Molecular Orbital Theory: Best Bonding Model Explained Simply

molecular orbital theory or mo theory for short gonna be the topic in this lesson and uh this could be a real pain

point for students i'll warn you but reality just happens to be more complicated than we'd like and it turns

out that mo theory here is gonna do a better job of describing bonding than either valence bond theory or even the

lewis structures we've uh gotten customary drawing now everything has its utility everything has its place but it

turns out this one actually gives the best description of reality uh we'll talk about why h2 you know hydrogen is

diatomic whereas helium is not and we'll talk about why o2 has some magnetic qualities that would not have been

predicted say from the lewis structure but mo theory allows us to explain those so

super useful but again it's a little bit complicated but we're going to hopefully bring it down exactly to a

level that's understandable my name is chad and welcome to chad's prep where my goal is to take the stress out of

learning science and this particular lesson is a really good one for this to be my objective so hopefully we

accomplish the task now in addition to high school and college science prep we also do mcat dat and oat prep as well

this lesson is part of my new general chemistry playlist i'm releasing several lessons a week throughout the school

year so if you want to be notified every time i post one subscribe to the channel click the bell notification all right so

we got to take a look at molecular orbital theory here which is going to be pretty much our best theory of bonding

and uh everything has their shortcomings nothing's perfect but this is the best

description of reality you're going to learn in your general chemistry course here and and the truth is it's actually

more complicated than we're even going to get into it but we're going to cover it at a level that's pretty much going

to suffice for most all of you in a general chemistry course so if we take a look at hydrogen here so we'll start

with valence bond theory and then we're going to build on it from there and see what's really going on so

in molecular hydrogen we saw with valence bond theory that if you've got two separate hydrogen atoms which have

their unpaired electron in a 1s orbital so that if these two atoms come and approach each other

you will get overlapping orbitals and valence bond theory just suffice it to say says yep and electrons live in those

overlapping orbitals life is good well it turns out it's actually a little more complex than that so these atomic

orbitals these 1s orbitals in this case those are wave functions so don't forget that all your atomic orbitals are

solutions to the schroding equation there are three dimensional mathematical equations themselves we call wave

functions well turns out when you overlap these wave functions you can add them or really a better word is combine

them in different ways so we're going to look at those different ways now to understand this

though we've got to talk about some two-dimensional wave functions you're maybe more familiar with and talk about

what happens when they overlap so we're going to go back and take a look at the sine function from your

trigonometry class for just a second if you take a look at a typical sine function here we'll focus in on this top

one first so from zero to pi or which is same as zero to 180 degrees so the sine function takes on positive values but

then from pi to 2 pi or 180 to 360 degrees it takes on negative values but right there right in

the middle so it takes on a value of zero in fact every multiple of pi takes on a value of

zero and for a wave function we refer to that as being a node so it's just a place where the function has a value of

zero now the corresponding to that so we're going to see we talked about orbitals these are for some of the more

complex orbitals it turns out there are no nodes in a 1s orbital but for pretty much every other orbital there's going

to be a node somewhere like p orbitals always have a node at the nucleus so and for

the function going to zero for a wave function for an orbital here that means you have zero likelihood of finding the

electron there so just keep that in mind now if we have two of these sine functions so and they overlap just like

so where the positive parts are perfectly aligned and the negative parts are perfectly aligned we refer to that

as being in phase so and when you have in-phase overlap so when you basically they overlap it's

just plus with plus and they add together essentially and you get constructive overlap and the function is

amplified and so the sum of these two when they're in phase like this is just a larger function

cool but you can also have it to where instead of having plus overlap with minus i'm sorry with plus and minus with

minus you can actually have them exactly out of phase as well so and now when they're exactly out of

phase and have the same magnitude they're actually going to cancel each other out in this case now it turns out

i've gone to the extremes here i've gone exactly in phase and exactly out of phase but you can have everything in

between so but the extremes are all we're going to be concerned with here but see every value and the function

here has a corresponding negative value here and when you add them together they add up to nothing to zero and so in this

case they canceled each other out this is destructive interference so and this is going to be important when we start

looking at adding wave functions because it turns out your atomic orbitals being three-dimensional mathematical equations

in some cases they're going to have positive values for the function and in some cases they're going to take on

negative values for the function now one thing i want to point out on your sine function is that as you're going from an

area where it takes on all positive values and you cross over to an area where it takes on all negative values

you do have to cross through 0 and get a node and we're going to see the same thing we look at the p orbitals which

