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 d3 d4 So, what is going on here!!

Strong field Weak field 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 Pairing Energy!!. Strong field = Low spin (2 unpaired) D0, Weak field = High spin (4 unpaired) P < Do P > Do

= sum of all Pc and Pe interactions Pairing Energy, P The pairing energy, P, is made up of two parts. Pc: Coulombic repulsion energy caused by having two electrons in same orbital. Destabilizing energy contribution of Pc for each doubly occupied orbital. 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 = sum of all Pc and Pe interactions How do we get these interactions?

Placing electrons in d orbitals High Low High Low High Low 1 u.e. 5 u.e. d5 0 u.e. 4 u.e. d6 1 u.e. 3 u.e. d7 2 u.e. d8 1 u.e. d9 0 u.e. d10

Detail working out…. d5 1 u.e. 5 u.e. High Field Low Field (Low Spin) (High Spin) What are the energy terms for both high spin and low spin? 1 u.e. 5 u.e. d5 Low Field Coulombic Part = 0 High Field Exchange part = for 3Pe + Pe Coulombic Part = 2Pc P = 4Pe Exchange part = for 3Pe LFSE = 3*(-2/5D0) + 2 (3/5D0) = 0 For 1Pe P = 2Pc + 4Pe High Field – Low Field = -2D0 +2Pe LFSE = 5 * (-2/5D0) = -2D0 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 d2 d3 d4 d5 d6 d7 d8 d9 d10 LFSE (in D0) .0 .4 .8 1.2 .6 .0 .4 .8 1.2 .6 .0

Splitting of d orbitals in a tetrahedral field Dt e Dt = 4/9Do Always weak field (high spin)

Extreme elongation: from octahedral to square planar Less repulsions along the axes where ligands are missing

A correction to preserve 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

Values of magnetic moment

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

The symmetry of metal orbitals in an octahedral environment T2g Eg

The symmetry of metal orbitals in an octahedral environment

Metal-ligand s interactions in an octahedral environment Six ligand orbitals of s symmetry approaching the metal ion along the x,y,z axes 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

non bonding anti bonding “metal character” “d0-d10 electrons” 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

We now look at things more closely. 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.

The bonding orbitals, essentially the ligand lone pairs, ML6 s-only bonding non bonding anti bonding “metal character” “d0-d10 electrons” The bonding orbitals, essentially the ligand lone pairs, will not be worked with further. 6 s ligands x 2e each 12 s bonding e “ligand character”

t2g eg eg t2g Stabilization 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) These are the SALC formed from the p orbitals of the ligands that can interac with the d on the metal. t2g (π*) t2g eg eg Do D’o Do has increased t2g Stabilization t2g (π) ML6 s-only ML6 s + π (empty π-orbitals on ligands)

eg eg t2g t2g t2g (π*) t2g (π) 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 eg D’o Do Do has decreased t2g (π*) 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) 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- Weak field, p donors small D high spin Strong field, p acceptors large D low spin s only

Turning to Square Planar Complexes 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 Sample π- bonding eg s-only bonding

A crystal-field aproach: from octahedral to tetrahedral Less repulsions along the axes where ligands are missing

A correction to preserve A crystal-field aproach: from octahedral to tetrahedral A correction to preserve center of gravity

“there cannot be unequal occupation of orbitals with identical energy” 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. 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’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 2 ¼ ¾ 3 4 5 6 7 1/3 8 9 10 11 3/16 9/16 12 1/4 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.