Coordination Chemistry II

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Coordination Chemistry II

• Bonding, including crystal field theory and
  ligand field theory

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Basis for Bonding Theories

• Models for the bonding in transition metal
  complexes must be consistent with observed
  behavior. Specific data used include stability
  (or formation) constants, magnetic
  susceptibility, and the electronic (UV/Vis)
  spectra of the complexes.

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Bonding Approaches

• Valence Bond theory provides the hybridization
  for octahedral complexes. For the first row
  transition metals, the hybridization can be
  d2sp3 (using the 3d, 4s and 4p orbitals), or
  sp3d2 (using the 4s, 4p and 4d orbitals).
• The valence bond approach isnt used because it
  fails to explain the electronic spectra and
  magnetic moments of most complexes.

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Crystal Field Theory

• In crystal field theory, the electron pairs on
  the ligands are viewed as point negative charges
  that interact with the d orbitals on the central
  metal. The nature of the ligand and the tendency
  toward covalent bonding is ignored.

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d Orbitals
7
Crystal Field Theory

• Ligands, viewed as point charges, at the
  corners of an octahedron affect the various d
  orbitals differently.

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Crystal Field Theory
9
Crystal Field Theory

• The repulsion between ligand lone pairs and the
  d orbitals on the metal results in a splitting of
  the energy of the d orbitals.

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d Orbital Splitting
__ __ dz2 dx2-y2
eg
0.6?o
?o
__ __ __ __ __ Spherical field
0.4?o
__ __ __ dxy dxz dyz
t2g
Octahedral field
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d Orbital Splitting

• In some texts and articles, the gap in the d
  orbitals is assigned a value of 10Dq. The upper
  (eg) set goes up by 6Dq, and the lower set (t2g)
  goes down by 4Dq.
• The actual size of the gap varies with the
  metal and the ligands.

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d Orbital Splitting

• The colors exhibited by most transition metal
  complexes arises from the splitting of the d
  orbitals. As electrons transition from the lower
  t2g set to the eg set, light in the visible range
  is absorbed.

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d Orbital Splitting

• The splitting due to the nature of the ligand
  can be observed and measured using a
  spectrophotometer. Smaller values of ?o result
  in colors in the green range. Larger gaps shift
  the color to yellow.

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The Spectrochemical Series

• Based on measurements for a given metal ion,
  the following series has been developed
• I-ltBr-ltS2-ltCl-ltNO3-ltN3-ltF-ltOH-ltC2O42-ltH2O
• ltNCS-ltCH3CNltpyridineltNH3ltenltbipyltphen
• ltNO2-ltPPh3ltCN-ltCO

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The Spectrochemical Series

• The complexes of cobalt (III) show the shift in
  color due to the ligand.
• (a) CN, (b) NO2, (c) phen, (d) en, (e) NH3,
  (f) gly, (g) H2O, (h) ox2, (i) CO3 2.

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Ligand Field Strength Observations

• 1. ?o increases with increasing oxidation number
  on the metal.
• Mn2ltNi2ltCo2ltFe2ltV2ltFe3ltCo3
• ltMn4ltMo3ltRh3ltRu3ltPd4ltIr3ltPt4
• 2. ?o increases with increases going down a group
  of metals.

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Ligand Field Theory

• Crystal Field Theory completely ignores the
  nature of the ligand. As a result, it cannot
  explain the spectrochemical series.
• Ligand Field Theory uses a molecular orbital
  approach. Initially, the ligands can be viewed
  as having a hybrid orbital or a p orbital
  pointing toward the metal to make s bonds.

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Octahedral Symmetry

• http//www.iumsc.indiana.edu/morphology/symmetry/o
  ctahedral.html

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Ligand Field Theory
Consider the sigma bonds to all six ligands in
octahedral geometry.
Oh E 8C3 6C2 6C4 3C2 (C42) i 6S4 8S6 3sh 6sd
Gs 6 0 0 2 2 0 0 0 4 2
This reduces to A1g Eg T1u
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Ligand Field Theory

• The A1g group orbitals have the same symmetry
  as an s orbital on the central metal.

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Ligand Field Theory

• The T1u group orbitals have the same symmetry
  as the p orbitals on the central metal.
• (T representations are triply degenerate.)

