Crystal-Field Theory Ligand-Field or Molecular Orbital Theory
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1 How can we explain bonding between metals and ligands? Crystal-Field Theory Ligand-Field or Molecular Orbital Theory October 4, 2010
2 The Periodic Table
3 Electronic structure of transition metals Filled ns, np shells; chemistry defined by unoccupied nd-orbitals Number of d-electrons = Z nearest noble gas e s charge e.g.: Fe(II) = =6 Fe(III) = = 5
4
5 d2z2-y2-x2
6 Valence Bond (VB) Theory developed by Pauling in the 1930s - used in VSEPR Useful in d-complexes sp 3 d, sp 3 d 2, sp 2 d useful in CN = 5 (sp, tbp), 6 (octahedral), and 4 (square plana Not much used for d- coplexes today, but some of the terminology is essential
7 Note limitations: M needs 3d x2-y2, 3d z2, 4s, 4p x, 4p y, 4p z to be unoccupied applying VB: 3d 4s 4p Cr +3 d 2 sp 3 [Cr(NH 3 ) 6 ] +3 OK for all d 3 Fe 3+ d 5 LS: OK 3d d 2 sp 3 Now consider Fe 3+ d 5 HS octahedral: d 2 sp 3 sp 3 d 2, but 4d?
8 d 8 octahedral case Ni +2 [Ni(NH 3 ) 6 ] +2 3d 4s 4p 4d high spin sp 3 d 2 again 4d [Ni(L) 4 ] 2+ Tetrahedral case: 4L e - Square planar case: dsp 2 pair goes to sp 3, OK, paramagnetic V B 3d(z 2, xy, xz, yz) (d x2-y2 )sp 2
9 VB can rationalize geometry and magnetic properties on a simple level cannot say anything about electronic spectra (color) and why some ligands lead to HS and some to LS complexes why LS d 6 complexes are kinetically inert etc.. Need better theory!
10 Crystal-Field Theory (gross over-simplification)
11 d2z2-y2-x2
12 INTERACTION OF d-orbitals with OCTAHEDRAL CRYSTAL FIELD of LIGANDS Chemistry of TM complexes controlled by where the d-electrons are d-electron energies controlled by ligand electrons
13 charges charges
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16 10Dq, a.k.a. Definition: energy splitting between the t 2g and e g orbitals Measurement: E = 10Dq e g hν t 2g [Ti(III)(H 2 O) 6 ] 3+ d-electrons = = 1 hν = 20,300 cm -1 = green light (complex = violet) = kcal/mol (on the order of a bond)
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18 Ti 3+ d 1 oct = E= hν
19 Spectrochemical series of ligands l
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21 Spectrochemical series of metal ions Mn 2+ <Ni 2+ <Co 2+ <Fe 2+ <V 2+ <Fe 3+,Co 3+ <Mn 4+ <Mo 3+ <Rh 3+ <Ru 3+ <Pd 4+ <Ir 3+ <Pt 4+
22 Strong and weak field Factors affecting 10 Dq -Increased charge on metal: draws ligands in more closely; more effect on d-orbital splitting -Ligand type: spectrochemical series -So named because strong field ligands have higher energy d-d transitions (shorter wavelength UV/vis maxima) I- < Br - < S 2- < Cl - < NO 3- < OH - ~ RCOO - < H 2 O ~ RS - < NH 3 ~ Im < 1,2-diaminoethane < bipy < CN -, CO
23 d 2 Case Electronic configuration is same for strong or weak field case
24 d 3 Case Electronic configuration is same for strong or weak field case
25 d 4 Weak Field High Spin (HS) Case o < E p, pairing energy S = 2
26 d 4 Strong Field Low Spin Case o > E p, pairing energy S = 1
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28 Electron pairing Ions with equal and greater than d 4 electronic configuration in octahedral (O h ) coordination can have low and high spin forms depending on value of o (10Dq) octahedral Fe 3+ (d 5 ) e g Low spin High spin o =10 Dq e g o =10 Dq P = t 2g spin pairing energy smaller than o : S = ½ LS: o > P t 2g spin pairing energy larger than o : S = 5/2 HS: o < P Unpaired (non-integer) spin: paramagnetic - detectable by magnetic measurement or sometimes by EPR
