Intro to Crystal Field Theory - Video Tutorials & Practice Problems
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1
concept
The study of ligand-metal interactions helped to form Ligand Field Theory which combines CFT with MO Theory.
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In this video on the intro to crystal field theory, we're going to see that transition metal coordination compounds form crystalline solids. Now if we take a look here, we see this beautiful gem, this red gem. Well, crystal field theory was developed to explain the color, as well as the magnetism or magnetic properties of coordination compounds. In fact, we're gonna say that coordination compounds form crystals. When we say crystal in the song, we're talking about crystals, hence the name for color within the name. And we're going to say it also focuses on the effects of ligands' electric field around the metal cations. Now ligands surround and create this type of magnetic well, this electric field around a metal cation. That's why the word field is also in the name. Later on, this helped to create what's known as ligand field theory. It's just a combination of crystal field theory with molecular orbital theory. So that's the origins of this whole idea of crystals and colors and magnetic properties. So as we delve into different types of complexes, we'll be touching on a little bit of each of these ideas within our videos.
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concept
The greater the interaction between the metal and its ligands then the greater the energy of its d orbitals
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When it comes to ligand orbital interactions, we're going to say that the interaction between them is electrostatic. And we're gonna say we're gonna have an increase in the energies of metal d orbitals, which in turn causes an increase in their interactions, which increases our energy. Just understand that we are gonna have like charges, and like charges repel one another. So we're gonna have the electrons of the metal cation interacting with the electrons of our ligands. This repulsion between them causes this increase in energy. So if we take a look here, we have our up arrow which is showing an increase in energy. And what we have here initially are 5 orbitals, 5 d orbitals. We're gonna say these are metal d orbitals without a ligand attached. Once we bring in a ligand and attach it to the metal cation, again, we have to compete. We have this repulsive behavior between the electrons of the metal cation and the electrons of the ligands. This is gonna cause an increase between the interactions of their electrons. So these higher energy orbitals here are just the metal d orbitals with the ligand or ligands attached. So take from this, as as we add ligands to our metal cations, we're gonna see an uptick in the energy of the d orbital electrons of the metal cation.
3
concept
For octahedral complexes, the greatest ligand-metal interactions occur on or along the axes.
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Now in terms of the interactions in octahedral complexes, we're going to say that the strength of ligand orbital interactions depend on complex geometry and d orbital orientation. We're gonna say here that for octahedral complexes, the ligands are on the axes. Remember, we say on the axis or along the axis. They're both synonymous with one another. We're gonna say on the axis, orbitals have the greatest interaction interactions with the ligands. So if we take a look here, what we have is a representation of our octahedral species. So think of it like 2 square pyramids that are stacked on top of each other or stacked inversely to each other, their bases touching one another. So we have these 6 points which represents our ligands, and in the center, we have our metal cation in theory. Now on the axes, we'd say that the greatest interaction again happens on the x and y axes here for this one, so it's d x squared minus y squared, and then this one we have the most interactions happening on the z axis, so d z squared. In these 2 on the axis examples, we'd say that an increase in interaction causes an increase in energy. Now in between the axis, we have our other 3 orbitals. These don't line up in the correct orientation to have the greatest interaction. So we're gonna say we have less interaction in this setup, which would cause a decrease in energy or less energy involved. So just remember, when it comes to octahedral species themselves, the greatest interaction is happening on the axes or along the axes. So in particular, we're talking about d sub x squared minus y squared and d sub z squared. So just keep that in mind.
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example
Example
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Here it says, which set of d orbitals below will interact the most with the ammonia ligands in within this coordination complex? Alright. So remember, this is our complex ion portion, and this is what we care about. The chlorine over here is just a counter ion. Now here we have 6 ammonia molecule ligands attached to our iron. So this is an octahedral complex. And when it comes to octahedral complexes, the greatest interactions are happening along the axes or on the axes. And that only happens for 2 types of orbitals, and they would be d sub x squared minus y squared, and d sub z squared. If we look at our options, the only one that has only those 2 orbitals and nothing else would be option e. So here, option e would be our final answer.
5
concept
For tetrahedral complexes, the greatest ligand-metal interactions occur in between the axes.
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Now with interactions in tetrahedral complexes, we're going to say that the ligands are aligned in between the axes. And we're gonna say in between the axes, the orbitals there have the greatest interactions with the ligands. So if we take a look here, think of a cube. The cube here, we have our 4 points in terms of this cube. And we're gonna say that this point and this point are the ones that are nearest us, and you can see that these two dots here are smaller because they're in the back. If you were to take those 4 points and have them represent our 4 ligands, you could shift this over and put it amongst all of these axes, your x, y, and z axes. Now remember, in between the axes deals with dxy, d y z, and d x z. Along where all the axes, well, that's reserved for d sub x squared minus y squared and d sub z squared. Now remember, for tetrahedral complexes, the greatest interaction is in between the axes. So here we have the greatest interaction amongst these 3 orbitals, which will result in the greatest amount of energy. For the ones on the axes, they don't quite line up in the way that has the greatest interaction between the ligand and the metal cation. Because of this, we're gonna see a decrease in interaction, which is gonna result in a decrease in energy. So remember, with tetrahedral complexes, the greatest interaction between the metal cation and the ligand, lies in between the axes, and keep in reference these particular d orbitals, dxy, d y z, and d x z.
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example
Example
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Identify the d orbital or orbitals with the highest energy in the complex shown below. Here we have zinc as our metal cation connected to 4 hydroxide ions. Doing this gives us an overall charge of 2 minus. Now the way that it's depicted shows that this is a tetrahedral complex. And with tetrahedral complexes, the greatest interaction happens in between the axes. Remember, the ordals that lie in between the axes would be dxy, d y z, and d x z. These remaining 2 are the ones that are along the axes or on the axes, so they would not have the greatest interaction. So a, b, and c are the correct orbitals, and because of that the answer would have to be option g. So we're talking about A, B, and C as being the d orbitals with the highest energy in this tetrahedral complex.
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Problem
Problem
For an octahedral complex, which set of d orbitals is expected to be at the lowest energy?
A
dxy, dyz, dz2
B
dyz, dxz, dz2
C
dxy, dyz, dxz
D
dxy, dyz, dx2–y2
E
dyz, dx2–y2, dz2
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