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**Physical Methods in Inorganic Chemistry 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) Physical Methods – Magnetic Resonance

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**Physical Methods in Inorganic Chemistry Magnetic Resonance**

Literature H. Friebolin One and Two Dimensional NMR Spectroscopy H. Günther NMR Spectroscopy P. J. Hore Nuclear Magnetic Resonance (primer) A. K. Brisdon Inorganic Spectroscopic Methods (primer) C. P. Slichter Principles of Magnetic Resonance R. Freeman Spin Choreography Physical Methods – Magnetic Resonance Website and

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Magnetic Resonance

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**Selected NMR properties of some elements**

Gyromagnetic ratio (107 rad T-1s-1) 26.75 8.58 6.72 1.93 -2.71 29.18 6.98 -5.31 10.84 7.05 6.35 5.12 -0.85 -1.25 -10.02 6.43 -8.50 1.12 0.50 5.80 4.82 Physical Methods – Magnetic Resonance

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**Trends in Chemical Shifts**

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. Physical Methods – Magnetic Resonance Opposite effects may be observed for transition metals (ligand effects).

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**Effect of Charge, Substituents**

and Oxidation State Physical Methods – Magnetic Resonance

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**The effect of coordination on the chemical shift of a transition metal**

Remember The paramagnetic shielding contribution sp ~ 1/DE 2. paramagnetic currents AUGMENT the magnetic field (sp is negative, hence a DESHIELDING parameter!) DE |sp|* d / ppm E / cm-1 Co(PF3)3- -4200 - Co(CN)63- 26300 Co(NH3)63+ 6940 23210 Co(en)33+ 7010 21400 Co(NO2)63- 7350 20670 Co(acac)3 12300 16900 Physical Methods – Magnetic Resonance 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 Examples of Fluxional inorganic systems.**

Remember: Physical Methods – Magnetic Resonance Examples of Fluxional inorganic systems. Axial-equatorial exchange in trigonal bipyramidal systems (PF5, SF4, PF4NMe2 , Fe(CO)5) Bridging/axial exchange in carbonyls. Bridging terminal exchange in boranes (B2H6 etc.);borohydrides (Al(BH4)3) Ring-whizzing in 1-cyclopentadienides (Cu(PMe3)( 1-C5H5) Interchange of ring bonding modes in compounds with mixed heptacity ( e.g. (1-C5H5)2(5C5H5)2Ti: (4-C6H6)(6-C5H5)Os

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17O spectrum of Co4(CO)12 Physical Methods – Magnetic Resonance

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**The 31P spectrum of PF4N(Me)2**

All 19F equivalent at high Temperature P Fa Fe N(Me)2 Physical Methods – Magnetic Resonance I(31P) = (19F) = 1/2 19Fe and 19Fea not equivalent at low Temperature

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**13C{H} spectrum of [(CH3)3C 6Li]4**

Recall: multiplets 2nI + 1 I(6Li) = 1 n = 4 Jav = (5.4 Hz x 3 + 0)/4 = 4.1 Hz Physical Methods – Magnetic Resonance J(13C-6Li) = 5.4 Hz n = 3

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**NMR Acronyms Nuclear Overhauser Spectroscopy**

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

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

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**Spin Lattice Relaxation and The Inversion-Recovery Experiment**

Physical Methods – Magnetic Resonance p/2 p/2 p/2 p/2

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**Inversion Recovery Method**

p/2 t3 t4 z z z z y y y y x x x x NMR Signal I(t) Physical Methods – Magnetic Resonance

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**Spin Spin Relaxation and the Spin Echo Experiment**

y p t echo z x y z x y = x y Physical Methods – Magnetic Resonance f m s t z x y = x y x y s m f

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**What is the effect of relaxation on the echo amplitude?**

Spin spin Relaxation random magnetic fields destroy phase coherence and are not refocused by p pulse Physical Methods – Magnetic Resonance NMR Echo of each signal:

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Echo Trains Physical Methods – Magnetic Resonance

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**The Method of Spin Decoupling**

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 (S2) with strength B2 in addition to transmitter S1 used for detection of spectrum (a so-called double resonance experiment). S2 is positioned at the resonance of a particular nucleus. Physical Methods – Magnetic Resonance 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**

I(X) = I(A) = 1/2 A X J 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 nX nA nX X( ) X( ) A( ) A( ) Physical Methods – Magnetic Resonance B2 of same order as 2pJAX nX should be sufficiently far away from nA Notation: A{X} nA