29 Crystal-field Stabilization Energy (CFSE) CFSE = x(-4dq) + y(+6dq) or since o = 10 Dq CFSE = x(-0.4 o ) + y(+0.6 o ) where x = number of electrons in t 2g (lower levels) y = number of electrons in e g (upper levels)
30 Crystal-Field Stabilization Energy, CFSE or Ligand-Field Stabilization Energy, LFSE CFSE = x(-0.4 o ) + y(0.6 o ) d 1 d 2 d 3 LFSE = -0.4 o = -0.8 o = -1.2 o High Spin Low Spin High Spin Low Spin d 4 d 5 LFSE = -0.6 o -1.6 o + P 0-2 o + 2P
31 Pairing Energy, P Two terms contribute to P: 1. loss of exchange energy p 3 or E 1 E 2 E 1 > E 2 total exchange energy = Σ N( N 1) K 2 N = number of e - with parallel spin K = exchange energy (characteristic of atom or ion) e.g., E = E 2 -E 1 2. coulombic repulsion between paired e -
32 Crystal-Field Stabilization Energy, CFSE or LFSE CFSE = x(-0.4 o ) + y(+0.6 o ) High Spin Low Spin High Spin Low Spin d 6 d 7 LFSE = -0.4 o + P -2.4 o + 2P -0.8 o -1.8 o + P d 8 d 9 d 10 LFSE = -1.2 o -0.6 o 0 Note: largest CFSE-LFSE for LS, d 6
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34 r Relationship between d-orbitals of TM surrounded by tetrahedral coordination of ligands
35 Octahedral vs Tetrahedral Splitting Pattern of d-orbitals tet = 4/9; tet 1/2 o octahedral tetrahedral O > T thus no strong field vs. weak field cases for tetrahedral complexes; note absence of subscript g in tetrahedral (t and e) Color of tetrahedral complexes different
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37 Octahedral HS tetrahedral
38 Co(II) d 7 S = 3/2 3 unpaired e - S = ½ 1 unpaired e - Total spin quantum #: S Σ s i N Σ = Summing over N electrons with s i spin quantum # on each elelctron s i = ±1/2
39 Jahn-Teller Effect: J-T theorem: any nonlinear molecule in a degenerate electronic state will be unstable and will undergo a distortion to a system of lower symmetry and lower energy thereby removing the degeneracy Cu 2+ d 9 J-T active ions: Strong JT: HS-d 4, d 9 [LS d 7 ] e g orbitals Weak JT: d 1, d 2, LS-d 4, LS-d 5, HS d 7 t 2g J-T does not predict if distortion is: elongation along z (as shown) or elongation along x-y, lowering d x2-y2
40 Would you expect JT in T d d 4 and d 9?
41
42 SQUARE PLANAR COMLEXES elongation of M-L along z second and third row d 8 complexes are square planar. E.g., Pd (II), Pt(II), Rh(I), Ir(I)
43 Square-planar Splitting Pattern of d- Orbitals Ni 2+, d 8 [Ni(CN) 4 ] -2 Square planar Ni 2+ complex is diamagnetic S = 0
44 Chapter 21 (20), self study on pg. 646 (564) d 8 complexes:[nicl 4 ] 2- paramagnetic, S=1; and Ni(CN) 4 ] 2- diamagnetic tetrahedral Squareplanar
45 Thermodynamic Aspects of LFSE
46 Lattice Energies of MCl 2 compounds M 2+ : Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Same for MF 2, MF 3 and [MF 6 ] 3- complexes
47 Deviation from d 0, d 5 and d 10 is due to thermochemical LFSE Agreement between e.g.: [Ni(H 2 O) 6 ] 2+, LFSE (thermochemical), 120 kj/mol and LFSE (spectroscopic), 126 kj/mol (1.2 oct deter. From spectra of [Ni(H 2 O) 6 ] 2+, oct 8500 cm -1 ) Must remember that LFSE is <10% of the total in reaction energies M 2+ (aq) + H 2 O (l) [M(H 2 O) 6 ] 2+ (aq) Ni 2+
