Transcript Coordination Chemistry II: Bonding

Coordination Chemistry II:
Bonding
Chapter 10
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.
Magnetic Susceptibility
• Diamagnetic versus paramagnetic complexes.
– Measurement (Figure 10-1).
• Commonly provides mass susceptibility per gram.
1
2
  2.828( T)   magnetic susceptibi lity
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
 S  L  g [ S ( S  1)]  [ 1 4 L( L  1)]
Contributions to the Magnetic
Moment
• Usually, the spin-only moment is sufficient
to calculate the magnetic moment.
– Especially for the first transition series
S  g S(S  1) or n(n  2)
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.
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.
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.
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).
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).
Crystal Field Theory
• The ligand octahedral field repels electrons in the d orbitals.
– Amount of repulsion depends on the orientation of the d orbitals.
• d z 2 and d x 2  y 2 are oriented directly toward these ligands.
• dxy, dxz, and dyz are directed between the ligands.
Which set is lower in energy?
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
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.
SF6
py orbitals
on fluorine
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.
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.
Low Spin Versus High Spin
• Energy of pairing electrons
  c  e
– 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).
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.
Low Spin Versus High Spin
• If O>, there is a lower energy upon
pairing in the lower levels (low spin).
• If O<, there is a lower energy with
unpaired electrons in the lower levels (high
spin).
• In Table 10-6, [Co(H2O)6]3+ is probably the
only complex that could be low spin.
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
Enthalpy Relationships
• M2+(g) + 6H2O(l) 
[M(H2O)6]2+
– 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.
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.
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.
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.
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.
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?
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?
Square-Planar Complexes
Sigma-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 .
Square-Planar Complexes
Including 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.
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.
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.
Angular Overlap
• Sigma-donor interaction (no pi-orbitals are
available).
– [M(NH3)6]n+
• 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.
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.
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)
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)6]2+ versus [Fe(H2O)6]3+
• Tables 10-13 and 10-14 (Angular Overlap)
– e > e (always)
– Values decrease with increasing size and decreasing
electronegativity
– Negative values for e. Why?
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.
Determining Four- and SixCoordinate 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.
Determining Four- and SixCoordinate 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.
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.