Download Chem 310 Lectures by: Dr. Muhammad D. Bala Office: Block H, 3

Chem 310 Lectures by: Dr. Muhammad D. Bala
Office: Block H, 3-64
Contacts:
phone Î extn. 2616;
e-mail Î [email protected]
Recommended texts:
• Shriver and Atkins: Inorg. Chem., 4th Ed.
• Cotton, Wilkinson and Gaus: Basic Inorg. Chem., 3rd Ed.
• David Nicholls: Complexes and 1st row transition elements
In this part of the course we have about 6 weeks to cover the
following topics:
1.Bonding: VBT, CFT, LFT and MOT
2.Magnetic and electronic properties of TM oxides
3.Reactivities of TM complexes
The Valence-Bond Theory
Covalent bonds by sharing pairs of electrons was first
proposed by G. N. Lewis in 1902.
It was not until 1927, however, that Walter Heitler and Fritz
London showed how the sharing of pairs of electrons holds a
covalent molecule together.
The Heitler-London model of covalent bonds was the basis of
the valence-bond theory.
The last major step in the evolution of this theory was the suggestion
by Linus Pauling that atomic orbitals mix to form hybrid orbitals,
such as the sp, sp2, sp3, dsp3, and d2sp3 orbitals.
The Valence-Bond Theory
It is easy to apply the valence-bond theory to some
coordination complexes, such as the Co3+ complexes below.
d2sp3- inner sphere complex Î low spin complex
sp3d2- outer sphere complex Î high spin complex
Note: Such a situation will not arise for for d1, d2 and d3 ion configuration.
Deficiencies of VB approach to bonding
• Assumes that all d orbitals in a complex are equal in energy.
• The arbitrary use of 3d and 4d orbitals for bonding Î energy
differential ignored.
• The theory is unable to adequately explain electronic and magnetic
properties of complexes.
•VBT is widely used in organic and main group element chemistry.
•In TM metal chemistry VBT is superseded by the Crystal Field
Theory (CFT).
•In combination with MOT it is often referred to as the Ligand Field
Theory (LFT).
The Crystal-Field Theory
Crystal Field Theory is based on the idea that a purely electrostatic
interaction exists between the central metal ion and the ligands.
Covalent bonding is ignored.
Crystal field theory was developed by considering two compounds:
manganese(II) oxide, MnO Î octahedral geometry,
copper(I) chloride, CuCl Î tetrahedral geometry.
Octahedral complexes
-
Each Mn2+ ion in manganese(II) oxide is
surrounded by six O2- ions arranged toward the
corners of an octahedron.
What happens to the energies of the 4s and 4p
orbitals on an Mn2+ ion?
z
y
-
Mn+
-
-
-
-
Let's assume that the six O2- ions that surround each Mn2+ ion
define an XYZ coordinate system. Two of the 3d orbitals (dx2-y2 and
dz2) on the Mn2+ ion point directly toward the six O2- ions. The other
three orbitals (dxy, dxz, and dyz) lie between the O2- ions.
Therefore, the five 3d orbitals on the Mn2+ ion are no longer
degenerate, i.e. no longer equal, or -of the same energy.
x
Octahedral Complexes
z
y
-
-
•The ligands approach the metal along x, y, z.
• e-s in d orbital are repulsed by –vely charged
ligands Î increase in potential energy.
-
Mn+
-
-
-
•Degree of e-static repulsion depends on the orientation of the d
orbitals.
• d orbitals (dz2 and dx2-y2) with lobes directed at the ligands
experience more repulsion Î placed at higher energy eg oebitals.
• d orbitals (dxy, dxz and dyx) with lobes in-between the ligands
experience less repulsion Î placed at lower energy t2g orbitals.
x
Octahedral Complexes
The s-orbital of the metal is spherically symmetric.
The three p-orbitals lie along the xyz axes, Î point directly towards the
ligands Î Therefore they all remain degenerate.
Energy of the s- and p-orbitals is raised due to the increased repulsion
between the negative point charges representing the ligands and the
negative charge of the electrons orbital Î orbitals are raised in energy.