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Ligand Field Theory

• The Eg group orbitals have the same symmetry as
  the dz2 and dx2-y2 orbitals on the central metal.
  
• (E representations are doubly degenerate.)

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Ligand Field Theory

• Since the ligands dont have a combination with
  t2g symmetry, the dxy, dyz and dxy orbitals on
  the metal will be non-bonding when considering s
  bonding.

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Ligand Field Theory

• The molecular orbital diagram is consistent
  with the crystal field approach.
• Note that the t2g set of orbitals is
  non-bonding, and the eg set of orbitals is
  antibonding.

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Ligand Field Theory

• The electrons from the ligands (12 electrons
  from 6 ligands in octahedral complexes) will fill
  the lower bonding orbitals.

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Ligand Field Theory

• The electrons from the 4s and 3d orbitals of
  the metal (in the first transition row) will
  occupy the middle portion of the diagram.

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Experimental Evidence for Splitting

• Several tools are used to confirm the splitting
  of the t2g and eg molecular orbitals.
• The broad range in colors of transition metal
  complexes arises from electronic transitions as
  seen in the UV/visible spectra of complexes.
• Additional information is gained from measuring
  the magnetic moments of the complexes.

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Experimental Evidence for Splitting

• Magnetic susceptibility measurements can be
  used to calculate the number of unpaired
  electrons in a compound.
• Paramagnetic substances are attracted to a
  magnetic field.

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Magnetic Moments

• A magnetic balance can be used to determine the
  magnetic moment of a substance. If a substance
  has unpaired electrons, it is paramagnetic, and
  attracted to a magnetic field.
• For the upper transition metals, the spin-only
  magnetic moment, µs, can be used to determine the
  number of unpaired electrons.
• µs n(n2)1/2

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Magnetic Moments

• The magnetic moment of a substance, in Bohr
  magnetons, can be related to the number of
  unpaired electrons in the compound.
• µs n(n2)1/2
• Where n is the number of unpaired electrons

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Magnetic Moments

• Complexes with 4-7 electrons in the d orbitals
  have two possibilities for the distribution of
  electrons. The complexes can be low spin, in
  which the electrons occupy the lower t2g set and
  pair up, or they can be high spin. In these
  complexes, the electrons will fill the upper eg
  set before pairing.

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High and Low Spin Complexes

• If the gap between the d orbitals is large,
  electrons will pair up and fill the lower (t2g)
  set of orbitals before occupying the eg set of
  orbitals. The complexes are called low spin.

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High and Low Spin Complexes

• In low spin complexes, the size of ?o is
  greater than the pairing energy of the electrons.

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High and Low Spin Complexes

• If the gap between the d orbitals is small,
  electrons will occupy the eg set of orbitals
  before they pair up and fill the lower (t2g) set
  of orbitals before. The complexes are called high
  spin.

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High and Low Spin Complexes

• In high spin complexes, the size of ?o is less
  than the pairing energy of the electrons.

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Ligand Field Stabilization Energy

• The first row transition metals in water are
  all weak field, high spin cases.

do d1 d2 d3 d4 d5 d6 d7 d8 d9 d10
LFSE 0 .4?o .8 1.2 .6 0 .4 .8 1.2 .6 0
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Experimental Evidence for LFSE

• The hydration energies of the first row
• transition metals should increase across the
  period as the size of the metal ion gets smaller.
• M2 6 H2O(l) ? M(H2O)62

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Experimental Evidence for LFSE

• The heats of hydration show two humps
  consistent with the expected LFSE for the metal
  ions. The values for d5 and d10 are the same as
  expected with a LFSE equal to 0.

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Experimental Evidence of LFSE
do d1 d2 d3 d4 d5 d6 d7 d8 d9 d10
LFSE 0 .4?o .8 1.2 .6 0 .4 .8 1.2 .6 0
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High Spin vs. Low Spin

• 3d metals are generally high spin complexes
  except with very strong ligands. CN- forms low
  spin complexes, especially with M3 ions.
• 4d 4d metals generally have a larger value of
  ?o than for 3d metals. As a result, complexes
  are typically low spin.

