chemistry 1000 lecture 26: crystal field theorypeople.uleth.ca/~roussel/c1000/slides/26color.pdf ·...
TRANSCRIPT
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Chemistry 1000 Lecture 26: Crystal field theory
Marc R. Roussel
November 6, 2018
Marc R. Roussel Crystal field theory November 6, 2018 1 / 18
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Crystal field theory
The d orbitals
−20−10−20
−20
−10
−10
0
0
0
10
10
20
2010 y
z
20x
−20
−10
−24
−20
−20
−16
−12
−10
−8
−400
0
4
8
10
12
16
20
20
24
10y
z
20x
3dx2−y2 3dz2
−20−10−20
−20
−10
−10
0
0
0
10
10
20
2010 y
z
20x
−20−10−20
−20
−10
−10
0
0
0
10
10
20
2010 y
z
20x
−20−10−20
−20
−10
−10
00
0
10
10
20
2010 y
z
20x
3dxy 3dxz 3dyz
Marc R. Roussel Crystal field theory November 6, 2018 2 / 18
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Crystal field theory
Crystal field theory
In an isolated atom or ion, the d orbitals are all degenerate, i.e. theyhave identical orbital energies.
When we add ligands however, the spherical symmetry of the atom isbroken, and the d orbitals end up having different energies.
The qualitative appearance of the energy level diagram depends onthe structure of the complex (octahedral vs square planar vs. . . ).
The relative size of the energy level separation depends on the ligand,i.e. some ligands reproducibly create larger separations than others.
Marc R. Roussel Crystal field theory November 6, 2018 3 / 18
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Crystal field theory
Octahedral crystal fields
In an octahedral complex, the dx2−y2 and dz2 orbitals point directly atsome of the ligands while the dxy , dxz and dyz do not.
This enhances the repulsion between electrons in a metal dx2−y2 ordz2 orbital and the donated electron pair from the ligand, raising theenergy of these metal orbitals relative to the other three. Thus:
∆
dddxy xz yz
z2 x2−y2dd
z2 x2−y2dd
isolated atom atom in octahedral field
dddxy xz yz
∆ = crystal-field splitting
Marc R. Roussel Crystal field theory November 6, 2018 4 / 18
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Crystal field theory
Crystal-field splitting
Note: Sometimes we write ∆o instead of ∆ to differentiate thecrystal-field splitting in an octahedral field from the splittingin a field of some other symmetry (e.g. ∆t for tetrahedral).
Marc R. Roussel Crystal field theory November 6, 2018 5 / 18
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Crystal field theory
Electron configurations
At first, just follow Hund’s rule, e.g. for a d3 configuration,
dddxy xz yz
z2 x2−y2dd
P = pairing energy = extra electron-electron repulsion energyrequired to put a second electron into a d orbital + loss of favorablespin alignment
Marc R. Roussel Crystal field theory November 6, 2018 6 / 18
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Crystal field theory
For d4, two possibilities:
P < ∆ P > ∆
2 x2−y2dd
dddxy xz yz
z
dddxy xz yz
z2 x2−y2dd
low spin high spin
Experimentally, we can tell these apart using the paramagnetic effect,which should be twice as large for the high-spin d4 than for thelow-spin d4 configuration.
Marc R. Roussel Crystal field theory November 6, 2018 7 / 18
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Crystal field theory
Spectrochemical series
We can order ligands by the size of ∆ they produce.
=⇒ spectrochemical series
A ligand that produces a large ∆ is a strong-field ligand.
A ligand that produces a small ∆ is a weak-field ligand.
(strong) CO ≈ CN− > phen > en > NH3 > EDTA4− > H2O >ox2− ≈ O2− > OH− > F− > Cl− > Br− > I− (weak)
Marc R. Roussel Crystal field theory November 6, 2018 8 / 18
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Crystal field theory
Example: Iron(II) complexes
Electronic configuration of Fe2+: [Ar]3d6
[Fe(H2O)6]2+ is high spin:
2 x2−y2dd
dddxy xz yz
z
From the spectrochemical series, we know that all the ligands afterH2O in octahedral complexes with Fe
2+ will also produce high-spincomplexes, e.g. [Fe(OH)6]
4− is high spin.
(strong) CO ≈ CN− > phen > en > NH3 > EDTA4− > H2O >ox2− ≈ O2− > OH− > F− > Cl− > Br− > I− (weak)
Marc R. Roussel Crystal field theory November 6, 2018 9 / 18
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Crystal field theory
Example: Iron(II) complexes (continued)
[Fe(CN)6]4− is low spin:
2 x2−y2dd
dddxy xz yz
z
Somewhere between CN− and H2O, we switch from low to high spin.
(strong) CO ≈ CN− > phen > en > NH3 > EDTA4− > H2O >ox2− ≈ O2− > OH− > F− > Cl− > Br− > I− (weak)
Marc R. Roussel Crystal field theory November 6, 2018 10 / 18
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Absorption spectroscopy
Color
Typically in the transition metals, ∆ is in the range of energies ofvisible photons.
Absorption:
2 x2−y2dd
dddxy xz yz
z
+hν →2 x2−y2dd
dddxy xz yz
z
Colored compounds absorb light in the visible range.The absorbed light is subtracted from the incident light:
White light Absorption spectrum Transmitted light
Inte
nsity
λ λ
Ab
so
rptio
n
Inte
nsity
λ
Marc R. Roussel Crystal field theory November 6, 2018 11 / 18
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Absorption spectroscopy
Example: copper sulfate
CuSO4 · 5 H2O CuSO4 solution vs blank
Marc R. Roussel Crystal field theory November 6, 2018 12 / 18
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Absorption spectroscopy
Example: copper sulfateVisible spectrum
CuSO4 in water
violet blue green red
ye
llo
w
ora
ng
e
Marc R. Roussel Crystal field theory November 6, 2018 13 / 18
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Absorption spectroscopy
The color wheel
Colors in opposite sectors are complementary.
Example: a material that absorbs strongly in the red will appear green.
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Absorption spectroscopy
Simple single-beam absorption spectrometer
sample detectormonochromatorsource
Marc R. Roussel Crystal field theory November 6, 2018 15 / 18
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Absorption spectroscopy
Dual-beam absorption spectrometer
source monochromator
beam
splitter
mirror
sample
blank
mirror
comparator
Marc R. Roussel Crystal field theory November 6, 2018 16 / 18
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Absorption spectroscopy
Example: Cobalt(III) complexes
The [Co(H2O)6]3+ ion is green.
From the color wheel, this corresponds to absorption in the red.
The [Co(NH3)6]3+ ion is yellow-orange.
It absorbs in the blue-violet.
The [Co(CN)6]3− ion is pale yellow.
It absorbs mostly in the ultraviolet, with an absorption tail in theviolet.
Note that these results are consistent with the spectrochemical series:The d level splitting is orderedH2O < NH3 < CN
−.
Marc R. Roussel Crystal field theory November 6, 2018 17 / 18
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Absorption spectroscopy
Examples: Colorless ions
Titanium(IV) ion =⇒ d0 configuration
Zinc(II) ion =⇒ d10 configuration
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Crystal field theoryAbsorption spectroscopy