Crystal (really “Ligand”) Field Theory
Ppt07(PS11) 1

Goals
• Learn that when ligands bind to a metal complex, the d orbital sublevel becomes further
“split” into sub-sublevels
– Electronic transitions between these sub-sublevels absorb visible light, causing “color”
• Learn what is meant by “strong field” and “weak field” cases, and how these impact the electron configuration (and paramagnetism).
• Use these ideas to explain why different complexes of the same TM cation have different colors (ruby vs emerald)
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Review, electron configurations for TM cations (& # d electrons)
• Earlier
(self study worksheet or exercise), you learned how to determine the number of d electrons in a transition metal (TM) cation
• Example, Ru 3+
– Ru, 44 electrons. Kr, 36 electrons

44-36 = 8

8 e s “past” Kr
– Ru 3+ , remove 3 electrons

8-3 = 5 e -
– All electrons go into d sublevel (not s )
[see next slide for “explanation” if you wish]

5 d electrons, [Kr] 5 s 0 4 d 5
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Creating Cations from Transition Metal
(TM) Atoms
• Recall that when filling up orbitals in ATOMS, the n s fills before the ( n -1) d (e.g., the 4 s fills before the 3 d , etc.).
– We said that this is because the 3d orbital is “higher in energy” than the 4s. (shapes/shielding issue)
• It turns out that once an electron (or more) is removed
(i.e., once you make a cation )
, the (n-1) d level becomes lower than the n s ! (see next slide)
[You are not responsible for knowing why this is so. Ask me in person if you wish.]
– This means that the electron configurations for the TM cations have no electrons in the ns subshell
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Effect of removing an electron on relative energies of orbital sublevels
3 d
4 s remove electron(s)
4 s
3 d
Neutral TM Atom
TM Cation
(I.e., once one or more electrons have been removed)
This switching of positions of the n s and ( n1)d sublevels is why there are no “s” electrons in TM cations. They would “fall down” to the ( n -1)d sublevel which is
(now) lower in energy. Electrons are not “removed from the s sublevel” first!
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Effect of removing an electron on relative energies of orbital sublevels
3 d
3 d
4 s remove electron
4 s
4 s
Fe: [Ar] 4 s 2 3 d 6
Neutral TM Atom
Fe +
3 d
: [Ar] 4 s 0 3
TM Cation d 7
NOTE: This example is for illustrative purposes. Fe is usually in the +2 or +3 oxidation states in complexes. However, see Nature Chemistry, 5 , pp 577 –
581 (2013) for an interesting example of a linear iron(I) complex.
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8
7

Review, Orbital Diagrams
• You also learned to make an orbital diagram for a TM cation:
• Ru 3+ : [Kr]
5 s 4 d
OR [Kr] __ __ __ __ __ __
5 s 4 d
• NOTE: This orbital diagram is for a “free” metal cation. I.e. With nothing bonded to it
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Ligand Field Theory
• Text refers to “crystal field theory”.
Simpler, but not “valid”.
• Ligand theory is better, but full treatment beyond the scope of this course
• KEY IDEA: When ligands bind to a metal cation, the ligand orbitals affect the energy of the metal’s d orbitals--some d orbitals’ energies go up, and some go down. We say that the d orbtial sublevel “splits” (into sub sublevels). See diagram, next slide.
Ppt07(PS11) 9

When 6 Ligands Surround a TM cation (octahedral environment), the d -orbital sublevel splits into two
“sub sublevels”
(my terminology)
Refer back to Slide 6 to see that this is what we did “before”
This is called the dorbital “splitting pattern” for an octahedral complex. This is the only splitting pattern you need to know for my class (it would change for different geometries and
C.N.s). You do not need to know that the top two orbitals are the z 2 and x 2 -y 2 , etc. Just know that there are “two up” and “three down”.
Light & Color 10

Splitting Pattern and
D
, the splitting energy
• The energy difference between the lower
“sub sublevel” and the higher one is called the “splitting energy”, with symbol D
• D is just short for
D
E
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D varies in different complexes, but is always small compared to “ s to p ” or “ p to d ” gaps!
(this is not obvious from text)
4 d
4 p
4 s
4 d
Free cation
D
4 p
4 s
Cation in octahedral complex
Light & Color 12

(earlier PowerPoint):
• Absorption of one photon of visible light corresponds to the excitation of one electron from a lower energy orbital to a higher energy one
• The bigger the D
E (energy difference or gap) between the orbitals, the greater the E photon absorbed
• Different gaps yield different colors absorbed, and thus different colors perceived
• Changing the D E in a metal complex (or other “dye” molecule) will change the color of the complex (or dye)
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The value of
D , although it varies, is “just right” to absorb photons of visible light!
( l 
400 – 800 nm)
This is why transition metal complex are usually colored! The small splitting that develops, results in
“gaps” that absorb some visible colors, leaving others to reach our eyes! (More on this later.)
Light & Color 14

The greater the value of
D
, the
“stronger the
(crystal or ligand) field”
• Recall that the reason for the splitting of the d orbitals sublevel was the presence of a
(crystal or ligand)
field.
– Think of this “field” as being like an
“environment”, imposed by the ligands.
• So hopefully it makes sense that the
“stronger the field” imposed by the ligands, the greater the
D
.
– “ strong field” means a bigger
D
– “ weak field” means a smaller
D
Ppt07(PS11) 15

