EPR Notes

Question 1

Paramagnetic

Answer 1

One or more unpaired electron(s)

Question 2

ms

Answer 2

(in presence of a magnetic field) Electron spin magnetic quantum number
- S, S-1, … , -S

Spin quantum number (ms) only has values of +/- 1/2

Question 3

How does EPR differ from NMR?

Answer 3

NMR - interactions of nuclear spins forming in an atom with a magnetic field applied to them
EPR - interaction of electron spins with the applied magnetic field

Since the electron magnetic moment is about 1000 times greater than the proton nuclear magnetic moment, there are significant differences in characteristic frequencies and sensitivities

Magnetic moment is inversely proportional to mass

Question 4

Materials studied by EPR

Answer 4

• Organic molecules with one unpaired electron (doublet state)
• Molecules with two unpaired electrons (triplet state, like O2)
• Transition metal complexes with incomplete 3d, 4d, or 5d orbitals

Question 5

Low spin complex

Answer 5

Minimum number of unpaired electrons
delta is greater than pairing energy (P)

Question 6

High spin complex

Answer 6

Maximum number of unpaired electrons
delta is less than the pairing energy (P)

Question 7

Geometry for coordination number 6 and 4

Answer 7

6 - octahedral
4 - weak field/high spin = tetrahedral
4 - strong field/low spin = square planar

Question 8

Spin multiplicity

Answer 8

n + 1 (where n = unpaired electrons)

n = 0, multiplicity = 1, singlet state
n = 1, multiplicity = 2, doublet state
n = 2, multiplicity = 3, triplet state

Question 9

Resonance condition: u = -gBJ

Answer 9

u = magnetic moment (passed by electron)
g = spectroscopic splitting factor, reflects nature of orbital
B = electron Bohr magneton, 9.274 x 10^-24 J/T
J = total angular momentum vector = L + S

• we neglect L in transition metal complexes, then J = S = (n/2) for n unpaired electrons
• equation becomes u = -gBS
• measurable components are g, B, ms

Question 10

Presence of a magnetic field (Bo or H)

Answer 10

The electron magnetic moments assume orientations with respect to the applied magnetic field, giving rise to 2S+1 energy states

Question 11

What does plotting the first derivative curve (dP/dBo) allow?

Answer 11

Allows us to improve resolution and decrease background/signal noise

Question 12

What causes hyperfine coupling in isotropic systems in EPR?

Answer 12

Interaction between electron spin magnetic moment and nuclear spin magnetic moment

Mechanism of couping is Fermi contact interaction which results from unpaired electron density at the nucleus in question

Unpaired electron density at the nucleus is only present when the electron is in an orbital having some s character
(Coupling provides indication of extent of electron delocalization over nuclei of nuclear spin I > 0)

Question 13

Ms

Answer 13

Total electron spin magnetic quantum number
- given by addition of electron spin magnetic quantum numbers (for a greater than doublet system)

Question 14

mi

Answer 14

Nuclear spin magnetic quantum number
(for one nucleus of nuclear spin one)

Question 15

Mi

Answer 15

Total nuclear magnetic spin magnetic quantum number
- given by addition of nuclear spin magnetic quantum numbers (for more than one nucleus of nuclear spin one)

Question 16

Summary of coupling

Answer 16

• hyperfine splitting patterns provide information about the numbers and types of nuclei couples to the unpaired electron
• the magnitude of the coupling constants (a) indicate the extent to which the unpaired electron is associated with a given nucleus (spin density)
• anisotropic g values may show whether the unpaired electron is transition metal based or ligand based

Question 17

What does coupling to a nuclei of nuclear spin (I) greater than 1/2 cause?

Answer 17

Produces a symmetrical multiplet whose intensities are different than a binomial multiplet (Pascal’s triangle)
Nature of a nonbinomial multiplet is deduced by a coupling tree

Question 18

Isotropy/anisotropy

Answer 18

In solution, molecules are tumbling at rates greater than the EPR spectrometer frequency
- anisotropic effects due to differences in molecular orientation with respect to magnetic field are averaged to 0 by rapid tumbling

Question 19

Consequence of isotropy

Answer 19

Any anisotropic effects due to differences in molecular orientation with respect to the magnetic field are averaged to 0 by rapid tumbling

Question 20

Consequence of anisotropy (solid, crystal, powder, frozen solution)

Answer 20

No symmetry - 3g, 3a values
Axial symmetry (symmetry about one axis) - 2g, 2a values (parallel and perpendicular)

Question 21

Molecular axis in parallel

Answer 21

larger a value
lower intensity

Question 22

Molecular axis in perpendicular

Answer 22

smaller a value
larger intensity