Three pulse recoupling and phase jump matching

Abstract

The paper describes a family of novel recoupling pulse sequences, called three pulse recoupling. These pulse sequences can be employed for both homonuclear and heteronuclear recoupling experiments and are robust to dispersion in chemical shifts and rf-inhomogeneity. These recoupling pulse sequences can be used in design of two-dimensional solid state NMR experiments that use powdered dephased antiphase coherence (γ preparation) to encode chemical shifts in the indirect dimension. Both components of this chemical shift encoded gamma-prepared states can be refocused into inphase coherence by a recoupling element. This helps to achieve sensitivity enhancement in 2D NMR experiments by quadrature detection.

Keywords: Gamma preparation; Hartmann–Hahn matching; MAS; Quadrature detection; Recoupling.

Fig. 1

Top left panel shows ramp of phase in Eq. (5). The Top right panel shows time derivative of phase in Eq. (5). Area under this curve gives the total phase change. The bottom panel shows the accumulation of phase area at the crossed points when the magnetization is rotated in the interaction frame of CF_x as in Eq. (5).

Fig. 2

Top panel in the figure shows the build up of transfer of magnetization in a basic ¹³C–¹³C correlation experiment on a 400 mHz (proton frequency) static field, using the TPR pulse unit with 18° as phase increment and no compensating phase decrement. Simulation uses internuclear distance of 1.52 Å and powder avaraging. a, b, c corresponds to inhomogeneity value ε of 0, .01 and .05 respectively. Middle Panel in the figure shows the build up basic ¹³C–¹³C correlation experiment using the TPR pulse unit with 18° as phase increment combined with an 18° decrement unit. a, b, c, d corresponds to inhomogeneity value ε of 0, .01, .05, and .1 respectively. In practice, the rf-inhomogeneity results in a weighted sum of these different ε. Offset of spin pair is assumed to be on resonance. Bottom panel in the figure shows the build up of basic ¹³C–¹³C correlation experiment using the TPR pulse unit with 18° as phase increment combined with an 18° decrement unit, with different chemical shift of the target spin. a, b, c, d, corresponds to chemical shift of 0, 5, 10 and 15 kHz on the target spin. In the bottom panel, we include a CSA value of 8.9 and 13.9 ppm for the two spins respectively with anisotropy parameter .13 and .98, representing the C_α–C_β spin pair in alanine respectively.

Fig. 3

Top panel in the figure shows the build up basic ¹³C–¹⁵N correlation experiment on a 400 mHz (proton frequency) static field, using the TPR pulse unit with 27° and 9° as phase increment and no compensating phase decrement on ¹³C and ¹⁵N respectively. a, b, c corresponds to inhomogeneity value ε of 0, .01 and .05 on Carbon channel. Middle Panel in the figure shows the build up using the TPR pulse unit with compensating phase decrement unit. Bottom panel in the figure shows the build up of basic ¹³C–¹⁵N correlation experiment using the TPR pulse unit, with different chemical shift of the ¹³C spin. a, b, c, d, corresponds to chemical shift of 0, 5, 7.5 and 10 kHz of the ¹³C spin.

Fig. 4

(A) shows the pulse sequence for a ¹³C_α–¹³C_β correlation experiment with TPR as the recoupling element. (B) Shows the pulse sequence for a ¹³C_α–¹³C_β correlation experiment using gamma preparation, with TPR as the recoupling element. (C) Shows the pulse sequence for a ¹³C_α–¹⁵N correlation experiment using gamma preparation, with TPR as the recoupling element. In (C) the last $\frac{\pi }{2}$ pulse on the carbon is toggled from −x to x during acquisition of second scan which is added and subtracted with first scan as described in (B).

Fig. 5

Top panel shows the build up curve for transfer of magnetization, shown every 2 rotor periods, at 10 kHz spinning, starting from one of the carbons, for ¹³C_α–¹³C_β correlation experiment, in uniformly labelled sample of Alanine, with TPR as the recoupling element as described in the text. Bottom panel shows a ¹³C_α–¹³C_β 2D correlation spectrum obtained using the TPR as the recoupling element.

Fig. 6

Top panel shows the build up of transfer of magnetization, shown every 8 rotor periods, at 10 kHz spinning, for the ¹³C_α → ¹⁵N experiment, in uniformly labelled sample of glycine, with TPR as the recoupling element as described in text. Middle panel shows the build up of transfer of magnetization, shown every 8 rotor periods for the ¹⁵N→¹³C experiment with same TPR as the recoupling element. Bottom panel shows the 2D spectrum for ¹³C_α–¹⁵N experiment with TPR as the recoupling element. The magntization precesses on ¹⁵N during indirect evolution.

Fig. 7

Top panel shows the 2D gamma-preparation spectrum for the pulse sequence shown in figure for ¹³C_α–¹³C_β correlation as described in the text. The frequencies in the indirect dimension are reflected around the carrier and down-shifted by rotor frequency of 10 kHz (100 ppm at 400 kHz) as described in the text. The carrier is at around 40 ppm. Middle panel shows the comparison of peak intensity of a slice through a cross-peak of a straight ¹³C_α–¹³C_β, correlation obtained with TPR, with magnetization evolving on C_β during indirect evolution as in bottom panel of Fig. 5, vs a slice through a larger gamma-preparation cross peak, where magnetization begins from C_β and precesses on C_α during t₁. Bottom panel shows the comparison of peak intensity of a slice through a cross-peak of a straight ¹³C_α–¹³C_β, correlation obtained with TPR, as in bottom panel of Fig. 5, with magnetization evolving on C_α during indirect evolution, vs a slice through a larger gamma-preparation cross peak, where magnetization begins from C_α and precesses on C_β during t₁.

Fig. 8

Figure shows the gamma preparation peak for the 2D hetrocuclear experiment which prepares an antiphase coherence on nitrogen to encode its chemical shift with preparation and refocussing done with TPR pulse sequence.