# Electron nuclear double resonance (ENDOR)

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Electron nuclear double resonance (ENDOR)
Gavin W Morley, Department of Physics, University of Warwick

Electron nuclear double resonance (ENDOR)
Overview Why do ENDOR? Continuous-wave ENDOR Pulsed ENDOR with: Selective pulses Non-selective pulses

Electron nuclear double resonance (ENDOR)
Why do ENDOR? More sensitive than NMR “EPR-detected NMR” (electron has a larger magnetic moment, flips faster and can be detected more sensitively) NMR may be impossible due to nearby electron spin Higher resolution than EPR Extra selection rules

Birth of ENDOR First paper: G Feher, Phys Rev 103, 834 (1956) George Feher (born 1924) Photo from AIP Emilio Segre Visual Archives Image by Manuel Vögtli (UCL)

Electron nuclear double resonance (ENDOR)
EPR-detected NMR: how?

Electron paramagnetic resonance
Iz = ½ Iz = -½ Photons reflected S = ½ I = ½ Magnetic field, B Energy of a spin system Here is a really simple Hamiltonian. We could have spins greater than a half. We could include some anisotropy of the g tensors and the hyperfine tensor. We could include a nuclear quadrupole interaction and various other terms, but we don’t need to do any of that now. This Hamiltonian describes Feher’s system and it’s a great model system for describing ENDOR. Magnetic field, B

Electron paramagnetic resonance
Iz = ½ Iz = -½ Photons reflected S = ½ I = ½ Magnetic field, B Energy of a spin system Here is a really simple Hamiltonian. We could have spins greater than a half. We could include some anisotropy of the g tensors and the hyperfine tensor. We could include a nuclear quadrupole interaction and various other terms, but we don’t need to do any of that now. This Hamiltonian describes Feher’s system and it’s a great model system for describing ENDOR. You need to record an EPR spectrum before trying ENDOR Magnetic field, B

ENDOR S = ½ I = ½ RF in Iz = ½ Iz = -½ Photons reflected
Magnetic field, B Energy of a spin system Send in RF and sweep the frequency. Where will the transitions occur? RF in Magnetic field, B

Two ENDOR transition frequencies
For isotropic A Microwave photons reflected “Weak coupling” RF frequency Microwave photons reflected “Strong coupling” RF frequency

Electron paramagnetic resonance
Iz = ½ Iz = -½ Photons reflected Magnetic field, B Energy of a spin system Let’s redraw the energy levels for a fixed magnetic field Magnetic field, B

Electron paramagnetic resonance
Energy of a spin system Magnetic field, B

Electron nuclear double resonance (ENDOR)
EPR-detected NMR: how? B0 is static magnetic field B1 is EPR magnetic field B2 is NMR magnetic field

Electron nuclear double resonance (ENDOR)
EPR-detected NMR: how? B0 is static magnetic field B1 is EPR magnetic field B2 is NMR magnetic field

Electron nuclear double resonance (ENDOR)
EPR-detected NMR: how? B0 is static magnetic field B1 is EPR magnetic field B2 is NMR magnetic field

Electron nuclear double resonance (ENDOR)
EPR-detected NMR: how? B0 is static magnetic field B1 is EPR magnetic field B2 is NMR magnetic field

Continuous Wave ENDOR EPR-detected NMR George Feher
Photo from AIP Emilio Segre Visual Archives Image by Manuel Vögtli (UCL)

Continuous Wave ENDOR Saturated EPR

Continuous Wave ENDOR Saturated EPR

Continuous Wave ENDOR Saturated NMR gives the biggest signal. ~3kHz linewidths CW ENDOR is the desaturation of a saturated EPR transition by providing an extra T1e relaxation route via NMR

Continuous Wave ENDOR (use FM and lock-in) νNMR (MHz)
Hale & Mieher, Phys Rev (1969) (following Feher, Phys Rev 114, 1219 (1959)) (use FM and lock-in) νNMR (MHz) Saturated NMR gives the biggest signal. ~3kHz linewidths CW ENDOR is the desaturation of a saturated EPR transition by providing an extra T1e relaxation route via NMR

Continuous Wave ENDOR νNMR (MHz)
Hale & Mieher, Phys Rev (1969) (following Feher, Phys Rev 114, 1219 (1959)) νNMR (MHz) The wavefunction is not just this envelope function which is s-like, but there is also a periodic modulation due to the periodic crystal. In order to assign all of these peaks to over 20 shells, they measured these spectra while rotating the crystal and studied the symmetry of each resonance. B Koiller, R B Capaz, X Hu and S Das Sarma, PRB 70, (2004) Image by Manuel Vögtli (UCL)