Electron-density distribution in the d orbitals
E
z
eg subset
y
x
x
dx2-y2
y
t2g subset
dz2
z
y
x
x
dxy
z
dxz
dyz
The Crystal-field parameter (Δ or 10 Dq)
• The Crystal Field splitting
parameter has been used to
correlate a wide range of
properties
of
first-row
transition metal complexes.
• This includes structure,
electronic
spectra
and
magnetic properties.
• It is perhaps the single most
useful
parameter
in
understanding coordination
chemistry.
eg
barycentre
+6Dq 3/5Δ ο
t2
2/5Δ τ
Δο
3/5Δ τ
-4Dq 2/5Δο
4/9 Δο
e
t2g
octahedral
field
free ion
tetrahedral
field
The Crystal-field parameter (Δ or 10 Dq)
eg
• The Crystal Field splitting parameter varies
systematically with the type of ligand.
3 /5 Δ ο
t2
2 /5 Δ τ
Δο
3 /5 Δ τ
2 /5 Δ ο
• E. g. in complexes of [CoX(NH3)5]n+ with
X = I-, Br-, Cl-, H2O and NH3 the colours
range from purple (for X = I-) thru to pink
(for Cl-) to yellow (with NH3).
•The same order was observed regardless of
the metal ion.
•Based on these observations Ryutaro
Tsuchida proposed the spectrochemical series
for ligands.
4 /9 Δ ο
e
t2 g
o cta h ed ral
field
free io n
tetra h ed ra l
fie ld
The Spectrochemical series
I- < Br- < SCN- ~ Cl- < F- < OH- ~ ONO- < C2O42- < H2O <
NCS- < EDTA4- < NH3 ~ pyr ~ en < bipy < phen < CN- ~ CO
weak-field ligand. E.g. Cl-
Î Low energy transition Î Δ = small
strong-field ligand. E.g. CO Î High energy transition Î Δ = LARGE
From a purely ionic basis we would expect CO < H2O < C2O42- <
EDTA4-.
That this is not the case is a reflection of covalent interactions: ignored
by CFT Î Limitation of the CFT. CFT cannot account for the
spectrochemical series.
Why the spectrochemical series?
Because the magnitude of the splitting energy Δ also determines the
colours and electronic spectra of the TM complex.
The Spectrochemical series
The Spectrochemical series
The splitting of d orbitals in the crystal field model depends on:
• the geometry of the complex Î octahedral, tetrahedral, sq. planar.
• the nature of the TM ion Î its group and period.
• the charge on the ion.
• the ligands that surround the metal.
Pt
4+
>
Ir
3+
>
Rh
3+
Strong-field ions
>
Co
3+
>
Cr
3+
>
Fe
3+
>
Fe
2+
>
Co
2+
>
Ni
2+
>
Weak-field ions
Mn
2+
Electron configuration of TM complexes
Degenerate orbitals are filled according to Hund's rules:
• One electron is added to each of the degenerate orbitals in a subshell
before a second electron is added to any orbital in the subshell Î lowest
energy subshell filled in first.
• Electrons are added to a subshell with the same value of the spin
quantum number until each orbital in the subshell has at least one
electron Î least electrostatic repulsion.
• Order of filling d-orbitals depend both on Δ and the pairing energy, P:
• If Δ > P Î Δ is large, strong field ligand Îe-s pair up in the lower
energy subshell first, e.g. t2g for octahedral CF Î Low spin complex
Î strong field Î inner sphere.
• If Δ < P Î Δ is small, weak field ligand Îe-s spread out among all
d-orbitals before any pairing, e.g. t2g and eg for octahedral CF Î
High-spin complex Î weak field Î outer sphere.
Octahedral electron configuration of octahedral TM complexes
•Îfor d1, d2, d3 and d8, d9, d10 Î the ligand type has same effect on
the d-orbital electron configuration.
