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Systems with 1 Unpaired Electron

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Systems with 1 Unpaired Electron I. Introduction to EPR II. EPR in heterogeneous catalysis by Song-I Han Assistant Professor University of California Santa Barbara PIRE-ECCI/ICMR Summer Conference August 14-25 University of California Santa Barbara I. Introduction to EPR • Basics of cw EPR • One electron in the magnetic field • Crystal field splitting and spin orbit coupling • Interaction with nuclear spins • Electron nuclear double resonance (ENDOR) • Electron spin echo envelope modulation (ESEEM) Nuclear Magnetic Resonance Electron Paramagnetic Resonance uses the interaction between the magnetic moments and the magnetic component of electromagnetic radiation in the presence of magnetic fields magnetic moments through non-zero spin angular momentum of unpaired electrons and a variety of nuclei spin angular momenta are quantized Which magnetic field strength and frequency? NMR: 1 – 21 Tesla and 10 – 900 MHz EPR: 0.06 – 3 Tesla and 2 – 90 GHz Low energy splitting Æ low Boltzmann polarization NMR: 1016 spins per 1 ml EPR: 1010-1011 spins per <1ml Which information? Atomic, molecular and lattice structure: perturbation of the magnetic moments through the neighboring electronic and nuclear spin network NMR: nuclear magnetic moments EPR: electron magnetic moment EPR brief • first EPR observation in 1945: CuCl2·H2O (133 MHz at 5 mT) • rapid exploitation of EPR thereafter through the availability of complete 9.5 GHz (λ=32 mm) systems after World War (II) Æ resonance at 0.35 T field • application to chemical systems since 1970 • technological availability of magnetic fields and frequency sources limits the common EPR frequency range to 1-100 GHz • fixed frequency and magnetic field sweep is most common • only the electronic ground state of species is relevant for EPR • uniquely applicable to paramagnetic state (net electron angular momentum) Typical systems studied by EPR 1. free radicals in the solid, liquid or gaseous phase 1 unpaired electron 2. transition ions including actinide ions up to 5 or 7 unpaired electron V4+, Ti3+, Mn2+, Fe3+, Co2+, Ni2+, Cu2+ ... 3. various point defects (localized imperfections) in solids electron trapped at a negative-ion vacancy (F center) or an electron hole 4. systems with more than one unpaired electron triplet state systems, biradicals 5. systems with conducting electrons semiconductors, metals One electron in the magnetic field Electron Zeeman Interaction (EZI): 2-level system Η = – µ ·B = γ ·S·B = ge·βe·S·B negative gyromagnetic ratio γ g-factor = 2.0023, and nearly isotropic for the simplest case S = ½, MS = 1/2, -1/2: |∆MS| = 1, E± = ± ½ g β B |∆MS| = 1 condition does not hold strictly when S>1/2, or when hyperfine interaction is present EPR detection: Magnetic field sweep with 100 kHz modulation EPR Η = ge·βe·Beff·S NMR Η = γ·Beff·I = βe·B0·g·S = γ·B0·(1-σ)·I One electron in the magnetic field: 2-level systems with resonance around g = 2 1. Free radicals 2. Ti(III), 98Mo(V), low-spin Fe(III) 3. F centers in alkali halides 4. Hydrogen atom trapped in crystal matrices 5. Conducting electrons in metals 1H gas, S=1/2, I=1/2 Ge3+, S=1/2, I=9/2 Much more complex EPR spectra due to … •effects of additional magnetic and electric fields from the unpaired electron’s environment • presence of more than one electron (e.g. transition metal ions with several unpaired d -electrons, up to 5 for high-spin Mn2+ or Fe3+) • organic molecules in triplet state IF such terms >> electron Zeeman term due to B0 • MW frequency may have too small bandwidth (e.g. in VO2+, Mn2+) • EPR spectra may only be observed in the ground state manifold Crystal-field splitting and spin-orbit coupling cause large energy splittings in transition metal ions condensed phase removes the orbital degeneracy for most transition metals “quenching of the orbital angular momentum” effective spin S=1/2 EPR spectra only through the unpaired electron in dx2-y2 orbital Æ one electron S=1/2, two-level system? figure: 3d9 transition metal ion Ligand field effect through second order SOC Most molecule’s ground state undergo orbital quenching by chemical bonding (e.g. radicals) or large CF’s (e.g. transition metal ions) Æ g-factor of free electrons But small amount of orbital angular momentum admixes to the ground state through interaction with the excited states Therefore electron spin becomes sensitive to crystalline environment Leading to anisotropic g-factor, i.e. the Zeeman splitting depends on the symmetry of the ligand field and the molecular orientation in B 0 Η = g·β·S·B g tensor! g anisotropy EPR spectra depend on orientation of samples in B0 in single crystals