Download Electronic structure and spectra Shriver, Chapter 19

Electronic structure and spectra
Shriver, Chapter 19
Crystal field theory
An ionic model, considers metal and its ligands as point charges
All 5 d-orbitals are isoenergetic in a spherical environment/crystal field (i.e., free atom)
Different arrangements of charges/ligands cause different splittings of the d-orbitals into
different energy levels, although the overall energy center (barycenter) does not change
Octahedral symmetry
dz2 and dx2-y2 orbitals (which point along the M-L bonds) are destabilized relative to dxy,
dxz, dyz (which point in between the M-L bonds)
the energy difference between them is Δ
dz2 and dx2-y2 orbitals are doubly degenerate in energy (symbol eg)
dxy, dxz, dyz are triply degenerate in energy (symbol t2g)
eg (z2, x2-y2)
0.6!
d
!
0.4!
t2g (xy, xz, yz)
spherical
symmetry
octahedral
symmetry
electronic transition (UV-visible spectrum) for a d1 ion is t2g  eg and its energy is Δ
(also called 10Dq in some books)
the magnitude of Δ depends on the nature of M
larger for higher oxidation states of the same metal ion and across a row, due to
the decreasing cation radius, resulting in more interaction with the ligands
increases down a triad as the extension of the d orbitals increases
the magnitude of Δ depends on the nature of L (empirically: the spectrochemical series)
halides < OH- < H2O < NH3 < PPh3 < CN- < CO
weak xtal field
strong xtal field
Crystal field stabilization energy (CFSE)/ligand field stabilization energy (LFSE)
CFSE = (0.4x – 0.6y) Δ
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where x is the number of t2g electrons and y is the number of eg electrons
should we fill all the t2g orbitals first? yes, when the CFSE is greater than the electron
pairing energy P
when does this occur? when Δ is large
i.e., in the second and third row
i.e., when L is a strong-field ligand
we put three unpaired e- into the t2g orbitals, but the fourth, fifth and sixth e- will be spinpaired
these will be low-spin complexes
however, if P > CFSE (i.e., Δ is small), then the fourth and fifth e- will go unpaired into
the eg orbitals
these will be high-spin complexes
similar considerations apply for seven ee.g., low-spin d4: t2g4eg0, 2 unpaired ee.g., low-spin d7: t2g6eg1, 1 unpaired e-
high-spin d4: t2g3eg1, 4 unpaired ehigh-spin d7: t2g5eg2, 3 unpaired e-
note: there is no classification of high- and low-spin for octahedral complexes with d0, d1,
d2, d3, d8, d9, d10 electron configurations
CFSE increases in high-spin complexes from d0 to d3, decreases to d5, then increases to d8
-
complexes with d3 and d8 electron configurations have a strong preference to be
octahedral
since there is no CFSE in d0, (weak field) d5 and d10 complexes, these show no
strong structural preference
Hydration enthalpies (water is a weak-field ligand) vary in the same way as the CFSE,
superimposed on the general increasing hydration enthalpy from right to left across the
3rd row
Lattice enthalpies show a similar trend
Spin can be detected experimentally by measuring magnetic dipole moment of a sample
- a compound with no unpaired electrons is repelled by an external magnetic field
(diamagnetic)
- a compound with unpaired electrons is attracted to an external magnetic field
(paramagnetic)
the magnetic moment µ contributed by the spin angular momentum of unpaired electrons
is
2
1
µ = 2{S ( S + 1)} 2 µB
!
where S is the total spin (quantized in units of ½) and µB is a constant called the Bohr
magneton:
µB =
!
eh
= 9.274 "10#24 JT #1
2me
Often the measured magnetic moment is not quite the same as the predicted spin-only
value, because of the contribution of orbital angular momentum
Tetrahedral symmetry
The ligands lie along the directions defined by the dxy, dxz and dyz orbitals – these are
destabilized while the dz2 and dx2-y2 orbitals are aligned between the M-L bonds and are
consequently stabilized (note: no gerade subscript in tetrahedral symmetry: there is no
center of symmetry)
t2 (xy, xz, yz)
0.4!
d
!
