Coordination ChemistryBonding in transition-metal complexes

Crystal field theory: an electrostatic model

+

-

-

--

-

-

The metal ion will be positive and therefore attract the negatively charged ligands

But there are electrons in the metal orbitals, which will experience repulsionswith the negatively charged ligands

Ligand/d orbital interactions

Orbitals point at ligands(maximum repulsion)

Orbitals pointbetween ligands

(less pronounced repulsion)

The two effects of the crystal field

o

3/5 o

2/5 o

o is the crystal field splitting

t2g

eg

E(t2g) = -0.4o x 3 = -1.2o

E(eg) = +0.6o x 2 = +1.2o

Splitting of d orbitals in an octahedral field

The magnitude of the splitting(ligand effect)

Strongfield

Weakfield

The spectrochemical series

CO, CN- > phen > NO2- > en > NH3 > NCS- > H2O > F- > RCO2

- > OH- > Cl- > Br- > I-

The magnitude of the splitting(metal ion effect)

Strongfield

Weakfield

increases with increasing formal charge on the metal ion

increases on going down the periodic table

o ≈ M ∑ nlLl x 103

Predicts value of (cm-1)nl is # of ligands Ll

The splitting constant must depend on both the ligand and the metal.

d1 d2

d3 d4

Placing electrons in d orbitalsStrong field Weak field Strong field Weak field

d4

Strong field =Low spin

(2 unpaired)

Weak field =High spin

(4 unpaired)

< o > o

When the 4th electron is assigned it will either go into the higher energy eg orbital at an energy cost of 0 or be paired at an energy cost of , the pairing energy.

Notes: the pairing energy, P, is made up of two parts. 1) Coulombic repulsion energy caused by having two electrons in same orbital

Pairing Energy, The pairing energy, , is made up of two parts.

1) Coulombic repulsion energy caused by having two electrons in same orbital. Destabilizing energy contribution of c for each doubly occupied orbital.

2) Exchange stabilizing energy for each pair of electrons having the same spin and same energy. Stabilizing contribution of e for each pair having same spin and same energy

= sum of all c and e interactions

Placing electrons in d orbitals

1 u.e. 5 u.e.

d5

0 u.e. 4 u.e.

d6

1 u.e. 3 u.e.

d7

2 u.e. 2 u.e.

d8

1 u.e. 1 u.e.

d9

0 u.e. 0 u.e.

d10

Positive favors high spin. Neg favors low spin.

Enthalpy of Hydration of hexahydrate

Splitting of d orbitals in a tetrahedral field

t2

e

t

t = 4/9o

Always weak field (high spin)

Magnetic properties of metal complexes

Diamagnetic complexesvery small repulsive

interaction with external magnetic field

no unpaired electrons

Paramagnetic complexesattractive interaction with

external magnetic fieldsome unpaired electrons

)2( nns

Measured magnetic moments include contributions from both spin and orbital spin. In the first transition series complexes the orbital contribution is small and usually ignored.

Coordination Chemistry:Molecular orbitals for metal complexes

The symmetry of metal orbitals in an octahedral environment

A1g

T1u

T2g

Eg

The symmetry of metal orbitals in an octahedral environment

The symmetry of metal orbitals in an octahedral environment

s

M

z

Metal-ligand interactions in an octahedral environment

Six ligand orbitals of symmetry approaching the metal ion along the x,y,z axes

We can build 6 group orbitals of symmetry as beforeand work out the reducible representation

s

If you are given , you know by now how to get the irreducible representations

= A1g + T1u + Eg

s

Now we just match the orbital symmetries

6 ligands x 2e each

12 bonding e“ligand character”

“d0-d10 electrons”

non bonding

anti bonding

“metal character”

Introducing π-bonding

2 orbitals of π-symmetryon each ligand

We can build 12 group orbitalsof π-symmetry

π = T1g + T2g + T1u + T2u

Anti-bonding LUMO(π)

The CN- ligand

Some schematic diagrams showing how p bonding occurs with a ligand having a d orbital (P), a * orbital, and a vacant p orbital.

6 ligands x 2e each

12 bonding e“ligand character”

“d0-d10 electrons”

non bonding

anti bonding

“metal character”

ML6 -only bonding

The bonding orbitals, essentially the ligand lone pairs, will not be worked with further.

t2g

eg

t2g

ML6

-onlyML6

+ π

Stabilization

(empty π-orbitals on ligands)

o’o o has increased

π-bonding may be introducedas a perturbation of the t2g/eg set:

Case 1 (CN-, CO, C2H4)empty π-orbitals on the ligands

ML π-bonding (π-back bonding)

t2g (π)

t2g (π*)

eg

t2g

eg

t2g

ML6

-onlyML6

+ π

π-bonding may be introducedas a perturbation of the t2g/eg set.

Case 2 (Cl-, F-) filled π-orbitals on the ligands

LM π-bonding

(filled π-orbitals)

Stabilization

Destabilization

t2g (π)

t2g (π*)

eg’o

oo has decreased

Strong field / low spin Weak field / high spin

Putting it all on one diagram.

Spectrochemical Series

Purely ligands:

en > NH3 (order of proton basicity)

donating which decreases splitting and causes high spin:: H2O > F > RCO2 > OH > Cl > Br > I (also proton basicity)

Adding in water, hydroxide and carboxylate

: H2O > F > RCO2 > OH > Cl > Br > I

accepting ligands increase splitting and may be low spin

: 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, acceptors large low spin

onlyWeak field, donors small high spin

Turning to Square Planar Complexes

y

x

zMost convenient to use a local coordinate system on each ligand with

y pointing in towards the metal. py to be used for bonding.

z being perpendicular to the molecular plane. pz to be used for bonding perpendicular to the plane, .

x lying in the molecular plane. px to be used for bonding in the molecular plane, |.

ML4 square planar complexesligand group orbitals and matching metal orbitals

ML4 square planar complexesMO diagram

-only bonding - bonding

A crystal-field aproach: from octahedral to tetrahedral

LM

L L

L

L

L

LM

L L

L

Less repulsions along the axeswhere ligands are missing

A crystal-field aproach: from octahedral to tetrahedral

A correction to preservecenter of gravity

The Jahn-Teller effect

Jahn-Teller theorem: “there cannot be unequal occupation of orbitals with identical energy”

Molecules will distort to eliminate the degeneracy

Angular Overlap Method

An attempt to systematize the interactions for all geometries.

M

1

65

4 2

3

M

109

78

M 2

6

1

12

11

The various complexes may be fashioned out of the ligands above

Linear: 1,6

Trigonal: 2,11,12

T-shape: 1,3,5

Tetrahedral: 7,8,9,10

Square planar: 2,3,4,5

Trigonal bipyramid: 1,2,6,11,12

Square pyramid: 1,2,3,4,5

Octahedral: 1,2,3,4,5,6

Cont’dAll 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-y2dxy dxz dyz

1 1 e 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) e

= 18/16 e in a trigonal bipyramid complex due to interaction. The dxy, equivalent by symmetry, is destabilized by the same

amount. The dz2 is destabililzed by 11/4 e.