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visit MIT OpenCourseWare at ocw.mit.edu. CATHERINE DRENNAN: All right. So moving to today's
handout, this is one of my favorite
parts of the course. Honestly, when I first
started teaching 5.111, I said transition metals
are rarely covered in the intro chemistry courses. Is it really necessary
to cover it here? And I was told it
absolutely was. It's one of the reasons
that a 5 on the AP exam is not good enough, that you
have to take the Advanced Standing exam. Because the people who
teach inorganic chemistry found that people who
placed out of 5.111 didn't do as well
in their course as people who took 5:111 here. So this is one of the reasons. And then I started
teaching it, and I realized this is
one of the-- even though people haven't
seen it before and sometimes will get a
little scare-- it's actually one of the most fun units. So I absolutely love
it, and hopefully you will love it by the end. People are like, we
never covered it. Why are you covering it? We're in chapter 16. It's fun. OK. So transition metals,
d-block metals, because they have
those d orbitals. Yes, we're going back to
talking about orbitals again. And they're called
transition metals because you transition from
this part of the periodic table with your, what
kind of orbitals? AUDIENCE: s. CATHERINE DRENNAN: s. To this part of your periodic
table with your, what kind of orbitals? AUDIENCE: p. CATHERINE DRENNAN: p. So they are the
transition metals, and they're often really
reactive and very cool. And many of them, since
we're on a biological theme, many of them are super
important in biology. And I have some of these
written down in your notes, but here they are up here. In the transition metals,
you have a lot of metals that we could not live without. Iron carries oxygen to
our blood, very important, hemoglobin. We talked about cobalt just now. That is the metal
in vitamin B12. So we know why that's important. We have zinc everywhere. Nickel's important for
bacteria, not so much for us. But bacteria is
important for us, so therefore nickel's
important to us. So all of these are
really important. Also, this part of the periodic
table is a part of the table that people love that want to
make pharmaceuticals or want to make new kinds of
electrodes or batteries or all sorts of things. There's a bunch that
are used as probes. We talked about imaging agents,
detecting cancer, and all sorts of different things like that. Many of these transition
metals are used in those probes and also in pharmaceuticals. And so this is sort
of a very rich part of the periodic table,
where those d orbitals allow for properties
that are incredibly useful for our health and
for doing all sorts of stuff. So I love this part. Again, some of the biological--
global cycling of nitrogen. We talked about nitrogen
fixation, that triple bond. It's really hard to
break nitrogen apart, but bacteria can do it. It does it using
transition metals. Fixing carbon,
hydrogenase, if you want to make hydrogen fuel
cells that are more biological. Again, biology uses
transition metals in this. Making vitamins, making
deoxynucleotides, respiration, photosynthesis, it's all
due to transition metals. All right. So we'll start with
just one example, or one of In Our
Own Words segment. And this focuses on
nickel, which is something very important in bacteria. And this is actually an example
from a collaborative project between my lab and course 6. And I know a lot
of you are thinking about being course
6 majors, so I thought I would tell you
about some research of Collin Stultz, a course 6 professor. So he was doing some
computational analysis on these proteins
that we're studying. So many of you at this
point in the semester probably feel like you
might be getting an ulcer. But unless you have
H. pylori in your gut, you probably are not
actually getting an ulcer. And you just take a little
B12, you'll feel a lot better. OK. So here's the video. [VIDEO PLAYBACK] - My name is Sarah Bowman, and
I am a post-doctoral fellow at MIT. I am working on
studying a protein from Helicobacter pylori,
which is pathogenic bacteria. Its kind of ecological niche
is in mammalian stomachs. It's actually very difficult
to treat using antibiotics, because a lot of times
when you're given antibiotics they're going
to actually be broken apart by the acidity of the stomach
before they actually ever get to killing the
Helicobacter pylori. Transition metals in
biological systems are actually really important. They increase the
range of reactivity that proteins and enzymes