•Î for CFSE calculation, strong or weak field ligand will be same.
d1
t2g1eg0
d8
t2g6eg2
d2
t2g2eg0
d9
t2g6eg3
d3
t2g3eg0
d10
t2g6eg4
Δ < P and Δ > P
Octahedral electron configuration of octahedral TM complexes
d4
t2g3eg1
t2g4eg0
d5
t2g3eg2
t2g5eg0
d6
t2g4eg2
t2g6eg0
d7
t2g5eg2
t2g6eg1
Δ < P High spin
Δ > P Low spin
Crystal–Field Stabilisation Energy (CFSE)
CFT predicts stabilisation for some electron configurations in the d
orbitals.
For an octahedral complex with d orbital configuration t2gxegy, with
respect to the barycentre:
An electron in the more stable t2g subset is treated as contributing a
stabilisation of 0.4Δo OR 4Dq.
An electron in the higher energy eg subset contributes to a
destabilisation of 0.6Δo OR 6Dq.
Therefore, the CFSE = (0.4x – 0.6y)Δo - P (P = pairing energy)
OR
CFSE = (4x - 6y)Dq - P (P = pairing energy)
Crystal–Field Stabilisation Energy (CFSE)
Q. Explain why the Co(NH3)63+ ion is a diamagnetic, low-spin
complex, whereas the CoF63- ion is a paramagnetic, high-spin
complex. Give the electron configuration and calculate the CFSE
of each complex in terms of Δ.
Answer:
Co = [Ar] 3d7 4s2 Î Co3+ = [Ar] 3d6
Co(NH3)63+ = strong field ligand, Δ > P Î pairing of electrons Î t2g6
electron configuration.
CoF63- = weak field ligand, Δ < P Î spreading of electrons Î t2g4 eg2
CFSE = (0.4x – 0.6y)Δo
1. Co(NH3)63+ Î x = 6 and y=0 Î CFSE = 2.4 Δ.
2. CoF63- Î x = 4 and y = 2 Î CFSE = 0.4Δ.
Crystal–Field Stabilisation Energy (CFSE)
Q. Determine which of the following are more likely to be high spin
complexes:
(1) [Fe(CN)6]3(2) [FeF6]3(3) [Co(H2O)6]+3
•(4) [Co(CN)6]-3
•(5) [Co(NH3)6]+3
•(6) [Co(en)3]+3
Solution: Compare the ligands on the spectrochemical series. Since
we want a high spin complex, we want weak field ligands. The weaker
field ligands in the above are H2O and F-, so complexes 2 and 3 are
more likely to be high spin. (The cyanide complexes are least likely.)
Crystal–Field Stabilisation Energy (CFSE)
Q1. Determine the CFSE if Dq = 2100 cm-1 for the following
configurations:
a) d4 high spin.
b) d4 low spin, assume the pairing energy P = 28,000 cm-1.
Q2. Given a Dq value of 1040 and 3140 cm-1 for high spin and low
spin d6 ion respectively, determine the CFSE in the following
configurations if the pairing energy P = 17,600 cm-1:
a ) weak field
b) strong field
Q1. a) d4 high spin.
Configuration = t2g3; eg1. Therefore from CFSE = (-4x +6y)Dq + P
CFSE = -4 x 3 + 6 = -6Dq = -12,600cm-1 ; remember for high spin
up to d5 configuration P = 0
b) d4 low spin, P = 28,000 cm-1.
Configuration = t2g4 Î CFSE = -4 x 4 = -16Dq + P = -5600 cm-1
Q2. a ) d6 in a weak field
Configuration = t2g4; eg2. Therefore from CFSE = (-4x +6y)Dq +dP
CFSE = -4 x 4 + 6 x 2 + P = -4Dq + P = 13,440cm-1
b) d6 in a strong field
Configuration = t2g6. Therefore from CFSE = (-4x)Dq + 3P
CFSE = -4 x 6 = -24Dq + 3P = -22,560cm-1
Tetrahedral complexes
• In the tetrahedral case the electrons go to the lower energy doubly
degenerate e orbital first.
• The upper triply degenerate t2 orbital is filled in afterwards.
• The subscripts g (gerund, german for even) and u (ungerund,
german for uneven) are missing for the tetrahedral geometry.
• g and u refer to inversion about a centre of symmetry which is
absent for the tetrahedron.
Tetrahedral complexes
Note: For tetrahedral complexes, those orbitals which point towards the
edges (dxy, dyz and dxz) Î e subset are raised to energy higher than
those which point towards the faces Î t2 subset.
That is, the exact opposite of the octahedral crystal field.
A tetrahedral complex has fewer ligands, only 4 to be exact.
The orbitals point in-between ligands rather than at the ligands Î
lower repulsion.
Due to the reasons above, the magnitude of the tetrahedral CF splitting
is smaller Î Δt = 4/9 Δo
Because Δt < Δo it is energetically favourable to spread out electrons Î
all tetrahedral complexes are high-spin.
Tetrahedral complexes
Also for low spin complexes to exist Δt > P, hence low spin tetrahedral
complexes of any TM configuration are very rare.
Some factors that favour formation of tetrahedral complexes:
Bulky ligands: inter-ligand repulsion exacerbated in an
arrangement Î Steric factors
octahedral
Weak field ligands: Many TM halides are tetrahedral
Electronic configuration of metal ion favours Δ = zero (d0, d5 and d10)
or low values of OSPE Î d1, d6 and to a lesser extent d2, d7
configurations.
Weak field ions: Central metal in low oxidation state Î Δ is low.
Octahedral Vs Tetrahedral
Summary: Field preference
1.2
Δtet = 4/9 Δoct.
octahedral
1.0
Octahedral Î d3 ; d8 then
d4 and d9
)
0.8
Tetrahedral (?) Î
d2; d7
d1;
d6
and
No influence Î d0; d5 (high
spin); and d10
Octahedral Site Preference
Energies, is defined as:
CFSE (units of
o
OSPE
tetrahedral
0.6
0.4
0.2
0
OSPE = CFSE (oct) CFSE (tet)
OSPE
1
2
3
6
7
4
5
Number of d electrons
8
9
10
Tetragonally distorted complexes: the Jahn-Teller Effect
The Jahn-Teller Theorem was published in 1937 and states:
“Any non-linear molecular system in a degenerate electronic state will be
unstable and will undergo distortion to form a system of lower symmetry
and lower energy thereby removing the degeneracy”
In simple terms it means that no nonlinear molecule can be stable in a
degenerate electronic state. The molecules must become distorted to
remove the degeneracy
In an octahedral crystal field, the t2g orbitals occur at lower energy than
the eg orbitals.
Only important for odd number occupancy of the eg level Î eg1 or eg3.
The effect of Jahn-Teller distortions is best documented for Cu2+
complexes (with 3 electrons in the eg level) where the result is that most
complexes are found to have elongation along the z-axis.
Tetragonally distorted complexes: the Jahn-Teller Effect
• Consider the octahedral Cu2+ ion Î d9 Î t2g6 eg3
• The eg levels are degenerate Î 3 electrons Î dx2-y2 1 dz2 2 or dx2-y2 2 dz2 1
• Hence the degeneracy of the eg levels is lifted Î ligands along the axes
experience different shielding effects Î 2 e-s vs. 1 e-.
• Resulting in z -axis contraction (dx2-y2 2 dz2 1) or elongation (dx2-y2 1 dz2 2).
As the z axis elongation increases Î the energy of the dz2 orbital drops
lower than the dxy orbital which along with dx2-y2 orbital rises in energy.
X'
X
X
Cu
X
2+
X
X'
X = Cl
X = Br
X=F
Cu---X
2.30
2.40
1.93
Cu---X΄
2.95
3.18
2.27
Tetragonally distorted complexes: the Jahn-Teller Effect
•(dx2-y21 dz2 2) due to the
2 electrons on the z axis
the dz2 orbital is more
shielded from the Cu2+
centre Î elongation
along this axes Î also
called tetragonal
distortion Î lower in
energy.
