just too much work than we can get very very very close to the exact answer for 2 plus and that's really reassuring because in the sample systems we better be able to get it right and we better be able to get it right to a lot of digits otherwise there might be something wrong with our whole underlying view In terms of wave functions in quantum mechanics no 1 believes that there is anything wrong with quantum mechanics it seems to predict everything very well even tho it may surprise some predictions about things like the doubles
the H 2 molecule no if I have another electron that's the simplest neutral molecules that we can have and it's just like helium now with the 2 electrons we have the electron electron repulsion we're back to that 1 over 1 2 there to integrate only now have been integrated over a much uglier and set of coordinates with the nuclear stretched out rather than being at 1 point and so it's harder and harder I'm not going to go through that because it's too hard and I think you've got the idea about how you undertake these calculations even a lot of detail on what we're going to do that is worth going to pretend that we can use orbitals that look rather like the ones that we had for H 2 plots and we can just slotted another electrons in recall that's what you do with Adam to start with a hydrogen atom where you know the exact answers and then it just started sliding electrons in the and of course what happens is the orbital energies get jumbled around and move around but he's still in the orbital approximation you think of feeding the orbital rather like something that you would find in hydrogen costs they holding on as the ads bigger and the nuclear charges bigger but qualitatively we still think in terms of these kinds of shades and we still think in terms of shells like the radial distribution function that we found in a much lecture but we know we can put 2 orbital 2 electrons Excuse me into the same spatial order and the same bonding orbital that we found was the low energy solutions and the overall molecular orbital them as the Slater determinant just like it was for added because we have to have the spins be antisymmetric so the total wave functions is antisymmetric and what we can write them if we can write that the bonding orbital it is a linear combination of 2 exponential let's say we just use the 1 essay and 1 SPD orbitals we normalize according to the overlap basked in the denominator here we get this formula than for the bonding orbital and that was later determined consists of this bonding orbital and the assortment of states so we start with the bonding orbital and spin the electron won a spot Ben Olsen and then the bottom orbital electrons no 1 has been down data and then the 2nd were referring to electron to we again the bonding moral for the spatial orbital electrons to his stand and the other a final entry in the 2 by 2 Slater determinant is the bonding orbital time suspend function for the electron to being down and I have expanded
this someone's life 601 and and this is what we have now we have the bonding orbital for electron 1 for the spatial hard times because remember that's how we do it we always take product times the bonding orbital for electron too and then we have to spend part which is the antisymmetric single part comes from taking on the job and in this case the special part of symmetric obviously and spent part is obviously antisymmetric which you can verify by swapping 1 and 2 and seeing the wave function changes as far
as we're concerned we're not doing anything with magnetic energy electron hats so we are turning on a magnetic field but In that case the Hambletonian in other words the operator for the energy of H 2 does not have the and been depended terms it doesn't have any energy which would indicate it's been obvious different than spend down if we turn on a magnetic field there are energy terms that depend on whether sped up at the electron spin and enact case we have to be careful because we have to include those terms is in the calculations but for us we don't have to do that and so the spatial part of the Hambletonian which is what we're going to focus on mostly is just a product of the molecular orbitals 1 has a 1 plus 1 being 1 or we could make it more elaborate we can always expand each starting molecular orbital that we started out with times the same thing for the 2nd electron and call this whole thing many signs and all of which would be the spatial part 1 over 2 times 1 sets and that this crop of the Orioles but if we do this are molecular orbital picture predicts a bond that's not too far air although it is by no means perfect the dissociation energies it's not perfect the bond length is not perfect but we do think that we do predicted upon for H 2 and so it seems like everything is we can
