Effective Hamiltonian and 1H-14N cross polarization/double cross polarization at fast MAS

Abstract

In this work we investigate in detail the underlying spin-dynamics associated with 1H-14N double CP experiments under fast MAS, recently demonstrated by Carnevale et al. We employ matrix logarithm and Floquet theory to compute numerically the effective Hamiltonian associated to the time-dependent problem. Certain common features related to construction of effective Hamiltonians by both approaches are discussed. The main observations related to 1H-14N CPMAS/double CP transfer are: (a) various spin terms of the effective Hamiltonian strongly depend on the crystallite orientation; (b) significant CP transfer occurs only when the magnitudes of the effective1H and 14N RF strengths are comparable, and simultaneously all pure 14N terms in the effective Hamiltonian are small, except for the longitudinal and the RF terms; (c) the sign of 14N CPMAS signal follows the sign of 14N effective RF strength; (d) sign of the double CP signal is largely independent of crystallite orientation. We predict and verify matching conditions employing multiples of the spinning frequency or involving different 14N RF strengths. We provide an analytical proof for (d). The proof also provides an estimate for the ratio of 1H-14N and 14N-1H transfer amplitudes which is further substantiated through simulations. In addition, we find that double CP signals include contributions from several single-quantum coherences present after the first CP process. The uneven contribution from different coherences leads to a reversal of signal at very short contact times, a feature noted experimentally by Carnevale et al. The connection between CPMAS transfer and efficient spin-lock is discussed and illustrated. The factors affecting second-order quadrupolar lineshapes in double CP experiment are examined. With a linear ramp of 1H RF amplitude we have observed that significant CP transfer occurs for more crystallite orientations resulting in improved sensitivity.