Office: Block H, 3-64 - University of KwaZulu-Natalcheminnerweb.ukzn.ac.za/Files/1...

Chem 310 Lectures by: Dr. Muhammad D. Bala

Office: Block H, 3-64

Contacts: phone extn. 2616; e-mail [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 MOT2.Magnetic and electronic properties of TM oxides3.Reactivities of TM complexes

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

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 low spin complex

sp3d2- outer sphere complex high spin complex

Note: Such a situation will not arise for for d1, d2 and d3 ion configuration.

• Assumes that all d orbitals in a complex are equal in energy.

• The arbitrary use of 3d and 4d orbitals for bonding 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•In TM metal chemistry VBT is superseded by the Crystal Field Theory (CFT).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).

Deficiencies of VB approach to bonding

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 octahedral geometry, copper(I) chloride, CuCl tetrahedral geometry.

The Crystal-Field Theory

Mn+-

- -

-

--

x

y zOctahedral 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 4porbitals on an Mn2+ ion?

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.

•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 placed at higher energy eg oebitals.

• d orbitals (dxy, dxz and dyx) with lobes in-between the ligands experience less repulsion placed at lower energy t2g orbitals.

Mn+-

- -

-

--

x

y zOctahedral Complexes

•The ligands approach the metal along x, y, z.

• e-s in d orbital are repulsed by –vely charged ligands increase in potential energy.

Octahedral Complexes

The s-orbital of the metal is spherically symmetric.

The three p-orbitals lie along the xyz axes, point directly towards the ligands 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 orbitals are raised in energy.

z y

x

dz2

y

y z

x

x x

z

dx2-y2

dxy dxz dyz

Electron-density distribution in the d orbitals

eg subset

t2g subset

E

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.

ΔοΔο4/9

t2

e

eg

t2g

free ionoctahedralfield

tetrahedralfield

3/5Δο

2/5Δο

2/5Δτ

3/5Δτ

barycentre

+6Dq

-4Dq

yellow

• The Crystal Field splitting parameter varies systematically with the type of ligand.

• 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 (with NH3).

•The same order was observed regardless of the metal ion.

•Based on these observations Ryutaro Tsuchida proposed the spectrochemical series for ligands.

The Crystal-field parameter (Δ or 10 Dq)

Δ οΔο4/9

t2

e

eg

t2 g

free ionocta hedralfield

tetra hedra lfie ld

3 /5Δ ο

2 /5Δο

2/5Δ τ

3/5Δ τ

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 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.

I- < Br- < SCN- ~ Cl- < F- < OH- ~ ONO- < C2O42- < H2O <

NCS- < EDTA4- < NH3 ~ pyr ~ en < bipy < phen < CN- ~ CO

The Spectrochemical series

weak-field ligand. E.g. Cl- Low energy transition Δ = small

strong-field ligand. E.g. CO High energy transition Δ = LARGE

The splitting of d orbitals in the crystal field model depends on:

• the geometry of the complex octahedral, tetrahedral, sq. planar.

• the nature of the TM ion its group and period.

• the charge on the ion.

• the ligands that surround the metal.

Pt4+ > Ir

3+ > Rh3+ > Co

3+ > Cr3+ > Fe

3+ > Fe2+ > Co

2+ > Ni2+ > Mn

2+

Strong-field ions Weak-field ions


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 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 least electrostatic repulsion.

• Order of filling d-orbitals depend both on Δ and the pairing energy, P:• If Δ > P Δ is large, strong field ligand e-s pair up in the lower energy subshell first, e.g. t2g for octahedral CF Low spin complex

strong field inner sphere.

• If Δ < P Δ is small, weak field ligand e-s spread out among all d-orbitals before any pairing, e.g. t2g and eg for octahedral CF High-spin complex weak field outer sphere.

Electron configuration of TM complexes

• for d1, d2, d3 and d8, d9, d10 the ligand type has same effect on the d-orbital electron configuration. • for CFSE calculation, strong or weak field ligand will be same.