solve the total energy as a function of ah with these 2 electrons in just like we did rates to plus we treat our as a parameter we move the nuclei we fix that we solve for for the lowest energy we put a point there we moved the nuclei again we solve again and so forth and is just the same thing as we did for extreme plus however if we do this something pretty odd happens as the Athens getting farther and farther apart the energy of H 2 does not go into the energy of 2 isolated age at because that would be minus 1 . 0 1 and a half of this hydrogen and hydrogen minus a hazardous hydrogen hydrogen B. That's not what happens when we take this molecular orbital which is our simplest 1 and therefore something's wrong because for Adams we really looked at predicting the correct ionization energy as part of a measure of quality as to whether we had the right idea or not if we could predict the ionization energy than we think we were aware that something was wrong and that something is wrong but what's wrong here is a little bit more so that it seems like but for some reason because it's all showing a 2nd the energy is way off on that we've done something inadvertently wrong because there's something about it but we still don't quite understand so it seems like when we look closer we've still got sort of a structural flaw In our approach and this is a very important structural flaws to appreciate if we
take same equals 1 the minimum energy your age 2 it is minus 1 . 0 9 9 1 Haji at the minimum radius of 1 . 6 0 3 any not that we do everything properly do all the other girls myself that's what we get if we let Zeta vary of course it expands a bit like it always tends to and we did say that 1 . 1 9 3 the minimum energy now proves to minus 1 . 1 2 8 2 and the the radius proves to 1 . 3 8 5 for the accepted values are minus 1 . 1 7 4 4 for the energy and 1 . 4 0 1 4 the into nuclear separation are so be it the we predicted by optimizing said a smaller but keep in mind the variation all fear refers only to the energy it doesn't say that the the engine nuclear distanced always has to be greater than the correct 1 it just as the energy is always higher then the correct 1 and so there is nothing wrong with predicting a tighter arrangement of nuclei that something to worry about however if we take our saying the equations and we just let their guard goes to infinity pulled out like that then the energy goes to limiting value of minus . 7 1 1 9 that's what we get and that's way off minus 1 something is wrong were predicting an elevated energy In the limit and and we have to take a look at that because that's the way to foreign air I want to just brush office has something in in fact even if we make our but also much more elaborate but but keep the same structure we still get a very bad answers the bond Association energy if you like for H to taking age to producing into a it must be then that we're doing something but that is different than that and to
see what we're doing here 605 what I've done is I've expanded at the all the terms we have the product of the electron 1 and it's it's immoral and an electron to it's a long and here's what we get we wanna say 1 1 to and now we get 1 SAY 1 SPT and then we get 1 has been 1 1 I say to you and then we get 1 of the 2 no 1 has to be 1 1 to excuse 1 of the sport terms me well let's let's just look at the 1st term a 1 1 as they too what is happening what that means both electrons are on a the a that's what that term means and that means there is no longer be this 1st term which is 25 per cent of total is 2 electrons over here and not over here and then what we've got In the middle because we've got 1 electron Asian 1 electron on B and then we got a from the on ,comma just the other way round the world labeling the electrons that that's saying and then the final terms here which is another but that 1 is 2 electrons on B and none of it well this this is the form of our molecular orbital and we can interpret these things when we square among others the probability of electron and if we let them too at Adams get very far apart of course when there close together everything's OK all the wrinkles are smoothed out but when we
let them get very far apart it's quite a different story because now we've got a big problem and the big problem is that were predicting 4 possibilities when we dissociate age 2 using the particularly wave functions where operating we need again h miners and H. plots he we get to major Adams was 2 Senate terms or we get age minus-10 age plots and the dissociation of age to what we want to think about is producing 2 major at not producing these weird excited states hydride being barely bound and then a proton but on the other side and yet that's the least these come out clearly in our way function In our molecular orbital and therefore the problem is that the way we set this up which was seen to be a very good way the most obvious way to it is no good because it includes too much ionic character it says half the the time to get 8 plus an age mine and the other half of the time you get to hydrogen atoms is not in fact what we want to have but if we know that then we can rationalize why limit comes out wrong and we the read the way we can do that as well we saw had the foresight you might think it planned to calculate the energy of the hydride and iron earlier on so we can go back to our notes on that and we've got that down pretty well so we can take that the energy Rivera protons and insanity and rest has no electrostatic energy at all because of potential energy 0 on the kinetic energies 0 it's just that the protons and so on we can figure out what's going on the optimum
