all right the subject of this lecture is molecular orbitals what we're going to do is we're going to come up with another way of describing what happens when two atoms form a Cove valent Bond our last Model veence Bond Theory described the bonding as an overlap between the orbitals of two atoms that's how we described the bond we're going to come up with a new way what we're going to do is we're going to view the process of bonding as having two atoms brought close together and instead of their atoms o instead of their orbitals overlapping them giving up their orbitals Al together to form joint orbitals known as molecular orbitals so let's define some terms here an atomic orbital remember is the wave function whose square gives the probability of finding an electron within a region of space around an atom in other words an atomic orbital is where an atom and electron is likely to be found a molecular orbital is the same concept it's a wave function whose square gives the probability of finding an electron in a molecule so instead of finding a electron within a atom we're now finding it within a orbital it's kind of the difference between saying where in the city of Elizabeth Town are you like L to be and where in the state of Kentucky are you likely to be so now we're looking at where in a molecule another thing about this view that's important is it views the formation of a bond between two atoms as that atom giving up all its individual orbitals once it forms a bond is kind of like the two atoms are getting married right when you get married you give up all your individual property right all your property suddenly becomes communal property until the divorce lawyers come in but anyway you view it all as communal property same way for these two atoms they come in with their own orbitals but when they merge and become a molecule they give up their individual orbitals and they form communal orbitals or molecular orbitals now the best way to describe this and I'm sure there's going to be a p chemist who's going to throw up a little bit in their mouth somewhere to hear me say this I like to think about molecular orbital formation um kind of along the lines of orbitals can't be created or destroyed if two orbitals are going to be hybridized or joined together to form a molecular orbital then two molecular orbitals have to be formed out of those two Atomic orbitals for example if two atoms come together to form a molecule they're 1s orbitals will add together and form an orbital their 1s orbitals will then subtract from each other as well and form a second orbital in other words I'm adding two s orbitals and out of those two s orbitals I'm getting two new orbitals I'm getting a what are known as a sigma bonding orbital and I'm getting what's known as a sigma asterisk or anti-bonding orbital or it's kind of like anytime somebody's writing a really bad comic book or a really bad movie what do they always do they cause the creation of the superhero and the villain in the same story right at the same time the hero is formed his evil opposite is formed at the same time that's exactly what happens when two Atomic orbitals join together to form a molecular orbital they form a low energy bonding orbital and a higher energy anti-bonding orbital if we look at our pictures here if we look at our pictures here the addition of the orbitals creates a bonding orbital this bonding orbital is lower in energy than um the the orbitals that it came from and the high area of finding an electron is between the two nuclei I can't seem to write it there let's see here the sigma bonding orbital has a high likelihood of finding the electron between the two orbitals this is in contrast to the anti-bonding orbitals the anti-bonding orbital formed by the addition of the two 2 s orbitals is higher energy than the orbitals from which it came and it has a node between the two orbitals your antibonding orbital I'm still here I can't handle silence can you handle silence here can you handle this did you think about your your bills your X your deadlines or when you're going to die well how appropr any sorry enough of my musical um interludes there so your antibonding or orbital has an anode has a has a anode has a node between the two nuclei and that node has a zero probability of finding the electron between the two nuclei and therefore it's considered anti-bonding high energy zero probability Bond Ord something we'll talk about a great deal here in a second is the number of bonding electron number of electrons and bonding orbitals minus the number of electrons and anti-bonding orbitals divided by two okay I feel the need to bullet point things so let's bullet point some things okay let's bullet point what we we've been talking about in molecular orbital Theory when two atoms form a bond they can Bine their orbitals to form molecular orbitals the merger of two Atomic orbitals results in the form of two new molecular orbitals a high energy anti-bonding orbital Bo yes Boo and a low energy bonding orbital the hero of our story a stable bond forms when the number of electrons in bonding orbitals is greater than the number of electrons in anti-bonding orbitals we form this rule right here using a formula and this formula is known as bond order bond order is equal to the number of electrons in bonding orbitals minus the number of electrons in anti bonding orbitals divided by two and if let's think about this a stable bond forms when the number of electrons in bonding orbitals is greater than the number of electrons in anti-bonding orbitals in other words whenever our bond order is greater than zero than a stable molecule results in other words a positive Bo promotes bonding the first time I learned this as an undergraduate I got really excited I said I can do boo no problem so I didn't shower for a couple weeks hoping that would produce promote my channel of bonding it turns out it didn't it actually had quite the opposite effect um but it turns out it works for atoms go