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Nature of the Ligands

• Crystal field theory and ligand field theory
  differ in that LFT considers the nature of the
  ligands. Thus far, we have only viewed the
  ligands as electron pairs used for making s bonds
  with the metal. Many ligands can also form p
  bonds with the metal. Group theory greatly
  simplifies the construction of molecular orbital
  diagrams.

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Considering p Bonding

• To obtain Gred for p bonding, a set of
  cartesian coordinates is established for each of
  the ligands. The direction of the s bonds is
  arbitrarily set as the y axis (or the py
  orbitals). The px and pz orbitals are used in p
  bonding.

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Considering p Bonding
z
x
z
y
x
y
x
y
y
x
Consider only the px and pz orbitals on each of
the ligands to obtain Gp.
z
z
y
z
x
y
z
x
Oh E 8C3 6C2 6C4 3C2 (C42) i 6S4 8S6 3sh 6sd
Gp 12 0 0 0 -4 0 0 0 0 0
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Considering p Bonding
Oh E 8C3 6C2 6C4 3C2 (C42) i 6S4 8S6 3sh 6sd
Gp 12 0 0 0 -4 0 0 0 0 0

• This reduces to T1g T2g T1u T2u. The T2g
  set has the same symmetry as the dxy, dyz and dxz
  orbitals on the metal. The T1u set has the same
  symmetry as the px, py and pz orbitals on the
  metal.

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Considering p Bonding

• ?p reduces to T1g T2g T1u T2u.
• The T1g and T2u group orbitals for the ligands
  dont match the symmetry of any of the metal
  orbitals.
• The T1u set has the same symmetry as the px, py
  and pz orbitals on the metal. These orbitals are
  used primarily to make the s bonds to the
  ligands.
• The T2g set has the same symmetry as the dxy, dyz
  and dxz orbitals on the metal.

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p Bonding

• The main source of p bonding is between the
  dxy, dyz and dxz orbitals on the metal and the d,
  p or p orbitals on the ligand.

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p Bonding

• The ligand may have empty d or p orbitals and
  serve as a p acceptor ligand, or full p or d
  orbitals and serve as a p donor ligand.

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p Bonding

• The empty p antibonding orbital on CO can
  accept electron density from a filled d orbital
  on the metal. CO is a pi acceptor ligand.

empty p orbital
filled d orbital
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p Donor Ligands (L?M)

• All ligands are s donors. Ligands with filled
  p or d orbitals may also serve as pi donor
  ligands. Examples of p donor ligands are I-,
  Cl-, and S2-. The filled p or d orbitals on
  these ions interact with the t2g set of orbitals
  (dxy, dyz and dxz) on the metal to form bonding
  and antibonding molecular orbitals.

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p Donor Ligands (L?M)

• The bonding orbitals, which are lower in
  energy, are primarily filled with electrons from
  the ligand, the and antibonding molecular
  orbitals are primarily occupied by electrons from
  the metal.

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p Donor Ligands (L?M)

• The size of ?o decreases, since it is now
  between an antibonding t2g orbital and the eg
  orbital.
• This is confirmed by the spectrochemical
  series. Weak field ligands are also pi donor
  ligands.

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p Acceptor Ligands (M?L)

• Ligands such as CN, N2 and CO have empty p
  antibonding orbitals of the proper symmetry and
  energy to interact with filled d orbitals on the
  metal.

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p Acceptor Ligands (M?L)

• The metal uses the t2g set of orbitals (dxy,
  dyz and dxz) to engage in pi bonding with the
  ligand. The p orbitals on the ligand are
  usually higher in energy than the d orbitals on
  the metal.

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p Acceptor Ligands (M?L)

• The metal uses the t2g set of orbitals (dxy,
  dyz and dxz) to engage in pi bonding with the
  ligand. The p orbitals on the ligand are
  usually higher in energy than the d orbitals on
  the metal.

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p Acceptor Ligands (M?L)

• The interaction causes the energy of the t2g
  bonding orbitals to drop slightly, thus
  increasing the size of ?o.

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Summary

• 1. All ligands are s donors. In general, ligand
  that engage solely in s bonding are in the middle
  of the spectrochemical series. Some very strong
  s donors, such as CH3- and H- are found high in
  the series.
• 2. Ligands with filled p or d orbitals can also
  serve as p donors. This results in a smaller
  value of ?o.

