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7/27/2019 Chemistry 445 Lecture 16 Crystal Field Theory
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Bonding in complexes of d-block
metal ions Crystal Field Theory.
energy eg
t2gCo3+ ion
in gas-phase
(d6)
Co(III) in
complex
3d sub-shell
d-shell
split by
presence
of liganddonor-atoms
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The d-orbitals: thet2gset
theegset
dyz dxy dxz
dz2 dx2-y2
x x x
x x
zzz
zz
y y y
y y
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Splitting of the d sub-shell in
octahedral coordination
dyz dz2 dx2-y2
the three orbitals of
thet2gset lie between
the ligand donor-atoms(only dyzshown)
the two orbitals of the egset lie along theCartesian coordinates, and so are adjacent
to the donor atoms of the ligands, which
raises the egset in energy
z z z
blue = ligand donor
atom orbitals theegsetthet2gset
y y y
x x x
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energy
eg
t2gCo3+ ion
in gas-phase(d6)
Co(III) in
octahedral
complex
3d sub-shell
d-shell
split by
presenceof ligand
donor-atoms
Splitting of the d sub-shell in
an octahedral complex
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The crystal field splitting parameter ()
Different ligands produce different extents of splitting betweenthe egand the t2glevels. This energy difference is the crystalfield splitting parameter, also known as 10Dq, and has unitsof cm-1. Typically, CN- produces very large values of, while F-produces very small values.
[Cr(CN)6]3- [CrF6]3-
eg eg
t2g
t2g
energy
= 26,600 cm-1 = 15,000 cm-1
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High and low-spin complexes:
energyeg eg
t2gt2g
low-spin d6
electrons fill the t2glevel first. In this
case the complex is diamagnetic
high-spin d6
electrons fill the whole d sub-
shell according to Hunds rule
The d-electrons in d4 to d8 configurations can be high-spin, where they
spread out and occupy the whole d sub-shell, or low-spin, where the t2glevel is filled first. This is controlled by whether is larger than the spin-
pairing energy, P, which is the energy required to take pairs of electrons
with the same spin orientation, and pair them up with the opposite spin.
> P < P
Paramagnetic
4 unpaired es
diamagnetic
no unpaired es
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energyeg eg
t2gt2g
low-spin d5 ([Fe(CN)6]3-)
electrons fill the t2glevel first. In this
case the complex is paramagnetic
high-spin d5 ([Fe(H2O)6]3+)
electrons fill the whole d sub-shell
according to Hunds rule
For d5 ions P is usually very large, so these are mostly high-spin. Thus,
Fe(III) complexes are usually high-spin, although with CN- is large enough
that [Fe(CN)6]3- is low spin: (CN- always produces the largest values)
> P < P
Paramagnetic
5 unpaired es
paramagnetic
one unpaired e
High and low-spin complexes of d5 ions:
[Fe(CN)6]3- = 35,000 cm-1
P = 19,000 cm-1[Fe(H2O)6]
3+ = 13,700 cm-1
P = 22,000 cm-1
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energyeg eg
t2g t2g
low-spin d7 ([Ni(bipy)3]3+)
The d-electrons fill the t2glevel first,
and only then does an electronoccupy the eglevel.
high-spin d7 ([Co(H2O)6]3+)
electrons fill the whole d sub-shell
according to Hunds rule
The d7 metal ion that one commonly encounters is the Co(II) ion. For metal
ions of the same electronic configuration, tends to increase M(II) < M(III) P < P
Paramagnetic
3 unpaired es
paramagnetic
one unpaired e
High and low-spin complexes of d7 ions:
[Ni(bipy)3]3+ [Co(H2O)6]
2+ = 9,300 cm-1
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energyeg eg
t2gt2g
low-spin d6 ([Co(CN)6]4-)
electrons fill the t2glevel first. In this
case the complex is diamagnetic
high-spin d5 ([CoF6]3-)
electrons fill the whole d sub-shell
according to Hunds rule
For d6 ions is very large for an M(III) ion such as Co(III), so all Co(III)
complexes are low-spin except for [CoF6]3-.high-spin. Thus,
Fe(III) complexes are usually high-spin, although with CN- is large enoughthat [Fe(CN)6]
3- is low spin: (CN- always produces the largest values)
>> P < P
Paramagnetic4 unpaired es
diamagnetic
no unpaired es
High and low-spin complexes of some d6 ions:
[Co(CN)6]3- = 34,800 cm-1
P = 19,000 cm-1
[CoF6]3- = 13,100 cm-1
P = 22,000 cm-1
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The spectrochemical series:
One notices that with different metal ions the order of
increasing with different ligands is always the same.
Thus, all metal ions produce the highest value of in
their hexacyano complex, while the hexafluoro complexalways produces a low value of. One has seen how in
this course the theme is always a search for patterns.
Thus, the increase in with changing ligand can be
placed in an order known as the spectrochemical series,
which in abbreviated form is:
I- < Br- < Cl- < F- < OH- H2O < NH3 < CN-
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The place of a ligand in the spectrochemical series is determined
largely by its donor atoms. Thus, all N-donor ligands are close to
ammonia in the spectrochemical series, while all O-donor ligands
are close to water. The spectrochemical series follows the positions
of the donor atoms in the periodic table as:
C N O F
P S Cl
Br
I
The spectrochemical series:
S-donors
between Br
and Cl
very little
data onP-donors
may be higher
than N-donors
?
spectrochemical
series followsarrows around
starting at I and
ending at C
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Thus, we can predict that O-donor ligands such as oxalate or
acetylacetonate will be close to water in the spectrochemical series.It should be noted that while en and dien are close to ammonia in
the spectrochemical series, 2,2bipyridyl and 1,10-phenanthroline
are considerably higher than ammonia because their sp2 hybridized
N-donors are more covalent in their bonding than the sp3 hybridized
donors of ammonia.
