Coordination Chemistry II: Bonding

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Coordination Chemistry II Bonding

• Chapter 10

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Thermodynamic Data

• Stability constants or formation constants are
  often used to indicate bond strengths.
• What does a high formation constant mean?
• Thermodynamic data is most valuable in predicting
  relationships among similar complexes.
• Formation constants can be affected by enthalpy
  and entropy changes.
• Table 10-2 and the chelate effect.

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Magnetic Susceptibility

• Diamagnetic versus paramagnetic complexes.
• Measurement (Figure 10-1).
• Commonly provides mass susceptibility per gram.

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Contributions to the Magnetic Moment

• Spin magnetic moment
• S maximum total spin in the complex
• O atom
• Orbital angular momentum
• Characterized by the quantum number L which is
  equal the maximum possible sum of ml values.
• O atom

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Contributions to the Magnetic Moment

• Usually, the spin-only moment is sufficient to
  calculate the magnetic moment.
• Especially for the first transition series
• where g is approximated to be 2 and n is the
  number of unpaired electrons.
• Determine the spin-only and complete magnetic
  moment for Fe.

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Electronic Spectra

• Orbital energy levels can be obtained directly
  from electron spectra (covered earlier).
• This chapter illustrates simple energy level
  diagrams that are commonly more complex.
• Based upon subtle differences in electronic
  spectra, the structure may be predicted with some
  success.

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Theories of Electronic Structure

• Valence Bond Theory Not commonly used, but the
  hybrid notation is still common.
• Crystal Field Theory An electrostatic approach
  used to describe the splitting in metal d-orbital
  energies. Does not describe bonding.
• Ligand Field Theory A more complete description
  of bonding in terms of the electronic energy
  levels of the frontier orbitals. Commonly does
  not include energy of the bonding orbitals.
• Angular Overlap Method Used to estimate the
  relative magnitude of the orbital energies in a
  MO calculation.

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Valence bond Theory (hybridization)

• A set of hybrid orbitals is produced to explain
  the bonding.
• Octahedral d2sp3 (6 hybrid orbitals of equal
  energy)
• Tetrahedral - ??
• Uses inner and outer orbitals to explain the
  experimentally determined unpaired electrons.
• The magnetic behavior determines which d orbitals
  (e.g. 3d or 4d) are used for bonding (Figure
  10-2).

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Valence Bond Description

• Two configurations are possible for d4-d7 ions.
• Fe(III) has 5 electrons in the d-orbitals.
• One unpaired electron, the ligands are strong
  and force the metal d electrons to pair up.
• Strong-field (bind strongly) ? low spin complex
• The hybridization orginates from the 3d inner
  orbitals (d2sp3).
• Five unpaired electrons, the ligands are weak
  and cannot force the metal d electrons to pair
  up.
• Weak-field (bind weakly) ?high spin
• The hybridization originates from the 4d outer
  orbitals (sp3d2).

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Crystal Field Theory

• The ligand octahedral field repels electrons in
  the d orbitals.
• Amount of repulsion depends on the orientation of
  the d orbitals.
• are oriented directly
  toward these ligands.
• dxy, dxz, and dyz are directed between the
  ligands.
• Which set is lower in energy?

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Crystal Field Theory

• The average energy of the d-orbitals in the
  present of the octahedral field is greater than
  than of the free ion.
• Energy difference between the two sets is equal
  to ?O.
• The t2g set is lowered by 0.4 ?O and the eg set
  is raised by 0.6 ?O.
• Crystal field stabilization energy (CFSE) The
  energy difference between the actual distribution
  of electrons and that for all electrons in the
  uniform field.
• Equal to LFSE (later)
• Drawbacks

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Ligand Field Theory Octahedral Complexes

• Consider ?-type bonding between the ligands and
  the metal atom/ion.
• Construct LGOs (performed previously).
• What is the reducible representation?
• Construct the LGOs (pictures).
• Construct the molecular orbitals with the metal
  orbitals.
• Same symmetry types.
• A group of metal orbitals do not have the
  appropriate symmetry?
• Which orbitals are these? Symmetry type?
  Bonding?
• Look at Figure 10-5.

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SF6 py orbitals on fluorine
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Ligand Field Theory Octahedral Complexes

• The six bonding orbitals are largely filled by
  the electrons from the ligands.
• The higher MOs (e.g. t2g and eg) are largely
  filled by the electrons on the metal atom/ion.
• The ligand field treatment largely focuses on the
  t2g and higher orbitals.
• The split between the two sets of orbitals, t2g
  and eg, is called ?O.

