Theory for cross effect dynamic nuclear polarization under magic-angle spinning in solid state nuclear magnetic resonance: The importance of level crossings
Abstract
We present theoretical calculations of dynamic nuclear polarization (DNP) due to the cross effect in nuclear magnetic resonance under magic-angle spinning (MAS). Using a three-spin model (two electrons and one nucleus), cross effect DNP with MAS for electron spins with a large g-anisotropy can be seen as a series of spin transitions at avoided crossings of the energy levels, with varying degrees of adiabaticity. If the electron spin-lattice relaxation time T1e is large relative to the MAS rotation period, the cross effect can happen as two separate events: (i) partial saturation of one electron spin by the applied microwaves as one electron spin resonance (ESR) frequency crosses the microwave frequency and (ii) flip of all three spins, when the difference of the two ESR frequencies crosses the nuclear frequency, which transfers polarization to the nuclear spin if the two electron spins have different polarizations. In addition, adiabatic level crossings at which the two ESR frequencies become equal serve to maintain non-uniform saturation across the ESR line. We present analytical results based on the Landau-Zener theory of adiabatic transitions, as well as numerical quantum mechanical calculations for the evolution of the time-dependent three-spin system. These calculations provide insight into the dependence of cross effect DNP on various experimental parameters, including MAS frequency, microwave field strength, spin relaxation rates, hyperfine and electron-electron dipole coupling strengths, and the nature of the biradical dopants.
- Publication:
-
Journal of Chemical Physics
- Pub Date:
- August 2012
- DOI:
- 10.1063/1.4747449
- Bibcode:
- 2012JChPh.137h4508T
- Keywords:
-
- dynamic nuclear polarisation;
- electron spin-lattice relaxation;
- hyperfine interactions;
- magic angle spinning;
- nuclear spin-lattice relaxation;
- paramagnetic resonance;
- quantum theory;
- 76.70.Fz;
- 71.70.Jp;
- 76.30.-v;
- 76.60.Es;
- Double nuclear magnetic resonance dynamical nuclear polarization;
- Nuclear states and interactions;
- Electron paramagnetic resonance and relaxation;
- Relaxation effects