Ligand field theory considers the effect of different ligand

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• 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).

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Relative energies of metal-ion 3d electrons.

• Because the 4s2 electrons are lost before the 3d,
  the highest occupied molecular orbitals (HOMOs)
  in transition metal complexes will contain the 3d
  electrons.
• M2 3d1 3d2 3d3 3d4 3d5
  3d6 3d7 3d8 3d9
  3d10
• 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 (?max) and intensities (e) 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.

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Oh
Td
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High-Spin and Low-Spin Complexes for 3d4 3d7
ions

• Octahedral 3d Complexes
• ?o P(pairing energy)
• Both low-spin (?o P) and high-spin (P
  ?o )
• complexes are found.
• Tetrahedral Complexes
• ?Td 4/9 ?o hence P gtgt ?Td and
  tetrahedral
• complexes are always high spin

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Electronic structure of high-spin and low-spin Oh
complexes
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Other factors influencing the magnitude of
?-splitting

• Oxidation State
• ?o (M3) gt ?o(M2)
• e.g. ?o for Fe(III) gt Fe(II).
• The higher oxidation state is likely to be
  low-spin
• 5d gt 4d gt3d
• e.g. Os(II) gt Ru(II) gt Fe(II)
• All 5d and 4d complexes are low-spin.

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• The nature of the ligand.
• Spectrochemical Ligand Series
• The ordering of the ligands in their ability to
  cause d-orbital splitting.
• I- lt Br- lt Cl- lt SCN- lt NO3- lt OH- lt C2O42- lt
  H2O RS- lt NCS- lt NH3
• imidazole lt en lt bipy lt phen lt NO2- lt PPh3
  lt CN- lt CO
• Variations are due to s-donating and ?-accepting
  properties of the ligand.
• Small ?-splitting ligands are called weak field
  ligands.
• Large ?-splitting ligands are called strong field
  ligands.
• Halide ions lt O-donors lt N-donors lt
  ?-unsaturated
• Weak field ligands _______________Strong field
  ligands

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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.
• ?SL
• 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

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Magnetic moments of high-spin and low-spin states
d4-d7
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n mS mSL

1 1.73 3.00
2 2.83 4.47
3 3.87 5.20
4 4.90 5.48
5 5.92 5.92

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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 t2g orbitals contribute to the
  orbital magnetic moment, but not when the t2g
  orbitals are filled or half-filled.

dxz and dyz equivalent after 90o rotation
dxy and dx2-y2 equivalent after 45o rotation but
have different energy in ligand field
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Account for the magnetic moments of the
following complexes

• V(H2O)6Cl3 m 3.10
• Co(NH3)6Br2 m 4.55

K4Fe(CN)6 m 0
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Antiferromagnetic Coupling of Electron Spin
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Relative energies of d-orbitals in tetragonal and
square planar geometries