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Ligand Field Theory Octahedral Complexes

• Ligands whose orbitals interact strongly with the
  metal orbitals are called strong-field ligands.
• Strong-field ? large ?O ? low spin (why?)
• Ligands with small interactions are called
  weak-field ligands.
• Weak-field ? small ?O ? high spin (why?)
• For d0 d3 and d8-d10 only one electron
  configuration is possible (no difference in net
  spin).
• For d4 d7 there is a difference between strong-
  and weak-field cases.

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Low Spin Versus High Spin

• Energy of pairing electrons
• ?c is the Coulombic energy of repulsion (always
  positive when pairing) and ?e is the quantum
  mechanical exchange energy (always negative).
• ?e relates to the number of exchangeable pairs in
  a particular electron configuration. This term
  is negative and depends on the number of possible
  states.
• Determine ?c and ?e for a d5 metal complex (low
  and high spin).

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Low Spin Versus High Spin

• The relationship between ?O, ?c, and ?e
  determines the orbital configuration.
• ? is largely independent on the ligands while ?O
  is strongly dependent.
• Look at Table 10-6 which gives these parameters
  for aqueous (aqua) ions.
• ?O for 3 ions is larger than ?O for 2 ions.
• ?O values for d5 are smaller than d4 and d6.

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Low Spin Versus High Spin

• If ?Ogt?, there is a lower energy upon pairing in
  the lower levels (low spin).
• If ?Olt?, there is a lower energy with unpaired
  electrons in the lower levels (high spin).
• In Table 10-6, Co(H2O)63 is probably the only
  complex that could be low spin.

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Ligand Field Stabilization Energies (LFSE)

• The difference (1) the total energy of a
  coordination complex with the electron
  configuration resulting from ligand field
  splitting of the orbitals and (2) the total
  energy for the same complex with all the orbitals
  equally populated is the LFSE.
• -2/5?O 3/5?O (d4 to d7 complexes)
• Table 10-7

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Enthalpy Relationships

• M2(g) 6H2O(l) ? M(H2O)62
• H2O is a weak field ligand.
• What accounts for the general decrease in ?H?
• What about the double hump?
• ?O is determined generally determined
  experimentally.

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Pi Bonding in Octahedral Complexes

• The x and z axes must be taken as a single set
  producing a combined LGO set. Why?
• Be able to derive the reducible representation.
• ?? T1g T2g T1u T2u
• How will the LGOs combine with orbitals from the
  metal atom/ion?
• Discuss the overlap between the ?-bonding LGOs
  and the p-orbitals of T1u symmetry.

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Pi Bonding in Octahedral Complexes

• The main addition to the interaction diagram is
  between the t2g orbitals of the metal and LGOs.
• These were nonbonding when only considering
  ?-type bonding (look at Figure 10-5).
• Pi bonding may occur when the ligands have
  available p or ? molecular orbitals.

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Ligands with Empty ? Orbitals

• Examine the example for the CN- ligand in the
  book (Figure 10-9).
• The HOMO forms the LGOs from ?-type bonding
  (already discussed previously).
• The LUMO, 1?, also forms a reducible set of LGOs
  (T1g T2g T1u T2u).
• Examine Figure 10-10 to illustrate effectiveness
  of overlap.

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Ligands with Empty ? Orbitals

• The resulting t2g LGOs are generally higher in
  energy than the initial t2g orbitals on he metal.
• Bonding/antibonding t2g orbitals will result.
• What will this do to ?O and the bond strength?
• Figure 10-11.
• This is termed as metal-to-ligand ? bonding or ?
  back-bonding.
• Some of the electron density in the d orbitals on
  the metal is donated back to the ligands.
• The ligands are termed as ?-acceptor ligands.

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Ligands with Filled ?-Type Orbitals

• Ligands such as F- or Cl- will possess molecular
  ? orbitals that possess electrons.
• This set of t2g orbitals are generally lower in
  energy than the t2g orbitals on the metal.
• What are the consequences?
• Examine Figure 10-11.
• Ligand-to-metal ? bonding (?-donor ligands).
• This bonding is generally less favorable. Why?

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Square-Planar Complexes

• The y-axis is pointed toward the center atom.
• LGOs for sigma-type bonding.
• The ?-bonding orbitals on the x- and z-axes have
  to be considered separately? Why?
• These are termed as ??? (px) and ?? (pz)
• Examine Table 10-9.
• What is the symmetry of a square-planar complex?

