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Physical Methods in Inorganic Chemistry Magnetic Resonance Physical Methods – Magnetic Resonance Lecture Course Outline Lecture 1: A quick reminder A few trends in Inorganic NMR A little more on Chemical Exchange Essential NMR Methods Spin Decoupling Spin Relaxation Measurements (again and more) Lecture 2: NMR Methods continued – 2D and others Correlated Spectroscopy (COSY) Nuclear Overhauser (NOE) Magic Angle Spinning (MAS) Lecture 3: Electron Paramagnetic Resonance The why and when of EPR in Inorganic Chemistry EPR methods (ENDOR, DEER)

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Physical Methods in Inorganic Chemistry Magnetic Resonance Physical Methods – Magnetic Resonance Literature H. Friebolin One and Two Dimensional NMR Spectroscopy H. Günther NMR Spectroscopy P. J. HoreNuclear Magnetic Resonance (primer) A. K. BrisdonInorganic Spectroscopic Methods (primer) C. P. SlichterPrinciples of Magnetic Resonance R. FreemanSpin Choreography Website and

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Magnetic Resonance

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Selected NMR properties of some elements Physical Methods – Magnetic Resonance Gyromagnetic ratio (10 7 rad T -1 s -1 )

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Trends in Chemical Shifts Physical Methods – Magnetic Resonance Remember: The diamagnetic shielding generally becomes smaller as the electron density at the nucleus decreases. Thus electronegative substituents, positive charge or increase in oxidation state usually result in decreased shielding and increased shift. Opposite effects may be observed for transition metals (ligand effects).

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Physical Methods – Magnetic Resonance Effect of Charge, Substituents and Oxidation State

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Physical Methods – Magnetic Resonance The effect of coordination on the chemical shift of a transition metal / ppm E / cm -1 Co(PF 3 ) Co(CN) Co(NH 3 ) Co(en) Co(NO 2 ) Co(acac) Remember 1.The paramagnetic shielding contribution p ~ 1/ E 2. paramagnetic currents AUGMENT the magnetic field ( p is negative, hence a DESHIELDING parameter!) EE p | * Typically, shifts follow the spectrochemical series: strong field ligands give small or negative chemical shifts whilst halogens give larger chemical shifts.

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Chemical Exchange Physical Methods – Magnetic Resonance Remember: Examples of Fluxional inorganic systems. Axial-equatorial exchange in trigonal bipyramidal systems (PF 5, SF 4, PF 4 NMe 2, Fe(CO) 5 ) Bridging/axial exchange in carbonyls. Bridging terminal exchange in boranes (B 2 H 6 etc.);borohydrides (Al(BH 4 ) 3 ) Ring-whizzing in 1 -cyclopentadienides (Cu(PMe 3 )( 1 -C 5 H 5 ) Interchange of ring bonding modes in compounds with mixed heptacity ( e.g. ( 1 -C 5 H 5 ) 2 ( 5 C 5 H 5 ) 2 Ti: ( 4 -C 6 H 6 )( 6 -C 5 H 5 )Os

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Physical Methods – Magnetic Resonance 17 O spectrum of Co 4 (CO) 12

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The 31 P spectrum of PF 4 N(Me) 2 Physical Methods – Magnetic Resonance P FaFa FaFa FeFe FeFe N(Me) 2 I( 31 P) = ( 19 F) = 1/2 All 19 F equivalent at high Temperature 19 F e and 19 Fe a not equivalent at low Temperature

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13 C{H} spectrum of [(CH 3 ) 3 C 6 Li] 4 Physical Methods – Magnetic Resonance I( 6 Li) = 1 Recall: multiplets 2nI + 1 J( 13 C- 6 Li) = 5.4 Hz J av = (5.4 Hz x 3 + 0)/4 = 4.1 Hz n = 3 n = 4

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Physical Methods – Magnetic Resonance NMR Acronyms Correlated Spectroscopy Nuclear Overhauser Spectroscopy Electron Nuclear Double Resonance Magic Angle Spinning

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Physical Methods – Magnetic Resonance Methods E B B h Continuous wave

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Physical Methods – Magnetic Resonance Spin Lattice Relaxation and The Inversion-Recovery Experiment

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Physical Methods – Magnetic Resonance Inversion Recovery Method z z z z x x x x y y y y NMR Signal I( )

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Physical Methods – Magnetic Resonance Spin Spin Relaxation and the Spin Echo Experiment z x y z x y x y = x y f m s x y s m f x y z x y = echo