have that node at the nucleus a little bit later on so let's go back and take a look at

these overlapping s orbitals for a second so because it turns out these s orbitals the wave functions again these

are just three-dimensional mathematical equations can take on either positive values or

negative values and for the 1s orbital it could be either one it could be all positive or all negative and so say that

these s orbitals here are all positive and so when they come to overlap

so then the region where they're overlapping all the values are positive and that region is going to get

amplified in the same way that our same sine functions were additive when they overlapped in phase and so this region

would get amplified and what you'd end up with is you'd end up with a big giant wave equation

that's kind of the combination of these two where it's amplified right down the middle and if we kind of draw in the

nuclei right here you'd find out so again these wave functions describe where an

electron might be found and it turns out it's really the wave function squared that describes that but i'm going to

gloss over that for now you'll get that a little more in your ochem class or a pecum class so but in this case

the most amplified region here is this region right in between the two nuclei right where the overlap was occurring

and so in this case it turns out that's going to be the most probable place to find an electron and that's a good thing

because the nuclei are positively charged the electrons are negatively charged and so having this region right

in between the two positively charged nuclei being the most likely place to find an electron well that's the place

the electron wants to be most and what we really mean when we say that because obviously electrons don't want anything

so but what that really means is that that's where they're going to be lowest in energy so when they have the most

attraction to the things they're attracted to and they're closest to both so that's right along there and that's

again now the most likely place they're going to be found and so it turns out that these two original atomic orbitals

have now combined to form this one giant we call molecular orbital hence the name of the theory here molecular orbital

theory so and this molecular orbital is lower in energy than either one of the

original atomic orbitals for one again the electrons now get to see two nuclei and the most probable place they'll be

found is right exactly in between those two nuclei and so that lowers the energy significantly it turns out also

according to the heisenberg uncertainty principle that the larger the volume of an orbital the lower its energy as well

and so in this case this molecular orbital is larger than either of the original atomic orbitals as well and so

this molecular is going to be lower in energy now it turns out this is end-to-end overlap that's occurring here

that's sigma overlap we learned earlier in the chapter and we'd refer to this guy right here as the sigma

1s orbital so in this case again it's a molecular

orbital so we can see the atomic orbitals that we started with before bonding occurred and now we can see the

molecular orbital they've overlapped to create now here's where things get a little bit weird so we said that the

atomic orbitals here these s-orbitals can be either be all positive or all-negative and the result would be the

sigma 1s whether they've been both all positive or both all negative we still would have got constructive overlap in

either case but what happens if instead one of them has the negative version of

the wave function well then when they go to overlap instead of constructive overlap

and amplification we're going to get destructive overlap now and it's going to cancel out this region right down the

middle and to draw this there's a couple different ways you can approach it but what i usually like to do is draw the

same thing i drew down here and then erase the part where they canceled each other out

and again one side's going to be now positive one side negative you find out another convention we'll use and we'll

probably use it with p orbitals uh a little more is that instead of writing in the plus and the minus we'll actually

like shade one and not shade the other or shade one one color and shade the other a different color and so i'll use

that convention a little bit too because that's something you're likely to encounter

so but in this case this is one new again molecular orbital up here so it has two areas of electron density so but

it is one molecular orbital so and we have created a node

right here where the function has a value of zero and what that means again is that you're never going to find the

electron right along that node and recall that's the actual best place an electron would want to be right in

between both of the positively charged nuclei and that's the one place it cannot be and so as a result so if if

letting the electrons be exactly where they want to be lowers the energy well then not letting them be there is going

to actually raise the energy also because part of again we had destructive overlap so the total volume here is

going to be lower than the total volume down here where there was amplification so because part again these original

atomic orbitals that overlapped cancelled each other out so to speak destructive interference and so the

overall volume of this uh levelly molecular orbital is less than the combined volume of these 1s orbitals and

definitely less than the sigma 1s here and so that's also going to raise the energy according to that heisenberg

uncertainty principle and so it turns out just like this sigma 1s was lower in energy than the original 1s orbitals

this new molecular orbital is going to be higher in energy and we'll call it the sigma 1s star

so and it turns out that again these molecular orbitals just like the original atomic orbitals can each hold

two electrons any orbital in the universe that you're ever likely to see is going to be able to hold a maximum of

two electrons whether that's atomic orbitals or these molecular orbitals and so you can fit two electrons into this

molecular orbital you can fit two electrons into this molecular orbital well in this case would i rather put two