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**The Method of Spin Decoupling**

i) irrad Fluorine Spectrum I(19F) = 1/2 A Fa Fe X ii) irrad i) Fe{Fa} Physical Methods – Magnetic Resonance ii) Fa{Fe} I(A) = I(X) = 0

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**31P(CH3CH2O)3 irrad 31P(CH3CH2O)3 31P(CH3CH2O)3**

I(31P)=1/2 irrad Physical Methods – Magnetic Resonance 31P(CH3CH2O)3

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**Recall: Exercise B = 1.41T Electron:**

Can we transfer this polarisation? Physical Methods – Magnetic Resonance 1H:

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**The Nuclear Overhauser Effect**

1) Enhancement of Sensitivity ie, the heteronuclear (13C – H) Nuclear Overhauser Effect g(1H) = rad T-1 s-1 g(13C) = rad T-1 s-1 Physical Methods – Magnetic Resonance 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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**The origin of the Nuclear Overhauser Effect**

Result: saturated proton transitions, 13C population difference increased 3-fold Irradiate proton resonances 2 1 13C H sat 1 3 4 1 4 2 H sat 13C Physical Methods – Magnetic Resonance 5 3 4 Boltzmann Protons saturated Cross Relaxation Takes spins from top to bottom level, competition with 13C relaxation (restoring Boltzmann in 13C population)

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**The maximum attainable enhancement (the fractional increase in intensity)**

hmax = 1/2 gI/gS where I is the saturated spin and S is the observed spin. Physical Methods – Magnetic Resonance 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 15N and 29Si have negative g.

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**Selective Nuclear Overhauser enhancements**

irrad a b g d Difference Spectrum Physical Methods – Magnetic Resonance Integration d g a b

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**29SiH(Ph)3 gSi = - 5.31 107 rad T-1s-1 Magnitude: 1+hmax = 1+1/2 gI/gS**

~ -1.5 gH = rad T-1s-1 29Si{1H} Proton Decoupled Physical Methods – Magnetic Resonance Coupled

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**Principles of 2-Dimensional NMR**

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

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What we know from FT NMR p/2 FT Physical Methods – Magnetic Resonance

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**2D NMR is a domain of FT and pulsed spectroscopy**

Physical Methods – Magnetic Resonance

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**Principles of 2-Dimensional NMR**

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

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**A 2-Dimensional Experiment**

evolution Series of one-dimensional NMR spectra must be recorded t1 evolution Physical Methods – Magnetic Resonance t1 evolution t1

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**Amplitude Modulation Phase Modulation t1 t1**

Physical Methods – Magnetic Resonance

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**Fourier transformation of FID signal, S(t1, t2) **

must be performed to obtain 2D spectrum as function of two frequency variables S(F1, F2) Physical Methods – Magnetic Resonance Spin-spin coupling was active during t1, hence F1 contains coupling constant Larmor precession active during t2, hence F2 contains chemical shift

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**What happens during the pulse sequences?**

p/2x p/2x t1 t2 Pulse Sequence z x y z x y z x y ?

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**What happens during the second p/2x Pulse?**

Pulse does not affect x-component! z x y z x y

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**? = Pulse Sequence: t1 t2 t2 p/2x z x y z x y x y x y**

Physical Methods – Magnetic Resonance = x y x y t2

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**A Simple 2D NMR Spectrum results**

F2 F1 W Physical Methods – Magnetic Resonance W

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**Correlated Spectroscopy (COSY)**

Pulse Sequence p/2x p/2x Aim : To discover spin-spin couplings in a molecule. Answer: Which resonance belongs to which nucleus? t1 t2 Physical Methods – Magnetic Resonance Schematic COSY spectrum of an AX system

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**Physical Methods – Magnetic Resonance**

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**Use of COSY to assign 11B NMR of B10H14.**

(no couplings via H-bridges) 2 2 4 2 3=4 1=2 5=6=7=8 9=10 a d b c a: 2B coupled to all kinds of B = 3,4 Physical Methods – Magnetic Resonance 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

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**2D-Nuclear Overhauser Spectroscopy**

p/2x p/2x p/2x p/2x t1 tm t2 D I S t1 t2 tm WI WS

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**And the resulting spectrum**

I S WI WS Physical Methods – Magnetic Resonance Cross Peaks tell us about interacting spins.