are able to access. Nickel is a transition metal. I mean, it's a transition
metal that's actually fairly rare in biological systems. So one of the big things that
H. pylori uses nickel for is an enzyme called urease. Urease requires something like
24 nickel ions, which is a lot. Urease is one of
the proteins that allows for a lot of buffering
capacity of the organism, of the H. pylori organism. The stomach pH is very
low, so pH 2-something. And this bacteria has to
swim through the stomach and then colonize it. And you'd think that the stomach
would just break it apart like it breaks apart your food. But in fact, the bacteria
itself has mechanisms in place that allow it to
create buffers that allow it to move
through the stomach and live in the stomach. And one of those enzymes, and
it's really important for that, is urease. In humans, nickel, as
far as we can tell, is not essential
for any enzymes, whereas in Helicobacter
pylori, for instance, nickel is an essential
transition metal. And so a really intriguing
thing to kind of think about is just whether we could somehow
target the nickel requirement in this organism and
in other bacteria that would allow us to kill these
pathogenic bacteria while not doing anything that would
be harmful to humans. [END PLAYBACK] CATHERINE DRENNAN:
So I like that video partly because it brings back
acid-base and buffers, as well as talking about
transition metals. And I love the bacteria
being attacked by the acid and then making a buffer
and saving itself. It's awesome. OK. So one of the reasons why
these transition metals are so powerful, they can
do so many things, is that they like
to form complexes, and they like to form complexes
with small molecules or ions. And those ions often will
have a lone pair of electrons, and the metal wants
that electron density. It wants the benefit
of that lone pair. So when you have this
lone pair, the metal will come in contact
with that lone pair, and it'll make a very
happy, very happy metal. And we can think
about this interaction here as the donor atoms
are called ligands. And now let's review something
we learned before about whether this is a Lewis
acid or a Lewis base then. OK, 10 more seconds. That's right. So it's a Lewis base. So if we put this
up here, donor atoms are called ligands,
which are Lewis bases, and the Lewis bases donate
the lone pair of electrons. And again, we can think about
the definition that we've been more used to, where
a base is taking H . It's accepting the
proton from the acid. But there, when it's taking
H , it's taking H without its electrons. So it's actually donating its
loan pairs to form a bond. And then we can think
about Lewis acids. So the acceptor atoms, which
are our transition metals, are Lewis acids. They accept the lone pair. And when an acid that has
a proton on it loses H , it is taking the
electrons with it, because H is leaving
without its electrons. So these definitions
work, but these are sort of more broad definitions. So here, our metals, any
of our transition metals, are going to be our
acceptors, our Lewis acids. And here are a bunch of ligands. We have water. We have NH3. We have CO. They have lone pairs. They can be donor atoms. And the ligands form
complexes with the metals. And the kind of
complexes-- they're often called
coordination complexes, and that's a metal that's
surrounded by ligands. And here's a little example,
a metal in the middle, and it has the
ligands around it. So let's consider this
coordination complex now and think about what this
picture is telling us. So we have our
coordination complex. We have cobalt in the middle,
and we have NH3 groups as our donor ligands. And here this bracket indicates
the overall charge is plus 3. Again, the transition metal
is going to be the Lewis acid. It's going to be accepting
the lone pairs from the Lewis bases, which are the
ligands, or the donor atoms. Now, we can think
about a new term called "coordination number." And that's simply
the number of ligands that are bound to the metal. So a CN number of 6 would
indicate six ligands make up what's called the
primary coordination sphere, which is the things
that are bound directly to the metal. So CN numbers for transition
metals range from 2 to 12, but 6 is probably
the most common. So before we think about the
shapes of these molecules, let's just look at
the notation for this, so coordination
complex notation. So I would write this
structure up here within brackets--
cobalt bracket NH3. You have parentheses around NH3. There's six of those. Another bracket here