value say there is 1 point over a hydrogen atom because that's where it came from but for the and we find out with a very occasional approach that the optimum value data was 11 over 16 so there are 2 of each form In a hydride age 2 have to wait to 8 and hydride and so the average value of data should be one-fourth of 2 times 1 was 2 times 1116 if we work better then and the state of Para few like the average value should be 27 over 32 which is about . 8 4 3 7 5 and that's in fact the optimum value of sales as you go To insanity that's the 1 that comes out of optimizing said the change is big on and also we can explain why the energy has a particular value might points 7 because the energy
of a hydrogen atom in a Slater orbital vis-a-vis square over to minus 8 and we found for hire but the energy analysts Slater orbital is status squared minus 11 over a state that's how we optimized if you recall there are 2 agents produced 1 aged 2 seperate 180 miners and age but with the plus no electronic energy the wants to you go two-way chat and 1 separate but if it separates this way you just get 1 hydride and nothing that you want to include equal parts of the world
so therefore terms but we only need to we don't need do the other 2 prison saying so what I want to do you figure out the energy this involves apart in this sport all it is 1 times 2 times the energy of a hydrogen and plus the energy hide and if I do that and I wouldn't say this word monsters 11 and everything what I find is that the energy Of the animal as our goes to infinity should be saved squared minus 27 over 60 but we know what exactly goes to because we just figured that out we said What should go to the average 27 over there too and so we got to put in 2007 over 30 to enter the formula and what we get the end after simplifying is minus 27 over 32 quantities Square which is minus . 7 1 1 9 exactly what is observed when you look at the numbers so sometimes numbers hide a lot of they seem to be just a number from nowhere and yet here it it's exactly 27 over 32 square and it's no coincidence that it has the value well we can
let our code is 0 2 if we let our code 0 what we're doing is we're compressing are age 2 into helium this is the great thing about I'm doing thought experiments is that you can do whatever you like and you can see whether it makes sense enough now costs what we better do is we better throw away the 1 over par repulsive tournaments unless they are good 0 and that's because when they touched worsening the strong force takes over and they would have to be some neutrons but they don't change our electronic energy and also we don't have to to really worry about enact cases and we have essentially helium at and what we find is that our parameters data for the orbital 27 over 60 as to 0 and that agrees with the calculation for helium exactly that's exactly what we find so the problem with the dissociation is that we're going to much weight class and age minus and the product and that's because of the way we set up the linear combination of atomic orbitals molecular orbital it's just too much it should be know is
far back as 1927 high-schooler in London were trying to explain chemical bonds and they wrote something which going call sigh surveillance bonds and the 1 after electron 1 times 1 has the 4 electron plots 1 has to be for electron 1 of us wants a electron to this seems very similar to the country we use when we finally got hired right 2 give us an answer and in fact if you use this particular way functions you can show that there is a chemical bond that exists and that as a pair of electrons and this led to the so-called valence bond theory and I what we're going to talk a little bit about them coming up and more qualitative way because in a certain sense it seems like whatever happened to the bonds whatever happened to the lines between the letters and the arrows moving electrons and all the things that might have done in organic chemistry seemed like bad stuff a sort of disappeared like the the Cheshire Cat but it's coming back don't worry because we can now actually incorporate are much more formal and insightful view of wanting to go back to a much more simplified to you when that expedition I usually computer programs are going to use molecular orbital approach so the valence bond approach is mostly of historical interest but it's not really used in modern computational programs but it is very important because it does suggest that approved instead of having
a 50 per cent higher on age plus minds that we have with or will we could try a new wave functions which is seeing 1 Times cited England's bonds plus C 2 times sci-fi on and then we go optimize C-1 and C-2 and get a better result and we know how to do that by now with the variation principle we've done that many times in this course already in fact go 10 it turns out there's a slightly different way of looking at it and it turns out that what we ought to do it seems a bit counterintuitive but what we ought to do it is concluded at the end of bonding orbital remember we have the combination of first-class and plus minus that have no if we include a little bit at the end of bonding orbital in the mix and in a single configuration interaction or just and we can get a much better result that turns out to be rather similar to taking this valence bond ionic approach but let's just look at In this way if we include CIA and we can get the right Association Limited for H 2 so
this solves the problem here is what we do we write the by now :colon CI for configuration interaction is equal to some coefficients and body horrible for electron 1 times the bonding orbitals for electron tubes good that's the part that's what we had before but now what we're going to do His Oregon expand our basis set to include C to some that mixture of science star and try bonding for electron 1 times signed star of states accused me Sigma amusing Sigma Nu side for electron to and these just because it's called signal bond until bond on and I know what these it be answered but are 1 minutes 1 is a plus 1 and B and the other 1 is 1 of 1 believed that I could multiply all these things out and when I get there and you see 1 for the same terms I before anyone too as 1 has to be too and so forth plus I get another term C 2 With the actor and interesting when I get 1 as it 1 1 6 2 and many others have the opposite side and then 1 has to be 1 of 1 of the 2 ministers because of the cemetery so the terms a very similar a few change signed and if I include more In my starting orbital and optimize the amounts of each you might think well if you can enter bonding orbital and it's going to come out 0 because after all we call and I want it but that's a little bit naive because this will see that's not quite how it works because C-1 and C-2 depend on ah and so there they turn colors and change as we change apart and it's this extra flexibility of having C-1 C-2 vary but let us get out of here so I'll just
cut to the chase if I simplified this that mixture that of the bonding in Yantai pondered what I get is compared to what I said before I get see 1 minus times side valence bond was higher in London Rome plus C 1 plus the 2 and sigh so they're very closely related to still the new combinations of the 2 but the difference here is that the coefficients themselves 1 and C 2 depended on when unchanged are now and I have my molecular orbital I have to really optimized every part of the molecular orbital the mixtures that I allow what percentages the Zetas Everything because 1 fact happens when the nuclei changed positions Is the electrons magically and quickly all of the born Oppenheim approximations instantly finds the optimal moral on so we have decided by clowning around a lot numerically but in actual fact in nature it's instantaneous and it doesn't take any great calculations do what we find that if we do this it is an hour goes to 0 goes to 0 that's perfect because as of 0 that means the end bonding power is out of our hair as far goes to to infinity however see 1 goes to 2 or 2 and seated now goes to minors from 2 0 2 and what that means is that
the 2nd of of second-term disappears and by substituting in the coefficients what we can see it is that on this configuration interaction wave function gears the correct answer for healing 1 side when our hostess Europe and it also gives 2 hydrogen atoms and nothing else as part goes to infinity and that's perfect means that we've solved the problem now only energy after dissociation correct we've got no more commander of course we could start all over we did this with 1 said was 1 be we saw before the even phrase to possibly should include 2 PC we go back we can put that in and and the bombing and I bonded and so forth and so on boy it gets complicated quickly but we get excellent results so if you're willing to work hard and you get a better answers and it's kind of satisfied but the simplest
calculation and wrapping up to whizzing equals 1 not optimizing and we get the energy if know what I call ECI for configuration interaction wave function is minus 1 . 1 1 8 6 5 and the radius is 1 . 6 6 8 8 if this is better than the 1st try with the bonding and if we optimize sale that it increases in the energy becomes smaller minus 1 . 1 4 7 9 4 and the radius in nuclear distances now 1 . 4 3 and if I put atomic orbitals I essentially the correct answer to as many digits as the experimentalists can tell you what this but of course you need a computer to do that because you just as many many many angles to do can hope to do them all hand and then you have even after you get them done you have a messy messy optimization problem which you may need some fairly sophisticated methods to to solve wage battle can be done and you get a very beautiful and so here's our
qualitative picture if we start to atomic orbitals we endeavored with 2 molecular orbitals and we can summarize things that with this qualitative pictures neurons 617 which is a molecular orbital diagram which some of you may already have used without understanding exactly what that meant in detail before we start out with the energy on the water and we put lines for the energy of the isolated at times we have 2 hydrogen atoms so the same energy but keep in mind that 2 different elements like CD and all that half all the levels were shifted because oxygen as much bigger positive charge in the center which is pulling down so you must image orbital 2 pct on oxygen and has the same energy to PC on carbon they do not but here out of do and then we take a good combination which is lower in energy than the isolated at times and the bad combination and upon which is higher in energy than the to isolate them and then we dropped 2 electrons in and to be strictly correct it's probably better to draw half for the electron so that a full error with a full point on the end means moved to electrons because when organic chemist right their reactions were usually have bonds moved sort of like a mousetrap standing onto another and they do know