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Electronic structure and spectra Shriver, Chapter 19 Crystal field theory An ionic model, considers metal and its ligands as point charges All 5 d-orbitals are isoenergetic in a spherical environment/crystal field (i.e., free atom) Different arrangements of charges/ligands cause different splittings of the d-orbitals into different energy levels, although the overall energy center (barycenter) does not change Octahedral symmetry dz2 and dx2-y2 orbitals (which point along the M-L bonds) are destabilized relative to dxy, dxz, dyz (which point in between the M-L bonds) the energy difference between them is Δ dz2 and dx2-y2 orbitals are doubly degenerate in energy (symbol eg) dxy, dxz, dyz are triply degenerate in energy (symbol t2g) eg (z2, x2-y2) 0.6! d ! 0.4! t2g (xy, xz, yz) spherical symmetry octahedral symmetry electronic transition (UV-visible spectrum) for a d1 ion is t2g eg and its energy is Δ (also called 10Dq in some books) the magnitude of Δ depends on the nature of M larger for higher oxidation states of the same metal ion and across a row, due to the decreasing cation radius, resulting in more interaction with the ligands increases down a triad as the extension of the d orbitals increases the magnitude of Δ depends on the nature of L (empirically: the spectrochemical series) halides < OH- < H2O < NH3 < PPh3 < CN- < CO weak xtal field strong xtal field Crystal field stabilization energy (CFSE)/ligand field stabilization energy (LFSE) CFSE = (0.4x – 0.6y) Δ 1 where x is the number of t2g electrons and y is the number of eg electrons should we fill all the t2g orbitals first? yes, when the CFSE is greater than the electron pairing energy P when does this occur? when Δ is large i.e., in the second and third row i.e., when L is a strong-field ligand we put three unpaired e- into the t2g orbitals, but the fourth, fifth and sixth e- will be spinpaired these will be low-spin complexes however, if P > CFSE (i.e., Δ is small), then the fourth and fifth e- will go unpaired into the eg orbitals these will be high-spin complexes similar considerations apply for seven ee.g., low-spin d4: t2g4eg0, 2 unpaired ee.g., low-spin d7: t2g6eg1, 1 unpaired e- high-spin d4: t2g3eg1, 4 unpaired ehigh-spin d7: t2g5eg2, 3 unpaired e- note: there is no classification of high- and low-spin for octahedral complexes with d0, d1, d2, d3, d8, d9, d10 electron configurations CFSE increases in high-spin complexes from d0 to d3, decreases to d5, then increases to d8 - complexes with d3 and d8 electron configurations have a strong preference to be octahedral since there is no CFSE in d0, (weak field) d5 and d10 complexes, these show no strong structural preference Hydration enthalpies (water is a weak-field ligand) vary in the same way as the CFSE, superimposed on the general increasing hydration enthalpy from right to left across the 3rd row Lattice enthalpies show a similar trend Spin can be detected experimentally by measuring magnetic dipole moment of a sample - a compound with no unpaired electrons is repelled by an external magnetic field (diamagnetic) - a compound with unpaired electrons is attracted to an external magnetic field (paramagnetic) the magnetic moment µ contributed by the spin angular momentum of unpaired electrons is 2 1 µ = 2{S ( S + 1)} 2 µB ! where S is the total spin (quantized in units of ½) and µB is a constant called the Bohr magneton: µB = ! eh = 9.274 "10#24 JT #1 2me Often the measured magnetic moment is not quite the same as the predicted spin-only value, because of the contribution of orbital angular momentum Tetrahedral symmetry The ligands lie along the directions defined by the dxy, dxz and dyz orbitals – these are destabilized while the dz2 and dx2-y2 orbitals are aligned between the M-L bonds and are consequently stabilized (note: no gerade subscript in tetrahedral symmetry: there is no center of symmetry) t2 (xy, xz, yz) 0.4! d ! 0.6! e (z2, x2-y2) spherical symmetry tetrahedral symmetry the value of Δ is smaller for tetrahedral symmetry than for octahedral symmetry, and therefore tetrahedral complexes are almost always high spin Square-planar symmetry Favored in a strong crystal field (usually, 2nd and 3rd row metals) with d8 configuration: oxidation state 0 in group 8: Ru(0), Os(0) oxidation state +1 in group 9: Rh(I), Ir(I) oxidation state +2 in group 10: Pd(II), Pt(II) oxidation state +3 in group 11: Ag(III), Au(III) Consider an octahedral complex from which the two axial ligands are removed: - one of the original eg orbitals, dx2-y2, remains destabilized (directly interacting with ligands) but the other one, dz2, is stabilized 3 - two of the original t2g orbitals, dxy and dyz, are stabilized relative to dxz x2-y2 eg xy d z2 spherical symmetry t2g octahedral symmetry xz, yz square planar symmetry (the energy ordering of the dxy and dz2 orbitals depends on the particular complex) this distribution of orbital energies allows the 7th and 8th d electrons to become paired, leaving the dx2-y2 orbital empty (compare to octahedral symmetry, which requires one electron in dx2-y2) note: stabilizing a filled d orbital at the expense of destabilizing another filled d orbital gains you nothing, but stabilizing a filled orbital while destabilizing an empty d orbital results in a lower overall energy (since an orbital costs nothing energetically if it is not occupied) Tetragonal distortion even if the value of Δ is not so large, a distortion away from octahedral symmetry (Oh) towards square planar symmetry (D4h) may be favorable, if the stabilization gained is greater than the price of destabilization this occurs when degenerate orbitals are filled unsymmetrically e.g., low-spin d7: d9: x2-y2 z2 eg x2-y2 z2 eg xy