with a plus 3 charge, indicating the
charge on everything, this whole structure. But often, coordination
complexes with a plus charge will have counterions around. So there might be, say, three
chlorine minus ions around, and so that could be
written like this, or it could be
written like this. If you see Cl3 outside
of those brackets, it means that
they're counterions. So if I looked at this, I'd
say NH3 is within the brackets. That means it's bound to the
cobalt. So that would tell you there are six things bound to
the cobalt. The Cl is outside. That indicates
it's a counterion. There are three of them. So there are three counterions,
which then tells you the charge must be plus 3. All right. So there is our notation. All right. So now we're back to
thinking about geometries. So this is one of the things
I love about this part. I feel like some
people in the course are just like, new
topic, new topic. Oh, man, when is the new
material going to end? Well, you find you get
enough into chemistry, and you start revisiting topics
you've already seen before. So this is great. All right. So coordination number 6. We haven't maybe heard
coordination number 6, but that's pretty
easy to remember. It's the number of atoms bound. What type of geometry is this? You can just yell it out. Right. So that's octahedral geometry. Again, the solid
triangles coming out indicate they're
coming out at you. Back dashes are going back,
and we have our axial. All right. So let's see how well you
remember CN 5 structures. And you can keep
this up here, and you can tell me what the name
of those two geometries are. All right. Why don't you take
10 more seconds. And here are our structures
in real life down here. People are just like,
I want to put see-saw. No, no. That is the parent
geometry of see-saw, but not see-saw itself. OK. So we have the
trigonal bipyramidal and the square pyramidal. So I'm holding up the
square pyramidal right now. And then we have the trigonal,
because it's trigonal along here, bipyramidal. So it's sort of like
one pyramid here, one pyramid there,
so bipyramidal. And if I took off one
and we had a lone pair, then we would get our
friend the see-saw. OK. Next we have this. What's that one called? AUDIENCE: Square. CATHERINE DRENNAN: Square-- AUDIENCE: Planar. CATHERINE DRENNAN: Planar, yep. And this one? Tetrahedral. And now CN number of 3. What is this one? AUDIENCE: Trigonal-- CATHERINE DRENNAN:
Trigonal planar. It's in a plane kind
of, if I hold the bonds and they don't fall off,
and it's kind of trigonal. And then what
about the last one? AUDIENCE: Linear. CATHERINE DRENNAN: Linear. OK. And let's just run through and
think about the angles as well. With octahedral,
what are our angles? AUDIENCE: 90. CATHERINE DRENNAN: 90. Trigonal bipyramidal? AUDIENCE: 90 and 120. CATHERINE DRENNAN: 90
and 120, that's right. So we have one 120 around here,
and then the top parts were 90. OK. We have the square pyramidal. 90. Square planar? AUDIENCE: 90. CATHERINE DRENNAN: 90. Tetrahedral? AUDIENCE: 109.7? CATHERINE DRENNAN: 109.5. Give credit for 0.7 too. That's quite close. Trigonal planar? AUDIENCE: 120. CATHERINE DRENNAN: 120. And linear? AUDIENCE: 180. CATHERINE DRENNAN: 180, right. So you're going to need to
remember these for this unit, but that's OK because you need
to remember them for the final anyway. So it gives you a nice review. All right. So we got every one. We got them down. Can look up your old notes. Just review. All right. So coordination complexes
also have another name. They can be called chelates. Just another name for
coordination complex. So chelates can be the thing. But you can also
say that the ligand will chelate as
another way of saying that it will bind to a metal. And it can bind more than
once with one or more sites of attachment. And the word "chelate"
comes from claws, and I like that picture. I feel like, yes, these
ligands coming in like claws and binding that metal. They're chelating that metal. So there are different
names depending on how many points of
attachment they have. And we have what's
known as monodentate-- "dent" for dentist or tooth. So that's one point
of attachment. And I bet that without having
seen this material ever before you can tell me
what the rest of these are. What do you think
bidentate means? AUDIENCE: Two. CATHERINE DRENNAN: Two. Tridentate? AUDIENCE: Three. CATHERINE DRENNAN: Tetradentate? AUDIENCE: Four. CATHERINE DRENNAN: Hexadentate? AUDIENCE: Six. CATHERINE DRENNAN: Six, right. There's not one for five. But this is good. So don't lose a point on this. I feel like sometimes