Different ligands tend to impose different “field strengths”
• Ligands that tend to make a smaller D are called
“weak field” ligands
• Ligands that tend to make a larger D are called
“strong field” ligands
– You do not need to memorize which ligands are of which type. You just need to know the concept (and meaning of “strong / weak field”
– Recall the “Fun with colors” expt! Ni 2+ with different ligands had different colors!
• The type of metal cation also affects D
(but again, you just need to know that this is “so”, not “how” or “who does what”)
Ppt07(PS11) 16

Next task…
• Now let’s see how we can “populate” the d -orbitals of a TM complex with electrons
– This is important because of some of the properties of TM complexes that we’ll discuss later (paramagnetism, color).
• This is similar to creating an orbital diagram, except there is a “new” consideration (as you will see)
• We’ll start with a review…
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Energy Considerations (reminder)
(briefly look back to slide 6 before looking below)
Why isn’t the config. for Ru 3+ this one?
[Kr]
4 d 5 p
Ans: Because that configuration would have higher energy than the one on the previous slide. This configuration would describe an “excited state” of Ru 3+ . That electron in the 5 p orbital wouldn’t stay there. It would
“fall down” to the 4 d .

When we write electron configurations or orbital diagrams, we assume ground state configurations .
We “want” the lowest overall energy possible.
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Hund’s Rule (revisited)
• OK, but what about this one? Why is this is not the correct config?
[Kr]
4 d
Ans: This also has a higher energy! This also represents an “excited state” configuration!
Why? Because it takes a bit of energy to put two electrons into the same orbital
(electrons repel, right? See next slide for more detail if you like).
I call the amount of
“energy cost” to put two electrons in the same orbital the pairing energy (P).
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Recap: It “costs” energy to pair up electrons in the same orbital
• Electrons repel, so having them in the same orbital makes the energy of the system a bit higher
• The amount of energy it “costs” to pair up two electrons is called the “pairing energy”
• P = “pairing energy”
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In the past, you could sort of ignore the pairing energy
• In the past, once you had put one electron into each sublevel of a “set”, you would then pair up the electrons before populating the next higher sublevel:
3s
Next electron would go into 2 p , paired, rather than putting it up
“higher” into the 3 s
2p
This is because the price to pair up the electron is much less than the energy needed to “get up to” that 3 s orbital (the 2 p – 3 s
“gap”). This was never addressed in 1 st semester, but please take a moment to make sure you understand this now.
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Summary of last slide’s “concept”
• When “filling up” an orbital diagram, you don’t pair up electrons unless the “price” to go up to the next level is more than the pairing energy
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Preparation for next slide
• On the following slide, two complexes are compared. Both involve Co 3+ , but in one case
(with F ’s), the ligands create a “weak field” and in the other
(with CN ’s),
, they create a “strong field”
• In the “weak field” case, the D is so small that it has become smaller than the pairing energy .
• As a result, the fourth electron placed into the diagram goes “up” into the higher level rather than pairing up in the lower one! (Click and look below to see the “sequence” of filling)
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Low enough
D results in electrons NOT pairing right away
P (fixed value)
 weak-field
 D
< P
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 strong-field
 D
> P
24

Explanation of the “high spin” and “low spin” designations on prior slide
• As will be discussed on the next couple of slides, an unpaired electron has something called a
“spin” and has its own magnetic field.
• Thus, the more unpaired electrons, the greater the total spin.
• The left complex had four unpaired electrons.
The right complex had none (which is fewer than four!). So the left one is called “high spin” and the right one “low spin”
• When there is a difference in total spin, the “high spin” one is always the “weak field” one.
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• Electrons have a “spin” (up or down)
• “Spin” is a Magnetic property
– single electron (spin) will attract a magnetic field (“ paramagnetic ”)
• If multiple electrons have the SAME spin in a complex, the complex will be MORE attracted to a magnetic field ( more paramagnetic)
– Two paired electrons (one up, one down) have no net “spin” (they cancel out)
• NOT attracted to a magnetic field
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• THUS:
• If a complex has ALL ITS ELECTRONS PAIRED
(“no spin”), then the complex:
– Will NOT attract a magnetic field
– Is called diamagnetic
• If a complex has ONE or MORE UNPAIRED electrons, it:
– WILL attract a magnetic field
• And the more unpaired electrons (the “higher the [total] spin”), the stronger the force of attraction
– Is called paramagnetic
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• D must have an energy that falls in the range of energies of visible light (photons)
– If too large, absorption band is in the UV (or higher) range
– If too small, absorption is in the IR (or lower) range
(almost never is this small for electronic transitions)
• “bottom” energy level must contain at least one electron
(or else nothing to “excite”!)
• “top” energy level must have at least one “vacancy” (or else nowhere for an electron to “go” to!)
• Result?
– If no d electrons, no color (Ti 4+ )
• Salts containing Al 3+ or Gp I and Gp II cations
– If 10 d electrons, no color
• Complexes/compounds containing Zn 2+ (or Gp III-Gp V metal cations)
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D
(per electron)
l
If l max for some absorption band is 795 nm (red end
 low energy):
D _
(per e )

E photon

 
8


(per photon)
(or electron)


2.500 x 10 electron
-19 J


6.022 x 10 emol of e-'s


 J mol
J mol

1000 J/kJ
 151 kJ/mol
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