Also arises due to ligand
dissimilarity, e.g. in MA4B2
Δ
Very
rare
Tetragonally distorted complexes: the Jahn-Teller Effect
• The distortion has resulted in lower energy for the system Î
stabilisation.
• Therefore many Cu2+ complexes are tetragonal even with six identical
ligands, e.g. [Cu(H2O)6]2+.
• The main reason for tetragonal distortion is to remove the instability
brought about by the non-linearity and achieve stability in TM complexes.
• No distortion for t2g3, t2g3 eg2 , t2g6, t2g6 eg2 , t2g6 eg4 .
•Important cases of distortion are: t2g3 eg1 (high spin Cr2+ and Mn3+) and
t2g6 eg1 (low spin Co2+ and Mn3+)
Tetragonally distorted complexes: the Jahn-Teller Effect
dx2-y2
dx2-y 2
dx2-y 2
eg
dz 2
dz 2
dxy
dz 2
dxy
t2g
dxz dyz
dxy
dxz
dyz
dxz
dyz
(a) Octahedral
field
(b) Small tetragonal
distortion
(c) Large tetragonal
distortion
Square planar complexes
Recall Jahn-Teller tetragonal distortion discussed above.
Mostly formed by metals with d8 ions with strong field ligands, e.g.
[NiII(CN)4]2-. Note that [NiIIX4]2- forms tetrahedral complexes, why?
All complexes of Pt(II) and Au(III) are square-planar, including those
with weak field ligands such as [PtCl4]2-. Also true for most complexes
of Rh(I), Ir(I) and Pd(II) Î 4d and 5d complexes.
z
y
dx2-y2
dxy
dz2
} dxz; dyz
x
A square planar complex is
obtained
when
it
is
energetically favourable to
have
the
configuration
dyz2dxz2dxy2dx2-y22 for 4d8 and
5d8 ions.
Full dz2 and empty dx2-y2 Î
Molecular Orbital Theory (MOT) and Ligand–Field Theory (LFT)
• The purely e-static approach of the CFT makes it unsuitable to
adequately explain metal-ligand bonding. TM compounds such as
Ni0(CO)4 with Ni in zero oxidation state must be purely covalent Î no
M-L e-static attraction.
• We have already seen that on purely e-static grounds, the order of the
spectrochemical series is unviable, e.g. we expect CO < H2O < C2O42- <
EDTA4- Î this is however not the case.
• Evidence from NMR & ESR Î unpaired e-n density on the ligands Î
sharing of e-ns Î strong evidence for M-L covalency.
•LFT is the theory that combines CFT with covalency (MOT)
• Essentially LFT is able to give an understanding of the true origins of Δo
and the spectrochemical series by taking into account the roles of σ- and
π- bonding in TM chemistry.
Oh σ bonding
z
z
y
x
+
y
+
+
+
+
+
x
+
s
z
z
y
+
y
+
x
x
-
-
Pz
z
z
y
y
-
-
x
+
+
x
Px
z
z
y
y
+
+
x
x
-
Py
z
-
-
x
-
+
dz2
x
+
-
y
y
-
-
y
+
y
+
z
z
+
z
+
dx2-y2
x
+
-
+
x
t2g:
Non
bonding
Orbitals
Remain
localised
on metal
atom
Oh σ bonding
In LFT the building up principle is
used in conjunction with a molecular
energy level diagram constructed from
metal orbitals and symmetry adapted
linear combination of atomic orbitals
(SALC).
For an octahedral geometry:
Six SALC with σ symmetry interact
with the metal orbitals
The orbitals of the central metal atom
divide by symmetry into 4 sets, viz:
Singly degenerate s
Triply degenerate p
Doubly degenerate d
Triply degenerate d
a1g
t1u
eg
t2g
Typical molecular energy levels diagram
of an octahedral complex showing the
frontier orbitals in the tinted box
Oh σ bonding
• The ligand-field model for octahedral TM complexes such as
Co(NH3)63+ and CoF63- assumes that the 3d, 4s, and 4p orbitals on the
metal overlap with one orbital on each of the six ligands to form a total
of 15 molecular orbitals.