electrons in this sigma 1s molecular orbital or just leave them as separate atoms in the 1s orbitals well this is

lower energy and so according to offball you know you fill in the lowest energy orbitals first and so i'd rather put

them here so and that's what makes this bonding so having this orbital that's lower energy

than the original atomic orbitals means that putting electrons there is likely to hold these atoms together into a

molecule rather than them being separate apart there's an advantage to being together however

so this orbital right here is higher in energy than the original 1s orbitals and so putting electrons in this orbital is

worse than having the separate atoms and so it serves to actually want the atoms to be just say separate and not come

together when you put electrons here and so as a result we call it an anti-bonding molecular orbital

and this is where things get weird so when you get the overlap between the atomic orbitals it always simultaneously

leads to the creation of both a lower energy bonding molecular orbital from constructive overlap and a higher energy

anti-bonding molecular orbital from destructive overlap both occur simultaneously and so notice the the

total number of orbitals you have is always going to be unchanged so we started with two 1s orbitals from two

separate atoms we had two orbitals when they came together those 1s orbitals ceased to exist once we form a molecule

what now exists are these molecular orbitals but it's still a total of two orbitals but that's what's really going

on and so here we're showing this with the 1s orbitals and we'll draw a lovely mo diagram to correspond to this a

little bit so but the big thing is that you know we're only going to consider what are

called the homonuclear diatomics and so we're actually only going to look at identical orbitals overlapping so here

we did it with an s and an s and a little bit we're going to do it with a p and a p in a couple of different ways

both sigma and pi versions of that so but in more complicated molecules you might have you know an s overlapping

with a p or maybe some hybrids you might consider something like this and the truth is it's actually even more

complicated than that once you get into many atom systems beyond just two atoms which is all we're going to consider in

this lesson so it turns out all the orbitals of all the atoms in the entire molecule are going to combine in

different ways to form molecular orbitals and this gets a little bit crazy to think about when you think

about you know proteins that can have thousands and thousands of atoms and you're going to have like molecular

orbitals that are some sort of combination of all the molecular you know all the atomic orbitals of all

those atoms that's crazy but it turns out there's a reality there and then you know like it's so complicated we can't

even deal with it but with things like methane ch4 which has a carbon and four hydrogen atoms sorry there we go four

hydrogen atoms so with that carbon and four hydrogen atoms you've got five atoms orbitals overlapping and we can

actually plot out their molecular orbitals and so uh just from you know take into account all the orbitals that

are actually overlapping and it's it's really complicated and it's beyond the scope of what i'm gonna present in this

lesson so but again it's complicated just for five atoms again get to a protein where you've got thousands of

atoms and it gets insane and it's nothing we can really visualize all that well in many cases so uh but again this

actually is going to give us a description of reality that's going to be pretty useful here so

all right so we've kind of looked at overlapping s orbitals so and how it leads to the lower energy bonding

molecular orbital from constructive overlap and the higher energy antibonding molecular orbital from

destructive overlap but let's see the same thing with p orbitals here all right so we're going to take a

couple of atoms and they're separate atoms right now with a p orbital and this it turns out is the pz orbital

there's a p orbital that lies on the x axis one on the y axis one on the z axis and the one that's on the z axis is

going to undergo sigma overlap when they come to these two atoms that come to approach each other

and in this case one reminder on the p orbital is there's a node right at the nucleus so for an

electron in a p orbital you will never find that electron at the nucleus there's a node there the function goes

to zero and it does just like we saw with the sine function because on one side of it it'll take on positive values

and on the other side negative values and it could be positive on the left and negative on the right or it could be you

know negative on the left and positive on the right it's arbitrary but they do have opposite signs just like in the

sine function you pass through that node and you're going through from positive values down to negative values or you're

going from negative values up to positive values when you cross through a value of zero for the function

so in this case instead of writing positives and negatives though what we often do

is just do a difference in shading and so the shading you know one of the shading could be positive and not

shading negative or vice versa we never actually go so far as to find it we just need opposites in this case and just a

reminder again this is not a charge this is the math so not plus and minus charges at all but the mathematical sign

of the function and so in this case i'm going to choose such a way where

the lobes of the p orbital that have the same sign are going to be the actual ones overlapping

and so in this case when these come to overlap so again this is the shaded region on

this one this is the shaded region on this one and so where they're overlapping they have the same

mathematical sign either both positive or both negative and that's going to lead to constructive overlap and just

like it did back here with the s orbitals constructive overlaps going to lead to a lower energy molecular orbital

that is a bonding molecular orbital and we kind of get an idea what this looks like here

and so this region where they overlapped got magnified amplified and again that's all got that sign whereas these have the

other sign and once again you can see now in this new molecular orbital this bonding molecular orbital we've created

you've got a change in sign of the function every time you cross a node we go from one sign to zero to a different

sign to zero to a different sign and so we have those two nodes notice those two nodes were already present there at both

nuclei and they're still present at both nuclei when you get constructive overlap you don't create any new nodes

so if you started out with two nodes in the individual atomic orbitals you're going to have two nodes in the overall

molecular orbital and again you're going to get an a region of ampli amplification right in

between the atoms in this case we'll call this the sigma 2p molecular orbital so it turns out

this is from we don't have p orbitals in shell number one so this would be for a 2p

but again just like we saw with the s orbitals destructive overlap will occur at the

same time we've got to consider both possibilities so going back here let's say we take this one on the left

and now we'll shade this side over here instead and that's going to make this a little

complicated and so i'm going to redraw it and so we've got shading over here but

now we've got the shading over here and so this region where they overlap now

so from the two different lobes of the two different p orbitals they're going to have opposite signs and they're going

to cancel each other out and it's going to create a new molecular orbital that's going to be anti-bonding and higher in

energy and once again when i want to draw an antibonding molecular orbital i'll do it the same way i did over here

i draw the bonding one and then i just erase that region down the middle where they were having some destructive

overlap so i'm just going to redraw this guy right here it's not a perfect drawing so spices say

we can see the creation of the new node and if we show the shading we go from

not shading to shading to not shading to shading and with the antibonding molecular orbital destructive overlap is

always going to lead to the creation of a new node right along between the two nuclei along that internuclear axis we

say and again this is going to be higher energy because it one the best place for the electrons to be would be right in

between the two nuclei and that's the place where they can't be and again because we canceled out part

of the orbital volume if you will it's also going to have lower volume and be higher energy according to the

heisenberg uncertainty principle cool so before these atoms came together we just had separate p orbitals but once

the atoms come together those p orbitals no longer exist those atomic orbitals no longer exist because those atoms have

come together to form a molecule it's now these two molecular orbitals that exist and again you form the lower

energy bonding one you also form the higher energy antibonding which we always designate with an

asterisk so this is sigma 2p and this is either sigma-2p and de-bonding some people would say or most commonly you'll

hear called sigma-2p star is the way they would refer to that cool so now we've seen how p-orbitals

and specifically the p-z can come together to do sigma overlap so however so those two orbitals are oriented in

such a way that they would when the atoms come together they would overlap end to end and that would be sigma

overlap but that's pz what about like py and px when the atoms come together they're going to overlap in side to side

fashion instead and that would be pi overlap and so let's take a look at that as well

and once again we're going to have these atoms coming together and so for example py when these come together we're going

to get side to side overlap now so and one we could consider the overlap to be in phase

in which case the areas where they overlap and again with pi overlap we get overlap in two regions so but the

overlap occurring both here and here has the same sign and it's going to lead to an amplified view here

and so there's our nuclei and we're going to get something with a big region of electron density there and

a big region of electron density there shaded up here not shaded down here and we still have a node right along

the nuclei there but we had that node to begin with in the original atomic orbitals as well

the big thing is that we have not created a new node right along this internuclear axis in between the nuclei

and again that's going to be characteristic of your bonding like orbitals you don't create a new node you

get constructive overlap rather than destructive and this guy right here we're just going

to call the pi 2p molecular orbital and again just like any other molecular

orbital it can hold two electrons so but we've also got to consider the opposite case where we get destructive

overlap where the p orbitals that are approaching each other have are exactly out of phase instead of in phase so

let's redraw that possibility and so now the sudden where we get the overlap occurring they're exactly

opposite signs and they're going to cancel each other out and if i want to draw what that would look like again my

favorite way is just to draw the bonding molecular orbital and then erase that region right down the middle

so i'm going to run out of room here just a little bit in fact i'll redraw this

in a second just to give myself enough room all right

i'll erase that region right down the middle again not a perfect drawing but it will

suffice and if we should look at our shading here to designate our signs it looks

something like this and so we still have that node right along the nuclei you're always going to have that for a pi

molecular orbital so created from p orbitals but we also have created a new node right down the middle