48 Octahedral vs Tetrahedral coordination Fig suggests that for d 0, d 5, and d 10 there should be no preference for octahedral or tetrahedral coordination; there is a large preference for octahedral for d 3 and HS d 8 Case of spinels: MgAl 2 O 6 mineral spinel; Mg 2+ in T d while Al 3+ in O h site many analogous normal spinel compounds with A 2+ (M 3+ ) 2 O 6 -LFSE can favor the formation of so-called inverse spinels: e.g. normal: Fe(II)[(Cr(III)] 2 O 4 LFSE [Cr(III) d oct ] > LFSE Fe(II) d 6 (HS, -0.4 oct ) Fe 3+ (Fe 2+, Fe 3+) O 4 LFSE = 0 for Fe 3+ (d 5 ), but Fe 2+ (d 6 ) provides -0.4 oct What about Mn 3 O 4, Co 3 O4
49 Review Chapter MO Theory: Chapter 2 Shriver and Atkins Molecular Orbital Theory of Octahedral Complexes-[ML 6 ] n+
50 See O h character Table on Appendix 3 s A 1g or a 1g totally symmetric irred. Rep p x, p y, p z T 1u or t 1u d xy, d xz, d yz T 2g or t 2g d x2-y2, d z2 E g or e g
51 X 2 +y 2 +z 2 2z 2 -x 2 -y 2, x 2 -y 2 xy, xz, yz x, y, z,
52 Molecular Orbital Theory Octahedral complexes
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57 X 2 +y 2 +z 2 2z 2 -x 2 -y 2, x 2 -y 2 xy, xz, yz x, y, z,
58 16 S [Ne] 3s 2 3p 4
59 M L σ - bonding in a [ML 6 ] n+ complex
60 M-L only σ bonding Bonding Model Example:[ Mo(CO) 6 ] Mo: 5s 1 4d 5 6e - 6CO: 12 e - Total of 18 e - fill into MOs: [CoF 6 ] 3- High Spin (HS) Co 3+ : d 6 6e - 6F - : 6x2-12e - Total: 18 e- a 1g2, t 1u6, e g4, t 2g 4 e g * 2 a 1g2, t 1u6, e g4, t 2g 6 Low Spin (LS) so far not so different from CFT as far as t 2g & e g orbital splitting, filling in [ML 6 ] n+
61 Considering M-L π Bonding difference between CFT and LFT
62 dπ-pπ dπ -dπ dπ-pπ* dπ-σ*
63 Consider t 2g set of ligand π-orbitals for O h complex along x and z directions interacting with d xz M orbital z p x and p z LGO π-interaction wirh d xz bonding and antibonding x
64 Effect of π bonding with π-donating ligands: e.g., F -, Br -, Cl -, I - electrons from π-donor L fill t 2g π orbitals electrons from M fill t 2g * hence O < no π-bonding
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66 M L π-bonding with π*-accapter ligands e.g., R 3 N, CN -, CO
67 M L π-bonding with π*-acceptor ligands: e.g., R 3 N, CN -, CO d-block metal organometallic complexes and related complexes tend to obey the effective atomic number rule, or 18-electron rule 6 L provide 12 σ-bonding, a 1g2, t 1u6, e g4, e- from M fill t 2g For π-acceptor ligands, d electrons from M occupy t 2g since occupation of e g * is detrimental to M-L bond formation ( O is large!), π-acceptor ligands are not favored for d 7, d 8, d 9, d 10 A low oxidation state organometallic complex contains π-acceptor Ls and the M center tends to acquire 18 e - in its valence shell (the 18-electron rule) and filling the valence orbitals: a 1g2, t 1u6, e g4, t 2g 6 LS
68 π-donor ligands π-acceptor ligands
69
70 Conclusions For complexes with σ-donor, π-donor and π-acceptor ligands: o decreases with π-bonding donor ligands Increased π donation stabilizes the t 2g orbitals, and destabilizes t 2g *, decreasing o π-acceptor ligands stabilize t 2g level, and increase o o is relatively large for π-acceptor ligands, thus they tend to be low spin Observed spectrochemical series is explained: I -, Br -, π-donating ligands are weak field (small o ) CO, NO, CN - π-acceptor ligands, are strong field (large o )
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