Lecture 3

Question 1

• Name 3 systems that produce isotropic EPR spectra

Answer 1

• 1. Unpaired electron in an s orbital. Spherically symmetric therefore probability of finding electron/radical same regardless of direction of magnetic field
• 2. Sample tumbling rapidly in solution. Direction doesn’t matter as averages over all possible directions
• 3. Unpaired electrons is in a cubic symmetry environment
• All result in orientation independent/symmetric EPR spectra that are simple to analyse.

Question 2

• Sketch the line shape for S= 1/2, I = 0 powder EPR spectrum that would be the result of an isotropically symmetric system.

Answer 2

• Any magnetic field, B direction results in derivative of resonance in exact same position as no anisotropy present

Question 3

• Describe the origin of anisotropy in terms of the g-tensor associated with the Hamiltonian of the hyperfine energy

Answer 3

• Deviation from g tensor associated with free electron spin where system xyz chosen such that diagonal g_xx/g_yy/g_zz elements relevant in Hamiltonian describing hyperfine energy
• In an isotropic system, orientation dependence of g tensor values are averaged by fast molecular motion and an isotropic g-value is observed
• g_iso = 1/3(g_xx + g_yy + g_zz)
• As tumbling not present in anisotropic system, how the magnetic field aligns with the axis of the non-symmetric (e.g. p-orbital) will change the contribution to the overall g value

Question 4

• Describe the origin of g_II/g_T terms of a radical in a p orbital in a magnetic field

Answer 4

• Position of resonance when orbital aligned parallel to magnetic field (z-axis) –> g_z/g_II
• Position of resonance when orbital aligned perpendicular to magnetic field (x/y-axis –> g_x,y/g_T

Question 5

• Sketch the line shape for S= 1/2, I = 0 powder EPR spectrum that would be the result of an axially symmetric system.

Answer 5

• Field modulation used to encode signal and lock in detect out gradient of line (higher sensitivity)
• This is a solid state powder spectrum os a system where no tumbling is occurring and is anisotropic and axially symmetric, and likely a radical in a p-orbital

Question 6

• Explain the intensities of the S= 1/2 , I=0 powder spectrum of an axially symmetric system

Answer 6

• Intensity is due to probability of spins aligning with magnetic field, B depending on orientation
• When aligned parallel with B (along z-axis), there is a low probability of spins being aligned where a radical is frozen in solution at this orientation
• Results in the g_II factor
• When aligned perpendicular to magentc field, B a higher intensity arises as more likely for a spin to be aligned anywhere in the xy plane relative to B
• Results in the g_T factor

Question 7

• How does the magnitude of a g factor in a powder spectrum relate to the magnetic field, B?

Answer 7

• g = hv/µ_BB
• Therefore, g varies inversely with B
• A low g factor occurs at a high field

Question 8

• What are the three types of powder EPR spectra and their conditions

Answer 8

Question 9

• Sketch an absorption and first derivative powder spectrum for an axial and orthorhombic system with labelled corresponding g values

Answer 9