Lecture 5

Question 1

• How many states will as S = 1 system form?

Answer 1

• 2S + 1 = 3
• 3 states à triplet

Question 2

• Describe the different spin configurations of a six-electron system

Answer 2

• a) singlet GS
• b) singlet after electronic excitation
• c) metastable triplet state (lower energy than b due to decreased interelectronic repulsion)
• d) configuration of four electron system with a triplet GS

Question 3

• If two electrons occupy the … spatial orbital, then only the …/singlet state is possible due to the … … …
• If each electron occupies a … orbital, then both the singlet and … states exist

Answer 3

• If two electrons occupy the same spatial orbital, then only the antisymmetric/singlet state is possible due to the Pauli exclusion principle
• If each electron occupies a different orbital, then both the singlet and triplet states exist

Question 4

• Briefly, what is zero field splitting?

Answer 4

• Zero-field splitting describes the various interactions of energy levels of a molecule/paramagnetic ion resulting form the presence of >1 electron (S > ½) in a crystals field.
• When two 2 unpaired electrons mutually interact 3 symmetric and 1 antisymmetric states form, giving rise to a triplet (m_s = -1, 0, +1) and a singlet (m_s = 0)
• Dipolar coupling causes the degeneracy of the three spin sublevels in the triplet to be lifted, even in the absence of a magnetic field, giving rise to a ZFS energy

Question 5

• Describe a system that exhibits an exchange interaction

Answer 5

• If exchange interactions (J_o), E_symmetric < E_{antisymmetric}­
• –> triplet energy < singlet energy
• This is a manifestation of the coulomb interaction between two electrons

Question 6

• What is the result of the exchange interaction, J₀ being > 0

Answer 6

• Would mean S = 0 singlet state is lowest in energy, implying the GS system is diamagnetic which cannot have EPR done on it.

Question 7

• Sketch and label an S =1 spin system’s energy level to describe the splitting that occurs in an increasing magnetic field, B where it is parallel to magnetisation.

Answer 7

Question 8

• What is the general case for ZFS in a system where B is likely not parallel to symmetry axis of magnetisation as before?

Answer 8

• Dm_s² – 1/3S(S+1)/2

Question 9

• Sketch and explain the ESR powder spectrum for a randomly oriented triplet system

Answer 9

• ZFS is axially symmetric
• D_II = -2D_T
• Chance of applying filed parallel to axis is unlikely but more likely when perpendicular
• This is reflected in the intensity of the spectra
• Similar pattern to anisotropic EPR data

Question 10

• What other interaction is present between two free electrons other than exchange interaction/coupling?

Answer 10

• Dipolar coupling, where an electron produces a magnetic field that the other is perturbed by.

Question 11

• What method can be used to measure the dipolar coupling between radicals and what result is indicated from it?

Answer 11

• Dipolar coupling between spatially separated unpaired electrons using pulsed EPR method Double Electron Electron Resonance (DEER)
• If electrons are close enough, coupling will produce an S=1 system, which gives a double-horns on a shelf powder spectrum (Pake pattern)

Question 12

• Describe an equilibrium system that can be used in an optically detected magnetic resonance system.

Answer 12

• Normally in a triplet GS system a m_s = 0 and m_s = ±1 spins are separated by a ZFS
• Populations of these states follow a Boltzmann distribution where lower energy m_s= 0 state predominates
• Optically pumping this system (e.g. with a laser pen) results in near 100% spin polarization to m_s=0
• This is due to photons exciting electrons to ES and relax via lowest energy pathway
  
  • m_s = 0; fluoresces as red light back down to m_s = 0 GS
  • m_s = ±1; ISC to singlet state and relax to GS via IR frequency (1024 nm ) photon
• pumping this process will eventually results in all spin density being in m_s = 0 state
• The conditions of this system make it subject to being spin manipulated through ODMR

Question 13

• How is spin manipulation carried out on the described system?

Answer 13

• Microwaves are used to drive transitions from m_s = 0 –> ±1
• This results in more ±1 spins being excited from the GS
• Observe a larger drop in fluorescence as higher population of spins relaxing via low energy dark photon pathway

Question 14

• What will an increase in magnetic field, B have on the fluorescence frequency spectrum of a spin manipulated system?

Answer 14

• Zeeman effect means single transition 0 –> 1 can be separated out in to 2 transitions due to splitting of m_s = ±1
• Spectra would also increasingly split with increasing B

Question 15

• What is an advantage of optically detected magnetic resonance? Give an example system

Answer 15

• A single spin manipulation can be carried out at room temperature with a small magnet
• An example of this would be a single NV centre, which is an extra electron in a diamond structure for example
• Analysis done atom by atom to work out structure instead of using a huge superconducting magnet in He(l)