along that axis between the nuclei which we're always going to do for a anti-bonding molecular orbital and so

this is our pi 2p antibonding so and here i showed it for kind of like p y but px would do the

same thing instead of being on the vertical axis on the horizontal axis as well and so you end up creating two sets

of these molecular orbitals from the two p orbitals for x and y so now we've got a better idea of what's

actually going on when atoms approach each other either if it's just hydrogen we're dealing with you know electrons in

shell number one or if we're dealing with the period two elements which not only will you have the uh s orbitals in

shell one you'll have the s orbital and shell two and the p orbitals also overlapping either in sigma fashion

which i said i would redraw this so sigma fashion or pi fashion so now we've got to put this

all together and create a what we call an mo diagram a molecular orbital diagram for a variety of different

molecules so but now we kind of got an idea of what these molecular orbitals look like and you may be on the hook for

identifying you know looking at a picture and being like what molecular orbital is that well you'd have to look

at this and be like oh that's the sigma overlap of p orbitals that's the sigma 2p so we're looking at something like

this and be like oh that resulted from side to side overlapping p orbitals but it was out of phase so that's the pi 2p

star pi 2p antibonding all right so let's create some mo diagrams here

so we're going to represent the atomic orbitals with a box like we did with electron configurations and we will do

the same thing with the molecular orbitals so we're not actually going to draw these shapes and that we saw

created so but we know that when two atoms come together in this case two hydrogen atoms so come together their s

orbitals are going to overlap to create a lower energy bonding molecular orbital that we'd call

sigma 1s and a higher energy antibonding molecular orbital which we call sigma 1s star

now in this case we know that we had a total of one electron each for the hydrogens a total of two and so we show

on the same diagram this gets a little confusing but we're going to show both the before and aft after picture of

bonding so before they've come together to bond these two separate atoms just have one electron in separate 1s

orbitals and so on the sides we show right here the atomic orbital diagram but now we're going to

show the molecular orbital diagram right up the middle here so there's really two points in time before bonding after

bonding and you really need to understand that there is two points in time so we've shown where the electrons

go before bonding now we need to show where they go after bonding well to fill in two electrons into the afterbonding

picture the molecular orbital picture you put them in the lowest energy spots and so they got two openings here and

that's where those two electrons would go kind of like just according to offball principle we saw earlier where

you fill in the lowest energy spots first and we can see now why hydrogen exists

as a diatomic because the after picture is lower in energy than the before picture so the electrons end up lower in

energy on average than the electrons of separate atoms and that's why it bonds together so typically things in the

universe want to be as low in energy as possible and and processes that lower the energy of

of of the universe and stuff like that tend to be spontaneous those are the kind of processes that happen and so

that's why two hydrogen atoms would want to bond together it lowers the energy of their

electrons now if we compare this to diatomic helium which does not exist and we can explain why it doesn't exist

now so each of those heliums has two electrons in the 1s orbital now

and again when they overlap they're going to create a lower energy bonding molecular orbital and a higher energy

antibonding molecular orbital so but now we've got four total electrons to fill into our molecular

orbitals and so we'll put the first two in the bonding but we'll put the second two

in the antibonding and so it turns out you know putting two electrons in a bonding molecule orbital

that's equivalent to a bond if you recall everything we've done so far like with lewis structures says that there's

two electrons in a single bond and so putting two electrons in a bonding like orbital that's equivalent to a bond

but putting two electrons in an antibonding molecular orbital kind of cancels that out it's an anti bond

and so in this case we can see that well the two bonding electrons are canceled out by the two antibonding electrons and

so it's kind of like it has no bonds which is why it doesn't exist now we've created what's called the bond order as

a way to kind of put a mathematical calculation on this and so the way this works for your bond order

you're going to take your number of bonding electrons and again you're going to just focus on the molecular orbital

diagram not the atomic part so you'll take the number of bonding electrons two subtract off the number of antibonding

in this case zero and then divide by two and that's going to get you your bond order which in this case two minus zero

is two divided by two is 1. and this would be the a bond order of 1 is kind of the equivalent of a single

bond of what you saw on a lewis diagram cool and so we see that yeah lewis showed this as a single bond and then

like the orbital theory kind of confirms that yeah it's essentially the equivalent of a single bond this bond

order so we do the same thing for helium though and i'll abbreviate this as bo

which might not have been the best choice but in this case we've got two bonding two antibonding so two minus two

and then all over two and again it's all over two because it takes two electrons to make a bond essentially so you just

