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تفترض هذه النظرية على ان المعقدات الفلرية عبارة هن تداخل الكتروستاتيكي ( يعني تآصر ايوني ) بين الذرة المركزية (تعتبر كشحنة نقطية موجبة تحتوي على اوربيتاالت dالخمسة ) و الليكاندات المحيطة بها (كشحنة نقطية سالبة تنجذب نحو الشحنات الموجبة و يحدث التآصر ,وقد فسرت هذه النظرية االلوان و السلوك المغناطيسي و الطيفي للمعقدات. األيون الفلزي وتأثير اقتراب الليكاندات اوربيتاالت dوالتوزيع الفراغي لها على طول المحاور Linear combination of dz2-dx2 and dz2-dy2 d2z2-x2-y2 Octahedral Field The d-orbitals: z z y dyz the t2g set x z y x dxy z x dxz z y dz2 y x y dx2-y2 x the eg set Splitting of the d sub-shell in octahedral coordination اوربيتاالت الليكاند الواهبة اوربيتاالت eg اوربيتاالت z z z y y x dx2-y2 t2g y x dz2 الذين يتجهان dz2,dx2-y2أوربيتالي مباشرة نحو الشحنات السالبة x dyz ألن فصوصها t2g تتجه مابين االحداثيات Splitting of d-orbital energies by an octahedral field of ligands. D is the splitting energy +0.6Δ₀ - o.4Δ₀ توزيع االلكترونات في حالة المجال الضعيف و القوي توزيع االلكترونات في حالة المجال الضعيف و القوي قياس مقدارطاقة انفصام المجال البلوري Δ₀ Crystal-Field Theory [Ti(H2O)6]3+ Color of Transition Metal Complexes DE = E2 - E1 = hn = hc l or l= hc DE Orbital occupancy for high- and low-spin complexes of d4 through d7 metal ions. high spin: weak-field ligand low spin: strongfield ligand high spin: weak-field ligand low spin: strongfield ligand High spin Low spin High-spin and Low-spin Complex Ions of Mn2+ مجال قوي خواص بارا مغناطيسية مجال ضعيف خواص بارامغناطيسية High and low-spin complexes of d5 ions: تكون في اغلب المعقدات طاقة االزدواج عالية لهذا تكون معقدات عالية البرم أما مع الليكاندات القوية فتنتج طاقة كافية الزدواج االلكترونات وتكوين معقدات ايونات d5بارامغناطيسية [Fe(H2O)6]3+ Δ = 13,700 cm-1 P = 22,000 cm-1 eg Δ<P t2g [Fe(CN)6]3- Δ = 35,000 cm-1 P = 19,000 cm-1 Paramagnetic 5 unpaired e’s eg paramagnetic one unpaired e Δ>P energy t2g )low-spin d5 ([Fe(CN)6]3- )high-spin d5 ([Fe(H2O)6]3+ تتوزع االلكترونات حسب قاعدة هوند اوربيتاالت تمال أوال بسبب قوة الليكاند t2g Splitting of the d sub-shell in an octahedral complex energy eg Δ 3d sub-shell Co3+ ion in gas-phase (d6) d-shell split by presence of ligand donor-atoms t2g Co(III) in octahedral complex High and low-spin complexes: energy eg Paramagnetic 4 unpaired e’s Δ > P diamagnetic no unpaired e’s t2g low-spin d6 t2g اوربيتاالت تمال أوال بسبب قوة الليكاند eg Δ<P t2g high-spin d6 تتوزع االلكترونات حسب قاعدة هوند High and low-spin complexes of some d6 ions: [CoF6]3- Δ = 13,100 cm-1 P = 22,000 cm-1 [Co(CN)6]3- Δ = 34,800 cm-1 P = 19,000 cm-1 eg energy Δ >> P t2g low-spin d6 ([Co(CN)6]4-) Paramagnetic 4 unpaired e’s diamagnetic no unpaired e’s eg Δ<P t2g high-spin d5 ([CoF6]3-) High and low-spin complexes of d7 ions: نفس العدد من االلكترونات و االختالف بحالة التأكسد [Co(H2O)6]2+ Δ = 9,300 cm-1 eg Δ<P [Ni(bipy)3]3+ Paramagnetic 3 unpaired e’s eg paramagnetic one unpaired e Δ>P t2g )high-spin d7 ([Co(H2O)6]3+ تملئ االوربيتاالت بااللكترونات حسب قاعدة هوند energy t2g )low-spin d7 ([Ni(bipy)3]3+ تملئ االوربيتاالت الواطئة الطاقة ومن ثم .