The spectrochemical series:
O
O-
O
-O O O
-
H3C CH3
H2N NH2
H2N NH
NH2N N N N
oxalate acetylacetonate en
dien bipyridyl 1,10-phen
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For the first row of donor atoms in the periodic table,namely C, N, O, and F, it is clear that what we areseeing in the variation of is covalence. Thus, C-donorligands such as CN- and CO produce the highest values
of because the overlap between the orbitals of the C-atom and those of the metal are largest. For the highlyelectronegative F- ion the bonding is very ionic, andoverlap is much smaller. For the heavier donor atoms,one might expect from their low electronegativity, more
covalent bonding, and hence larger values of. Itappears that is reduced in size because ofoverlapfrom the lone pairs on the donor atom, and the t2gsetorbitals, which raises the energy of the t2gset, and solowers.
The bonding interpretation of
the spectrochemical series:
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When splitting of the d sub-shell occurs, the occupation
of the lower energy t2glevel by electrons causes astabilization of the complex, whereas occupation of the
eglevel causes a rise in energy. Calculations show that
thet2glevel drops by 0.4, whereas the eglevel is raisedby 0.6. This means that the overall change in energy,the CFSE, will be given by:
CFSE = (0.4n(t2g) - 0.6n(eg))
where n(t2g) and n(eg) are the numbers of electrons in
the t2gand eglevels respectively.
Crystal Field Stabilization
Energy (CFSE):
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The CFSE for some complexes is calculated to be:
[Co(NH3)6]3+: [Cr(en)3]
3+
egeg
t2gt2g
= 22,900 cm-1 = 21,900 cm-1
CFSE = 22,900(0.4 x 6 0.6 x 0) CFSE = 21,900(0.4 x 3 0.6 x 0)
= 54,960 cm-1
= 26,280 cm-1
Calculation of Crystal Field
Stabilization Energy (CFSE):
energy
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The CFSE for high-spin d5 and for d10 complexes iscalculated to be zero:
[Mn(NH3)6]2+: [Zn(en)3]
3+
egeg
t2gt2g
= 22,900 cm-1 = not known
CFSE = 10,000(0.4 x 3 0.6 x 2) CFSE = (0.4 x 6 0.6 x 4)
= 0 cm-1
= 0 cm-1
Crystal Field Stabilization Energy
(CFSE) of d5 and d10 ions:
energy
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For M(II) ions with the same set of ligands, the variation of is not large.One can therefore use the equation for CFSE to calculate CFSE in terms of
for d0 through d10 M(II) ions (all metal ions high-spin):
Ca(II) Sc(II) Ti(II) V(II) Cr(II) Mn(II) Fe(II) Co(II) Ni(II) Cu(II) Zn(II)
d0 d1 d2 d3 d4 d5 d6 d7 d8 d9 d10
CFSE: 0 0.4 0.8 1.2 0.6 0 0.4 0.8 1.2 0.6 0
This pattern of variation CFSE leads to greater stabilization in the complexes
of metal ions with high CFSE, such as Ni(II), and lower stabilization for the
complexes of M(II) ions with no CFSE, e.g. Ca(II), Mn(II), and Zn(II). The
variation in CFSE can be compared with the log K1 values for EDTA
complexes on the next slide:
Crystal Field Stabilization Energy
(CFSE) of d0 to d10 M(II) ions:
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CFSE as a function of no of d-electrons
0
0.2
0.4
0.6
0.8
1
1.2
1.4
0 1 2 3 4 5 6 7 8 9 10 11
no of d-electrons
CFSE
inmultiplesof
Crystal Field Stabilization Energy (CFSE) of
d0 to d10 M(II) ions:
Ca2+ Mn2+ Zn2+
double-humped
curve
Ni2+
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log K1(EDTA) as a function of no of d
electrons
10
12
14
16
18
20
0 1 2 3 4 5 6 7 8 9 10 11
no of d-electrons
logK1(EDTA
).
Log K1(EDTA) of d0 to d10 M(II) ions:
Ca2+
Mn2+
Zn2+
double-
humped
curve
= CFSE
rising baseline
due to ioniccontraction
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log K1(en) as a function of no of d-
electrons
0
2
4
6
8
10
12
0 1 2 3 4 5 6 7 8 9 10 11
no of d-electrons
logK1(en).
Log K1(en) of d0 to d10 M(II) ions:
double-
humpedcurve
Ca2+ Mn2+
Zn2+
rising baseline
due to ionic
contraction
= CFSE
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log K1(tpen) as a function of no of d-
electrons
0
5
10
15
20
0 1 2 3 4 5 6 7 8 9 10 11
no of d-electrons
logK1(tpen).
Log K1(tpen) of d0 to d10 M(II) ions:
Ca2+
Mn2+
Zn2+
double-
humpedcurve
N N NN
N Ntpen
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Irving and Williams noted that because of CFSE, the logK1 values for virtually all complexes of first row d-blockmetal ions followed the order:
Mn(II) < Fe(II) < Co(II) < Ni(II) < Cu(II) > Zn(II)
We see that this order holds for the ligand EDTA, en,
and TPEN on the previous slides. One notes that Cu(II)
does not follow the order predicted by CFSE, which
would have Ni(II) > Cu(II). This will be discussed under
Jahn-Teller distortion of Cu(II) complexes, which leads to
additional stabilization for Cu(II) complexes over what
would be expected from the variation in CFSE.
The Irving-Williams Stability Order: