Quantized field description of rotor frequency-driven dipolar recoupling

Abstract

A formalized many-particle nonrelativistic classical quantized field interpretation of magic angle spinning (MAS) nuclear magnetic resonance (NMR) radio frequency-driven dipolar recoupling (RFDR) is presented. A distinction is made between the MAS spin Hamiltonian and the associated quantized field Hamiltonian. The interactions for a multispin system under MAS conditions are described in the rotor angle frame using quantum rotor dynamics. In this quasiclassical theoretical framework, the chemical shift, the dipolar interaction, and radio frequency terms of the Hamiltonian are derived. The effect of a generalized RFDR train of π pulses on a coupled spin system is evaluated by creating a quantized field average dipolar-Hamiltonian formalism in the interaction frame of the chemical shift and the sample spinning. This derivation shows the analogy between the Hamiltonian in the quantized field and the normal rotating frame representation. The magnitude of this Hamiltonian peaks around the rotational resonance conditions and has a width depending on the number of rotor periods between the π pulses. Its interaction strength can be very significant at the n = 0 condition, when the chemical shift anisotropies of the interacting spins are of the order of their isotropic chemical shift differences. © 2000 American Institute of Physics.