االوربيتاالت العالية الطاقة Crystal-Field Theory Weak-field ligands )تمتلك (small D تميل االلكترونات الى االنتقال إلى االوربيتاالت العالية الطاقة على ازدواج .االلكترونات )تمتلك Strong-field ligands (large D تميل الى الملئ التدريجي لاللكترونات في االوربيتاالت الواطئة الطاقة High and Low Spin Octahedral Complexes المعقدات العالية البرم و الواطئة البرم ممكنة في الترتيب االلكتروني d4, d5, d6, and d7 Crystal Field Splitting Energy (CFSE) • In Octahedral field, configuration is: t2gn egn CFSE = -0.4 Δo nt2g + 0.6 Δo neg DO = 10 Dq • In weak field: DO P, => t2g3eg1 • In strong field DO P, => t2g4 • P - paring energy CFSE حساب طاقة استقرار المجال البلوري t2g3 eg0 CFSE = -1.2 Δ₀ t2g2 eg0 CFSE =-0.8 Δ₀ ويبين الجدول التالي ملخص لتركيب وطاقة استقرار المجال البلوري ) )CFSEوعدد االلكترونات المزدوجة للتراكيب من d1→d10في حالتي المجال الضعيف و المجال القوي : P P P P P 3P 3P 3[Fe(CN)6] Example: explain +3 [Fe(H2O)6] more stable? [Fe(CN)6]3- Δ = 35,000 cm-1 P = 22,000 cm-1 eg energy Δ>P t2g CFSE=(5X-0.4Δ₀)+(0X0.6Δ₀) +2P =-2.0Δ₀ + 2P or [Fe(H2O)6]3+ Δ = 13,700 cm-1 P = 22,000 cm-1 eg Δ<P t2g CFSE=(3X-0.4Δ₀)+(2X0.6Δ₀) =-1.2Δ₀ + 1.2Δ₀ = 0 Crystal Field Stabilization Energy (CFSE) of d5 and d10 ions: The CFSE for high-spin d5 and for d10 complexes is calculated to be zero: [Zn(en)3]3+ [Mn(NH3)6]2+: energy eg eg t2g t2g Δ = 22,900 cm-1 Δ = not known CFSE = 10,000(0.4 x 3 – 0.6 x 2) = 0 cm-1 CFSE = Δ(0.4 x 6 – 0.6 x 4) = 0 cm-1 جدول يبني قيم طاقة استقرار اجملال البلوري وطاقة االزدواج لبعض املعقدات هذه المعقدات لها نفس العدد التناسقي وااليون الفلزي وااليون المرافق • Effect of ligands on the colors of coordination compounds Slide of 53 Tetrahedral & Square Planar Ligand Field Figure 20.28: Crystal field diagrams for octahedral and tetrahedral complexes مستويات الطاقة النفصام اوربيتاالت للمعقدات الرباعية السطوح و المربع المستوي square planar tetrahedral متثيل انفصام اوربيتاالت ملعقدات املربع املستوي square planer Z out octahedral dx2-y2 dx2-y2 eg dx2-y2 dz2 dz2 dxy dxy t2g dz2 dxy dxz dyz dxz dyz dxz dyz ايونات d8تكون معقدات مربعة مستوية تجريبيا ً وجد إن المربع المستوي هو ناتج من إزالة ليكاندين من المعقدات الثمانية السطوح L L dx2-y2 M L L z L y L L x M L dx2-y2 dz2 dxy dz2 dxy dxz,dyz dxz,dyz Square Planar Octahedral L L dn High spin (HS) Low spin (LS) Tetrahedral d Octahedral Octahedral Complexes d1 Complexes -0.4 complexes -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 ويالحظ في المعقدات الرباعية السطوح إن اعلي استقرارية يضفيها المجال الليـــــكاندي هي في نظـــــــــــــــــامي ) d2,d7(high spinولهذا السبب يتخذ نظام d2أو d7الشكل المنتظم لرباعي السطوح. 