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Square-Planar ComplexesSigma-Type Bonding Only

• Finding the LGOs.
• ?red A1g B1g Eu
• What are the orbitals on the central metal atom
  that can interact with these LGOs?
• Inspecting the character table reveals that the
  metal d-orbitals are split into three
  representations. Why?
• Examine Figure 10-13.
• The energy difference between the eg/b2g
  nonbonding orbitals and the a1g antibonding is ?.

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Square-Planar ComplexesIncluding Pi-Bonding

• ?px A2g B2g Eu (???)
• What are the interacting orbitals on the metal?
• ?pz A2u B2u Eg (??)
• What are the interacting orbitals on the metal?
• The effective overlap of the p orbitals on the
  metal to form ? bonds is small. Why?
• Examine Figure 10-15.

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The Sets of Orbitals in Figure 10-15

• The 1st set contains bonding orbitals (mostly
  sigma).
• 8 electrons from the ligands largely fill these
  orbitals.
• The 2nd set contains 8 ?-donor orbitals of the
  ligands.
• This interaction is small and decreases the
  energy differences in orbitals the next higher
  set.
• The 3rd set is primarily metal d-orbitals with
  some modifications due to interactions with the
  ligands.
• ?3, ?2, and ?1 are in this set.
• The 4th set largely originates from the ?
  orbitals of the ligands (if present).
• One of the main effects of these orbitals is the
  increase in the gap energy labeled ?1.

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Angular Overlap (Crystal Field)

• Estimates the strength of interaction between
  individual ligand orbitals and d-orbitals based
  on the overlap between them. These values are
  then combined for all ligands and d-orbitals.
• The value for a given d-orbital is the sum of the
  numbers for the appropriate ligands in a column.
• This number can be positive or negative depending
  on location of the ligand and d-orbitals.
• The value for a given ligand is the sum of the
  numbers for all d-orbitals in the row.
• This number can also be positive or negative
  depending on location of the ligand and
  d-orbitals.

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Angular Overlap

• Sigma-donor interaction (no pi-orbitals are
  available).
• M(NH3)6n
• The strongest interaction is between the metal
  dz2 orbital and a ligand p-orbital (or
  appropriate MO).
• Describe the interaction based on this method.
• Table 10-11 and Figure 10-20.

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Angular Overlap

• Pi-acceptor ligands (available ?-type orbitals).
• Strongest interaction is between dxz and ? on
  the ligand.
• The ? orbitals are almost always higher in
  energy.
• Reverse the signs.
• Figure 10-22 and Table 10-12
• There is a lowering of 4e? due to this
  interaction.
• Why is magnitude e? always smaller than that of
  e??
• Understand ?-donor interactions.

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The Spectrochemical Series

• ? depends on the relative energies and the degree
  of overlap.
• How ligands effect ?
• ?-donor ligands
• ?-donating
• ?-accepting (or back bonding)
• Understand the spectrochemical series (page 368)

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Magnitude of e?, e?, and ?

• Changing the metal and/or ligand effects the
  magnitudes of e? and e?, thereby changing the
  value of ?.
• Aqua species of Co2 and Co3
• Fe(H2O)62 versus Fe(H2O)63
• Tables 10-13 and 10-14 (Angular Overlap)
• e? gt e? (always)
• Values decrease with increasing size and
  decreasing electronegativity
• Negative values for e?. Why?

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The Jahn Teller Effect

• There cannot be unequal occupation of orbitals
  with identical energies. The molecule will
  distort so that these orbitals are no longer
  degenerate.
• Cu(II) d9 ion, The complex will distort. How?
• The low-spin Cr(II) complex is octahedral with
  tetragonal distortion (Oh ? D4h)
• Two absorption bands are observed instead of one.

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Determining Four- and Six-Coordinate Preferences

• General angular overlap calculations of the
  energies expected for different number of d
  electrons and different geometries can give us
  some indication of relative stabilities.
• Larger number of bonds usually make the
  octahedral complexes more stable. Why are the
  energies equal in the d5, d6, and d7 cases?
• Figure 10-27.

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Determining Four- and Six-Coordinate Preferences

• The success of these simplistic calculations is
  variable.
• The s- and p-orbitals of the metal are not
  included.
• No ?-type interactions are included in Figure
  10-27.
• The orbital potential energies for the metals
  change with increasing atomic number (more
  negative).
• Can add 0.3e? ? (increase in Z) as a rough
  correction to the total enthalpy.

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The Process for a Complex of D3h Symmetry

• Construct the sigma-type bonding LGOs for the
  complex.
• Determine the interacting orbitals on the center
  atom.
• Construct a table to determine e? (and e? if
  appropriate).
• Construct the MO diagram and overlap energy
  figure.
• Homework Determine the e? contribution.