wanna find out what's the balance of excess bonding electrons and then by divide by two to get the equivalent

number of bonds that means so but in this case it's just going to equal zero and a bond order of zero means there's

no bond there which is means that this doesn't exist there's no bond this diatomic helium

does not even exist so typically if you've got a positive bond order anything higher than

zero we think there's a chance that that could exist but a bond order of zero that is something that does not

exist and so in this case we've now explained according to molecular orbital theory why hydrogen is a diatomic

whereas helium is not a diatomic and doesn't exist as a diatomic cool and this is kind of the way it

works now notice you know we could go and you know start looking at different things so we we already talked

about so helium diatomic here doesn't exist but what if i had helium diatomic with a plus charge

so with a plus charge with ions you're supposed to know that with cations you lose electrons with anions you gain

electrons and so here with a helium a diatomic helium cation instead of having a total of four electrons it would only

have three and so it turns out the atomic part i can just choose whichever one i want to erase it doesn't really

matter so but in the molecular part i have to erase one of the highest energy electrons and i'd be left with a picture

looking like this and that's going to change our calculation for bond order now

and so we'd have 2 minus 1 all over 2 and we'd get a bond order of 1 half

and that's greater than zero it's equivalent of like half a bond which we don't really have a lewis structure uh

analog for that so but because it's higher than zero we might consider he2 plus as actually having a chance of

existing of uh there being some sort of uh correspondence to reality so again

diatomic helium itself not so much but he2 plus that might actually exist again because we do have a positive bond order

associated with it cool this is going to get a little more complicated we start dealing with the

period 2 elements we're just going to have more molecular orbitals to kind of diagram out let's

take a look all right so now we'll deal with the homonuclear diatomics for the period 2

elements and we're going to start with o2 f2 ne2 and that homonuclear just refers to two identical atoms so two

oxygens two fluorines two neons there is such a thing as heteronuclear diatomics like no would be an example of that but

i'm gonna totally not cover that most of you will not be on the hook for the heteronuclear diatomics so if we look at

these homonuclear diatomics so it turns out that oxygen fluorine and neon this is what the diagram would look like

you're gonna get the 1s orbitals overlapping to create the lower energy bonding sigma 1s and the higher energy

sigma 1s star antibonding you're going to get the 2s orbitals overlapping in the same fashion giving a lower energy

sigma 2s and a higher energy sigma 2s antibonding then you're going to get the p orbitals overlapping and the pz's are

going to overlap end to end to give the lower energy sigma 2p and higher energy sigma 2p antibonding so but then px

and py when they overlap side to side it's going to lead to lower energy pi 2p uh molecular orbitals and pi 2p star

anti-bonding molecular orbitals that are higher energy so this is what the diagram would look like

now we'll find out for everybody left of auction the periodic table in period two there the diagram is

going to switch just a little bit and we'll talk about why and and you know point it out and stuff like this but

this is the diagram we've got to fill in so if we take a look at starting with say oxygen well oxygens 1s2

2s2 2p4 and so that's what each of the options

are going to look like now one thing to know let's just deal with those 1s electrons for a second

so those 1s electrons are full and because they're full then when they

overlap and those again one s orbital cease to exist you will end up filling both the sigma

1s and the sigma 1s antibonding and that's not going to really tell us much because the bonding molecular

orbital electrons are going to get cancelled out by the antibonding ones and so it's not going to contribute to

the bond order and so the truth is a lot of times we'll just leave out the core electrons off the diagram and only

diagram out the valence because again these aren't really going to contribute the electrons are always going to be

paired up they're always going to cancel each other out in terms of a bond order calculation and so they don't really

tell us anything we don't already know so oftentimes you'll just see this kind of eliminated i drew it in once i

probably won't draw it on the next diagram as you'll see so but here now we can focus on these

valence electrons and so 2s2 and so four electrons total so we'll fill in two here and

two here so but the p electrons are not full we've got four for each of the oxygen so

one two three four one two three four and so we've got a total of eight

electrons to fill into the molecular orbitals and we'll just work our way up so first two go here one two and then

the two the pi two piece here are degenerate and when you've got degenerate orbitals everybody gets one

before you start pairing them up that's two four six and we've got eight so once again we'll put electrons right there

cool and this is what the structure the mo diagram here for o2 looks like now this tells us a couple of things so one

we take a look at that bond order calculation so in this case and if we do for the