Octahedral electron configuration of octahedral TM complexes

Δ < P and Δ > P

d3 d10t2g3eg

0 t2g6eg

4

d1 d8t2g1eg

0 t2g6eg

2

d2 d9t2g2eg

0 t2g6eg

3

Octahedral electron configuration of octahedral TM complexes

Δ < P High spin

d7 t2g5eg

2 t2g6eg

1

d4

d6

t2g3eg

1

t2g4eg

2

t2g4eg

0

t2g6eg

0

d5 t2g3eg

2 t2g5eg

0

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 t2g

xegy, 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)

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 Co3+ = [Ar] 3d6

Co(NH3)63+ = strong field ligand, Δ > P pairing of electrons t2g

6

electron configuration.

CoF63- = weak field ligand, Δ < P spreading of electrons t2g

4 eg2

CFSE = (0.4x – 0.6y)Δo

1. Co(NH3)63+ x = 6 and y=0 CFSE = 2.4 Δ.

2. CoF63- x = 4 and y = 2 CFSE = 0.4Δ.


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.)


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 = t2g

3; 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 = t2g

4 CFSE = -4 x 4 = -16Dq + P = -5600 cm-1

Q2. a ) d6 in a weak field Configuration = t2g

4; 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 fieldConfiguration = t2g

6. Therefore from CFSE = (-4x)Dq + 3PCFSE = -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.


Note: For tetrahedral complexes, those orbitals which point towards the edges (dxy, dyz and dxz) e subset are raised to energy higher than those which point towards the faces 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 lower repulsion.

Due to the reasons above, the magnitude of the tetrahedral CF splitting is smaller Δt = 4/9 Δo

Because Δt < Δo it is energetically favourable to spread out electrons all tetrahedral complexes are high-spin.


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 octahedral arrangement Steric factors

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 d1, d6 and to a lesser extent d2, d7

configurations.

Weak field ions: Central metal in low oxidation state Δ is low.

Octahedral Vs TetrahedralSummary: Field preference

Δtet = 4/9 Δoct.

Octahedral d3 ; d8 then d4 and d9

Tetrahedral (?) d1; d6 and d2; d7

No influence d0; d5 (high spin); and d10

Octahedral Site Preference Energies, is defined as:

OSPE = CFSE (oct) -CFSE (tet)

0 1 2 3 4 5 6 7 8 9 10

0.2

0.4

0.6

0.8

1.0

1.2

Number of d electrons

CFS

E (u

n its

of

)o

octahedral

tetrahedral

OSPE OSPE

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 beunstable 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 eg1 or eg

3.

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.


• Consider the octahedral Cu2+ ion d9 t2g6 eg

3

• The eg levels are degenerate 3 electrons dx2-y

2 1 dz2 2 or dx

2-y

2 2 dz2 1

• Hence the degeneracy of the eg levels is lifted ligands along the axes experience different shielding effects 2 e-s vs. 1 e-.• Resulting in z -axis contraction (dx

2-y

2 2 dz2 1) or elongation (dx

2-y

2 1 dz2 2).

As the z axis elongation increases the energy of the dz2 orbital drops

lower than the dxy orbital which along with dx2-y

2 orbital rises in energy.

Cu2+

X'

X'

X

X X

X

Cu---X Cu---X΄X = Cl 2.30 2.95X = Br 2.40 3.18X = F 1.93 2.27


Δ

Veryrare

Also arises due to ligand dissimilarity, e.g. in MA4B2

•(dx2-y

21 dz2 2) due to the

2 electrons on the z axis the dz

2 orbital is more shielded from the Cu2+

centre elongation along this axes also called tetragonal distortion lower in energy.


• The distortion has resulted in lower energy for the system 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, t2g

3 eg2 , t2g

6, t2g6 eg

2 , t2g6 eg

4 .