people lose a point on this on the exam. You knew it in class
before I taught it. You don't want to like
somehow work backwards. So this is easy
points right here. Just remember on the
exam, wait a minute, maybe I already know this. All right. So let's look at some
examples of chelating ligands that bind with
multiple points of attachment. And the first one--
we're kind of on a theme today-- is vitamin B12 that
we're going to look at. So this is called
the corrin ring. Cobalt is in the
middle, and that ring binds with four
points of attachment. So it is a tetradentate
ligand, this corrin ring. There is also an
upper ligand, which is 5 prime-deoxyadenosine,
and a lower ligand that's called dimethylbenzimidazole. You don't need to
know their names. Overall, it has six ligands
in octahedral geometry. But the corrin ring is a
very nice biological example of a multidentate ligand. Heme would be the same. I thought I would show you
this rotating around so you get a better sense and tell
you that this structure of this vitamin was determined
by Dorothy Hodgkin, who won the Nobel Prize in
1964 for determining the structure by
crystallography and also solving the structure of penicillin. This was the most
complicated molecule to be solved by crystallography,
and a lot of people said that technique
could never be used to do something that big. She showed that they were wrong. In terms of determining the
structure of penicillin, it was during the war. And people wanted to
make more penicillin, but they had no idea what
the structure was so they didn't know what to make. And she figured
out the structure. And it's a
weird-looking molecule, so no one would have guessed it
without knowing the structure. So for her pioneering
work in crystallography she won the Nobel Prize. All right. So vitamin B12 is one
example of a chelate. Another that's probably more
that you probably hear about the most-- it's almost
synonymous with the word "chelate"-- is EDTA. Here is the EDTA
molecule, and you see that it has
lots of lone pairs that are just dying
to grab onto a metal. So we have six. We have 1, 2, 3,
4, 5, 6, six things that are capable of
chelating that metal. And so here is what
the complex looks like. So the red oxygen can chelate. The green oxygen
here can chelate, the nitrogen here in dark
blue, the other nitrogen in dark blue here, light
blue oxygen here, and also the purple oxygen.
So now why don't you tell me what the
geometry of this would be as a clicker question. You ready? AUDIENCE: Yeah. CATHERINE DRENNAN: Yeah. 10 more seconds. Should be fast hopefully. Yeah, great, 86%. It is octahedral. And sometimes it's a little
bit hard to see that, but I helped you out by
drawing those bonds in black that you needed to look at. So we have four that are in
the plane here, one above and one below here. So that is octahedral geometry. Also, how many
points of attachment? What kind of dentate
ligand is this? It's hexadentate as well. So it has six points
of attachment here. All right. So EDTA is a really
good metal chelator. And part of the reason that
it is such an awesome metal chelator is because of entropy. So we're back to entropy again. So the binding of EDTA to the
metal is entropically favored. And the reason for this is
that metals that are, say, in your body, like if you
happen to eat some lead paint, and that lead is hanging out. It's not just by itself. It's coordinating hopefully
just to water and not to proteins in your body. But when you take some EDTA to
prevent your lead poisoning, one molecule of EDTA
will bind to metal, and all of these waters
are going to be released. So I have over here some
lead with a whole bunch of little waters. This is quite an ordered system. But if I take out all
of those waters here, that's a lot more entropy
going on than what we had. And then you have one
chelating ligand here, and that's a pretty
simple system. So this is ordered. This is disordered. So the binding of EDTA, one EDTA
releases six water molecules, and that makes it very
favorable to do this. And because of that,
chelating molecules, or the chelate effect,
molecules that are chelates, like metal bound to EDTA,
are unusually stable because of this favorable
entropic effect, this release of water. So the release of water, the
release of increasing entropy, drives that metal chelation,
and you sequester your metal, which is really good if you're
trying to avoid lead poisoning. So I think this is a nice
example of our friend entropy driving a reaction. So a lot of you did really