xz, yz t2g Oh xy xz, yz t2g Oh D4h 4 D4h the effect is also seen in complexes with high-spin complexes: e.g., d4: x2-y2 z2 eg xy xz, yz t2g Oh D4h examples of metal cations which commonly show strong tetragonal distortions (JahnTeller distortion) are Cu2+ (d9) and Cr2+ (d4) the distortion results in enhanced lability of ligands in complexes with these metals compare Cr(H2O)63+, d3, octahedral with large CFSE this complex is inert, the release of water ligands (exchange) is very slow (k = 3 x 10-6 s-1, t1/2 = 60 h) with Cr(H2O)62+, d4, pseudo-octahedral with strong Jahn-Teller distortion this complex is labile, the release of the axial water ligands occurs very rapidly (k = 3 x 108 s-1, t1/2 = 2 ns) tetragonal distortions are much less important in tetrahedral complexes because the overall d-orbital splitting is much smaller Ligand field theory Takes into account the molecular orbitals created by the overlap of ligand orbitals with metal orbitals (instead of treating the ligands as point charges, as in crystal field theory) Ligands can be σ-donors, π-donors, or π-acceptors We have already seen one important consequence of this, in the π-backbonding of ligands like CO and CN- to the metal What is the effect of this covalent bonding on Δ? Consider first the case of ligands which are σ-donors only, e.g., NH3 In octahedral symmetry, the six metal valence orbitals with the correct symmetry to form metal-ligand σ-bonds are s, px3 and the eg set of d orbitals (dz2, dx2-y2). 5 The filled ligand σ-orbitals are lower in energy than the metal valence orbitals. The overlap of the ligand orbitals with the eg orbitals causes eg* to rise in energy (it becomes the major contributor to the antibonding orbital) which increases Δ p s eg* eg ! t2g t2g metal complex ligands but consider that H2O is higher in the spectrochemical series than OH-, so the strength of σ-donation is not the only effect ligands often have more than one lone pair, and the additional lone pairs can participate in π-donation to the metal via overlap of the filled p orbitals with the t2g orbitals this raises the energy of t2g, decreasing Δ eg* ! eg t2g* t2g lone pairs metal complex ligands clearly, in comparing OH- and H2O, the stronger π-donation by OH- is a more important effect than its stronger σ-donation Some ligands do not have additional lone pairs but they do have empty (antibonding) orbitals of π-symmetry: they are π-acceptors 6 examples are CO, CNthese π* orbitals lie above the energy of the t2g orbitals. Overlap between empty π* and filled t2g causes the latter to decrease in energy. The consequence is an increase in Δ. eg* "* eg ! t2g t2g metal complex ligands This accounts for strong π acceptors at the top of the spectrochemical series. Electronic spectra Arise from electronic transitions, i.e., promotion of a valence electron from a lower energy orbital to a higher energy orbital Usually requires energy in the visible or the UV part of the electromagnetic spectrum Transitions between (mostly metal-based) orbitals in a partly-filled d subshell are called d-d transitions for example, t2g1eg0 t2g0eg1 , one d-d transition, with energy Δ but, t2g3eg0 t2g2eg1, two d-d transitions the electron promoted to an eg orbital can occupy either dz2 or dx2-y2 same energy: dxz dz2, dyz dz2, dxy dx2-y2 different energy: dxz dx2-y2, dyz dx2-y2, dxy dz2 don't worry about term symbols! Selection rule 1 (spin-selection rule): spin must be conserved during an electronic transition Therefore a transition in which spin must change is spin-forbidden (has very low intensity) e.g., Mn(H2O)62+, high spin d5, t2g3eg2, d-d transitions are spin-forbidden, pale pink e.g., Cr(H2O)62+, high spin d4, t2g3eg1, d-d transition is spin-allowed, bright blue 7 Selection rule 2 (Laporte selection rule): parity must change during an electronic transition For octahedral symmetry, this means the orbital symmetry must change from g to u or from u to g Therefore d-d transitions are Laporte-forbidden (have low intensity) They become “a little bit allowed” due to molecular vibrations that temporarily reduce the symmetry The intensity of an electronic transition is reflected by its extinction coefficient ε (Beer’s Law, Abs = ε C l) For spin-allowed, Laporte-forbidden d-d transitions, ε = ca. 100 M-1 cm-1 For spin-forbidden, Laporte-forbidden d-d transitions, ε = ca. 1 M-1 cm-1 A transition from a (mostly ligand-based) orbital to a (mostly metal-based) orbital is called a ligand-to-metal charge transfer (LMCT) These are generally spin-allowed and Laporte-allowed, with ε = ca. 104-105 M-1 cm-1 Important in d0 complexes where no d-d transitions are possible e.g., MnO4-, d0, LMCT gives intense purple color A transition from a (mostly metal-based) orbital to a (mostly ligand-based) orbital is called a metal-to-ligand charge transfer (MLCT) Important in electron-rich metals with ligands that have π* orbitals e.g., Ru(bpy)32+ Luminescence A molecule in its ground state (lowest electronic energy level) that absorbs a photon and undergoes an electronic transition finds itself in an excited electronic state, designated * e.g., [Ru(bpy)32+] + hν [Ru(bpy)32+]* [Ru(bpy)32+] + energy The energy is then lost and the molecule returns to the ground state Can be lost through transfer of thermal energy to the surroundings (non-radiative decay) Or by emission of a photon – luminescence (radiative decay) Two kinds: (1) fluorescence – spin-allowed, same spin-state in excited and ground states rapid, few ns (2) phosphorescence – spin-forbidden, different spin-state in excited and ground states: slower, few µs how does the spin-state in the excited state become different from the ground-state? Intersystem crossing from one excited state to another (e.g., singlet to triplet) 8