Theory and simulations of homonuclear spin pair systems in rotating solids

Abstract

The theory of nuclear magnetic resonance (NMR) on a solid sample containing pairs of coupled homonuclear spins-1/2, rotating in a large magnetic field, is presented. The time dependence introduced by the sample rotation, in conjunction with the spin–spin coupling, makes it appear that each of the central two levels in the four-level system split into a pair of ‘‘virtual states.’’ Each of the eight possible single-quantum coherences between the virtual states and the two outer levels in general contribute to the spectrum, although four of these contributions are forbidden unless a rotational resonance occurs (matching of an integer multiple of the spinning speed with the difference in isotropic shifts). Analytical line shapes for the case of vanishing shift anisotropy are given and techniques for numerical simulation in the general case demonstrated. The theory of Zeeman magnetization exchange in the presence of zero-quantum dephasing is presented.

SIMPSON: A general simulation program for solid-state NMR spectroscopy

“…This is ascribed to the presence of "homogeneous" interactions [61] which effectively call for a quite time-consuming time-ordered integration of the spin dynamics during sampling of the FID [17,62]. Several breakthroughs, among which range efficient powder averaging [45,49] and exploitation of time-translational symmetries [52,53,54], have greatly improved the conditions for such simulations and their combination with iterative fitting for extraction of accurate structural parameters.…”

“…This may be the case for desired as well as undesired terms of the Hamiltonian implying that accurate determination of structural parameters from the desired terms as well as evaluation of the multiple-pulse building blocks providing suppression of undesired terms very often depend on the ability to numerically simulate the spin dynamics of the actual NMR experiment. This applies, for example, to the solid-state NMR experiments for which dipolar recoupling (e.g, rotational resonance [16,17], REDOR [18], DRAMA [19], DRAWS [20], RFDR [21], RIL [22], HORROR [23], BABA [24], C7 [25,26], RF-DRCP [27]), multiple-pulse homo-or heteronuclear decoupling (e.g., BR-24 [28], FSLG [29], MSHOT-3 [30], TPPM [31]), cross-polarization [32,33], QCPMG-MAS [34], or MQ-MAS [35] pulse sequences are indispensable building blocks. Thus, considering the very large number of advanced experiments already available, the large number of possible combinations between these, and the rapidly increasing number of new experimental procedures presented every year there is a substantial need for a general and consistent simulation tool to support experiment design, user-specific method implementation, and evaluation of spectral data.…”

Towards homonuclear J solid-state NMR correlation experiments for half-integer quadrupolar nuclei: experimental and simulated 11B MAS spin-echo dephasing and calculated 2JBB coupling constants for lithium diborate

“…41 For two dipolar-coupled spin I = 1/2 nuclei, the 15 well-known rotational-resonance phenomena arise from the non-commutation (and hence incomplete refocusing under MAS) of the homonuclear dipolar coupling and the chemical shift anisotropy (CSA). [42][43] In analogy to this, Edén and Frydman have introduced the term "spontaneous quadrupolar-20 driven recoupling" for the incomplete removal by MAS of the homonuclear dipolar coupling between two quadrupolar (I > 1/2) nuclei that arises from the non-commutation of the dipolar and quadrupolar couplings. This analysis builds upon work by Gan and Robyr 44 and Facey et al 45 for the case of a 25 dipolar coupling between two 2 H (spin I = 1) nuclei.…”

“…Note that a quadrupolardriven recoupling effect is observed for the case of parallel quadrupolar tensors (that are not colinear with the dipolar coupling); this is different to the spin I = 1/2 n=0 rotational resonance effect, where no effect is observed if the two CSA 60 tensors are parallel. [42][43] In this study, the effect of 11 B-11 B dipolar couplings on 11 B spin-echo dephasing is investigated using samples of polycrystalline lithium diborate, Li 2 O.2B 2 O 3 , with three different degrees of 11 B depletion/enrichment: 5%, 25% and 65 100%. (At natural abundance, 80% of boron nuclei are 11 B, with the remainder (20%) being 10 B.).…”

Complete resolution of the solid-state NMR spectrum of a uniformly 15 N-labeled membrane protein in phospholipid bilayers

“…Solid-state NMR spectroscopy is well suited for peptides and proteins immobilized in phospholipid bilayers, and several complementary approaches are under development (4)(5)(6)(7)(8). However, up until now experimental studies have required samples labeled with stable isotopes in one or a few selected sites.…”