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**2D NOESY vs 1D NMR Physical Methods – Magnetic Resonance**

69 amino acids, M = 7688 Physical Methods – Magnetic Resonance

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**2 D NOESY – Why? Advantages wrt 1D 1H{1H} NOE:**

Simplification of crowded spectra No need for selective excitation of individual resonances Higher efficiency Physical Methods – Magnetic Resonance

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**NMR in Solids Problems:**

Through Space dipolar coupling not averaged out (broadened spectra) Hence, long spin lattice relaxation times T1 (lack of modulation of dipolar coupling) and therefore restriction of pulse repetition rate, consequently, poor S/N Fast spin-spin relaxation times T2 (line broadening) Chemical Shift anisotropy not averaged out (line broadening) Distance dependent – information on spin separations! Physical Methods – Magnetic Resonance Often broad, structureless resonance

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**Temperature dependence of line width**

Proton resonance line Physical Methods – Magnetic Resonance Solid complex adduct

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**The Dipolar Coupling-Through Space Coupling**

repulsion attraction Every nucleus with non-zero I, has a magnetic dipole m=gI x y z Bmz Bmx Physical Methods – Magnetic Resonance r q m Anisotropic quantity

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**In a single crystal, this is simple:**

Recall: D A X Physical Methods – Magnetic Resonance KAX: splitting in spectrum of X caused by dipolar coupling to A

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**Magic Angle Spinning = 0 for q = 54.7o**

Physical Methods – Magnetic Resonance 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, B0 ± BAmz where BAmz is the dipolar field generated by A on X.

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But what about a powder? Every molecule AX has a unique q but different molecules have different q. We need a trick. 54.7o 54.7o 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. Also removes chemical shift anisotropy (also follows the (3cos2q-1) law).

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**How fast can you spin? - Or the relevance of the spinning speed.**

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. Physical Methods – Magnetic Resonance

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(Ph)331PO sper spar Typical spectrum of a system with axial chemical shift anisotropy. static 1.9kHz At low spinning rates, observation of side bands (info about principal components of shielding tensor). 3.8kHz Physical Methods – Magnetic Resonance At high spinning rate we see a single resonance at isotropic chemical shift. siso

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**CP-MAS 15N spectrum of (NH4)NO3 CPMAS**

Physical Methods – Magnetic Resonance The CP(Cross polarisation)-MAS (Magic Angle Spinning) 15N spectrum of NH4NO3 shows two interesting effects: 1) the bigger chemical shift anisotropy for NO3- as compared with NH4+ 2) the greater intensity for NH4+ due to magnetisation transfer from 1H.

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2Ca(CH3CO2)2.H2O Physical Methods – Magnetic Resonance

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**Electron Paramagnetic Resonance (EPR) = Electron Spin Resonance (ESR)**

Physical Methods – Magnetic Resonance

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**EPR is developing fast… …because its APPLICATIONS**

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

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**E R samples P Paramagnetic**

Most substances do not contain paramagnetic species and are hence EPR silent Advantage Easier to interpret Introduction of “Spin Spies” Disadvantage Fewer accessible systems a) b) O N O H2N OH Physical Methods – Magnetic Resonance S S N O O + Protein-SH S S Protein N O

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**Applications of EPR Study of Electron Transfer Processes**

Physical Methods – Magnetic Resonance

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**Applications of EPR Study of N@C60 (and others) Quantum Computing**

Phase transition temp: 260K 4S3/2 (14N) = 1 FT-EPR Physical Methods – Magnetic Resonance K.P. Dinse

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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**

Physical Methods – Magnetic Resonance

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**Energy Splittings and Selection Rule**

ES= +mSgemBB0 DmS=±1 -geh = gemB cf. EI = - mIghB0 (nucleus) 200 400 1H – frequency/MHz mS = -1/2 mS = +1/2 B0/T 10 20 Physical Methods – Magnetic Resonance 100 300 ESR frequency/GHz X Q W

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**The g-value E = mSgemBB0 E = mSgmBB0 ge = 2.00232**

The g-value is a unique property of the molecule as a whole and independent of any electron – nuclear hyperfine interactions. E = mSgemBB0 E = mSgmBB0 SO coupling (SO constant l) leads to derivation of g from that of free electron ge = In case the electron is the only source of magnetism in the sample Physical Methods – Magnetic Resonance When unpaired electron couples to 1) Empty orbital (e.g., d1), g<ge 2) Occupied orbital (e.g., d9), g>ge

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**For most organic radicals, g ≈ ge **

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

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**Isotropic Coupling between an electron and a nuclear spin 1/2**

S in field S I I in field Hyperfine Coupling aiso/4 wI wS wS Physical Methods – Magnetic Resonance |aiso| wS

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**More than one nucleus aSaI bSaI bSbb aSbb bSaI1aI2aI3 aSaI1aI2aI3**

