Broadband dipolar recoupling in the nuclear magnetic resonance of rotating solids: A compensated C7 pulse sequence

Abstract

We introduce an improved variant of the C7 pulse-sequence for efficient recoupling of spin-1/2 pair dipolar interactions in magic-angle spinning solid-state NMR spectroscopy. The tolerance of C7 toward isotropic as well as anisotropic chemical shift offsets and rf inhomogeneity is improved considerably by replacing the original basic element Cφ44̄=(2π)φ(2π)φ+π with the cyclically permuted element Cφ14̄3=(π/2)φ(2π)φ+π(3π/2)φ. The improved performance of this permutationally offset stabilized variant of C7 is analyzed by average Hamiltonian theory to fifth order, numerical simulations, and demonstrated by experiments on powder samples of doubly 13C-labeled barium oxalate hemihydrate and diammonium fumarate.

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

“…Finally, we should briefly address attention to a number of additional elements used to speed up the simulations: (i) for diagonal Hamiltonians (i.e., Hamiltonians without mutually non-commuting elements) the integration in Eq. (3) is conducted using analytical solutions, (ii) since the internal Hamiltonian commutes with the Zeeman operator(s) evolution under pulses with phase φ i = 0 is most efficiently accomplished by calculating the propagator for a pulse with phase φ i = 0 (i.e., H is real) followed by the appropriate z rotation [26], and (iii) a particularly efficient variant of γ-COMPUTE is applied when the start and detect operators fulfill the relation ρ(0) = 1 2 (Q det + Q † det ) [54].…”

“…8 investigates 13 C to 15 N heteronuclear coherence transfer using a heteronuclear variant of the POST-C7 [26] pulse sequence as visualized in Fig. 8a and represented by the SIMPSON input file in Appendix A.…”

“…RFDR represents a frequently used dipolar recoupling experiment, which as a disadvantage is not γ-encoded such as the HORROR [23] and C7 [25,26] class of recoupling experiments, but benefits from an attractive experimental robustness and forgiveness with respect to isotropic and anisotropic chemical shifts (unless the isotropic shift differences for the involved spin pairs are very small). These features have rendered the 2D RFDR pulse sequence shown in Fig.…”

“…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.…”

Triple-quantum correlation NMR experiments in solids using J-couplings

“…In this context, various experiments have been developed to obtain two-dimensional (2D) double-quantum -singlequantum (DQ-SQ) correlation spectra of coupled spin-½ systems under magic angle spinning (MAS) which is required for enhanced spectral resolution and sensitivity. Many of these methods employ pulse sequences which reintroduce the MAS-averaged through-space homonuclear dipolar interaction, to obtain DQ-SQ correlation spectra which reflect the through-space atomic proximities [3][4][5][6][7][8][9][10]. Alternatively, pulse sequences based on throughbond isotropic J-couplings, like the INADEQUATE [11] and refocused INADEQUATE [12] experiments, have also been applied efficiently to obtain through-bond DQ-SQ correlation spectra for large range of materials [12][13][14][15][16][17][18][19][20][21][22][23].…”