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Bonding in complexes of d-block metal ions – Crystal Field Theory.
energy eg
t2g
Co3+ ionin gas-phase
(d6)
Δ
Co(III) in complex
3d sub-shell
d-shellsplit bypresenceof liganddonor-atoms
The d-orbitals: the t2g
set
the eg
set
dyz dxy dxz
dz2 dx2-y2
x x x
x x
zzz
zz
y y y
y y
Splitting of the d sub-shell in octahedral coordination
dyz dz2 dx2-y2
the three orbitals of
the t2g set lie between
the ligand donor-atoms
(only dyz shown)
the two orbitals of the eg set lie along the
Cartesian coordinates, and so are adjacentto the donor atoms of the ligands, which
raises the eg set in energy
z z z
blue = ligand donor atom orbitals the egsetthe t2g set
y y y
x x x
energy
eg
t2gCo3+ ion
in gas-phase(d6)
Δ
Co(III) in octahedral
complex
3d sub-shell
d-shellsplit bypresenceof liganddonor-atoms
Splitting of the d sub-shell in an octahedral complex
The crystal field splitting parameter (Δ)
Different ligands produce different extents of splitting between
the eg and the t2g levels. This energy difference is the crystal field splitting parameter Δ, also known as 10Dq, and has units of cm-1. Typically, CN- produces very large values of Δ, while F- produces very small values.
[Cr(CN)6]3- [CrF6]3-
eg eg
t2g
t2g
energy
Δ = 26,600 cm-1 Δ = 15,000 cm-1
High and low-spin complexes:
energy
eg eg
t2gt2g
low-spin d6
electrons fill the t2g level first. In this case the complex is diamagnetic
high-spin d6
electrons fill the whole d sub-shell according to Hund’s 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 t2g
level is filled first. This is controlled by whether Δ 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.
Δ > P Δ < P
Paramagnetic4 unpaired e’s
diamagneticno unpaired e’s
energy
eg eg
t2gt2g
low-spin d5 ([Fe(CN)6]3-)electrons fill the t2g level first. In this case the complex is paramagnetic
high-spin d5 ([Fe(H2O)6]3+)electrons fill the whole d sub-shell
according to Hund’s 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- Δ is large enoughthat [Fe(CN)6]3- is low spin: (CN- always produces the largest Δ values)
Δ > P Δ < P
Paramagnetic5 unpaired e’s
paramagneticone unpaired e
High and low-spin complexes of d5 ions:
[Fe(CN)6]3- Δ = 35,000 cm-1
P = 19,000 cm-1
[Fe(H2O)6]3+ Δ = 13,700 cm-1
P = 22,000 cm-1
energy
eg eg
t2gt2g
low-spin d7 ([Ni(bipy)3]3+)The d-electrons fill the t2g level first,
and only then does an electronoccupy the eg level.
high-spin d7 ([Co(H2O)6]3+)electrons fill the whole d sub-shell
according to Hund’s rule
The d7 metal ion that one commonly encounters is the Co(II) ion. For metalions of the same electronic configuration, Δ tends to increase M(II) < M(III) < M(IV), so that Co(II) complexes have a small Δ and are usually high spin. The (III) ion Ni(III) has higher values of Δ, and is usually low-spin.