0.6!
e (z2, x2-y2)
spherical
symmetry
tetrahedral
symmetry
the value of Δ is smaller for tetrahedral symmetry than for octahedral symmetry, and
therefore tetrahedral complexes are almost always high spin
Square-planar symmetry
Favored in a strong crystal field (usually, 2nd and 3rd row metals) with d8 configuration:
oxidation state 0 in group 8: Ru(0), Os(0)
oxidation state +1 in group 9: Rh(I), Ir(I)
oxidation state +2 in group 10: Pd(II), Pt(II)
oxidation state +3 in group 11: Ag(III), Au(III)
Consider an octahedral complex from which the two axial ligands are removed:
- one of the original eg orbitals, dx2-y2, remains destabilized (directly interacting
with ligands) but the other one, dz2, is stabilized
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- two of the original t2g orbitals, dxy and dyz, are stabilized relative to dxz
x2-y2
eg
xy
d
z2
spherical
symmetry
t2g
octahedral
symmetry
xz, yz
square planar
symmetry
(the energy ordering of the dxy and dz2 orbitals depends on the particular complex)
this distribution of orbital energies allows the 7th and 8th d electrons to become paired,
leaving the dx2-y2 orbital empty (compare to octahedral symmetry, which requires one
electron in dx2-y2)
note: stabilizing a filled d orbital at the expense of destabilizing another filled d orbital
gains you nothing, but stabilizing a filled orbital while destabilizing an empty d orbital
results in a lower overall energy (since an orbital costs nothing energetically if it is not
occupied)
Tetragonal distortion
even if the value of Δ is not so large, a distortion away from octahedral symmetry (Oh)
towards square planar symmetry (D4h) may be favorable, if the stabilization gained is
greater than the price of destabilization
this occurs when degenerate orbitals are filled unsymmetrically
e.g., low-spin d7:
d9:
x2-y2
z2
eg
x2-y2
z2
eg
xy
xz, yz
t2g
Oh
xy
xz, yz
t2g
Oh
D4h
4
D4h
the effect is also seen in complexes with high-spin complexes:
e.g., d4:
x2-y2
z2
eg
xy
xz, yz
t2g
Oh
D4h
examples of metal cations which commonly show strong tetragonal distortions (JahnTeller distortion) are Cu2+ (d9) and Cr2+ (d4)
the distortion results in enhanced lability of ligands in complexes with these metals
compare Cr(H2O)63+, d3, octahedral with large CFSE
this complex is inert, the release of water ligands (exchange)
is very slow (k = 3 x 10-6 s-1, t1/2 = 60 h)
with Cr(H2O)62+, d4, pseudo-octahedral with strong Jahn-Teller distortion
this complex is labile, the release of the axial water ligands occurs very
rapidly (k = 3 x 108 s-1, t1/2 = 2 ns)
tetragonal distortions are much less important in tetrahedral complexes because the
overall d-orbital splitting is much smaller
Ligand field theory
Takes into account the molecular orbitals created by the overlap of ligand orbitals with
metal orbitals (instead of treating the ligands as point charges, as in crystal field theory)
Ligands can be σ-donors, π-donors, or π-acceptors
We have already seen one important consequence of this, in the π-backbonding of ligands
like CO and CN- to the metal
What is the effect of this covalent bonding on Δ?
Consider first the case of ligands which are σ-donors only, e.g., NH3
In octahedral symmetry, the six metal valence orbitals with the correct symmetry to form
metal-ligand σ-bonds are s, px3 and the eg set of d orbitals (dz2, dx2-y2).
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The filled ligand σ-orbitals are lower in energy than the metal valence orbitals.