whole thing we could be like two i'm sorry let's go bonding two four six eight ten

and then two four five six

all over 2 is going to get us a bond order of 2. and if we just left off the core electrons entirely and redid the

calculation so leaving those out we would have had 2 4 6 8 bonding and then 2 4 antibonding and so instead of 10

minus 6 we would have got 8 minus 4 both numbers would have just been

reduced by 2 but it would still lead us to getting a bond ordered calculation of 2 and so that's what i meant by you know

leaving these out of the bond order calculation and stuff like that doesn't tell us anything we don't already know

we're gonna get the same calculation of bond order but this tells us that this has the equivalent in o2 of a double

bond and that corresponds nicely with what we know about the lewis structure so the lewis structure even shows a

double bond and this corresponds to a bond order of two and so this confirms or at least is consistent with what we

know of the lewis structure but it tells us something the lewis structure does not so we got a couple new vocab words

here so one is paramagnetic and one is diamagnetic so it turns out for a paramagnetic

substance it is attracted in a magnetic field whereas for a diamagnetic it has a very very very weak repulsion in a

magnet when placed in a magnetic field and what causes this is the presence or absence of unpaired electrons so it

turns out electrons you learned have a spin associated with them but when you pair up electrons their spins are

opposites and they cancel and so it turns out if all your electrons are paired up then their spins all cancel

and you don't experience an attraction in the magnetic field in fact you get that really really weak repulsion it

turns out and that's what makes you diamagnetic all your electrons are paired there's not a single unpaired

electron to be found in you so and if we look at the lewis structure it looks like all the electrons exist in

pairs so pairing a bond there a pair and a bond there a lone pair lone pair lone pair lone pair and according to the

lewis structure we might think that o2 is diamagnetic unfortunately though it does experience an attraction when

placed in a magnetic field and lewis is not going to help us understand that but molecular orbital theory will we can see

here we've got two unpaired electrons in the pi 2p star antibonding molecular orbital and

so molecular orbital theory allows us to figure out that yeah o2 is indeed paramagnetic as we

know in practice and now we can explain why and before we got to mo theory we couldn't explain why and so here's one

of the big successes of mo theory over the earlier bonding theories it allows us to predict paramagnetism and

diamagnetism better than the earlier bonding theories like the lewis theory in this case

okay let's say we switch this up and take a look at f2 if we draw the lewis structure in f2

so this is what it looks like and it looks like it has a single bond and we'll find that that's going to

correspond to a bond order of one in a little bit uh and it turns out that f2 is diamagnetic and so hopefully we'll

realize from the mo diagram in a second that it doesn't have any unpaired electrons and if we take a look at

fluorine here we got 1s 2 2s2 2p5

and so how would this be different than what we saw with oxygen well all we'd have to do is add one more electron in

to the 2p orbitals and adding one more there means we have to add in so one more for each of these add another two

electrons to the mo diagram which means adding them in there and so now if we go to do our bond order

calculation well we just added two more anti-bonding electrons and so instead of eight minus four over two

it's now going to be eight minus six over two which equals

one and so f2 has a bond order of one which is consistent with the single bond we

know exists according to lewis structures and life is good we also see that all the electrons are now paired up

and f2 we can explain that yeah it's consistent with the idea that it is indeed diamagne

now if we move on to neon here and notice we wrote neon too but notice neon being a noble gas

doesn't exist as a diatomic and so we're not going to explain any properties of neon 2 we're going to explain again just

like we did with helium why it doesn't exist diatomic neon does not exist either and in this case we move on to

neon 1s2 2s2 2p6 and we'd have to again add

one additional electron for each of the neon atoms which means two additional electrons

into the mo diagram and now we see when we go to calculate out that bond order we've now got

again looking at just the valence two four six eight bonding and two four six eight anti-bonding

and eight minus eight over two is a zero and with a zero bond order we predict that it does not exist and so we also

can use here molecular orbital theory to show that any two is not something we'd anticipate

existing okay so again this is the mo diagram for o2 f2 ne2 but

if you want to take a look at everybody left of oxygen so uh n2 uh c2 b2 be2 or li2 in those period two

elements uh we're going to switch up the diagram just a little bit let's take a look

all right so here i've got the mo diagram now for the other period to homonuclear diatomics

and we see one major change here and that major change here is the sigma 2p and pi2ps have switched places

so if you notice here this was nice because it was all symmetrical so you had the pi 2p lower in energy than the

original 2p atomic orbitals just as the pi 2p star was just as equally high in energy above

