6 s ligands x 2e each

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ML6 s-only bonding
d0-d10 electrons
The bonding orbitals, essentially the ligand lone
pairs, will not be worked with further.
6 s ligands x 2e each
2
p-bonding may be introduced as a perturbation of
the t2g/eg set Case 1 (CN-, CO, C2H4) empty
p-orbitals on the ligands M?L p-bonding (p-back
bonding)
These are the SALC formed from the p orbitals of
the ligands that can interac with the d on the
metal.
t2g (p)
t2g
eg
eg
t2g
t2g (p)
ML6 s-only
ML6 s p
(empty p-orbitals on ligands)
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p-bonding may be introduced as a perturbation of
the t2g/eg set. Case 2 (Cl-, F-) filled
p-orbitals on the ligands L?M p-bonding
eg
eg
t2g (p)
t2g
t2g
t2g (p)
ML6 s-only
ML6 s p
(filled p-orbitals)
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Putting it all on one diagram.
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Spectrochemical Series
Purely s ligands D en gt NH3 (order of proton
basicity)

• donating which decreases splitting and causes
  high spin
• D H2O gt F gt RCO2 gt OH gt Cl gt Br gt I (also proton
  basicity)

p accepting ligands increase splitting and may be
low spin
D CO, CN-, gt phenanthroline gt NO2- gt NCS-
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Merging to get spectrochemical series
CO, CN- gt phen gt en gt NH3 gt NCS- gt H2O gt F- gt
RCO2- gt OH- gt Cl- gt Br- gt I-
Weak field, p donors small D high spin
Strong field, p acceptors large D low
spin
s only
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Turning to Square Planar Complexes
Most convenient to use a local coordinate system
on each ligand with y pointing in towards the
metal. py to be used for s bonding. z being
perpendicular to the molecular plane. pz to be
used for p bonding perpendicular to the plane,
p. x lying in the molecular plane. px to be
used for p bonding in the molecular plane, p.
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ML4 square planar complexes ligand group orbitals
and matching metal orbitals
s bonding
p bonding (in)
p bonding (perp)
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ML4 square planar complexes MO diagram
eg
s-only bonding
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A crystal-field approach from octahedral to sq
planar
Less repulsions along the axes where ligands are
missing
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A crystal-field aproach from octahedral to sq
planar
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The Jahn-Teller effect
Jahn-Teller theorem there cannot be unequal
occupation of orbitals with identical energy
Molecules will distort to eliminate the degeneracy
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Angular Overlap Method
An attempt to systematize the interactions for
all geometries.
The various complexes may be fashioned out of the
ligands above
Linear 1,6 Trigonal 2,11,12 T-shape 1,3,5
Square pyramid 1,2,3,4,5 Octahedral 1,2,3,4,5,6
Tetrahedral 7,8,9,10 Square planar
2,3,4,5 Trigonal bipyramid 1,2,6,11,12
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Contd
All s interactions with the ligands are
stabilizing to the ligands and destabilizing to
the d orbitals. The interaction of a ligand with
a d orbital depends on their orientation with
respect to each other, estimated by their overlap
which can be calculated. The total
destabilization of a d orbital comes from all the
interactions with the set of ligands. For any
particular complex geometry we can obtain the
overlaps of a particular d orbital with all the
various ligands and thus the destabilization.
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ligand dz2 dx2-y2 dxy dxz dyz
1 1 es 0 0 0 0
2 ¼ ¾ 0 0 0
3 ¼ ¾ 0 0 0
4 ¼ ¾ 0 0 0
5 ¼ ¾ 0 0 0
6 1 0 0 0 0
7 0 0 1/3 1/3 1/3
8 0 0 1/3 1/3 1/3
9 0 0 1/3 1/3 1/3
10 0 0 1/3 1/3 1/3
11 ¼ 3/16 9/16 0 0
12 1/4 3/16 9/16 0 0
Thus, for example a dx2-y2 orbital is
destabilized by (3/4 6/16) es 18/16 es in a
trigonal bipyramid complex due to s interaction.
The dxy, equivalent by symmetry, is destabilized
by the same amount. The dz2 is destabililzed by
11/4 es.
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Coordination Chemistry Electronic Spectra of
Metal Complexes
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Electronic spectra (UV-vis spectroscopy)
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Electronic spectra (UV-vis spectroscopy)
hn
DE
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The colors of metal complexes
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Electronic configurations of multi-electron atoms
What is a 2p2 configuration?
n 2 l 1 ml -1, 0, 1 ms 1/2
These configurations are called microstates and
they have different energies because of
inter-electronic repulsions
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Electronic configurations of multi-electron
atoms Russell-Saunders (or LS) coupling
For the multi-electron atom L total orbital
angular momentum quantum number S total spin
