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

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

Electron Spin as a Probe 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

Spin Angular Momentum S e |m s > =  ½ |m s > In energy units of h/2  I N |m N > =  ½ |m N >

Gives “Fingerprint” Spectra Spectrum when no Magnetic nuclei present Spectrum when one Magnetic nucleus present S e = 1/2 S e =  1/2 I m = 1/2 I m =  1/2 I m = 1/2  E = g e  e H + a/2 E = g e  e H E = g e  e H  a/2 Selection rules  S e =  1  I m = 0

Microwave Transitions Energy differences depend on the external magnetic field Electronic energy differences between pure electron spin states are about a thousand times larger (  e = 9.27 × 10  28 J/G) than energy differences between pure nuclear states (  N = 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)

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, k B T = eV = 208 cm  1

Intensity patterns No magnetic nuclei yields one line One magnetic nucleus yields two lines 2 equivalent nuclei get pattern equivalent nuclei get pattern equivalent nuclei get pattern

TRESR (Boxcar) H 2 N-  C(CH 3 ) 2 25 G H 2 N-C(CH 3 ) 2 CO 2  +  OH  H 2 N-  C(CH 3 ) 2 + CO 2 + OH 

Block Diagram of ESR Spectrometer