Ligand field theory considers the effect of different ligand environments (ligand fields) on the energies of the d- orbitals. The energies of the d orbitals in different environments determines the magnetic and electronic spectral properties of transition metal complexes. Ligand field theory combines an electrostatic model of metal-ligand interactions (crystal field theory) and a covalent model (molecular orbital theory).

Relative energies of metal-ion 3d electrons. Because the 4s 2 electrons are lost before the 3d, the highest occupied molecular orbitals (HOMOs) in transition metal complexes will contain the 3d electrons. M 2+ 3d 1 3d 2 3d 3 3d 4 3d 5 3d 6 3d 7 3d 8 3d 9 3d 10 Sc Ti V Cr Mn Fe Co Ni Cu Zn The distribution of the 3d electrons between the d-orbitals in any given complex will determine the magnetic properties of the complex (the number of unpaired electrons, the total spin (S) and the magnetic moment of the complex). Electronic transitions between the highest occupied d-orbitals will be responsible for the energies (λ max ) and intensities (  ) of the d-d bands in the electronic spectra of metal complexes. Electronic transitions to and from the highest occupied d-orbitals will be responsible for the energies and intensities of the ligand-to-metal (LMCT) and metal-to-ligand (MLCT) charge transfer bands appearing in the electronic spectra of metal complexes.

O h T d

 Octahedral 3d Complexes Δ o ≈ P(pairing energy) Both low-spin (Δ o ≤ P) and high-spin (P ≥ Δ o ) complexes are found.  Tetrahedral Complexes Δ Td = 4/9 Δ o hence P >> Δ Td and tetrahedral complexes are always high spin High-Spin and Low-Spin Complexes for 3d 4 – 3d 7 ions

Electronic structure of high-spin and low-spin O h complexes

Other factors influencing the magnitude of Δ-splitting Oxidation State Δ o (M 3+ ) > Δ o (M 2+ ) e.g. Δ o for Fe(III) > Fe(II). The higher oxidation state is likely to be low-spin 5d > 4d >3d e.g. Os(II) > Ru(II) > Fe(II) All 5d and 4d complexes are low-spin.

The nature of the ligand. Spectrochemical Ligand Series The ordering of the ligands in their ability to cause d-orbital splitting. I - < Br - < Cl - < SCN - < NO 3 - < OH - < C 2 O 4 2- < H 2 O ~ RS - < NCS - < NH 3 ~ imidazole < en < bipy < phen < NO 2 - < PPh 3 < CN - < CO Variations are due to σ-donating and Π-accepting properties of the ligand. Small Δ-splitting ligands are called weak field ligands. Large Δ-splitting ligands are called strong field ligands. Halide ions < O-donors < N-donors < Π-unsaturated Weak field ligands _______________Strong field ligands Small Δ-splitting Large Δ-splitting

Magnetic properties of transition metal complexes. Paramagnetism arises from the spin and orbital motions of unpaired electrons Diamagnetism arises from filled-shell electrons. Origin of Paramagnetism Spin angular momentum of unpaired electrons  obs = Orbital angular momentum of unpaired electrons Spin-orbit coupling Magnetic Moments of Transition Metal Ions The magnetic moment is related theoretically to the total spin quantum number (S) and total orbital angular momentum quantum number (L) of the ion.  S+L = For many transition metal complexes, the measured magnetic moment,  obs, is very close to the spin-only magnetic moment (orbital motion quenched).  obs ≈ = where n = number of unpaired electrons

Magnetic moments of high-spin and low-spin states d 4 -d 7

n SS  S+L =

Orbital contributions to magnetic moments. Quenching of orbital motion The ligand field restricts “orbital motions” of metal ion electrons. “An electron will have orbital motion about an axis only when the orbital it occupies can be transformed into an equivalent (and equal energy) orbital by a simple rotation about that axis” Only electrons in t 2g orbitals contribute to the orbital magnetic moment, but not when the t 2g orbitals are filled or half-filled. d xy and d x2-y2 equivalent after 45 o rotation but have different energy in ligand field d xz and d yz equivalent after 90 o rotation

Account for the magnetic moments of the following complexes [V(H 2 O) 6 ]Cl 3  = 3.10 [Co(NH 3 ) 6 ]Br 2  = 4.55 K 4 [Fe(CN) 6 ]  = 0

Antiferromagnetic Coupling of Electron Spin

Relative energies of d-orbitals in tetragonal and square planar geometries