well on the exam talking about factors of delta H and entropy
and when you'd have favorable delta G's. Here's another
nice example where the chelate effect explains why
metal chelates are so unusually stable. All right. So uses of EDTA. I already just told you one. Lead poisoning-- all ambulances
have EDTA in case someone is eating some lead paint. Another thing that EDTA is
used for, which I think is fun, you should all go check if
you buy little packaged goods, and they have a long list
of chemical ingredients. Look for EDTA. It's often there. And it says it's "added
for freshness," which means that bacteria need metals. You have EDTA. EDTA sequesters the metals. The bacteria can't live on
the food that you're eating. So instead of
saying, food additive added to kill the bacteria
that were otherwise growing on your food, they say
added for freshness. And I do think that
is an improvement. All right. Another thing, we've already
talked about the importance of cleaning bathtubs. To chelate calcium
out of bathtub scum, you have EDTA or
other metal chelates. And then I have my
favorite other example of the use of EDTA. This favorite example is in
Hollywood, the movie Blade. How do you kill a vampire? Vampires drink what? AUDIENCE: Blood. CATHERINE DRENNAN: Blood. Blood has? AUDIENCE: Iron. CATHERINE DRENNAN: Iron. EDTA chelates? AUDIENCE: Iron. CATHERINE DRENNAN: Iron. So you get a little
dart, and you have-- you can kind of see
them maybe up here-- they're filled with liquid. That's EDTA. You shoot the vampire with
EDTA, and the vampire just disappears, just kind of
turns to sort of dust. [LAUGHTER] Because it's like mostly iron,
and the iron gets chelated. But it happens right away. But anyway, I think that's cool. Yes, what a good way
to kill a vampire. EDTA, it's brilliant. Excellent use on
Hollywood's part for EDTA. OK. Metal chelates, all
sorts of potential values that they have. OK. So when we're talking about
coordination complexes, we're talking about geometries. Sometimes the atoms can be
arranged in different ways. And when you have these
geometric isomers, they can have very
different properties. So just look at an example here. It's a platinum compound,
a platinum compound who has two NH2 groups
and two chlorine groups. And you could arrange those
in two different ways. You could put the NH3 groups
on one side and the chlorine groups on the other side,
and that would be cis. These are cis to each other. Or you could put a
transconfiguration, where chlorine is here, and
then another chlorine is trans on the other side. And the same with this. So cisplatinum here is a
potent anti-cancer drug. And it has to be cisplatinum
because it binds to DNA, and the two bases of DNA
displace these chlorines. So if they're not on the same
side, it can't bind to the DNA. And so this prevents
the cancer cells from being repaired
from damaging agents. Transplatinum does absolutely
nothing that anyone knows. So it's exactly the
same composition, but because they are different
isomers from each other-- and I have, let's see, ah,
over here-- different isomers of each other-- and so
chlorines on the same side, cis versus the trans--
have completely different properties. So cisplatinum got a lot
of fame because it cured Lance Armstrong of cancer. Lance Armstrong now, of course,
is a much more controversial figure than he was at the time. But still he created
an amazing charity that hopefully is still doing
well despite some of his fall from fame. OK. So another type of
isomer are called optical isomers, also
called enantiomers or chiral molecules. And these are one, again, you
have the same composition, but they are non-superimposable. They are, in fact, mirror
images of each other. So if my head was
a mirror, these would be mirror
images of each other. And I could try very
hard to superimpose them, bringing the blue
molecules over here, but then the green and
the red don't match. You can come and try. These are, in fact,
non-superimposable mirror images from each other. And sometimes they can have
very similar properties. It depends. But if you put
molecules like that that are known as chiral,
chiral molecules, i.e. enantiomers--
non-superimposable mirror images. The human body is very much
of a chiral environment. You have enzymes
designed to bind things in a particular way. So they can have very,
very different properties. OK. So we have to do some d-electron
counting before we end today. And I love this because
it's really pretty simple to count d-electrons. And so we're going to just
take a look at some examples. And for doing this
