Transcript Lecture 2 - City University of New York

Placing electrons in d orbitals (strong vs weak field)
Strong field
Weak field
Strong field
Weak field
d1
d2
Strong field
Weak field
Strong field
Weak field
d4
d3
So, what is going on here!!
When the 4th electron is assigned it will either go into the higher energy
eg orbital at an energy cost of D0 or be paired at an energy cost of P, the
pairing energy.
Strong field Weak field
d4
Strong field =
Low spin
(2 unpaired)
Pairing
Energy!!.
P < Do
Weak field =
High spin
(4 unpaired)
D0,
P > Do
Pairing Energy, P
The pairing energy, P, is made up of two parts.
1) Pc: Coulombic repulsion energy caused by having two electrons
in same orbital. Destabilizing energy contribution of Pc for each
doubly occupied orbital.
2) Pe: Exchange stabilizing energy for each pair of electrons having
the same spin and same energy. Stabilizing contribution of Pe for
each pair having same spin and same energy
P = sum of all Pc and Pe interactions
How do we get these interactions?
Placing electrons in d orbitals
High
Low
High
Low
d5
1 u.e.
5 u.e.
0 u.e.
2 u.e.
Low
d6
4 u.e.
d8
2 u.e.
High
d7
1 u.e.
3 u.e.
d9
1 u.e.
1 u.e.
d10
0 u.e.
0 u.e.
Detail working out….
High Field
(Low Spin)
Low Field
(High Spin)
d5
1 u.e.
5 u.e.
What are the energy terms for both high spin and
low spin?
Low Field
Coulombic Part = 0
High Field
Exchange part = for
Coulombic Part = 2Pc
Exchange part = for
For
1Pe
3Pe + Pe
P = 4Pe
3Pe
P = 2Pc + 4Pe
LFSE = 5 * (-2/5D0) = -2D0
LFSE = 3*(-2/5D0) + 2 (3/5D0) = 0
High Field – Low Field = -2D0 +2Pe
When D0 is larger than Pe the high field arrangement
(low spin) is favored.
Positive
favors high
spin. Neg
favors low
spin.
Interpretation of Enthalpy of Hydration of hexahydrate using LFSE
d0 d1
LFSE (in D0) .0
.4
d2 d3 d4
.8 1.2 .6
d5 d6 d7
.0 .4
.8
d8
d9 d10
1.2 .6
.0
Splitting of d orbitals in a tetrahedral field
t2
Dt
e
Dt = 4/9Do
Always weak field (high spin)
Extreme elongation: from octahedral to square planar
L
L
L
M
L
L
M
L
L
L
L
L
Less repulsions along the axes
where ligands are missing
A crystal-field aproach: from octahedral to square planar
A correction to preserve
center of gravity
Magnetic properties of metal complexes
Diamagnetic complexes
very small repulsive
interaction with external
magnetic field
no unpaired electrons
Paramagnetic complexes
attractive interaction with
external magnetic field
some unpaired electrons
s  n(n  2)
Values of magnetic moment
Coordination Chemistry:
Molecular orbitals for metal complexes
The symmetry of metal orbitals in an octahedral environment
A1g
T1u
The symmetry of metal orbitals in an octahedral environment
T2g
Eg
The symmetry of metal orbitals in an octahedral environment
s
Metal-ligand s interactions in an octahedral environment
Six ligand orbitals of s symmetry approaching the metal ion along the x,y,z axes
z
M
We can build 6 group orbitals of s symmetry as before
and work out the reducible representation
s
If you are given G, you know by now how to get the irreducible representations
G = A1g + T1u + Eg
Now we just match the orbital symmetries
s
“d0-d10 electrons”
anti bonding
“metal character”
non bonding
6 s ligands x 2e each
12 s bonding e
“ligand character”
Introducing π-bonding
2 orbitals of π-symmetry
on each ligand
We can build 12 group orbitals
of π-symmetry
Gπ = T1g + T2g + T1u + T2u
The T2g will interact with the metal d t2g orbitals. The ligand pi
orbitals do not interact with the metal eg orbitals.
We now look at things more closely.
Anti-bonding LUMO(π)
First, the CN- ligand
Some schematic diagrams showing how p bonding occurs
with a ligand having a d orbital (such as in P), or a p*
orbital, or a vacant p orbital.
ML6 s-only bonding
“d0-d10 electrons”
anti bonding
“metal character”
non bonding
6 s ligands x 2e each
The bonding orbitals, essentially the ligand lone pairs,
12 s bondingwill
e
not be worked with further.
“ligand character”
π-bonding may be introduced
as a perturbation of the t2g/eg set:
Case 1 (CN-, CO, C2H4)
empty π-orbitals on the ligands
ML π-bonding (π-back bonding)
t2g (π*)
These are the SALC
formed from the p
orbitals of the ligands
that can interac with
the d on the metal.
t2g
eg
eg
Do
D’o
Do has increased
t2g
Stabilization
t2g (π)
ML6
s-only
ML6
s+π
(empty π-orbitals on ligands)
π-bonding may be introduced
as a perturbation of the t2g/eg set.
Case 2 (Cl-, F-)
filled π-orbitals on the ligands
LM π-bonding
eg
Do has decreased
eg
D’o
t2g (π*)
Do
Destabilization
t2g
t2g
Stabilization
t2g (π)
ML6
s-only
ML6
s+π
(filled π-orbitals)
Putting it all on one
diagram.
Strong field / low spin
Weak field / high spin
Spectrochemical Series
Purely s ligands:
D: en > NH3 (order of proton basicity)
p donating which decreases splitting and causes high spin:
D: H2O > F > RCO2 > OH > Cl > Br > I (also proton basicity)
p accepting ligands increase splitting and may be low spin
D: CO, CN-, > phenanthroline > NO2- > NCS-
Merging to get spectrochemical series
CO, CN- > phen > en > NH3 > NCS- > H2O > F- > RCO2- > OH- > Cl- > Br- > I-
Strong field,
p acceptors
large D
low spin
s only
Weak field,
p donors
small D
high spin
Turning to Square Planar Complexes
z
y
x
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|.
ML4 square planar complexes
ligand group orbitals and matching metal orbitals
s bonding
p bonding (in)
p bonding
(perp)
ML4 square planar complexes
MO diagram
eg
s-only bonding
Sample bonding
Angular Overlap Method
An attempt to systematize the interactions for all geometries.
1
1
4
M
7
8
3
11
M
M
2
9
5
6
2
12
10
6
The various complexes may be fashioned out of the ligands
above
Linear: 1,6
Tetrahedral: 7,8,9,10
Trigonal: 2,11,12 Square planar: 2,3,4,5
T-shape: 1,3,5
Trigonal bipyramid: 1,2,6,11,12
Square pyramid: 1,2,3,4,5
Octahedral: 1,2,3,4,5,6
Cont’d
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.
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.