or powder samples ⎡ ⎤ Η = ge·βe·Beff·S ⎢ ⎥ principal values contain ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ symmetry of the inner field = βe·B0·g·S ⎣ ⎦ B0 along one of the PAS g = gx, gy or gz arbitrary orientation of B0 2 2 2 2 2 2 2 g = gx ·lx + gy ·ly + gz ·lz CF with axial symmetry g(θ )2 = g 2 sin 2 θ + g 2 cos2 θ ⊥ g|| > g B0(g||) < B0(g) EPR of solutions Molecular motion leads to simplification of spectra due to averaging of anisotropic interactions S=1/2, I=7/2 Typical vanadyl solution spectrum (of VO(acac)2) EPR at low temperature (frozen solids) in order to increase relaxation times through freezing of molecular motion Æ identical to powder spectra Æ concept of anisotropy is of importance 1st derivative S=1/2, I=0 Interaction with nuclear spins (hyperfine interaction) local magnetic fields by neighboring nuclear magnetic moments (µn) Nuclear Zeeman interaction Η = gn·βn·Beff·I = γ·B ·(1-σ)·I NZI << EZI 0 e.g. gn=5.58 for proton depend on the orientation of µn with respect to B0 Æ splitting of each electron spin state into (2I+1) levels. 1H, S=1/2, I=1/2 nitroxide radical, S=1/2, I=1 Cobalt (II), 3d7 (single crystal) Co(II), V(IV), VO(II) S=1/2, I=7/2 8 lines 2+ Co in Mg(CH3COO)2·4H2O crystal High-spin manganese (II), S=5/2 S=5/2, 3d5 character in bound form; 5 line EPR spectrum I=5/2, 6-fold splitting of EPR line 2+ Mn in ScPO4 single crystal Origin of hyperfine interactions • dipole-dipole interaction between the magnetic moments 1 µ ⎡ 3 ⎤ Η = 0 g β g β S ⋅ − ( ⋅ )( ⋅ ) anisotropic δδ 3 e e n n ⎢ 2 ⎥ 4π r h ⎣ r ⎦ unpaired electrons in p-, d-, or f- orbitals • Fermi-contact interaction through finite electron spin density at the nucleus 2 µ 2 Η = 0 g β g β Ψ(0) S ⋅ isotropic contact 3 h e e n n unpaired electrons in mainly s- or p-,d-. f- orbitals or π electrons or transition metals The hyperfine interaction matrix A Η = Η FS + β ⋅ ⋅ ⋅ + ⋅ ⋅ + ⋅ ⋅ + ⋅ ⋅ − gnβn ⋅ ⎡ ⎤ ⎡ δ ⎤ = ⎢ ⎥ = a + ⎢ δ ⎥ 1 iso ⎢ ⎥ ⎢ ⎥ δ ⎣ ⎦ ⎣⎢ ⎦⎥ • isotropic EZI and HFI for I=3/2 (e.g. Cu2+) • selection rule: ∆mS=±1 and ∆mI=0 • 4 allowed transition • centered around giso and split by aiso Powder and single crystal EPR spectra of Cu2+ complexes S=1/2, I=3/2 g|| is larger than g┴ g, A values: copper ion is surrounded by oxygen 2+ Cu doped into CaCd(CH3COO)4·6H2O Powder EPR of Cu2+ complexes S = 1/2, I = 3/2 EZI >> HFI coaxial and axially symmetric g and A matrices powder EPR spectrum for an axially elongated copper complex Powder EPR of Cu2+ coordinated to sulfur, nitrogen or oxygen coordination to close nuclei through gII and A|| values by CW X-band EPR (a) copper (II) diethyldithiocarbamate (b) copper (II) tetrapyridyl porphyrazine (c) copper (II) in calcium cadmimum acetate hexahydrate ESR observation of the formation of an Au(II) complex in zeolite Y divalent state of gold is rare and most interesting oxidation state in transition metal chemistry zeolites are very promising as support for stablizing cations and metalic species because of their crown-ether-like ring strcutures in their cages and channels. first observation of square-planar Au(II) -complex with N4 in the supercage of Y-zeolite was observed via EPR Z.Qu, L. Giurgiu, E. Roduner, Chem. Commun. (2006) 2507-2509. Effect of nuclear Zeeman interaction vs. hyperfine interaction at the nucleus weak coupling: e.g. water protons in the first coordination sphere of copper-hexaaquo complex strong coupling: typical for most systems The complete Hamiltonian Η = β ⋅ ⋅ ⋅ + ⋅ ⋅ + ⋅ ⋅ + ⋅ ⋅ − gnβn ⋅ 1. ... so far one electron spin in magnetic fields of different origins were discussed 2. Zero-field splitting more than one electron spins (S > 1/2) in magnetic fields strong dipole-dipole interactions between the electrons e.g. transition metal ions with up to five unpaired d-electrons or spin triplets in organic molecules can be much larger than the electron Zeeman interaction 3. Nuclear Quadrupole Interaction from nuclei with a nuclear spin quantum number I > ½ impact on EPR spectrum is usually small Relaxation times and linewidths T1 spin-lattice relaxation: through dissipation of energy via the thermal vibration of the lattice T2 spin-spin relaxation: mutual spin flips caused by dipolar and exchange interactions among the spins 1 1 1 linewidth determined by: = + (T2 is much shorter than T1) T2,eff T2 2T1 for transition metal complexes, T2 = several µs at liquid helium temperatures Sensitivity and resolution e.g. for a commercial X-band spectrometer 5·1010 spins can be detected at a SNR of 1.5 for a 1 gauss wide line e.g. linewidths of transition ions in crystals, present at low concentrations, or in ~1mM solutions, are typically 10–100 gauss A list of paramagnetic ions observed in EPR no.
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