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Physical Methods – Magnetic Resonance What is the effect of relaxation on the echo amplitude? random magnetic fields destroy phase coherence and are not refocused by pulse NMR Echo of each signal: Spin spin Relaxation

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Physical Methods – Magnetic Resonance Echo Trains

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The Method of Spin Decoupling Physical Methods – Magnetic Resonance FACT: Spin–Spin Coupling yields important information but NMR data interpretation complicated by line splittings. A SOLUTION: simplify spectra by removing some (chosen) splittings and learn about which nuclei couple to which. HOW: apply a second Radiofrequency source (S 2 ) with strength B 2 in addition to transmitter S 1 used for detection of spectrum (a so-called double resonance experiment). S 2 is positioned at the resonance of a particular nucleus. RESULT: decoupled spectra are less crowded and have much higher sensitivity as all available NMR intensity concentrated into single line (and Nuclear Overhauser).

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The Origin of the Spin Decoupling Effect Physical Methods – Magnetic Resonance A X J I(X) = I(A) = 1/2 X( ) A A( ) X Irradiation of X at its resonance frequency induces rapid transitions from X( ) to X( ) and vice versa. A “sees” a single, averaged field. irrad at X A B 2 of same order as 2 J AX X should be sufficiently far away from A Notation: A{X}

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The Method of Spin Decoupling Physical Methods – Magnetic Resonance A FaFa FaFa FeFe X X I(A) = I(X) = 0 Fluorine Spectrum I( 19 F) = 1/2 i) irrad ii) irrad F e {F a } F a {F e } i) ii)

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Physical Methods – Magnetic Resonance 31 P(CH 3 CH 2 O) 3 I( 31 P)=1/2 31 P(CH 3 CH 2 O) 3 irrad 31 P(CH 3 CH 2 O) 3

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Recall: Exercise B = 1.41T 1 H: Electron: Can we transfer this polarisation? Physical Methods – Magnetic Resonance

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( 1 H) rad T -1 s -1 ( 13 C) = rad T -1 s -1 The Nuclear Overhauser Effect 1) Enhancement of Sensitivity ie, the heteronuclear ( 13 C – H) Nuclear Overhauser Effect 2) Information about proximity of two nuclei (ie, protons) 3) Dependent on Cross Relaxation between different spins. Prerequisite for this cross relaxation experiment is that the spin lattice relaxation of the nuclei is dominated by dipole-dipole interaction with the other nuclear spins.

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Physical Methods – Magnetic Resonance The origin of the Nuclear Overhauser Effect Irradiate proton resonances C H H BoltzmannProtons saturatedCross Relaxation Takes spins from top to bottom level, competition with 13 C relaxation (restoring Boltzmann in 13 C population) sat Result: saturated proton transitions, 13 C population difference increased 3-fold

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Physical Methods – Magnetic Resonance The maximum attainable enhancement (the fractional increase in intensity) max I / S where I is the saturated spin and S is the observed spin. Maximum effect occurs when there is no “leakage” as a result of relaxation mechanisms other than the dipole- dipole interaction (a through space interaction!). For homonuclear systems, maximum enhancement is 50%. Remember that 15 N and 29 Si have negative .

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Physical Methods – Magnetic Resonance Selective Nuclear Overhauser enhancements irrad Difference Spectrum Integration

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29 SiH(Ph) 3 Physical Methods – Magnetic Resonance Proton Decoupled Coupled Si 10 7 rad T -1 s Si{ 1 H} H 10 7 rad T -1 s -1 Magnitude: max I / S ~ -1.5

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Physical Methods – Magnetic Resonance Principles of 2-Dimensional NMR Father of 2D NMR: Jeener, Belgium Main Developers: RR Ernst (Switzerland), R Freeman (UK, Oxford)

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What we know from FT NMR FT Physical Methods – Magnetic Resonance

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2D NMR is a domain of FT and pulsed spectroscopy

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Physical Methods – Magnetic Resonance Principles of 2-Dimensional NMR The time-intervals of 2D NMR

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Physical Methods – Magnetic Resonance A 2-Dimensional Experiment evolution t1t1 t1t1 t1t1 Series of one- dimensional NMR spectra must be recorded

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Physical Methods – Magnetic Resonance Amplitude Modulation Phase Modulation t1t1 t1t1

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Physical Methods – Magnetic Resonance Fourier transformation of FID signal, S(t 1, t 2 ) must be performed to obtain 2D spectrum as function of two frequency variables S(F 1, F 2 ) Spin-spin coupling was active during t 1, hence F 1 contains coupling constant Larmor precession active during t 2, hence F 2 contains chemical shift

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What happens during the pulse sequences? Pulse Sequence z x y z x y z x y t1t1 t1t1 x ? t2t2

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What happens during the second x Pulse? z x y z x y /2 x Pulse Pulse does not affect x-component!

