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Crystal Field Theory

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نظرية المجال البلوري. Crystal Field Theory. - PowerPoint PPT Presentation

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الفلرية المعقدات ان على النظرية هذه تفترضايوني ) ( تآصر يعني الكتروستاتيكي تداخل هن عبارة ( موجبة نقطية كشحنة تعتبر المركزية الذرة بين

اوربيتاالت على ( dتحتوي الليكاندات و الخمسة ( نحو تنجذب سالبة نقطية كشحنة بها المحيطة

, هذه فسرت وقد التآصر يحدث و الموجبة الشحناتالطيفي و المغناطيسي السلوك و االلوان النظرية

للمعقدات.

األيون الفلزي وتأثير الليكاندات اقتراب

والتوزيع الفراغي لها على طول Linear combination of اوربيتاالتd المحاور

dz2-dx

2 and dz2-dy

2

d2z2-x

2-y2

Octahedral Field

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

t2g ألن فصوصهاتتجه مابين االحداثيات

الذين dz2,dx2-y2 أوربيتالييتجهان مباشرة نحو الشحنات السالبة

z z z

اوربيتاالت الليكاند الواهبة eg اوربيتاالت

t2gاوربيتاالت

y y y

x x x

Splitting of d-orbital energies by an octahedral field of ligands.

is the splitting energy

+0.6Δ₀

- o.4Δ₀

توزيع االلكترونات في حالة المجال الضعيف و القوي

توزيع االلكترونات في حالة المجال الضعيف و القوي

Crystal-Field TheoryCrystal-Field Theory

[Ti(H2O)6]3+

Δ₀ قياس مقدارطاقة انفصام المجال البلوري

or

Ehc

=

E = E2 - E1 = h =hc

Orbital occupancy for high- and low-spin 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

High spin Low spin

High-spin and Low-spin Complex Ions of Mn2+

مجال قوي مجال ضعيف

خواص بارا مغناطيسية خواص بارامغناطيسية

High and low-spin complexes of d5 ions:

energy

eg eg

t2gt2g

low-spin d5 )[Fe)CN(6]3-(t2gاوربيتاالت تمال أوال بسبب قوة الليكاند

high-spin d5 )[Fe)H2O(6]3+(

تتوزع االلكترونات حسب قاعدة هوند

تكون في اغلب المعقدات طاقة االزدواج عالية لهذا تكون معقدات عالية البرم أما مع الليكاندات القوية

فتنتج طاقة كافية الزدواج االلكترونات وتكوين ايونات d5 معقدات بارامغناطيسية

Δ > P Δ < P

Paramagnetic5 unpaired e’s

paramagneticone unpaired e

[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

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

High and low-spin complexes:

energyeg

eg

t2g t2g

low-spin d6

t2g اوربيتاالت تمال أوال بسبب قوة الليكاند

high-spin d6

تتوزع االلكترونات حسب قاعدة هوند

Δ > P Δ < P

Paramagnetic4 unpaired e’s

diamagneticno unpaired e’s

High and low-spin complexes of some d6 ions:

energy

eg eg

t2gt2g

low-spin d6 )[Co)CN(6]4-( high-spin d5 )[CoF6]3-(

Δ >> P Δ < P

Paramagnetic4 unpaired e’s

diamagneticno unpaired e’s

[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

High and low-spin complexes of d7 ions:

energy

eg eg

t2gt2g

low-spin d7 )[Ni)bipy(3]3+(تملئ االوربيتاالت الواطئة

الطاقة ومن ثم االوربيتاالت .العالية الطاقة

high-spin d7 )[Co)H2O(6]3+(تملئ االوربيتاالت

بااللكترونات حسب قاعدة هوند

نفس العدد من االلكترونات و االختالف بحالة التأكسد

Δ > P Δ < P

Paramagnetic3 unpaired e’s

paramagneticone unpaired e

[Ni(bipy)3]3+ [Co(H2O)6]2+ Δ = 9,300 cm-1

Crystal-Field TheoryCrystal-Field Theory

Weak-field ligands (small تمتلك)

االلكترونات تميلإلى االنتقال الىالعالية االوربيتاالتعلى الطاقة

االلكترونات ازدواج .