1 spin ½ nucleus bSaI1aI2aI3 aSaI1aI2aI3 bSaI1aI2bI3 aSaI1aI2bI3 bSaI1bI2aI3 aSaI1bI2aI3 bSbI1aI2aI3 aSbI1aI2aI3 bSbI1bI2aI3 aSbI1bI2aI3 bSbI1aI2bI3 aSbI1aI2bI3 bSaI1bI2bI3 aSaI1bI2bI3 bSbI1bI2bI3 aSbI1bI2bI3 3 spin ½ nuclei bSaI1aI2 aSaI1aI2 2 spin ½ nuclei bSbI1aI2 aSbI1aI2 bSaI1bI2 bSbI1bI2 Physical Methods – Magnetic Resonance

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**Allowed Transitions for N nuclei with spins Ik**

N nuclei couple to S Total Number of states: Total number of allowed transitions Physical Methods – Magnetic Resonance Frequencies of allowed transitions

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**The EPR signal is typically in the first derivative form**

Employ modulation technique Physical Methods – Magnetic Resonance

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**EPR of a Simple Isotropic C-centred radical**

1mT e Physical Methods – Magnetic Resonance

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**Another isotropic system in solution: BH3-.**

EPR spectrum of [BH3●]— in solution. The stick diagram marks the resonances for the 11B(I=3/2) and the three protons. The remaining weak resonances are due to the radicals containing 10B(I=3). Physical Methods – Magnetic Resonance

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**Oxidation of a Chromium (III) porphyrine derivative**

Oxidation of a Chromium (III) porphyrine derivative* (still, isotropic in solution) S(Cr5+) = 1/2 I(14N) = 1 I(53Cr) = 3/2 (9.6% abundant) * Physical Methods – Magnetic Resonance

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**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) Physical Methods – Magnetic Resonance Recall: Description of physical quantities Isotropic: scalars Directional: vectors Interactions between vectorial quantities: tensors

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**g is anisotropic and varies with direction**

Diagonalise Principal values where Physical Methods – Magnetic Resonance Isotropic g: Anisotropy: Asymmetry:

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**For an arbitrary orientation of a crystal in a magnetic field**

In spherical coordinates: Physical Methods – Magnetic Resonance

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**And the resulting powder spectrum for a rhombic g-tensor**

Low spin Fe3+ in cytochrome P450 Powder spectrum 1st derivative Physical Methods – Magnetic Resonance

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**Often the g tensor has axial symmetry**

Then: ║ ┴ And: ║ ┴ Physical Methods – Magnetic Resonance

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**ESR spectrum of a simple d1 system**

║ ┴ Physical Methods – Magnetic Resonance

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**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 Physical Methods – Magnetic Resonance

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**A Model Cu2+ system Axial symmetry I(65Cu) = 3/2 d9, S=1/2 ║ ┴**

Physical Methods – Magnetic Resonance

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**Li+(13CO2─) 12C I(13C) = ½, I(7Li) = 3/2**

Physical Methods – Magnetic Resonance A(13C)>>A(7Li): Spin density mainly on 13C

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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 Physical Methods – Magnetic Resonance Systems: Ti3+(d1)S=1/2 Fe3+(d5) S=5/2 (high spin) often high anisotropy, S=1/2 (low spin) Cu2+(d9) S=1/2 I=3/2 for 63Cu and 65Cu Co2+(d7) S= 3/2 (high spin) S=1/2 (low spin)

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**Multiple Resonance Techniques**

EPR spectrum of the phenalenyl radical Physical Methods – Magnetic Resonance

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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**

…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. Physical Methods – Magnetic Resonance 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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**Electron Nuclear Double Resonance**

Physical Methods – Magnetic Resonance

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**Isotropic Coupling between an electron and a nuclear spin 1/2**

Recall: S I aiso/4 wI wS S wS Physical Methods – Magnetic Resonance

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**The ENDOR experiment (simplified)**

NMR transition(3-4) at Recall: Thermal Equil. EPR 1-3 saturated. sat 4 3 Physical Methods – Magnetic Resonance 2 1

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Previous overhead Relative populations are given by Boltzmann at thermal equilibrium (wI<<wS, 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 |wI-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 |wI + 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**

EPR spectrum Physical Methods – Magnetic Resonance ENDOR

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**Orientation Selection**

EPR Hyperfine couplings not resolved 1H ENDOR Toluene Solvent Physical Methods – Magnetic Resonance Two wide doublets which give the hyperfine couplings to protons in the C8H8 and C5H5 rings directly. Repeat for parallel components and find spin densities.

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