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t2t2 Pulse Sequence: t1t1 t1t1 z x y z x y z x y x ? z x y x y = t2t2 x y Physical Methods – Magnetic Resonance

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A Simple 2D NMR Spectrum results F1F1 F2F2 Physical Methods – Magnetic Resonance

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Correlated Spectroscopy (COSY) x t1t1 t2t2 Pulse Sequence x Aim : To discover spin-spin couplings in a molecule. Answer: Which resonance belongs to which nucleus? Schematic COSY spectrum of an AX system Physical Methods – Magnetic Resonance

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Use of COSY to assign 11 B NMR of B 10 H 14. a: 2B coupled to all kinds of B = 3,4 3=4 1=2 5=6=7=8 9=10 b: 4B coupled to 2 kinds of B = 5,6,7,8 c: 2B coupled to 1 kind of B = 9,10 d: 2B coupled to 2 kinds of B = 1,2 (no couplings via H-bridges) a b d c

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2D-Nuclear Overhauser Spectroscopy x t1t1 mm t2t2 t1t1 mm t2t2 I S D II SS

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Physical Methods – Magnetic Resonance And the resulting spectrum I S D II SS Cross Peaks tell us about interacting spins.

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Physical Methods – Magnetic Resonance 2D NOESY vs 1D NMR 69 amino acids, M = 7688

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Physical Methods – Magnetic Resonance 2 D NOESY – Why? Advantages wrt 1D 1 H{ 1 H} NOE: Simplification of crowded spectra No need for selective excitation of individual resonances Higher efficiency

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Physical Methods – Magnetic Resonance NMR in Solids Problems: Through Space dipolar coupling not averaged out (broadened spectra) Hence, long spin lattice relaxation times T 1 (lack of modulation of dipolar coupling) and therefore restriction of pulse repetition rate, consequently, poor S/N Fast spin-spin relaxation times T 2 (line broadening) Chemical Shift anisotropy not averaged out (line broadening) Often broad, structureless resonance Distance dependent – information on spin separations!

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Temperature dependence of line width Physical Methods – Magnetic Resonance Solid complex adduct Proton resonance line

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The Dipolar Coupling-Through Space Coupling r x y z BxBx BzBz N N NN S S S S repulsion attraction Every nucleus with non-zero I, has a magnetic dipole I Anisotropic quantity Physical Methods – Magnetic Resonance

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K AX : splitting in spectrum of X caused by dipolar coupling to A A X D In a single crystal, this is simple: Recall:

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Magic Angle Spinning Physical Methods – Magnetic Resonance = 0 for At this angle all dipolar interactions disappear! Recall here that the resonance frequency of a given nucleus X coupled to a nucleus A is determined by the total field it experiences in z-direction, ie, B 0 ± B A z where B A z is the dipolar field generated by A on X.

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But what about a powder? Every molecule AX has a unique but different molecules have different We need a trick. Physical Methods – Magnetic Resonance A powder sample is mounted for magic angle spinning and gives the internuclear vectors an average orientation at the spinning angle o Also removes chemical shift anisotropy (also follows the (3cos 2 -1) law).

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How fast can you spin? - Or the relevance of the spinning speed. Physical Methods – Magnetic Resonance Assume: Static line width of resonance to be studied (ie, undesired interaction) is f Hz then spinning speed must exceed f Hz if all broadening interaction are to be nullified. Spinning speeds of up to 35 kHz possible.

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(Ph) 3 31 PO Physical Methods – Magnetic Resonance At low spinning rates, observation of side bands (info about principal components of shielding tensor). At high spinning rate we see a single resonance at isotropic chemical shift. static 1.9kHz 3.8kHz Typical spectrum of a system with axial chemical shift anisotropy. per par iso

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CP-MAS 15 N spectrum of (NH 4 )NO 3 CPMAS Physical Methods – Magnetic Resonance The CP(Cross polarisation)-MAS (Magic Angle Spinning) 15 N spectrum of NH 4 NO 3 shows two interesting effects: 1) the bigger chemical shift anisotropy for NO 3 - as compared with NH 4 + 2) the greater intensity for NH 4 + due to magnetisation transfer from 1 H.

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2Ca(CH 3 CO 2 ) 2.H 2 O Physical Methods – Magnetic Resonance

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Electron Paramagnetic Resonance (EPR) = Electron Spin Resonance (ESR) Physical Methods – Magnetic Resonance

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Möbius & coworkers 360GHz ENDOR at 275 GHz (Schmidt et al 2005). The HIPER project “Bringing the NMR paradigm to ESR” Graham Smith et al. EPR is developing fast… …because its APPLICATIONS so demand Physical Methods – Magnetic Resonance

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E R samples Paramagnetic Most substances do not contain paramagnetic species and are hence EPR silent Disadvantage Fewer accessible systems Advantage 1)Easier to interpret 2)Introduction of “Spin Spies” N O H2NH2N OH N O S S O O + Protein-SH N O S S Protein a)b)

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Physical Methods – Magnetic Resonance Applications of EPR Study of Electron Transfer Processes

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Physical Methods – Magnetic Resonance Applications of EPR Study of 60 (and others) Quantum Computing K.P. Dinse 4 S 3/2 ( 14 N) = 1 Phase transition temp: 260K FT-EPR

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Local Structure ENDOR/ESEEM in proteins Physical Methods – Magnetic Resonance

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Applications of EPR Long range structure Use of Spin Labels Light Harvesting complexes

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Physical Methods – Magnetic Resonance Energy Splittings and Selection Rule m S = -1/2 m S = +1/2 B 0 /T ESR frequency/GHz X Q W H – frequency/MHz E S = +m S g e B B 0 m S =±1 - e h = g e B cf. E I = - m I hB 0 (nucleus)

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The g-value E = m S g e B B 0 E = m S g B B 0 g e SO coupling (SO constant ) leads to derivation of g from that of free electron Physical Methods – Magnetic Resonance In case the electron is the only source of magnetism in the sample The g-value is a unique property of the molecule as a whole and independent of any electron – nuclear hyperfine interactions. When unpaired electron couples to 1) Empty orbital (e.g., d 1 ), g

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For most organic radicals, g ≈ g e For transition metals, large deviations from g e possible g can be measure to high accuracy (±0.0001) g is the “chemical shift” of NMR Note: later, we will discuss that g is anisotropic and not actually a scalar but a tensor. g depends on structure of radical, excitation energies, strengths of spin-orbit couplings Physical Methods – Magnetic Resonance

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SS S in field Hyperfine Coupling SS SS S S S I I S I I I in field |a iso | SS a iso /4 Isotropic Coupling between an electron and a nuclear spin 1/2 II II Physical Methods – Magnetic Resonance

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More than one nucleus S I S I S b S b 1 spin ½ nucleus S I1 I2 S I1 I2 2 spin ½ nuclei S I1 I2 S I1 I2 S I1 I2 S I1 I2 S I1 I2 S I1 I2 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 S I1 I2 I3 3 spin ½ nuclei

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Allowed Transitions for N nuclei with spins I k Physical Methods – Magnetic Resonance N nuclei couple to S Total Number of states: Total number of allowed transitions Frequencies of allowed transitions

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Physical Methods – Magnetic Resonance The EPR signal is typically in the first derivative form Employ modulation technique

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Physical Methods – Magnetic Resonance EPR of a Simple Isotropic C- centred radical e 1mT

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Physical Methods – Magnetic Resonance Another isotropic system in solution: BH 3 -. EPR spectrum of [BH 3 ● ] — in solution. The stick diagram marks the resonances for the 11 B(I=3/2) and the three protons. The remaining weak resonances are due to the radicals containing 10 B(I=3).

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Physical Methods – Magnetic Resonance Oxidation of a Chromium (III) porphyrine derivative* (still, isotropic in solution) S(Cr 5+ ) = 1/2 I( 14 N) = 1 I( 53 Cr) = 3/2 (9.6% abundant) *

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Physical Methods – Magnetic Resonance But nothing is ever that simple… Anisotropic Interactions (of significance in solids, frozen solutions, membranes etc.) with the applied field with surrounding magnetic nuclei between electron spins (if more than one, obviously) Recall: Description of physical quantities Isotropic: scalars Directional: vectors Interactions between vectorial quantities : tensors

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Physical Methods – Magnetic Resonance g is anisotropic and varies with direction where Diagonalise Principal values Isotropic g: Anisotropy: Asymmetry:

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Physical Methods – Magnetic Resonance For an arbitrary orientation of a crystal in a magnetic field In spherical coordinates:

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Physical Methods – Magnetic Resonance And the resulting powder spectrum for a rhombic g-tensor Low spin Fe 3+ in cytochrome P450 Powder spectrum 1 st derivative

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Physical Methods – Magnetic Resonance Often the g tensor has axial symmetry Then: ║ ┴ ║ ┴ And:

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Physical Methods – Magnetic Resonance ESR spectrum of a simple d 1 system ║ ┴

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Physical Methods – Magnetic Resonance But things are not that easy… The hyperfine couplings can also be anisotropic (and often are!) Recall: Fermi contact Interaction (discussion of J) Density of unpaired electron at nucleus (s-orbital character in SOMO) ISOTROPIC Recall: Dipolar Interaction, D p,d,f orbital character in SOMO Averages out in solution ANISOTROPIC

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Physical Methods – Magnetic Resonance A Model Cu 2+ system Axial symmetry I( 65 Cu) = 3/2d 9, S=1/2 ║ ┴

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Physical Methods – Magnetic Resonance Li + ( 13 CO 2 ─ ) I( 13 C) = ½, I( 7 Li) = 3/2 12 C A( 13 C)>>A( 7 Li): Spin density mainly on 13 C

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Physical Methods – Magnetic Resonance Transition Metal EPR Complicated by the fact that transition metal systems might have several unpaired electrons and several approximately degenerate orbitals 3d elements important as only moderate spin-orbit coupling Ability to distinguish between high spin and low spin complexes (in ligand fields): coordination number and geometry accessible via EPR Difficult to observe EPR on systems with integer S Systems: Ti 3+ (d 1 )S=1/2 Fe 3+ (d 5 ) S=5/2 (high spin) often high anisotropy, S=1/2 (low spin) Cu 2+ (d 9 ) S=1/2 I=3/2 for 63 Cu and 65 Cu Co 2+ (d 7 ) S= 3/2 (high spin) S=1/2 (low spin)

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Physical Methods – Magnetic Resonance Multiple Resonance Techniques EPR spectrum of the phenalenyl radical

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Physical Methods – Magnetic Resonance “The problems of resolving the hyperfine lines may be linked to that of a man with several telephones on his desk all of which ring at the same time. If he tries to answer them all, he hears a jumble of conversations as all callers speak to him at once. Of course his callers have no problem – they only hear one voice.

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This is analogous to recognising Physical Methods – Magnetic Resonance …that each nucleus experiences the hyperfine field of only one electron. Each (spin-1/2) nucleus then gives rise to two resonance conditions depending on whether the electron hyperfine field opposes or augments the applied field. How? A strong radiofrequency (NMR) field induces NMR transitions which are observed as a change in the intensity of an electron resonance condition. Electron Nuclear Double Resonance (ENDOR)

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Physical Methods – Magnetic Resonance Electron Nuclear Double Resonance

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SS SS SS S S S I I S I I a iso /4 Isotropic Coupling between an electron and a nuclear spin 1/2 II II Physical Methods – Magnetic Resonance Recall:

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Physical Methods – Magnetic Resonance Recall: Thermal Equil. EPR 1-3 saturated. sat The ENDOR experiment (simplified) NMR transition(3-4) at

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Previous overhead Relative populations are given by Boltzmann at thermal equilibrium ( I << S, hence populations of 1 & 2, 3 & 4 assumed identical) Irradiate 1-3 transition (saturate at high power) – same populations in 1&3 now Irradiate system with RF (NMR) and sweep frequency whilst continually saturating EPR transition; observe the intensity of its absorption When RF frequency matches | I -a/2|, transition 3-4 will be induced, restoring some population difference between levels 1&3 More EPR absorption now possible – this is an ENDOR signal Equally, when RF frequency matches | I + a/2| (1-4 transition), this time a pumping from 1-4 occurs (as 4 has the higher population) and a population difference between 1&3 is again achieved and EPR transition enhance – the second ENDOR signal In practice, need to consider spin lattice relaxation processes Physical Methods – Magnetic Resonance

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Tetracene cations in sulphuric acid Physical Methods – Magnetic Resonance EPR spectrum ENDOR

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Physical Methods – Magnetic Resonance Toluene Solvent Hyperfine couplings not resolved EPR 1 H ENDOR Orientation Selection Two wide doublets which give the hyperfine couplings to protons in the C 8 H 8 and C 5 H 5 rings directly. Repeat for parallel components and find spin densities.

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