•Important cases of distortion are: t2g3 eg

1 (high spin Cr2+ and Mn3+) andt2g

6 eg1 (low spin Co2+ and Mn3+)


eg

t2g

(a) Octahedralfield

(b) Small tetragonaldistortion

(c) Large tetragonaldistortion

dxy

dxz

dyz

dx2-y

2

dz2

dz2

dz2

dx2-y

2

dx2-y

2

dyz

dyz

dxzdxz

dxydxy

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) 4d and 5d complexes.

z

y

x

A square planar complex is obtained when it is energetically favourable to have the configuration dyz

2dxz2dxy

2dx2-y

22 for 4d8 and 5d8 ions.

dx2-y

2

dz2

dxy

} dxz; dyzFull dz

2 and empty dx2-y

2

• 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 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 < C2O4

2- < EDTA4- this is however not the case.

• Evidence from NMR & ESR unpaired e-n density on the ligands sharing of e-ns 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 Δoand the spectrochemical series by taking into account the roles of σ- and π- bonding in TM chemistry.

Molecular Orbital Theory (MOT) and Ligand–Field Theory (LFT)

z

y

x

Px

+-

z

y

x

Pz

-

+

z

y

x

Py

-+

z

y

x

-

+

z

y

x- +

z

y

x

s

+

z

y

x

++++

++

z

y

x++-

-

z

y

x++-

-

dx2-y2

Oh σ bonding

z

y

x-

+

z

y

x

+

+

--

--

t2g:Non bondingOrbitalsRemain localised on metal atom+

+

z

y

x

dz2

- -

Typical molecular energy levels diagram of an octahedral complex showing the frontier orbitals in the tinted box

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 orbitalsThe orbitals of the central metal atom divide by symmetry into 4 sets, viz:

Singly degenerate s a1gTriply degenerate p t1uDoubly degenerate d egTriply degenerate d t2g

• The ligand-field model for octahedral TM complexes such as Co(NH3)6

3+ 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

Oh σ bonding

• Summary:

• 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 metal-ligand overlap 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 σ-bonding only ligands, such as CH3

- and H-

π-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

Oh σ bonding

Answer:

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 strong or weakstrong field = low spin weak field = high spin

• Draw the energy level diagram

Oh σ bonding

4p

4s

3d

x2-y2 z2 xy xz yz NB MOs

Bonding MOs

Six donor orbitals

6NH3 each donating 2 e-s

Antibonding MOs

Atomic orbitals in metal ion Atomic orbitals in ligand ionMolecular orbitals

Molecular Orbital diagram for [CoIII(NH3)6]3+

Δο

Oh σ bonding

4p

4s

3d

x2-y2 z2 xy xz yz NB MOs

Bonding MOs

Six donor orbitals

6 F- each donating 2 e-s

Antibonding MOs

Atomic orbitals in metal ion Atomic orbitals in ligand ionMolecular orbitals

Molecular Orbital diagram for CoF63-

Δο

Oh σ bonding

Clearly good σ donor ligandResult in good M-L overlap

Strongly antibonding eg set

Ligand–Field Theory: π bonding

π bonding is important for ligands with orbitals of local π symmetry with respect to the M-L axis e.g. metal dxy and ligand py orbitals.These interaction with the previously NB metal t2gorbitals influences Δo. π-donor ligand has filled orbitals of π symmetry

These are π-bases, e.g. Cl-, Br-, OH- and H2O. These have L→M e-n donation.π-acceptor ligand has empty π orbitals that are available for occupation These are π acids, e.g. CO and PR3 ligands 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

Increasing Δo →π donor < weak π donor < no π effects < π acceptor

e.g. I-, Br- Cl- F- H2O NH3 PR3, CO

Summary:strong σ- or π-donor

weak field ligands.

π-acceptors strong field ligands.π donor ligands

lower in E than t2g.π acceptor ligands higher in E than t2g.

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