• Six of these orbitals are bonding molecular orbitals, whose energies are
much lower than those of the original atomic orbitals.
• Another six are antibonding molecular orbitals, whose energies are higher
than those of the original atomic orbitals.
• Three are best described as nonbonding molecular orbitals, because they
have essentially the same energy as the 3d atomic orbitals on the metal.
• Note: The d-orbitals of LFT are the molecular orbitals and not the
atomic orbitals of the CFT
• Summary:
Oh σ bonding
• The allocation of electrons is similar to CFT
•12 ligand electrons are accommodated in the bonding orbitals.
• metal electrons are accommodated in the NB (t2g) and AB (eg*)
orbitals.
• The separation between the frontier orbitals (Δo) is similar to CFT.
• The type of complex that is obtained will also depend on Δo and P.
• The origin of Δo and the spectrochemical series are clearer:
• good σ-donor ligands (e.g. CH3- and H-) result in strong metalligand overlap Î larger value of Δo due to a more strongly AB eg*.
•Except for ligands in which there are no orbitals of π symmetry
available for bonding Î σ-bonding only ligands, such as CH3- and Hπ-bonding is the main determinant of Δo and the spectrochemical
series for TM complexes.
Oh σ bonding
Q. Construct molecular orbital energy level diagrams for CoIII ion in
the following octahedral crystal fields:
1. Low spin
2. High spin
Clearly show:
•
the relative positions of the metal, ligand and complex orbitals
•
10Dq
•
placement of electrons in each case
Answer:
Oh σ bonding
Steps for determining d-orbital energy level diagrams for TM complexes:
• Determine the oxidation state of the metal
• Determine the number of d electrons
• Determine ligand field Îstrong or weak
Î strong field = low spin
Î weak field = high spin
• Draw the energy level diagram
Oh σ bonding
Antibonding
MOs
4p
Δο
4s
Six donor orbitals
6NH3 each donating
2 e-s
3d
2
x2-y2 z
xy
xz
yz
NB MOs
Bonding MOs
Atomic orbitals in metal ion
Molecular Orbital diagram for [CoIII(NH3)6 ]3+
Molecular orbitals
Atomic orbitals in ligand ion
Oh σ bonding
Antibonding
MOs
4p
Δο
4s
Six donor orbitals
6 F- each donating
2 e-s
3d
2
x2 -y2 z
xy
xz
yz
NB MOs
Clearly good σ donor ligand
Result in good M-L overlap
Î Strongly antibonding eg set
Atomic orbitals in metal ion
Molecular Orbital diagram for CoF63-
Bonding MOs
Molecular orbitals
Atomic orbitals in ligand ion
Ligand–Field Theory: π bonding
π bonding is important for ligands with orbitals of
local π symmetry with respect to the M-L axis Î
e.g. metal dxy and ligand py orbitals.
These interaction with the previously NB metal t2g
orbitals Î influences Δo.
π-donor ligand Î has filled orbitals of π symmetry
Î These are π-bases, e.g. Cl-, Br-, OH- and H2O.
These have L→M e-n donation.
π-acceptor ligand Î has empty π orbitals that are
available for occupation Î These are π acids, e.g.
CO and PR3 ligands Î capable of M→L back
donation to form π- bonds.
Summary of influence of π-bonding on Δo:
π-donor ligands decrease Δo.
π-acceptor ligands increase Δo.
π-donor
ligands
decrease Δo.
π-acceptor
ligands
increase Δo.
Ligand–Field Theory: π bonding
Summary:
strong σ- or π-donor
Î weak field ligands.
π acceptor ligands
higher in E than t2g.
π donor ligands
lower in E than t2g.
π-acceptors Î strong
field ligands.
Increasing Δo →
π donor < weak π donor < no π effects < π acceptor
e.g. I-, Br- Cl- FH2O
NH3
PR3, CO