3 8 3+ 2+ ً d (Cr , Niو dلوحظ تجريبيا أن االيونين يفضالن إلى حد كبير التناظر الثماني السطوح , dx2-y2 dx2-y2 dz2 dxy dxz,dyz dxy dxy dxz,dyz dx2-y2 dz 2 H2O H2O Ni dxz,dyz Tetrahedral Octahedral OH2 dz 2 2 OH2 Cl OH2 H2O Octahedral Coordination number =6 Ni(II) d8 S = 1 Cl Square Planar 2- N N Cl C C Ni 2- Ni Cl Tetrahedral (CN=4) C N C N Square Planar (CN=4) Ni(II) d8 S =1 Ni(II) d8 S = 0 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 spectrochemical series: 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: F O N Cl S P C ? very little data on P-donors – may be higher than N-donors Br I S-donors ≈ between Br and Cl spectrochemical series follows arrows around starting at I and ending at C The spectrochemical series: 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 Ndonors are more covalent in their bonding than the sp3 hybridized donors of ammonia. O O - - O O oxalate H 2N dien N H H 3C CH3 O H 2N O- acetylacetonate NH 2 N bipyridyl N NH 2 en N N 1,10-phen The bonding interpretation of 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. Crystal Field Stabilization Energy (CFSE): 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: 0.6n(eg)) - Δ(0.4n(t2g) CFSE = where n(t2g) and n(eg) are the numbers of electrons in the t2g and eg levels respectively. Calculation of Crystal Field Stabilization Energy (CFSE): The CFSE for some complexes is calculated to be: [Cr(en)3]3+ [Co(NH3)6]3+: energy eg eg t2g t2g Δ = 22,900 cm-1 Δ = 21,900 cm-1 CFSE = 22,900(0.4 x 6 – 0.6 x 0) = 54,960 cm-1 CFSE = 21,900(0.4 x 3 – 0.6 x 0) = 26,280 cm-1 Crystal Field Stabilization Energy (CFSE) of d0 to d10 M(II) ions: 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 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: 0 Crystal Field Stabilization Energy (CFSE) of d0 to d10 M(II) ions: CFSE as a function of no of delectrons doublehumped curve 1.4 CFSE in multiples of Δ. Ni2+ 1.2 1 0.8 0.6 0.4 0.2 0 Ca2+0 1 2 3 4 5 6 Mn72+ 8 no of d-electrons 9 10 112+ Zn Log K1(EDTA) of d0 to d10 M(II) ions: log K1(EDTA) as a function of no of delectrons = CFSE logK1(EDTA). 20 doublehumped curve 18 16 Zn2+ 14 Mn2+ 12 Ca2+ 10 0 1 2 3 4 5 6 rising baseline due to ionic contraction 7 no of d-electrons 8 9 10 11 Log K1(en) of d0 to d10 M(II) ions: log K1(en) as a function of no of delectrons = CFSE 12 doublehumped curve logK1(en). 10 8 6 Zn2+ 4 Ca2+ 2 rising baseline due to ionic contraction Mn2+ 0 0 1 2 3 4 5 6 7 no of d-electrons 8 9 10 11 Log K1(tpen) of d0 to d10 M(II) ions: log K1(tpen) as a function of no of delectrons doublehumped curve logK1(tpen). 20 15 Zn2+ 10 Mn2+ 5 N N N N N tpen N Ca2+ 0 0 1 2 3 4 5 6 7 no of d-electrons 8 9 10 11 The Irving-Williams Stability Order: 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.