Electronic and geometric structure
Oxidation state → number of d electrons
atomic number - oxidation state = number of electrons
(neutral atom) (electron deficiency)
# electrons - # for preceding noble gas = # d electrons
Fe3+
Cu+
26 - 3 = 23,
_________
23 - 18 = 5
_________
Oxidation state is ‘formal’.
Charge is actually distributed over the ligands.
A.-F. Miller, 2008, pg
1
Coordination
3
Coordination
number
4
5
6
A.-F. Miller, 2008, pg
2
Figure 2.4
Lippard & Berg
Coordination geometries
associated with different
common coordination
numbers.
d-orbital energies
Crichton Figure 2.1: d orbital shapes
Crystal-Field theory: the arrangement of ligands around
the central metal ion determines the energies of the d
orbitals via electrostatic repulsion between metal ion d
electrons and electron density of ligands.
eg
}
gas phase ion
A.-F. Miller, 2008, pg
3
t2g
dz2, dx2-y2
3/5Δoct
2/5Δoct
dxy, dxz, dyz
L
L
L
M
L
L
L
Strong field / weak field
low-spin / high-spin
eg
L
Δ
S=1/2
L
spin pairing
t2g
L
L
Strong field,
Low spin
L
Weak field,
High spin
L
M
t2g
A.-F. Miller, 2008, pg
M
L
L
S=5/2
eg
L
L
4
L
L
Different coordination geometries: Ni2+
Td
distortion towards SqPl
Oh
eg
t2g
L
L
L
L
M
5
L
M
L
L
A.-F. Miller, 2008, pg
L
L
L
L
L
L
M
L
L
L
Crystal field splitting
A.-F. Miller, 2008, pg
6
Crichton Figure 2.5
Spectrochemical series
Small Δ
I- < Br- < SCN- < S2- < Cl- < NO3- < F- < OH- ~ RCOOH2O ~ RS- < NH3 ~ Im < bpy < CN- < CO
Large Δ
Δ ≈ doubles over this series
Mn2+< Ni2+<Co2+<Fe2+<V2+<Fe3+<Co3+<Mn3+<Mo3+<Ru3+<Pd4+
Im = imidazole, bpy = 2,2’-bipyridine
ispga rule
of thumb, and exceptions exist.
A.-F.This
Miller, 2008,
7
Problems with crystal field model
The observed spectroelectrochemical series does not agree
with electrostatics as the dominant interaction
between ligands and d electrons. Eg. halides I- and Bshould not be so weak, OH- should not be weaker than
H2O.
When bonding and overlap between orbitals of different
symmetries is taken into account, we obtain ligand field
theory.
σ bonds are ‘head-on’, along the line of a bond.
π bonds are ‘side-to-side’ with electron density above and
below the line of the bond, but with no density on the line.
π bonding is more polarizable and allows electron density to
be more
delocalized (lower energy).
A.-F. Miller, 2008, pg
8
Orbitals vs. bond types
Each ligand forms a σ bond first, eg. with a lone pair.
π bonds may be from metal ion d orbitals to ligand p or π
orbitals.
σ bonds can use metal ion s, p. dz2 or dx2-y2. (ligands along
x,y,z)
π bonds can be made of metal ion dxy, dxz or dyx orbitals.
A.-F. Miller, 2008, pg
9
Example MOs produced by the
ligand-field model.
Metal-like: “d”
Ligand-like
Critchton Figure 2.6
Ligands each donate a PAIR of electrons (and fill an MO).
Metal ion electrons → t2g or eg* Retain the FORM of the Xtal field diagram.
A.-F. Miller, 2008, pg
10
Ligand-field effects on Δ
π donors
Crichton Fig. 2.7
Lower-E ligand orbitals that are populated. Upon hybridization with t2g , the set
that drop are ligand-like & populated. The metal-like orbitals move to higher E (➘Δ).
A.-F. Miller, 2008, pg
11
Ligand-field effects on Δ
π acceptors
Crichton Fig. 2.7
Higher-E ligand orbitals are vacant. Upon hybridization with t2gs , the set
that drop are metal-like (➚Δ). They remain vacant. Examples: CN- and CO.
A.-F. Miller, 2008, pg
12
Ligand-field effects on Δ
Crichton Fig. 2.7
Electrostatic repulsion can still raise the energy of any metal electrons in eg*.
NEW: consideration of π bonding provides for lowering the energy of the t2g
orbitals.
Full-full interactions or empty-empty interactions have no net effect.
π acceptor ligands partially oxidize the metal, stabilize formal low oxidation states.
-, OH-.
π donor ligands
stabilize
high
formal
oxidation
states
:
F
A.-F. Miller, 2008, pg
13