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High Spin Ground States: d2, d3, d6, and d7
We have taken care of the d0, d1, d4, d5, d6, d9, and d10 configurations. Now have to do d2, d3, d6, and d7 configurations. It turns out that all we have to do is solve d2.
We saw earlier that F in octahedral environment splits to A2g + T1g + T2g; in tetrahedral we would get A2 + T1 + T2. Our problem is the energy ordering. Which is GS?
Thus the 3F GS for d2 splits into 3A2g + 3T1g + 3T2g. The 4F GS for d3 splits into 4A2g + 4T1g + 4T2g. Where did the spin multiplicities come from??
But it is not so easy. Here is our approach:
We know the symmetry of the GS of the free d2 ion. How? We can get the terms for d2 using the methods applied earlier to p2, etc. They are 3F, 1D, 3P, 1G, 1S.
We identify the GS as 3F. How?
But how do we decide on what becomes the GS after the splitting due to the ligands?
We use a correlation diagram. It shows the affect of increasing the ligand field strength from zero (free ion) to very high where energy ordering is determined solely by the occupancy of the t2g and the eg orbitals.
d2
1
3
electrons
d7 = d5 + d2
2 d3=d5-hole2
3
1
2
d8=d10-hole2
holesd2 and d7 both are electrons on top of a spherical shell yielding a splitting pattern: 1, 2, 3
d3 and d8 are both two d-holes in a spherical shell, yielding reversed splitting: 3, 2, 1
d2
Real complexes
We have two electrons in the eg orbitals. It can be shown that these give rise to 1A1g,
1Eg, and 3A2g which have same energy in strong ligand field.
Connect the terms of the same symmetry without crossing.
Splitting of free ion terms.
Similarly, splitting occurs for these occupancies.
We have included the 3T1g originating from the 3P. We will need it immediately. Same symmetry as lower energy 3T1g from the 3F.
Free Ion terms
Configurations based on splitting of d electrons. Dominant in very strong fields.
F
P
Ligand field strength (Dq)
Energy
Orgel diagram for d2, d3, d7, d8 ions
d2, d7 tetrahedral d2, d7 octahedral
d3, d8 octahedral d3, d8 tetrahedral
0
A2 or A2g
T1 or T1g
T2 or T2g
A2 or A2g
T2 or T2g
T1 or T1g
T1 or T1g
T1 or T1g
And now
d2 and d7 in tetrahedral (reversed due to tetrahedral field)
and
d3 and d8 in octahedral (reversed due to d-holes).
Note the reversed ordering of the splitting coming from F (T1/T2/A2). The lower T1(g) now aims up and should cross the upper T1(g) but does not due to interaction with the upper T1(g). Now have strong curvature to avoid crossing.
Same symmetry; crossing forbidden
T1 or T1g
T1 or T1g
First look at
d2 and d7 in octahedral (2 elecs on a spherical cloud)
and
d3 and d8 in tetrahedral (double reversal: d-holes and tetrahedral)
All states shown are of the same spin. Transitions occur between them but weakly.
Note the weak interaction of the two T1, the curvature.
This curvature will complicate interpretation of spectra.
Move to Tanabe-Sugano diagrams. d1 – d3 and d8 – d9 which have only high spin GS are easier. Here is d2.
Correlation diagram for d2.
Convert to Tanabe-Sugano.
Tanabe-Sugano
Electronic transitions and spectra
d2 Tanabe-Sugano diagram
V(H2O)63+, a d2 complex
Configurations having only high spin GS
d1 d9
d3
d2
d8
Note the two lines curving away from each other.
Note the two lines curving away from each other.
Slight curving.
Configurations having either high or low spin GS
The limit betweenhigh spin and low spin
Determining o from spectra
d1d9
One transition allowed of energy o
Exciting electron from t2g to eg
Exciting d-hole from eg to t2g
Exciting d-hole from eg to t2g
Exciting electron from t2g to eg
Lowest energy transition = o
mixing
mixing
Determining o from spectra
Here the mixing is not a problem since the “mixed” state is not involved in the excitation.
d3
d8
Ground state and excited state mixing which we saw earlier.
E (T1gA2g) - E (T1gT2g) = o
For d2 and d7 (=d5+d2) which involves mixing of the two T1g states, unavoidable problem.
Make sure you can identify the transitions!!
But note that the difference in energies of two excitations is o.
d2
d7
Can use T-S to calculate Ligand Field Splitting. Ex: d2, V(H2O)63+
Again, the root, basic problem is that the two T1 s have affected each other via mixing. The energy gap depends to some extent on the mixing!
E/B
O/B
Technique: Fit the observed energies to the diagram.
We must find a value of the splitting parameter, o/B, which provides two excitations with the ratio of 25,700/17,800 = 1.44
Observed spectrum
17,800 cm-1
2: 25,700 cm-1
First, clearly 1 should correspond to 3T1 3T2 But note that the 2 could correspond to either 3T1 3A2 or 3T1 3T1. The ratio of 2/1 = 1.44 is obtained at o / B= 31
Now can use excitation energies
For1: E/B = 17,800 cm-1 /B = 29 yielding B = 610 cm-1
By using 31 = o/B = o/610 obtain o = 19,000 cm-1
The d5 case
All possible transitions forbiddenVery weak signals, faint color
Jahn-Teller Effect found if there is an asymmetrically occupied e set.
octahedral d9 complex
z2 x2-y2
xy xz yz
effect of octahedral field elongation along thex axis
x2-y2
z2
xy
xz yz
b1g
a1g
b2g
eg
Can produce two transitions.
This picture is in terms of the orbitals. Now for one derived from the terms.
Continue with d9
2D
Free ion termfor d9
2T2g
2Eg
effect ofoctahedral field
Eg
B2g
A1g
B1g
effect of elongation along z
GS will have d-hole in either of the two eg orbitals. ES puts d-hole in either of the three t2g orbitals.
For example, the GS will have the d-hole in the x2-y2 orbital which is closer to the ligands.
Some examples of spectra
Charge transfer spectra
LMCT
MLCT
Ligand character
Metal character
Metal character
Ligand character
Much more intense bands
Coordination ChemistryReactions of Metal Complexes
Substitution reactions
MLn + L' MLn-1L' + L
Labile complexes <==> Fast substitution reactions (< few min)Inert complexes <==> Slow substitution reactions (>h)
a kinetic concept
Not to be confused withstable and unstable (a thermodynamic concept; Gf <0)
Inert Intermediate Labile
d3, low spin d4-d6& d8 d8 (high spin) d1, d2, low spin d4-d6& d7-d10
MLnX + Y MLnY + X
Mechanisms of ligand exchange reactionsin octahedral complexes
Ia if associationis more important
Id if dissociationis more important
Dissociative (D)
MLnX-x
MLn
YMLnY
Associative (A)
MLnXY
YMLnX-X
YMLn
Interchange (I)
MLnXY
Y- -MLn- -X-X
YMLn
Association or Dissociation step may be more important and the process classifiedas such.
Kineticsof dissociative reactions
Using Steady State Approximation, concentration of ML5 is always very low; rate of creation = rate of consumption
Kineticsof interchange reactions
Fast equilibriumK1 = k1/k-1
k-1 >> k2
Again, apply Steady State.
For [Y] >> [ML5X]common experimental
condition!
Kinetics of associative reactions
Principal mechanisms of ligand exchange in octahedral complexes
ML5Xk1
slowML5 + X
k2
fast
+YML5Y
r = k1 [ML5X]
ML5X + Yk1
slowML5XY
k2
fast
-XML5Y
r = k1 [ML5X][Y]
Dissociative
Associative
Dissociative pathway(5-coordinated intermediate)
Associative pathway(7-coordinated intermediate)
MOST COMMON
Experimental evidence for dissociative mechanisms
Rate is independent of the nature of L
Experimental evidence for dissociative mechanisms
Rate is dependent on the nature of L
Inert and labile complexesSome common thermodynamic and kinetic profiles
Exothermic(favored, large K)
Large Ea, slow reaction
Exothermic(favored, large K)
Large Ea, slow reactionStable intermediate
Endothermic(disfavored, small K)Small Ea, fast reaction
LM
L L
L
L
X
L
ML L
L
L
X
L
ML L
L
L
G
Ea
Labile or inert?
LFAE = LFSE(sq pyr) - LFSE(oct)
Why are some configurations inert and some are labile?
Inert !
Substitution reactions in square-planar complexesthe trans effect
T
M
L X
L T
M
L Y
L
+X, -Y
(the ability of T to labilize X)
Synthetic applicationsof the trans effect
Cl- > NH3, py
Mechanisms of ligand exchange reactions in square planar complexes
-d[ML3X]/dt = (ks + ky [Y]) [ML3X]
LM
L L
X
LM
L L
Y
LM
L L
X
LM
L L
X
LM
L L
S
LM
L L
S
S
Y
Y
+Y
+S
-X
+Y
-S
-X
Electron transfer (redox) reactions
M1(x+)Ln + M2
(y+)L’n M1(x +1)+Ln + M2
(y-1)+L’n
-1e (oxidation)
+1e (reduction)
Very fast reactions (much faster than ligand exchange)
May involve ligand exchange or not
Very important in biological processes (metalloenzymes)
Outer sphere mechanism
[Fe(CN)6]4- + [IrCl6]2- [Fe(CN)6]3- + [IrCl6]3-
[Co(NH3)5Cl]2+ + [Ru(NH3)6]2+ [Co(NH3)5Cl]+ + [Ru(NH3)6]3+
Reactions ca. 100 times fasterthan ligand exchange(coordination spheres remain the same)
r = k [A][B]
Ea
A B+
A B
A' B'+
G
"solvent cage"
Tunnelingmechanism
Inner sphere mechanism
[Co(NH3)5Cl)]2+ + [Cr(H2O)6]2+ [Co(NH3)5Cl)]2+:::[Cr(H2O)6]2+
[Co(NH3)5Cl)]2+:::[Cr(H2O)6]2+ [CoIII(NH3)5(-Cl)CrII(H2O)6]4+
[CoIII(NH3)5(-Cl)CrII(H2O)6]4+ [CoII(NH3)5(-Cl)CrIII(H2O)6]4+
[CoII(NH3)5(-Cl)CrIII(H2O)6]4+ [CoII(NH3)5(H2O)]2+ + [CrIII(H2O)5Cl]2+
[CoII(NH3)5(H2O)]2+ [Co(H2O)6]2+ + 5NH4+
Inner sphere mechanism
Reactions much faster than outer sphere electron transfer(bridging ligand often exchanged)
r = k’ [Ox-X][Red] k’ = (k1k3/k2 + k3)
Ox-X + Red Ox-X-Redk1
k2
k3
k4Ox(H2O)- + Red-X+
Ea
Ox-X Red+
Ox-X-Red
G
Ox(H2O)- + Red-X+
Tunnelingthrough bridgemechanism