Δ > P Δ < P
Paramagnetic3 unpaired e’s
paramagneticone unpaired e
High and low-spin complexes of d7 ions:
[Ni(bipy)3]3+ [Co(H2O)6]2+ Δ = 9,300 cm-1
energy
eg eg
t2gt2g
low-spin d6 ([Co(CN)6]4-)electrons fill the t2g level first. In this
case the complex is diamagnetic
high-spin d5 ([CoF6]3-)electrons fill the whole d sub-shell
according to Hund’s rule
For d6 ions Δ 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- Δ is large enoughthat [Fe(CN)6]3- is low spin: (CN- always produces the largest Δ values)
Δ >> P Δ < P
Paramagnetic4 unpaired e’s
diamagneticno unpaired e’s
High and low-spin complexes of some d6 ions:
[Co(CN)6]3- Δ = 34,800 cm-1
P = 19,000 cm-1
[CoF6]3- Δ = 13,100 cm-1
P = 22,000 cm-1
The spectrochemical series:
One notices that with different metal ions the order of increasing Δ with different ligands is always the same. Thus, all metal ions produce the highest value of Δ in their hexacyano complex, while the hexafluoro complex always produces a low value of Δ. One has seen how in this course the theme is always a search for patterns. Thus, the increase in Δ 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-
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 Brand Cl
very littledata onP-donors –may be higherthan N-donors
?
spectrochemicalseries followsarrows aroundstarting at I andending at C
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, 2,2’bipyridyl 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
For the first row of donor atoms in the periodic table, namely C, N, O, and F, it is clear that what we are seeing in the variation of Δ is covalence. Thus, C-donor ligands such as CN- and CO produce the highest values of Δ because the overlap between the orbitals of the C-atom and those of the metal are largest. For the highly electronegative F- ion the bonding is very ionic, and overlap is much smaller. For the heavier donor atoms, one might expect from their low electronegativity, more covalent bonding, and hence larger values of Δ. It appears that Δ is reduced in size because of π–overlap from the lone pairs on the donor atom, and the t2g set orbitals, which raises the energy of the t2g set, and so lowers Δ.
The bonding interpretation of the spectrochemical series:
When splitting of the d sub-shell occurs, the occupation of the lower energy t2g level by electrons causes a
stabilization of the complex, whereas occupation of the eg level causes a rise in energy. Calculations show that the t2g level drops by 0.4Δ, whereas the eg level is raised by 0.6Δ. This means that the overall change in energy, the CFSE, will be given by:
CFSE = Δ(0.4n(t2g) - 0.6n(eg))
where n(t2g) and n(eg) are the numbers of electrons in
the t2g and eg levels respectively.
Crystal Field Stabilization Energy (CFSE):
The CFSE for some complexes is calculated to be:
[Co(NH3)6]3+: [Cr(en)3]3+
egeg
t2gt2g
Δ = 22,900 cm-1 Δ = 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
The CFSE for high-spin d5 and for d10 complexes is calculated to be zero:
[Mn(NH3)6]2+: [Zn(en)3]3+
egeg
t2gt2g
Δ = 22,900 cm-1 Δ = not known
CFSE = 10,000(0.4 x 3 – 0.6 x 2) CFSE = Δ(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
For M(II) ions with the same set of ligands, the variation of Δ is not large. One can therefore use the equation for CFSE to calculate CFSE in terms of Δ 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 0.4Δ 0.8Δ 1.2Δ 0.6Δ 0 0.4Δ 0.8Δ 1.2Δ 0.6Δ 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:
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
CF
SE
in m
ult
iple
s o
f Δ
.
Crystal Field Stabilization Energy (CFSE) of d0 to d10 M(II) ions:
Ca2+ Mn2+ Zn2+
double-humpedcurve
Ni2+
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
log
K1(E
DT
A) .
Log K1(EDTA) of d0 to d10 M(II) ions:
Ca2+
Mn2+
Zn2+
double-humpedcurve
= CFSE
rising baselinedue to ioniccontraction
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
log
K1(e
n) .
Log K1(en) of d0 to d10 M(II) ions:
double-humpedcurve
Ca2+Mn2+
Zn2+
rising baselinedue to ioniccontraction
= CFSE
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
log
K1(
tpen
).
Log K1(tpen) of d0 to d10 M(II) ions:
Ca2+
Mn2+
Zn2+
double-humpedcurve
N N NN
N Ntpen
Irving and Williams noted that because of CFSE, the log K1 values for virtually all complexes of first row d-block metal 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:
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