that with a double-headed arrow so but that's kind of difficult because Powell .period for example doesn't have or have had an of the year to make them by hand took the trouble to make a few buying and here that I put in on the lines in between like the tennis tournament all they are meant to qualitatively indicate his wish for but also present in the linear combination that's giving you the bonding around on the north end of the month nothing more than that really I mean you did to actually know the amount we have to do some kind of calculation we can can't just get what amounts of gold where easily the energies themselves unless they been calculated some and for you if you're just trying yourself the energies of gasses and you have to keep in mind that they move around a lot as you add electron spin so you must just assume that a molecular orbitals like a static tennis tournament or something and then players to feature the it's not like that at all if they move around the actual tournament itself moves around and sometimes things that were above and 1 combination go below In another will see that the next lecture the bond border
is an important concept when you look at the molecular orbital diagram it's the number bonding electrons minus the number and type bonding electrons divided by 2 and for H 2 we've got to London electrons and 0 and bonding electron so the bond order is the average or divide by 2 of 2 minus 0 which is what they're for we would predict a single forward between 2 hydrogen atoms and that's why we draw line usually if we're talking about double triple bomb dropped to work through the line for a
student from where we only have 1 bonding electron the bondholders 1 that explains why it's on very weakly bound compare it 2 and for helium to Daimler Allianz AG to plus for the 1st 3 electron there's no to bonding and 1 in the end bond and so the bond orders again one-half for a change there's 2 bonding electron and there are 2 antidotes bonding electrons and therefore the order is one-half of 2 minus 2 or 0 if the bond order is 0 that's what we're predicting his Noll basically to helium atoms trying to form a bond at about the same energy at studio in without bonded so why should they do you prefer to maintain their independence from entropy considerations these are really qualitative pictures because as we have more electrons we have all those 1 over a 1 2 1 over our won 3 1 over 2 3 and we never did any of those injured we just have kept the same qualitative pictures here with these 2 levels and started pumping electrons but in actual fact they move around and if we want to get it right we have to actually do some work and but if we
make qualitative measurements so here's some accepted data for H 2 Class are invigoration as 1 acid Majidi the bond orders that have an exact was measured as the bomber this 162 meters and the binding energy in chemistry and some soldiers more this 269 for age we have won a segment in square and the bond orders was the bond length is 75 the commuters and the binding energies 458 killed jewels from all 4 he had 2 plus time we now have 1 answered when you press at bondage as well as the other 1 being full the bottom line is back to 162 meters that's probably a coincidence don't see what should be exactly the same as the binding energy is Back to ascend value for H E to worry about that from the bottom a 0 the bond length is listed as 6 thousand the meters and the binding energy is listed as about .period 1 of those tools from all what that means is that the physical chemist very stubborn and if you say you can't make a bond or you can make something stable at all they will try very hard so it could be that there is an experiment where you pull down to helium atoms and major sure nothing else is around and there's just those 2 and they have minor fluctuations in charge and so they they kind of vaguely attract each other at this very very long distance and people like to do that the same way like to get a gigantic telescope and see how far they can't see out into the universe but that doesn't mean that the helium dying it exists under normal circumstances it does exist in this very excellent care way with these very specialized experiments that have been done by experts but we never see the helium under ordinary circumstances and that's why we consider him to be a fairly ideals monitoring the get OK I will leave it there were done now we are sort of very detailed exposition of bonding in the simple systems cost to make a detailed we had a simple system because if we have 3 electrons on the ceremony on that we forget it we're going to have so many integral to do and it's going to take forever and so what we have to do is learn how to zoom in on what's important and leave the rest of society especially it's going to be a ton of work we don't want to end digging a ditch with a teaspoon that's a very bad idea we just want cut to the chase and say Look here's the the valence electrons here is what we have to calculate how accurately we have together and here's qualitatively what means in terms of structure bonding and reactive so pick it up next time blacks again in the 2nd row on the periodic table which will be exciting because there will be some catches sight of hydrogen and helium which is a little bit of to stick with this


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