The overlap of the ligand orbitals with the eg orbitals causes eg* to rise in energy (it
becomes the major contributor to the antibonding orbital) which increases Δ
p
s
eg*
eg
!
t2g
t2g
metal
complex
ligands
but consider that H2O is higher in the spectrochemical series than OH-, so the strength of
σ-donation is not the only effect
ligands often have more than one lone pair, and the additional lone pairs can participate
in π-donation to the metal via overlap of the filled p orbitals with the t2g orbitals
this raises the energy of t2g, decreasing Δ
eg*
!
eg
t2g*
t2g
lone
pairs
metal
complex
ligands
clearly, in comparing OH- and H2O, the stronger π-donation by OH- is a more important
effect than its stronger σ-donation
Some ligands do not have additional lone pairs but they do have empty (antibonding)
orbitals of π-symmetry: they are π-acceptors
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examples are CO, CNthese π* orbitals lie above the energy of the t2g orbitals. Overlap between empty π* and
filled t2g causes the latter to decrease in energy. The consequence is an increase in Δ.
eg*
"*
eg
!
t2g
t2g
metal
complex
ligands
This accounts for strong π acceptors at the top of the spectrochemical series.
Electronic spectra
Arise from electronic transitions, i.e., promotion of a valence electron from a lower
energy orbital to a higher energy orbital
Usually requires energy in the visible or the UV part of the electromagnetic spectrum
Transitions between (mostly metal-based) orbitals in a partly-filled d subshell are called
d-d transitions
for example, t2g1eg0  t2g0eg1 , one d-d transition, with energy Δ
but, t2g3eg0  t2g2eg1, two d-d transitions
the electron promoted to an eg orbital can occupy either dz2 or dx2-y2
same energy: dxz  dz2, dyz  dz2, dxy  dx2-y2
different energy: dxz  dx2-y2, dyz  dx2-y2, dxy  dz2
don't worry about term symbols!
Selection rule 1 (spin-selection rule): spin must be conserved during an electronic
transition
Therefore a transition in which spin must change is spin-forbidden (has very low
intensity)
e.g., Mn(H2O)62+, high spin d5, t2g3eg2, d-d transitions are spin-forbidden, pale pink
e.g., Cr(H2O)62+, high spin d4, t2g3eg1, d-d transition is spin-allowed, bright blue
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Selection rule 2 (Laporte selection rule): parity must change during an electronic
transition
For octahedral symmetry, this means the orbital symmetry must change from g to u or
from u to g
Therefore d-d transitions are Laporte-forbidden (have low intensity)
They become “a little bit allowed” due to molecular vibrations that temporarily reduce
the symmetry
The intensity of an electronic transition is reflected by its extinction coefficient ε
(Beer’s Law, Abs = ε C l)
For spin-allowed, Laporte-forbidden d-d transitions, ε = ca. 100 M-1 cm-1
For spin-forbidden, Laporte-forbidden d-d transitions, ε = ca. 1 M-1 cm-1
A transition from a (mostly ligand-based) orbital to a (mostly metal-based) orbital is
called a ligand-to-metal charge transfer (LMCT)
These are generally spin-allowed and Laporte-allowed, with ε = ca. 104-105 M-1 cm-1
Important in d0 complexes where no d-d transitions are possible
e.g., MnO4-, d0, LMCT gives intense purple color
A transition from a (mostly metal-based) orbital to a (mostly ligand-based) orbital is
called a metal-to-ligand charge transfer (MLCT)
Important in electron-rich metals with ligands that have π* orbitals
e.g., Ru(bpy)32+
Luminescence
A molecule in its ground state (lowest electronic energy level) that absorbs a photon and
undergoes an electronic transition finds itself in an excited electronic state, designated *
e.g., [Ru(bpy)32+] + hν  [Ru(bpy)32+]*  [Ru(bpy)32+] + energy
The energy is then lost and the molecule returns to the ground state
Can be lost through transfer of thermal energy to the surroundings (non-radiative decay)
Or by emission of a photon – luminescence (radiative decay)
Two kinds:
(1) fluorescence – spin-allowed, same spin-state in excited and ground states
rapid, few ns
(2) phosphorescence – spin-forbidden, different spin-state in excited and ground
states: slower, few µs
how does the spin-state in the excited state become different from the ground-state?
Intersystem crossing from one excited state to another (e.g., singlet to triplet)
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