Strong-field ligands (large تمتلك) في لاللكترونات التدريجي الملئ الى تميل

الطاقة الواطئة االوربيتاالت

dd44, d, d55, d, d66, and d, and d7 7 المعقدات العالية المعقدات العالية في الترتيب االلكترونيفي الترتيب االلكتروني البرم و الواطئة البرم ممكنةالبرم و الواطئة البرم ممكنة

Crystal Field Splitting Energy (CFSE)

• In Octahedral field, configuration is: t2gn eg

n

O = 10 Dq• In weak field: O P, => t2g

3eg1

• In strong field O P, => t2g4

• P - paring energy

CFSE = -0.4 Δo nt2g + 0.6 Δo neg

t2g2 eg0 t2g3 eg0

CFSE =-0.8 Δ₀ CFSE = -1.2 Δ₀

CFSE حساب طاقة استقرار المجال البلوري

البلوري المجال استقرار وطاقة لتركيب ملخص التالي الجدول ويبينCFSE) )من للتراكيب المزدوجة االلكترونات حالتي d1→d10وعدد في

القوي : المجال و الضعيف المجال

P

P P

P

P

3P3P

Example: explain [Fe(CN)6]3- or [Fe(H2O)6]+3 more stable?

energy

eg eg

t2gt2g

CFSE=)3X-0.4Δ₀)+(2X0.6Δ₀) =-1.2Δ₀ + 1.2Δ₀ = 0

Δ > P Δ < P

[Fe)CN(6]3- Δ = 35,000 cm-1

P = 22,000 cm-1

[Fe)H2O(6]3+ Δ = 13,700 cm-1

P = 22,000 cm-1

CFSE=)5X-0.4Δ₀)+(0X0.6Δ₀) +2P =-2.0Δ₀ + 2P

The CFSE for high-spin d5 and for d10 complexes is calculated to be zero:

[ Mn(NH3)6]2+: ] ( )Z n en3[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

جدول يبين قيم طاقة استقرار المجال البلوري وطاقة االزدواج لبعض المعقدات

Effect of ligands on the colors of coordination compounds

Slide of 53

• هذه المعقدات لها نفس العدد التناسقي وااليون الفلزي وااليون المرافق

Tetrahedral & Square Planar Tetrahedral & Square Planar Ligand FieldLigand Field

مستويات الطاقة النفصام اوربيتاالت للمعقدات الرباعية

السطوح و المربع المستوي

tetrahedralsquare planar

تمثيل انفصام اوربيتاالت لمعقدات المربع المستوي

dx2-y2

dxy

dz2

dxz dyz

dx2-y2

dxy

dz2

dxz dyz

dxz dyzdxy

dx2-y2 dz2

t2g

eg

square planerZ outoctahedral

d8تكون معقدات مربعة مستوية ايونات

L

M

L

L L

LLM

L L

LL

z

x

y

تجريبيا� وجد إن المربع المستوي هو ناتج من إزالة ليكاندين من

المعقدات الثمانية السطوح

dx2-y2

dz2

dxy

dxz,dyz

dx2-y2

dz2

dxydxz,dyz

Octahedral Square Planar

dn High spin (HS) Low spin (LS) Tetrahedral

d Octahedral

Complexes

Octahedral

complexes

Complexes

d1 0.4- o.4- 0.6-

d2 0.8- 0.8- 1.2-

d3 1.2- 1.2- 0.8-

d4 -o.6 -1.6 o.4-

d5 0 2.0- 0

d6 0.4- 2.4- 0.6-

d7 0.8- 1.8- 1.2-

d8 -1.2 1.2- 0.8-

d9 0.6- 0.6- 0.4-

d10 0 0 0

الرباعية المعقدات في ويالحظاستقرارية اعلي إن السطوح

هي الليـــــكاندي المجال يضفيهانظـــــــــــــــــامي d2,d7(highفي

spin) نظام يتخذ السبب d2 ولهذالرباعي d7 أو المنتظم الشكل

.السطوحااليونين أن تجريبيا� d8 و d3 لوحظ

)Cr3+, Ni2+ كبير حد إلى يفضالنالسطوح الثماني , التناظر

Octahedral

dxz,dyzdxy

dz2

dx2-y2

dxz,dyzdxy

dz2

dx2-y2

TetrahedralSquare Planar

dxz,dyz

dxy

dz2

dx2-y2

OH2

Ni

H2O

OH2

OH2

H2O

H2O

2

Octahedral Coordination number =6

Ni

Cl

ClCl

Cl2-

Tetrahedral (CN=4)

Ni(II) d8 S =1

Ni

C

C

C

C

N

N

N

N

2-

Square Planar (CN=4)

Ni(II) d8 S = 0Ni(II) d8 S = 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:

CNOF

PSCl

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.

O

O-

O

-O O O-

H3C CH3

H2N NH2

H2N NH

NH2N N N N

oxalate acetylacetonate en

dien bipyridyl 1,10-phen

The spectrochemical series:

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+: ] ( )C r en3[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

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

(.

N N NN

N N

Log K1)tpen( of d0 to d10 M)II( ions:

Ca2+

Mn2+

Zn2+

double-humpedcurve

tpen

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: