The multiple quantum NMR dynamics in systems of equivalent spins with the dipolar ordered initial state

TL;DR

This paper develops analytical and numerical methods to study multiple quantum NMR dynamics in large systems of equivalent spins with dipolar ordered initial states, revealing exponential coherence profiles and comparing different initial conditions.

Contribution

It introduces new methods for analyzing MQ NMR in large spin systems with high symmetry, providing detailed coherence profiles from first principles.

Findings

Coherence profiles can be approximated by exponential functions.

The dynamics differ between dipolar ordered and thermal equilibrium initial states.

Analytical and numerical approaches are validated for systems of hundreds of spins.

Abstract

The multiple quantum (MQ) NMR dynamics in the system of equivalent spins with the dipolar ordered initial state is considered. The high symmetry of the MQ Hamiltonian is used in order to develop the analytical and numerical methods for an investigation of the MQ NMR dynamics in the systems consisting of hundreds of spins from "the first principles". We obtain the dependence of the intensities of the MQ NMR coherences on their orders (profiles of the MQ NMR coherences) for the systems of $200 - 600$ spins. It is shown that these profiles may be well approximated by the exponential distribution functions. We also compare the MQ NMR dynamics in the systems of equivalent spins having two different initial states, namely the dipolar ordered state and the thermal equilibrium state in the strong external magnetic field.