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Laporte Selection Rule (Only for Systems with Inversion Symmetry)

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Laporte Selection Rule (Only for Systems with Inversion Symmetry) UV/Vis-Spectroscopy = investigation of electronic transitions within a molecule Energy Electronic transition Emission Excited state Ea hn Ground state E Absorption g c Conversion factors ~ –1 –1 E Ea Eg hn h hcn 1 eV = 8066 cm = 96.5 kJ•mol 1 eV = 1.602•10–19 J n+ UV/Vis spectra of the [M(H2O)6] cations general observation: d1, d4, d6, d9 (one band) d2, d3, d7, d8 (three bands) d5 (several sharp, relatively weak bands) (only high-spin compounds) d0, d10: no absorption bands Intensities of absorption bands –1 –1 emax (extinction coefficient), dimension M cm SiO2 cuvette Lambert-Beer law: emax = E / (c·l) 5 –1 –1 range: emax = 0 to > 10 M cm l = diameter e of cuvette emax 1 n n~ c 400 nm = 25000 cm-1 200 nm = 50000 cm-1 max Selection rules* spin multiplicity MS = 2S+1 S = Ss = n/2 (total spin quantum 1. Spin selection rule S = 0 or MS = 0 number) (Transition between same spin states allowed: singlet -> singlet, triplet -> triplet, others are forbidden: singlet -> triplet, doublet -> singlet, etc.) 2+ [Mn(H2O)6] Pauli-Principle not obeyed hn S = 5/2 S = 5/2 S = 3/2 S = 1, forbidden e < 1 M‒1cm‒1 .. only one electron is involved in any transition max * were developed for metal atoms and ions (where they are rigorously obeyed), not complexes Spin selection rule 2+ [Co(H2O)6] 3+ Pauli Prinziple [Cr(NH3)6] obeyed hn S = 3/2 S = 3/2 S = 0, allowed ‒1 ‒1 emax = 1-10 M cm In the case of spin orbit coupling (as is the case for trans.-metal complexes), the spin-selection rule is partially lifted (=> weak, so-called inter-combination bands arise with e = 0.01 – 1.0 M‒1cm‒1) 4 2 III III II (example: A2g→ Eg- transition, in the case of Cr , l.s.-Co , or Mn ) an e ~ 0.01 M‒1cm‒1 is hardly detectable Orbital selection rule L = 1 2. d-d-transitions are forbidden Transitions that are allowed must involve an overall change in orbital angular momentum of one unit, i.e. L = +1 or -1. Transitions within the same sub-level are forbidden allowed: s p, p d forbidden: d d, p p Mixing d, p and s functions can lead to partial lifting of the rule (this explains, why d-d-transitions are observed at all, as all MO‘s have also some s and p character) Laporte selection rule (only for systems with inversion symmetry) Laporte rule: parity must change allowed: g u, u g forbidden: g g, u u parity: g(even), u(uneven); index refers to symmetry behaviour of the wave function (orbital, state) with respect to an inversion operation about origin This rule is a specific variant of the symmetry selection rule (will be explained later) g, even: u, uneven: s and d orbitals p and f orbitals s-, n- and p* bonds s-, n- and p* bonds Laporte rule / An Example LaPorte rule: parity must change (holds for systems with inversion symmetry) allowed: g u, u g forbidden: g g, u u parity: g(even), u(uneven); index refers to symmetry behaviour of the wave function (orbital, state) with respect to an inversion operation about origin for octahedral complexes, all d-d transitions are forbidden (d-orbitals are „g“) intensities of bands in non-centrosymmetric molecules generally higher (since the Laporte ban is lifted) see next page Examples cis/trans-[CoCl2(NH3)4]Cl (cis-complex has more intense absorption bands) tetrahedral complexes are more intensely colored than octahedral ones Form of the bands Half width at half height > 3000 cm–1 Franck-Condon-Principle Fine structure (vibrations) not resolved Form of the bands • Transitions are vertical • The electronic transitions will be from the ground electronic to a vibrationally excited electronic state (no→nn‘). As M-L bonds are constantly vibrating, light strikes the molecules in various vibrational positions. Thus the bands are broad. • Transitions that are forbidden by the spin selection rule (but which are observed very weakly as the result of spin-orbit coupling) are much narrower. The corresponding 6 4 2+ lines of the terms (e.g. the A1g and the A1g terms for Mn ) are almost parallel to each other, and thus do not vary much with o. Other effects that are of interest, but of the scope of this lecture: band splitting due to symmetry reduction, band polarisation, dichroism, see the text books. Summary: three rules: spin S=0, Laporte (ug; gu), orbit l = 1 typical values for emax: 2+ ‒1 ‒1 [Mn(H2O)6] spin forbidden, Laporte forbidden, emax < 1 M cm 2+ ‒1 ‒1 [Co(H2O)6] spin allowed, Laporte forbidden, emax = 1-10 M cm 2– ‒1 ‒1 [CoCl4] spin allowed, emax = 600 M cm all are l forbidden (d→d) Bands with larger intensity in general due to ‒ charge-transfer transitions (e.g. MnO4 , LMCT) or p-p* transitions within the ligand Rule of thumb: 3 ‒1 ‒1 KMnO4 charge transfer transitions have emax > 10 M cm * were developed for metal atoms and ions (where they are rigorously obeyed), for complexes, these rules are not so strictly obeyed; i.e. vibronic coupling, heavy atom effect; s.p.d-mix Ligands are unsymmetric Exercise How many d-d transitons do you expect for an octahedral Scandium(II) complex? Are these transitions spin allowed? Sc2+-Ion, d1, => one band; d→d transitions are forbidden (orbit selection rule); the absorption is spin allowed, the absorption is Laporte forbidden (T2g→Eg); parity does not change e is expected to be 1-10 M–1cm–1 (this is experimentally observed) 2+ 1 [Sc(H2O)6] , d hn doublet doublet 2T 2 2g Eg S = 1/2 S = 1/2 S = 0, spin allowed Exercise Sc2+ is instable in solution 2+ Sc is stable only in solid state: CsScCl3, CsScBr3, CsScI3 III (prepared by reduction of Cs3Sc 2X9 with Sc metal) e.g. Inorg. Chem. 1981, 20, 2627-2631 (no UV/vis data reported) Ti3+ complexes have e ~ 10-50 M–1cm–1 as predicted Jahn-Teller Theorem Any non-linear molecular system in a degenerate electronic state will Be unstable and will undergo distortion to form a system of lower symmetry and lower energy thereby removing the degeneracy D4d D4d 2 2 Oh x -y z2 ' ' z2 x2-y2 xy xz, yz 2/3 1/3 free Ion 1/3 2/3 xz, yz xy octahedral crystal field z elongated z compressed octahedron octahedron ' > (two long, 4 short) (two short, 4 long) D4h Oh D4h.
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