part, we're going to start using our friend
the periodic table again. And we need to find oxidation
numbers, which we just talked about in the last unit. So if we have a coordination
complex with cobalt, and this cobalt has those
six NH3 groups and our plus 3 charge-- so this is the complex
that we have been talking about-- let's now figure
out what the oxidation number of this is. And so this NH3 is neutral,
so that's given as a hint. Many of our ligands are
going to be neutral ligands. So if that is 0, what is
the charge on the cobalt? AUDIENCE: Plus 3. CATHERINE DRENNAN: Plus 3. Now we're going to use
the rules of d-count. So we have a d-count. We need to look up the group
number from the periodic table, which, in this case, is 9. Then we have minus the oxidation
number, so we have 9 minus 3, or 6. And so this is a d6 system. And that is all there is
to doing these counts. So let's just try another one. So we heard about nickel. We'll do nickel. Nickel is coordinated
by carbon monoxide, and there are four of those. So what is my charge on
the nickel going to be, my oxidation number
of the nickel? So what's my overall
charge of this complex? AUDIENCE: 0. CATHERINE DRENNAN: 0. CO is also going to be 0. There's no charge on CO. So what is the oxidation
number of nickel? AUDIENCE: 0. CATHERINE DRENNAN: 0. So then we can do our d-count. The d-count, what is the
group number for nickel? AUDIENCE: 10. CATHERINE DRENNAN: What is it? AUDIENCE: 10. CATHERINE DRENNAN: 10. This is the kind of math that
always makes me very happy. 10 minus 0 is 10. So that is a d10 system. All right. We'll do one more over here. And the next one is
a clicker question. Gives me time to write AUDIENCE: Whenever you're ready. We're out of time. CATHERINE DRENNAN: Yep. All right. Let's just do 10 more seconds. Yep. So here our overall
charge is minus 1. We have the chlorines
are minus 1. NH3 is 0. Water is 0. So this has to be plus 2 because
plus 2 minus 3 is minus 1. We have 9 minus 2 is
7, so it's a d7 system. All right. So Wednesday, d orbitals. I cannot wait. Yes. All right, 10 seconds. OK. Does someone want to tell me
why that's the right answer? Anybody? We got a nice dangly
thing for your keys or ID. No? All right. So here we're thinking about
whether things are better reducing agents or
better oxidizing agents. And here we're given two
different redox potentials-- minus 600 and minus 300. So the one that is going
to be the lower number is going to be better at
reducing other things. It wants to be oxidized itself. And then we can think
about whether it's a favorable process in terms
of whether the thing that likes to reduce is actually
doing the reducing. That's going to make it
a spontaneous process. All right. So these are the
kinds of questions for the oxidation-reduction
unit that we just finished. And this will be on exam 4,
which, amazingly, we just finished an exam, and
there's another one. So exam 4 is two
weeks from today. All right. From Friday, sorry,
two weeks from Friday. All right. So today we're going to continue
with this unit on transition metals. The next exam is going to
have oxidation-reduction and transition metals and
a little bit of kinetics. Kinetics is our last unit. So we're getting very close
to the end of the semester. So we're finishing up the
handout from last time. Again, we're back to
the periodic table. We're thinking about
transition metals. We're thinking about that middle
part of the periodic table, and so we're thinking
about d orbitals. So there are five d orbitals. How many s orbitals are there? AUDIENCE: One. CATHERINE DRENNAN: One. How many p orbitals are there? AUDIENCE: Three. CATHERINE DRENNAN: Three. And so d orbitals have five. And we're not going to
talk about really anything beyond d orbitals in this class. And frankly, not
very many people do. But d orbitals are amazing,
so we have to fit them in. All right. So there are five d orbitals. And they're up
here, and you need to be able to draw their shapes. And the bar for drawing the
shapes is actually pretty low. So these are my
drawings that I made. And so you can probably
do just about as well. All right. So the one that has
the most unusual shape is the dz squared. And so it has its maximum
amplitude along the z-axis. And for this unit,
our z-axis is always going to be up and down here. y is in the plane of the screen,
and x is coming out toward you and also going into the screen. And so dz squared has its
maximum amplitude along z, and it also has a
doughnut in the xy-plane. And so I also brought