angular momentum quantum number Spin multiplicity
2S1 ML ?ml (-L,0,L) MS ?ms (S, S-1,
,0,-S)
For each 2p electron n 1 l 1 ml -1, 0,
1 ms 1/2
ML/MS define microstates and L/S define states
(collections of microstates) Groups of
microstates with the same energy are called terms
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Determining the microstates for p2
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Spin multiplicity 2S 1
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Determining the values of L, ML, S, Ms for
different terms
1S
1P
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Classifying the microstates for p2
Electrons must have different quantum numbers 1
1 illegal 1 1- is same as 1- 1
(indistinguishable)
Spin multiplicity columns of microstates
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Energy of terms (Hunds rules)
Lowest energy (ground term) Highest spin
multiplicity 3P term for p2 case
3P has S 1, L 1
If two states have the same maximum spin
multiplicity Ground term is that of highest L
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Determining the microstates for s1p1
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Determining the terms for s1p1
Ground-state term
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Coordination Chemistry Electronic Spectra of
Metal Complexes cont.
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Electronic configurations of multi-electron
atoms Russell-Saunders (or LS) coupling
For the multi-electron atom L total orbital
angular momentum quantum number S total spin
angular momentum quantum number Spin multiplicity
2S1 ML ?ml (-L,0,L) MS ?ms (S, S-1,
,0,-S)
For each 2p electron n 1 l 1 ml -1, 0,
1 ms 1/2
ML/MS define microstates and L/S define states
(collections of microstates) Groups of
microstates with the same energy are called terms
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before we did
p2
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For metal complexes we need to consider d1-d10
For 3 or more electrons, this is a long tedious
process
But luckily this has been tabulated before
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Transitions between electronic terms will give
rise to spectra
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Selection rules (determine intensities)
Laporte rule g ? g forbidden (that is, d-d
forbidden) but g ? u allowed (that is, d-p
allowed)
Spin rule Transitions between states of different
multiplicities forbidden Transitions between
states of same multiplicities allowed
These rules are relaxed by molecular vibrations,
and spin-orbit coupling
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Group theory analysis of term splitting
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High Spin Ground States
An e electron superimposed on a spherical
distribution energies reversed because tetrahedral
dn Free ion GS Oct. complex Tet complex
d0 1S t2g0eg0 e0t20
d1 2D t2g1eg0 e1t20
d2 3F t2g2eg0 e2t20
d3 4F t2g3eg0 e2t21
d4 5D t2g3eg1 e2t22
d5 6S t2g3eg2 e2t23
d6 5D t2g4eg2 e3t23
d7 4F t2g5eg2 e4t23
d8 3F t2g6eg2 e4t24
d9 2D t2g6eg3 e4t25
d10 1S t2g6eg4 e4t26
Holes in d5 and d10, reversing energies relative
to d1
A t2 hole in d5, reversed energies, reversed
again relative to octahedral since tet.
Holes dn d10-n and neglecting spin dn d5n
same splitting but reversed energies because
positive.
Expect oct d1 and d6 to behave same as tet d4 and
d9
Expect oct d4 and d9 (holes), tet d1 and d6 to be
reverse of oct d1
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d1 ? d6 d4 ? d9
Orgel diagram for d1, d4, d6, d9
Energy
D
0
D
ligand field strength
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Orgel diagram for d2, d3, d7, d8 ions
Energy
A2 or A2g
T1 or T1g
T1 or T1g
P
T2 or T2g
T1 or T1g
F
T2 or T2g
T1 or T1g
A2 or A2g
d2, d7 tetrahedral d2, d7 octahedral d3, d8
octahedral d3, d8 tetrahedral
0
Ligand field strength (Dq)
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d2
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Tanabe-Sugano diagrams
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Electronic transitions and spectra
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Other configurations
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Other configurations
The limit between high spin and low spin
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Determining Do from spectra
d1
d9
One transition allowed of energy Do
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Determining Do from spectra
Lowest energy transition Do
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Ground state is mixing
E (T1g?A2g) - E (T1g?T2g) Do
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The d5 case
All possible transitions forbidden Very weak
signals, faint color
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Some examples of spectra
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Charge transfer spectra
Metal character
LMCT
Ligand character
Ligand character
MLCT
Metal character
Much more intense bands