Continuous Wave ENDOR νNMR (MHz)
Hale & Mieher, Phys Rev (1969) (following Feher, Phys Rev 114, 1219 (1959)) νNMR (MHz) CW ENDOR effect is typically a few % of the EPR signal

Continuous Wave ENDOR Advantage of CW ENDOR:
Observe sharpest ENDOR resonances Disadvantage of CW ENDOR: CW ENDOR line intensity depends on a delicate balance between relaxation rate and excitation power. Jack Freed did the relaxation theory for this for molecules in solution. George Feher Photo from UCSD Feher went on to make HUGE contributions to photosynthesis This is compared with experiments in solution in: Plato, Lubitz & Mobius, J Phys Chem 85, 1202 (1981)

Pulsed ENDOR Use a π pulse for nuclei, but there are two main pulse sequences for electrons: Davies ENDOR: π pulse then echo readout with all selective (long) pulses. Mims ENDOR uses a stimulated echo with non-selective (short) pulses How can you fit in the long RF pulse within the electron spin T2 time? Preparation

Davies ENDOR π π/2 π π MW: RF:
Roy Davies, Royal Holloway, University of London RF: Davies is a professor of Machine Vision. He developed Davies ENDOR while a postdoc at Oxford. As with CW ENDOR, sweep RF frequency to get a spectrum. Use long, selective MW pulses to burn a hole  smaller signal However, there are no “blind spots” which is an advantage over Mims ENDOR.

Rotating frame

Rotating frame

Spin echo Hahn echo In rotating frame

Spin echo Hahn echo In rotating frame

Davies ENDOR Product operator notation:
Electron-nuclear two-spin order, 2SzIz

Davies ENDOR RF pulse duration is an important parameter to set

Davies ENDOR Davies ENDOR efficiency, FDavies= 50% Echo height
RF frequency

Davies ENDOR Start again… Product operator notation:
Electron-nuclear two-spin order, 2SzIz Start again…

Davies ENDOR Off-resonance RF does nothing

Davies ENDOR Echo height RF frequency

Davies ENDOR Start again again… Product operator notation:
Electron-nuclear two-spin order, 2SzIz Start again again…

Davies ENDOR

Davies ENDOR Davies ENDOR efficiency, FDavies= 50% Echo height
RF frequency

Davies ENDOR Davies ENDOR disadvantage: selective pulses on electron spins mean many spins are ignored if the resonance is inhomogeneously broadened

Mims ENDOR τ τ π MW: RF: sweep RF frequency
MW: τ τ π RF: sweep RF frequency (Bill Mims: Schweiger & Jeschke dedicated their book to him calling him the Spiritus Rector of pulsed EPR). Initially need to vary RF pulse length to find pi pulse. Then must also vary tau Non-selective (short) MW pulses excite more spins  bigger signal. However, ENDOR efficiency, FMims = ¼ (1 – cos (A τ)) so there are “blind spots” with no signal for some τ

Mims ENDOR Initially need to vary RF pulse length to find pi pulse. Then must also vary tau

Beware Mims ENDOR blind spots
C Gemperle & A Schweiger, Chem Rev 91, 1481 (1991) ENDOR efficiency, FMims = ¼ (1 – cos (A τ)) Initially need to vary RF pulse length to find pi pulse. Then must also vary tau

Beware short RF pulses in pulsed ENDOR
C Gemperle & A Schweiger, Chem Rev 91, 1481 (1991) This problem is avoided by “time-domain pulsed ENDOR”, instead of the standard frequency domain experiments.

Beware short RF pulses with frequency-domain pulsed ENDOR
C Gemperle & A Schweiger, Chem Rev 91, 1481 (1991)

Beware short microwave pulses with Davies ENDOR
C Gemperle & A Schweiger, Chem Rev 91, 1481 (1991)

ENDOR – orientation dependence at high magnetic field
M Rohrer, F MacMillan, T F Prisner, A T Gardiner, K Möbius & W Lubitz, J Phys Chem B 102, 4648 (1998) For more info see the book

ENDOR – orientation dependence at high magnetic field
M Rohrer, F MacMillan, T F Prisner, A T Gardiner, K Möbius & W Lubitz, J Phys Chem B 102, 4648 (1998) duroquinone

ENDOR for Quantum Information Processing
We can control electronic qubits fast, but nuclear qubits have longer coherence times

Pulsed ENDOR For more details including TRIPLE (ENDOR with two RF frequencies) see: Schweiger & Jeschke, Principles of pulse electron paramagnetic resonance, OUP 2001 C Gemperle & A Schweiger, Chem Rev 91, 1481 (1991)

ENDOR conclusions ENDOR is much more sensitive than NMR and has much higher resolution than EPR Continuous-wave ENDOR for very sharp resonances Pulsed ENDOR with: Selective pulses (Davies) Non-selective pulses (Mims)

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