¹⁴N overtone transition in double rotation solid-state NMR

Abstract

Solid-state NMR transitions involving outer energy levels of the spin-1 (14)N nucleus are immune, to first order in perturbation theory, to the broadening caused by the nuclear quadrupole interaction. The corresponding overtone spectra, when acquired in conjunction with magic-angle sample spinning, result in lines, which are just a few kHz wide, permitting the direct detection of nitrogen compounds without the need for labeling. Despite the success of this technique, "overtone" resonances are still broadened due to indirect, second order effects arising from the large quadrupolar interaction. Here we demonstrate that another order of magnitude in spectral resolution may be gained by using double rotation. This brings the width of the (14)N solid-state NMR lines much closer to the region commonly associated with high-resolution solid-state NMR spectroscopy of (15)N and demonstrates the improvements in resolution that may be possible through the development of pulsed methodologies to suppress these second order effects.

Fokker-Planck formalism in magnetic resonance simulations

“…Secondly, only a two-angle spherical grid is required because rotor phase averaging is built-in. Thirdly, the lack of explicit time dependence in the evolution generator permits frequency domain detection which, for overtone peaks, is much faster than the time domain approach [46,59]. The equation of motion is: (37) with the following spin Liouvillian (assuming, to match the available experimental literature, 14 N to be the quadrupolar nucleus and 1 H to be the polarisation source): The matrix representation for Equation (37) is built in a similar way to the previous sections, by discretising the RF phase and the rotor phase on finite grids and using Equation (13) to obtain matrix representations for the phase derivative operators.…”

14N overtone NMR under MAS: Signal enhancement using cross-polarization methods

“…Currently, most NMR users favour expensive 15 N enriched substances, but a significant minority never gave up on 14 N and significant progress has been made in the solid-state: its quadrupole moment interacts with local electric fields and provides structural and dynamic information that would not otherwise be available [5][6][7] . Even the resolution problem is gradually being overcome: the NMR signal of the double-quantum ("overtone", OT) transition between the outer Zeeman levels of the 14 N spin is orders of magnitude sharper than the single-quantum transition signal [8][9][10][11][12][13][14][15] .…”

Quantitative analysis of14N quadrupolar coupling using1H detected14N solid-state NMR

“…Methods for detection of overtone (Dm = AE2) transitions on static samples, [4][5][6] and more recently under MAS [7][8][9][10][11][12] and DOR 13 have provided alternative methods for characterizing 14 N sites. Unlike Dm = AE1 14 N signals, overtone signals are not affected by the large (MHz) quadrupole broadening.…”

“…However, there are sensitivity concerns when exciting this ''forbidden'' transition, which are further exacerbated by the slow nutation and correspondingly low excitation bandwidth of overtone signals, making simultaneous detection of multiple 14 N overtone signals difficult. 8 A third strategy for detection of 14 N is the indirect detection method, pioneered independently by Gan and Bodenhausen's laboratories, [14][15][16][17][18][19][20][21][22][23][24][25] where 14 N sites are detected via their interaction with coupled spin-1/2 'spy' nuclei; typically 1 H or 13 C, using pulse sequences qualitatively similar to HMQC experiments. Transfer of polarisation between the 14 N and the 'spy' nucleus occurs due to high-order cross-terms between the quadrupolar and 14 N'spy' dipolar Hamiltonians, known as the 'residual dipolar splitting' (RDS), as well as a contribution from the J-coupling, in experiments known as J-HMQCs.…”