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

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.