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Metal-Ligand bonding in transition metal
complexes

A covalent bond forms between two atoms
when an orbital on one atom overlaps with
the orbital on another atom
Total number of electrons on both orbitals is no
more than two.
 In transition metal complexes, covalent bonds
are formed via overlap of a completely filled
ligand orbital and a vacant hybrid orbital on metal
ion.
 Hybridization determines the geometry of the
molecule
If geometry is known, the hybrid orbitals of
the metal ion used in the bonding is known.
Hybrid orbitals for common geometries in complexes
CN
2
4
4
6
Geometry
linear
tetrahedral
square planar
octahedral
Hybrid orbitals
sp
sp3
dsp2
d2sp3, sp3d2
Color and Magnetism
Color of a complex depends on; (i) the metal, (ii) its oxidation state & (iii) ligands (i.e.,
everything)
For example, pale blue [Cu(H2O)6]2+ versus dark blue
[Cu(NH3)6]2+.
Partially filled d orbitals usually give rise to colored
complexes because they can absorb light from the
visible region of the spectrum.
 The color of the complex is the sum of the light not
absorbed (reflected) by the complex.
 A plot of absorption intensity of light versus
wavelength is called an absorption spectrum for the
complex or compound.
Since the spectrum for [Ti(H2O)6]3+ has a maximum absorption at 510 nm
(green & yellow), & transmits all other wavelengths, the complex is
purple.
Transition metal complexes that are paramagnetic
have unpaired e-’s & those that are diamagnetic have
no unpaired e-’s.


Consider the d6 Co metal ion:
[Co(NH3)6]3+ has no unpaired electrons, but [CoF6]3has four unpaired electrons per ion.
(note, s e-’s are lost first before d e-’s in a metal cation)
We need to develop a bonding theory to account for both
color and magnetism in transition metal complexes.
 A Spectrochemical series is a listing of ligands in order of
their ability to increase :
Cl- < F- < H2O < NH3 < en < NO2- (N-bonded) < CN Weak field ligands (Cl- & F-) lie on the low end of the
spectrochemical series.
 Strong field ligands (CN-) lie on the high end of the
spectrochemical series.
Octahedral Complexes
Recall that the s e-’s are lost first for the metal ion. So, Ti3+ is
d1, V3+ is a d?? and Cr3+ is a d?? ion.
 We apply Hund’s rule to the 2 sets of 5 d-orbitals.
 The first three e-’s go into different d orbitals with
their spins parallel.
 We have a choice for the placement of the fourth
electron:
 if it goes into a higher energy orbital, then there is an
energy cost associated with promotion ();
 if it goes into a lower energy orbital, then there is an
energy cost associated with e- spin pairing.
Weak-field ligands
(which have a small )
tend to favor adding
electrons to the higherenergy orbitals (high-spin
complexes) because  is
less than the spin-pairing
energy.
Strong-field ligands (which have a large ) tend to
favor adding electrons to lower-energy orbitals (lowspin complexes) because  is greater than the spinpairing energy.
Tetrahedral & Square-Planar
In a tetrahedral field the dxy, dyz, & dxz orbitals are
of higher E than the dx2-y2 and the dz2 orbitals.
 Because there are only 4 ligands,  for a tetrahedral
field is smaller than  for an octahedral field.
 This causes all tetrahedral complexes to be high spin
(unless told otherwise).
Figure 23.24A Splitting of d-orbital energies by a tetrahedral
field of ligands.
The splitting of d-orbital energies is less in a tetrahedral
than an octahedral complex, and the relative d-orbital
energies are reversed. Only high-spin tetrahedral
complexes are known because Δ is small.
Square planar complexes can be thought
of as octahedral complexes with the two
ligands along the z-axis removed.
 As a consequence the four planar ligands are drawn
in closer towards the metal.
 Relative to the octahedral field, the dz2 orbital is
greatly lowered in energy, the dyz, and dxz orbitals
lowered in energy, the dxy, and dx2-y2 orbitals are
raised in energy.
Most d8 metal ions
form square planar
complexes.
The majority of
complexes are low
spin (i.e.
diamagnetic).
Examples: Pd2+,
Pt2+, Ir+, and Au3+.
Figure 23.24B Splitting of d-orbital energies by a square planar
field of ligands.
Square planar complexes are low-spin and usually diamagnetic
because the four pairs of d electrons fill the four lowest-energy orbitals.
The Magnetic Properties of Transition
Metal Complexes
Magnetic properties are determined by the number of
unpaired electrons in the d orbitals of the metal ion.
Hund’s rule states that e- occupy orbitals of equal energy
one at a time. When all lower energy orbitals are halffilled:
- The next e- can enter a half-filled orbital and pair up by
overcoming a repulsive pairing energy, (Epairing).
- The next e- can enter an empty, higher, energy orbital by
overcoming Δ.
The number of unpaired e- will depend on the relative
sizes of Epairing and Δ.
Figure 23.22
High-spin and low-spin octahedral complex
ions of Mn2+.
Figure 23.23 Orbital occupancy for high-spin and low-spin
octahedral complexes of d4 through d7 metal ions.
high spin:
weak-field
ligand
low spin:
strong-field
ligand
high spin:
weak-field
ligand
low spin:
strong-field
ligand
Sample Problem 23.6 Identifying High-Spin or Low-Spin Complex
Ions
PROBLEM: Iron (II) forms a complex in hemoglobin. For each of the
two octahedral complex ions [Fe(H2O)6]2+ and [Fe(CN)6]4,
draw an energy diagram showing orbital splitting, predict
the number of unpaired electrons, and identify the ion as
low spin or high spin.
PLAN:
Fe2+ electron configuration shows the number of d
electrons, and the spectrochemical series shows the
relative ligand strengths. We draw energy diagrams and
separate the t2g and eg orbital sets more for the strong-field
ligand. Then we add electrons, noting that a weak-field
ligand gives the maximum number of unpaired electrons
and a high-spin complex, whereas the strong-field ligand
will give the minimum number of unpaired electrons and a
low-spin complex.
Sample Problem 23.6
↑
↑↓ ↑
eg
↑
eg
↑
t2g
Potential energy
Potential energy
SOLUTION:
↑↓ ↑↓ ↑↓ t2g
[Fe(H2O)6]2+
[Fe(CN)6]4-
high-spin
low-spin