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Electron Spin as a Probe for Structure

Electron Spin as a Probe for Structure. Spin angular momentum interacts with external magnetic fields g e b e HS e and nuclear spins I m Hyperfine Interaction + a I m S e. Hamiltonian = g e b e S e H  g N b N I m H + aI m S e. Energy of electron in external Magnetic field H.

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Electron Spin as a Probe for Structure

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  1. Electron Spin as aProbe for Structure • Spin angular momentum interacts with • external magnetic fieldsgebeHSe • and nuclear spins Im • Hyperfine Interaction + aImSe Hamiltonian = gebeSeHgNbNImH + aImSe Energy of electron in external Magnetic field H Energy of magnetic nucleus in external Magnetic field H

  2. Magnetic parameters • Lande g-factor about 2 for organic radicals • For free electron g = 2.00232 • Actual value of g is dependent on spin-orbit coupling in the radical • Determines center of spectrum of a radical • Bohr magneton, be = 9.274 × 10−28 J / G • Hyperfine coupling depends on the electron’s spin density at the magnetic nuclei

  3. Electron Spin as aProbe for Structure • The main reason it acts as a sensitive probe of free radical structure is that the Hyperfine Interaction or Fermi Contact Term is large only at the nucleus of a magnetic atom

  4. Spin Angular Momentum In energy units of h/2 Se |ms> =  ½ |ms> IN |mN> =  ½ |mN>

  5. Gives “Fingerprint” Spectra Selection rules DSe = 1 DIm = 0 Im = 1/2 Se = 1/2 Im = 1/2 E = gebeH  E = gebeH a/2 E = gebeH+ a/2 Im = 1/2 Se = 1/2 Im = 1/2 Spectrum when no Magnetic nuclei present Spectrum when one Magnetic nucleus present

  6. Microwave Transitions • Energy differences depend on the external magnetic field • Electronic energy differences between pure electron spin states are about a thousand times larger (be = 9.27 × 1028 J/G) than energy differences between pure nuclear states (bN = 5.05 × 1031 J/G) • Since energy differences are small, it is possible to saturate transitions • Stimulated emission is also seen because of Chemically Induced Dynamic Electron Polarization (CIDEP)

  7. Microwaves (Units) • Magnet field of about 3400 G = H • X-band microwaves 3.0 to 3.3 cm • Frequency around 9.4 GHz • Energy 0.3 to 0.33 cm1 • At 300 C, kBT = 0.025 eV = 208 cm1

  8. Intensity patterns • No magnetic nuclei yields one line • One magnetic nucleus yields two lines • 2 equivalent nuclei get pattern 1-2-1 • 3 equivalent nuclei get pattern 1-3-3-1 • 4 equivalent nuclei get pattern 1-4-6-4-1

  9. TRESR (Boxcar) H2N-C(CH3)2 H2N-C(CH3)2CO2-+OH H2N-C(CH3)2 + CO2 +OH- 25 G

  10. Block Diagram of ESR Spectrometer http://www.chm.bris.ac.uk/emr/Phil/Phil_1/p_1.html

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