those two p orbitals and same thing with the sigma 2p and sigma 2p star and so there was this nice symmetry here and

that symmetry is now broken so and again reality is often more complicated than we'd like it to be

so but it turns out with fewer electrons in the p orbitals so it turns out the the screening that's going on here is

actually going to lead for these lovely elements here for the 2s and the 2p to be closer in energy

than they were over here for oxygen fluorine or neon so and having them be closer in energy has some significant

impacts it turns out that when orbitals are overlapping in this kind of mo fashion they have to be somewhat similar

in energy for there to be any kind of uh meaningful overlap and so in the case here this 2s

orbital right here and one of the the 2pz that's up here are so far apart that there's really no meaningful overlap

going on there but here they're much closer in energy now and as a result so uh your 2s orbitals not only overlap

with each other but the 2s orbital of one can overlap with the 2pz of the other and so what that ultimately

does is it's going to actually increase or really just increase the separation here between the sigma 2p here raising

it higher in energy above that of the pi 2p so that's why these are switched here and we call this sp mixing so here with

the the 2s and the two piece their energies being far enough apart we really don't consider any significant

amount of sp mixing but for the rest of these elements in period 2 because the 2s and 2b are much closer in energy we

will have this sp mixing one thing to note here i did leave the 1s off just like i said it probably would because it

doesn't really contribute anything to our understanding so i'm going to be looking at just

the valence electrons here cool so this is our diagram here we don't

have to work all of these but i do want to work one of them and that one i want to work is nitrogen so because we know

something about diatomic nitrate now these other diatomics i don't know that we really encounter in significant

fashion especially for some of these like lithiums of metal and stuff so but diatomic nitrogen that's the

biggest portion of the air that you're breathing right now yes there's oxygen that's the stuff you need but 78 of that

air is nitrogen that's diatomic nitrogen and we know according to mr lewis we diagram it out to look like this and it

has a triple and if we take a look at the electron configuration for nitrogen

so 1s2 2s2 2p3 having that half filled p subshell

and again we're only going to focus on the valence electrons here and so we've got

to fill those in and we've got 2s2 so two electrons there for each of these nitrogen atoms and what that means we'll

fill in the sigma 2s and the sigma 2s antibonding so there's those four electrons are now filled in here on the

molecular part of the diagram and then we've got 2p3 so we've got an electron on each of the p orbitals

for both nitrogens and so we've got six total p electrons to fill in and the first four

well let's get those with the correct spin that would be disastrous first four go there and then five six

and we go to calculate our bond order now and we've got two four six eight bonding

electrons and only two antibonding so eight minus two all over two equals three and a bond order of three

does indeed correspond to what lewis would have us draw as a triple bond and so it's consistent with that and notice

all of our electrons are also paired in the molecular orbital part of the diagram and so we'd expect n2 mo theory

would predict it to be diamagnetic and indeed it is

so great this is pretty much the level of mo theory you've got to understand so again you should know again here's the

diagram you should know that we've got the atomic part of the diagram before atoms you know separate atoms before

they're bonded together and then we have the molecular part of the diagram down the middle so a lot of students don't

get that and they get lost on filling in the electrons so but the electrons that are filled into the atoms are the same

electrons that are filled into the molecule here so but it's only the molecule that

exists after they come together it's only the atoms that would exist before they've come together but we're

representing both realities at the same time on the same diagram you should be able to calculate bond

orders you should know what those molecular orbitals look like both the bonding and the antibonding that we drew

out earlier so both like the sigma you know and sigma star for the s orbitals uh the sigma and sigma star for the p

orbitals and then the pi and the pi stars for those p orbitals as well uh finally you should be able to draw

the mo diagram for any one of the homonuclear diatomics and you some of you will be on the hook for actually

knowing which diagram you need to use for which of these but quite a few of you are probably actually going to even

be provided the appropriate diagram so and go from there so you should ask your professor and ask him or her

am i gonna have to memorize these lovely mo diagrams for all the period two homonuclear diatomics and do i have to

know which follows this and which follows this or will they be provided for you and you just need to know how to

fill them in so and again most you probably will just have to fill them in but some of you will be on the hook for

actually memorizing the diagrams my apologies if that's the case for you now if you found this lesson helpful would

you consider hitting that like button best thing you can do to make sure other students get to see this lesson as well

and if not you should just smile because hopefully mo theory is just a little more understandable than it was 40

minutes ago happy studying