Chemistry 445 Lecture 16 Crystal Field Theory

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-)


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+)



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-)


case the complex is diamagnetic

high-spin d5 ([CoF6]3-)



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


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.


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):


15/22

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


16/22

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+


19/22

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


20/22

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


21/22

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


22/22

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:

Chemistry 445 Lecture 16 Crystal Field Theory

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