figure so what do we mean by this can we see an actual practical application of this that we can relate to sure let's start with the simplest molecule there is hydrogen I have a hydrogen atom here and that hydrogen atom has an electron configuration of 1 S1 and for our purposes here we're actually going to do an orbital diagram here where energy is increasing up the page there I have another hydrogen atom over here also with one electron in this 1 s we know that hydrogen exists as a diatomic molecule according to molecular orbital Theory when these two hydrogen atoms get together and form the hydrogen molecule they give up their individual orbitals to form molecular orbitals since we start with two orbitals we can't create or destroy orbitals so to speak we have to wind up with two so we wind up with a bonding orbital referred to as the 1s Sigma orbital that promotes bonding because it has lower energy so it creates one orbital of lower energy and then it also forms a 1s antibonding orbital and that anti-bonding orbital is higher energy than the original orbitals and it shifts the electron density and it shifts the electron density away from the area between the two nuclei whereas this lower energy bonding orbital promotes electron density between now remember uh um a fundamental rule here is that a bond only wants to form Bond's only going to form if it's energetically favorable and most of the time by energetically favorable we're meaning it achieves a lower energy state right isn't our goal at the end of the day to get to the point where we're having to expend less energy on work instead of more energy on work same way for these electrons they are always looking to a lower energy State as opposed to a higher one so our two hydrogens merge their orbitals they form a low energy bonding and a high energy antibonding their electrons are going to enter into the low energy bonding orbital first so in our hydrogen molecule the electron configuration of our hydrogen molecule could be viewed as having a 1 s Sigma 2 electron configuration so that's the bonding situation for our hydrogen according to molecular orbital theory if we were to calculate the bond order for our hydrogen molecule we would say that we have two electrons right here in our bonding orbitals minus zero electrons from our antibonding orbital it's empty divided by two that gives us a bond order of one this means two things first our bond order is greater than zero so the molecule is stable and the second thing is this bond order actually tells us the number of bonds that forms it actually tells us the number of bonds that form since we have a bond bond order of one that means that our hydrogen molecule has a single bond between them and remember what did we always refer to a single Bond as we always said a sigma Bond was a sigma Bond and what orbital are our electrons in for our s for our single Bond my word they're in the 1s Sigma or orbital the same thing that we've been referring to a sigma Bond a single Bond as and now you know and knowing is half the battle why don't you write down a sooko everybody write down aano ad Anakin's Pana sotano a h o k a a h s o k a space t a n o t a n o so that's an example or hydrogen is an example of how bonding order can predict that a will form and why it's stable let's look at an example of where bond order predicts something isn't going to be stable before we do that however I need you to write down a Soo write down a sotano a h s o k a let me repeat that a h s o k a space Tano t a n o t n Anakin's Apprentice right ahsokatano we know that helium exists in a monatomic form helium diatomic does not exist naturally doesn't happen not going to do it wouldn't be prudent molecular Thor molecular orbital Theory can explain why if we look at Helium the electron configuration of helium in the atomic form is 1 S 2 1 s orbital with the two electrons in it if helium diatomic was to try to form what would its electron configuration be well the 1 s's would merge again and they would form a 1s Sigma bonding orbital and they would form for a higher energy 1 s Sigma antibonding orbital so we have started with two orbitals we have two orbitals now this time instead of having just two electrons to find homes for we have four electrons that need home two from this one two from this one so we start off filling our low energy bonding orbital but that fills up an orbital can only hold two electrons so so we then have to place electrons in the higher energy antibonding orbital what does that do to our bond order if we look at our bond order for our helium now we have two electrons in the bonding orbitals but we also have two electrons in the anti-bonding orbitals so our bond order winds up being zero which means that they're going to form zero bonds those two helium so we have a molecule that would not be stable and is not going to form that Bond and not want to form that Bond so we can see how bond order can tell us if a molecule form and be stable and if it does form how many bonds will be between the two atoms up till now we've looked at scenarios where we've simply merged s orbitals and when we merge two s orbitals we get two orbitals out a 1s Sigma and a 1s Sigma antibonding what we want to look at now is a situation that the where the complexity increases we want to look at a situation where instead of moving of just merging s orbitals we merge a p orbital the situation involving P orbitals increases the complexity dramatically first of all I've got three orbitals in each molecule that I have to merge so I have to figure out a way to combine these three orbitals the lowest what when these atoms merge we're going to get a sigma orbital out an anti-bonding Sigma orbital out and then we're going to get two Pi orbitals out so we have three p orbitals and those three p orbitals combined with three p orbitals from another atom are going to give us a sigma a sigma antibonding a pi orbital a pi orbital and then a pi antibonding orbital and a pi