Tutorial on analytic theory for cross‐polarization in solid state NMR

Abstract

This tutorial aims to be a self-contained and explicit analysis of the basic cross polarization (CP) solid-state NMR experiment (SSNMR) in the isolated spin-pair approximation using standard quantum mechanical arguments. The general result of obtaining coherence transfer between two dipolar coupled spin-active nuclei while applying radio frequency fields to both nuclei is described, with emphasis on the origin of the well known Hartmann-Hahn matching conditions. No new theory is presented; rather several common analytical methods in SSNMR are demonstrated in the context of cross-polarization under static and magic-angle spinning (MAS) conditions. A background in NMR and quantum mechanics is assumed, however this work attempts to minimize the need for excursions into the literature. This article was written to aid a reader in advancing into more detailed descriptions of CP and dipolar recoupling in general.

Persistent dark states in anisotropic central spin models

“…DNP works by harnessing the flip-flop interactions ( S + 0 S − j + S − 0 S + j ) already present in the Hamiltonian H. This transfer can be achieved with several methods, e.g. tuning external fields to resonant Hartmann-Hahn conditions where flip-flop interactions dominate 24,25 . By Eq.…”

“…This model belongs to the class of integrable XXX Richardson-Gaudin models [21][22][23] . The second is the fully anisotropic XX model ( α = 0 and arbitrary γ ), which describes resonant exchange interactions in dipolar spin systems in rotating frames [24][25][26][27] . It was only recently established that the XX model is integrable, arising as a singular limit of the class of hyperbolic XXZ Richardson-Gaudin models 10 .…”

Chapter 2. Solid‐State NMR in Drug Discovery and Development

“…48 When combined with MAS, the Hartmann-Hahn condition that enables CP splits into a manifold of sidebands, such that actual CP matches in CP-MAS experiments normally are set to occur at the stronger sidebands (normally designated þ/-1). 49,50 Heteronuclear dipolar decoupling is commonly used to narrow or simplify spectral resonances by removing the broadening effects of coupling 1 H to nuclei when observing 13 C, 15 N, 19 F or other nuclei. 51 The two-pulse phase modulation (TPPM) scheme and the related small phase incremental alteration (SPINAL) decoupling sequence are currently popular methods for heteronuclear dipolar decoupling.…”

On the Fer expansion: Applications in solid-state nuclear magnetic resonance and physics

“…CP is probably the gateway method into solidstate NMR, especially for biomolecules and encompass core concepts in dipolar coupling, and magic angle spinning [239]. Recently, Takegoshi et al calculated the effective Hamiltonians and propagators of the Fer expansion to understand the spin dynamics for cross polarization in solid-state NMR [238].…”