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Summary

• 3. Ligands with empty p, d or p orbitals can
  also serve as p acceptors. This results in a
  larger value of ?o.
• I-ltBr-ltCl-ltF-ltH2OltNH3ltPPh3ltCO
• p donorlt weak p donorlts onlylt p acceptor

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4 Coordinate Complexes

• Square planar and tetrahedral complexes are
  quite common for certain transition metals. The
  splitting patterns of the d orbitals on the metal
  will differ depending on the geometry of the
  complex.

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Tetrahedral Complexes

• The dz2 and dx2-y2 orbitals point directly
  between the ligands in a tetrahedral arrangement.
  As a result, these two orbitals, designated as e
  in the point group Td, are lower in energy.

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Tetrahedral Complexes

• The t2 set of orbitals, consisting of the dxy,
  dyz, and dxz orbitals, are directed more in the
  direction of the ligands.
• These orbitals will be higher in energy in a
  tetrahedral field due to repulsion with the
  electrons on the ligands.

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Tetrahedral Complexes

• The size of the splitting, ?T, is considerable
  smaller than with comparable octahedral
  complexes. This is because only 4 bonds are
  formed, and the metal orbitals used in bonding
  dont point right at the ligands as they do in
  octahedral complexes.

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Tetrahedral Complexes

• In general, ?T 4/9 ?o. Since the splitting
  is smaller, all tetrahedral complexes are
  weak-field, high-spin cases.

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Tetragonal Complexes

• Six coordinate complexes, notably those of
  Cu2, distort from octahedral geometry. One such
  distortion is called tetragonal distortion, in
  which the bonds along one axis elongate, with
  compression of the bond distances along the other
  two axes.

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Tetragonal Complexes

• The elongation along the z axis causes the d
  orbitals with density along the axis to drop in
  energy. As a result, the dxz and dyz orbitals
  lower in energy.

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Tetragonal Complexes

• The compression along the x and y axis causes
  orbitals with density along these axes to
  increase in energy.
• .

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Tetragonal Complexes

• For complexes with 1-3 electrons in the eg set
  of orbitals, this type of tetragonal distortion
  may lower the energy of the complex.

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Square Planar Complexes

• For complexes with 2 electrons in the eg set of
  orbitals, a d8 configuration, a severe distortion
  may occur, resulting in a 4-coordinate square
  planar shape, with the ligands along the z axis
  no longer bonded to the metal.

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Square Planar Complexes

• Square planar complexes are quite common for
  the d8 metals in the 4th and 5th periods Rh(I),
  IR(I), Pt(II), Pd(II) and Au(III). The lower
  transition metals have large ligand field
  stabalization energies, favoring four-coordinate
  complexes.

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Square Planar Complexes

• Square planar complexes are rare for the 3rd
  period metals. Ni(II) generally forms
  tetrahedral complexes. Only with very strong
  ligands such as CN-, is square planar geometry
  seen with Ni(II).

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Square Planar Complexes

• The value of ?sp for a given metal, ligands and
  bond length is approximately 1.3(?o).

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The Jahn-Teller Effect

• If the ground electronic configuration of a
  non-linear complex is orbitally degenerate, the
  complex will distort so as to remove the
  degeneracy and achieve a lower energy.

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The Jahn-Teller Effect

• The Jahn-Teller effect predicts which
  structures will distort. It does not predict the
  nature or extent of the distortion. The effect
  is most often seen when the orbital degneracy is
  in the orbitals that point directly towards the
  ligands.

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The Jahn-Teller Effect

• In octahedral complexes, the effect is most
  pronounced in high spin d4, low spin d7 and d9
  configurations, as the degeneracy occurs in the
  eg set of orbitals.

d4 d7 d9
eg t2g
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The Jahn-Teller Effect

• The strength of the Jahn-Teller effect is
  tabulated below (wweak, sstrong)

e- 1 2 3 4 5 6 7 8 9 10
High spin s - w w
Low spin w w - w w - s - s -
There is only 1 possible ground state
configuration. - No Jahn-Teller distortion is
expected.
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Experimental Evidence of LFSE
do d1 d2 d3 d4 d5 d6 d7 d8 d9 d10
LFSE 0 .4?o .8 1.2 .6 0 .4 .8 1.2 .6 0