a little model of this. So here's dz squared. We have maximum amplitude
along the z-axis, up and down. And we have our little
doughnut in our xy-plane. So then we have dx squared
minus y squared, which has maximum amplitude
along x and along y. And that would look like this. So we have our
maximum amplitudes that are right on axis. So if this is y-axis and x
is coming out toward you, those orbitals are
pointing right along that coordinate frame. The other three orbitals
look a little bit like dx squared minus y squared,
but they're not on-axis. They're off-axis. They're in between the axes. So we have dyz. It has its maximum
amplitude 45 degrees off of the y and the z-axis. So if this is
z-axis here, there's no maximum amplitude along here. It's 45 degrees off. So it's right in the middle
between the z and the y. So dxz has its maximum amplitude
45 degrees between x and z. So that would be
pointing the other way. And so I tried to
draw this keeping the reference frame the same. It's a little hard
to see the orbitals, but it would be kind of this. So we rotate that
around, and so that's what that would look like. And then dxy we have maximum
amplitude 45 degrees in between the x and the y. So x coming out, y in the plane. And so this is, again, a
little bit hard to draw. If I drew it absolutely
perfectly and not tilted at all, you kind of
wouldn't see anything. But that's what that
would look like. So again, the names
of this, it tells you about the relationship
between that orbital, that maximum amplitude, and
the axis that we have defined. So this is very
important to know that these guys are in
between the axes, right in the middle, 45 degrees. And you'll see why in a few
minutes why that's important. OK. So just to practice, here are
some slightly better pictures of the orbitals. And this is the coordinate
frame over here, and now we have the
orbitals inside that. So again, z is going up, y is
in the plane of the screen, and x is going back and
also coming out toward us. So which is this d orbital? You can just yell it out. AUDIENCE: dz squared. CATHERINE DRENNAN: dz. Yeah, that's easy to remember. That's the unique-looking one. What about this one? First think about the plane. So it's the xy-plane. And then, is it on or off-axis? So which one is this? AUDIENCE: [INAUDIBLE] CATHERINE DRENNAN: Yeah. So this one is on-axis. You can see the
maximum amplitude of the orbital pointing
right along those axes. So it's right in the corners
of that square there. And then what about
this one down here? AUDIENCE: [INAUDIBLE] CATHERINE DRENNAN: Yep. So that would be dxy. So it's in the xy-plane, but
it's 45 degrees off the axes. So it's in between
the axes here. And what about that one? AUDIENCE: . CATHERINE DRENNAN: Right. So it's along both z and y here. And then this last
one, which is drawn to kind of come out toward you,
so that is along x as well. So that's dxz, and
it's going up along z. So you can look at the
coordinate frame, which we'll try to keep consistent,
and ask yourself, is it on-axis or off-axis,
and which plane is it in? And that will allow you to name
them and also to draw them. So just to kind of give you more
of a three-dimensional sense, there's these little movies
that I'll show you now. And so you can get a better
sense of that awesome doughnut. It's going to make you hungry. They even colored it like a
really nice original doughnut that you would get
at Dunkin' Donuts. So the doughnut is
in the xy-plane, and these other
lobes are along z. So now we have dx
squared minus y squared, and you can see that the
maximum amplitudes, again, are along the axes. Key-- they're along
the axes here. I don't know why it
comes out towards you and-- I didn't, yeah. But it gives you a good
three-dimensional sense of this. All right. So dxy now, again,
in the xy-plane. But instead of being on-axis,
it's 45 degrees off-axis. So you can see, I think,
in this really nicely, it's right between the axes,
but it's not touching them. The axes sort of
separate these orbitals. And then we have xz. So now we're going up along
the z-axis and in the x-plane. And here it comes at you again,
45 degrees in between z and x. And then our last
one, we have yz. So the shapes of
those later three, actually even four of
them, are the same. It's just a matter if
they're on or off-axis and which plane they're in. So this is not too hard to draw. All right. So why is this important? Why should we care exactly
how the orbitals are oriented? And the reason that you
should care about that is because it can explain a
lot of the special properties of transition metals.