anti-bonding orbital so that's what we're going to get when we merge these orbitals here you might want to write that down because I need to erase it now what makes this a little bit difficult is depending on what atoms are merging it's going to depend on the energy relationship between those sigmas and those Pi bonds for example when we look at when we look at oxygen and oxygen merges its Pi orbitals I mean sorry it's p orbitals what you discover is you get a and once again just so that you know we've got a energy increasing whoops energy increasing up that direction so we merge our two P orbitals and the first orbital we get is a 2p Sigma out then with slightly higher energy we get two Pi orbitals 2 p Pi orbitals which just really sounds silly to me two 2 p Pi I guess it's because it's hard to say or something then you get your anti-bonding orbitals and the anti-bonding orbitals have that reverse energy order you get your 2 p Pi anti-bonding orbitals and then you get your 2 p Sigma anti-bonding orbital and in this and in the oxygen molecule and this goes for Florine as well in case you're keeping track of your elements at home the sigma has lower energy than the pies the sigma bonding than the pi bonding and whenever I go to do molecular orbital Theory I always usually default to this um configuration however experimental work has suggested that that's not the case for all molecules for example nitrogen when it merges its P orbitals is going to be contrary nitrogen is going to be difficult instead it's going to form oh know is it really going to make me erase this just a second I'm going to do magic tricks here Tada look at everything disappearing there um when nitrogen forms its orbitals it actually does it a little bit differently what it does is when it merges its P orbitals the first two orbitals that form are actually Pi orbitals in nitrogen the pi orbitals have the lower energy the pi bonding and then you have the 2p Sigma bonding so you have lower energy in those pies than you do in the sigma that's a a um example of differentiation from the rule this isn't something you're going to be able to predict as a general rule it's something based on experimental results um and not something you'd be responsible for on an exam as long as we have nitrogen in front of us let's take a look at what its electron configuration would be nitrogen in its p 2 p orbitals here it has it has 1 2 3 1 2 3 p electrons so where would those P electrons be located the P electrons would be located in the actually I don't want to do it just for nitrogen as a part let's um let's summarize what I'm saying about the orbitals and then we will um look at oxygen and nitrogen entirely instead of just looking at those P subshells for nitrogen also why don't you write down the U name Captain Rex I mean if you we've got a so you got to have Captain Rex matter of fact they just brought him in back in Rebels yes Captain Rex Rex Captain Rex let's take a look at the oxygen molecule here is something you would be expected to be able to do on an exam if I gave you the combined molecular orbitals like I've done here right I've written out what those molecular orbitals are for your oxygen so that you know that your Sigma is lower energy than your 2 pi for oxygen I'd expect you to be able to place the electrons and tell me the bond order so let's get started first we have two 1s orbitals and two 1s orbital orbital electrons so two electrons there two electrons there now our two s orbitals two two so we've got to put two electrons in the bonding two electrons in the um unbonding then we've got two electrons in RPS two electrons in our PS so that's four electrons so we're going to place one two electrons in the sigma and I have two Pi orbitals of equal energy right so I place one electron in each of those Pi orbitals this is really important and really cool for a couple reasons first let's take a look at the bond order of oxygen here what would the bond order of oxygen be well remember bond order is the number of electrons in bonding orbitals so I've got 1 2 3 4 5 6 7 8 I have eight electrons in bonding orbitals minus the number in anti-bonding orbitals 1 2 3 4 4 / 2 gives me two so the bonding order for oxygen is two meaning it's going to form a double bond and you're saying wait a second we knew oxygen was going to form a double bond based on our veence bond theory true but here's something that you can't predict based from valence Bond Theory here's where molecular orbital Theory gives us some important information that um here's where molecular orbital Theory gives us something that veence Bond Theory wouldn't if we look at this electron configuration for our oxygen here you'll notice that our oxygen has some unpaired electrons if we looked at it here let me look La this molecular orbital theory if we looked at it based on veence bond Theory based on veence bond Theory all of Oxygen's electrons are paired up and molecular orbital Theory we have two lone electrons there's an easy way to experimentally determine whether or not a molecule has paired electrons or unpaired electrons that simply apply it to a magnetic field if you have unpaired electrons then in the presence of a magnetic field your molecules when placed in the presence of a magnetic field will go to a positive or negative pole whereas if they don't have unpaired electrons they won't be affected by the presence of that magnetic field it turns out that when you place oxygen in the presence of a magnetic field it responds to that presence of the magnetic field it actually does in fact split into two streams which means that the oxygen molecule has unpaired electrons according to veence bond Theory it doesn't but according to molecular or orbital Theory it does that's why molecular orbital theory is important to us one of the many reasons is it helps us explain properties such as the response to a magnetic field that veence Bond Theory over here can't this also brings us the opportunity to talk about a couple new terms paramagnetic means the chemical species has unpaired electrons to remember it I often refer to it as unpaired to Magnetic unpaired to Magnetic unpaired a magnetic and that's how I usually remember it paramagnetic means a chemical species is unpaired electrons and responds to the presence of a magnetic field the opposite of paramagnetic is di magnetic diamagnetic are substances whose electron pairs are spinned and they weakly are repelled by magnetic fields so di magnetic are repelled weakly by magnetic fields because they have electrons that are paired paramagnet unpaired to Magnetic and it's paramagnetic but I always say unpair to Magnetic as a pneumonic device so it's unpaired to Magnetic substances with unpaired electrons are attracted by a magnetic field molecular orbital Theory allows us to predict and explain di magnetism and paramagnet magism whereas veence Bond Theory often fails to do so another place where molecular um orbital Theory and veence bond Theory differ is in resonance veence Bond Theory remember we really don't have a good way to explain resonance I mean the way we draw those leis structures we're kind of admitting G wiiz we can't come up with a good way to cope with this molecular orbital Theory however is able to explain resonance it's saying that the pi orbital or the molecular orbital here doesn't belong to just one atom it's saying instead these Pi orbitals belong to all three atoms after all if an orbital belongs to more than one atom there's no good reason the electrons can't be spread among all three of them and have a probability of existing around all three of them so molecular orbital Theory helps us explain resonance um and resonance uh coincides I guess is the best way to say it with with molecular orbital Theory much more so than it does veence Bond theory in case you are having trouble with my chicken scratch I thought I'd show you the figure from the book what we have is we have energy increasing this way and we see the orbital diagrams for nitrogen and for oxygen notice they're the same except for the difference in the energies of the bonding pies and the bonding sigmas in nitrogen the bonding pies are lower energy than the sigma whereas in oxygen the sigma's lower energy than the Pi's we haven't done a orbital diagram a molecular orbital diagram for our nitrogen let's take the time and fill one out so that nitrogen doesn't fill left out if we were to write the veent shell electron configuration for our nitrogen atoms that's what we'd get right SP2 sp3 so now we have to place those electrons in the bonding orbitals so I've got four four S electrons I have to find home in again I'm starting at the bottom going to the top I now have three + 3 is six six electrons I have to place in my 2 p molecular orbitals so I start at the bottom 1 2 2 3 4 1 2 and now I found a home for all six electrons so what my would my bond order for nitrogen be my bond order for nitrogen would be my number of electrons in bonding orbitals 1 2 3 4 5 6 7 8 8 8 minus my number of electrons and antibonding orbitals in this case 1 2 divide by two and that gives me a bond order of three which we know from veence Bond Theory means that nitrogen forms a triple bond so see molecular orbital theory is isn't really that bad at this level particularly since we're going to be giving you these orbital diagrams and just asking you to make conclusions about bond order or filling them in let's work a couple examples before we work those couple examples why don't you write down um Ventress write down a assaji Ventress as a JJ let me repeat as a JJ and then Ventress v n t SS v n t SS aaji ESS all right nitrogen monoxide usually called nitric oxide is a diatomic molecule with molecular orbital diagram similar to that of nitrogen show the molecular orbital diagram for nitrogen oxide predict its bond order is it nitrog is nitrogen monoxide diamagnetic or paramagnetic to answer this question you have to recognize they're telling you a very important piece of information there it's telling you it has a molecular orbital diagram similar to that of nitrogen remember nitrogen has the pi orbitals having less energy than the sigma so when we look at the diagram here or when we draw our diagram we're going to have to take that into account and I'm going to get a new sheet of paper here to draw with all right let's do some drawing here we have nitrogen with 1 s 2s 1 2 3 2 p come in and right so there's our electron configuration for nitrogen 1 S2 2 S2 2 p 3 oxygen remember is 1 S2 2s 2 2 p 4 2 3 2 p I know I'm doing an evil thing here and doing them backwards and four all right so there's the electron configuration for our two neutral atoms when they form a molecule according to hybrid orbital Theory they're going to hybridize their orbitals so we're going to hybridize our sr1 s's here when we do that we get a very sloppily drawn um 1 s Sigma 1 s Sigma antibonding then we're going to do the same with our 2 S's we get a 2s Sigma a 2s Sigma antibonding then our PS we do the same thing but remember because they told us they told us it was like nitrogen which was their way of saying that our the two Pi bondings we're going to make are going to have less energy than the 2 Sigma we're going to make and antibonding and whoops antibonding so now that we've got our orbital diagram all laid out now we can fill in our electrons four in the S one s's four in the 2 S's then we have let's count it 1 2 3 4 5 six seven to place in these hybridized P orbitals so I'm going to go 1 2 3 4 5 6 7 so what is my bonding order going to be based on this all right let's shrink it all down here my bonding orbit order would be the number in my bonding orbitals so 2 4 6 8 10 minus the number in my anti-bonding orbitals 2 4 5 divided by 2 and I get a bond order of 2.5 next is this paramagnetic or di paramagnetic well we've got one unbonded orbital one unbonded electron so we know it's going to be unpaired a magnetic or paramagnetic chemistry is easy life is hard yes