General theoretical formalism for describing the high-order effects of the dipolar coupling between spin-1/2 and quadrupole nuclei

Abstract

Articles you may be interested inNuclear magnetic relaxation induced by exchange-mediated orientational randomization: Longitudinal relaxation dispersion for a dipole-coupled spin-1/2 pair Measuring dipolar and J coupling between quadrupolar nuclei using double-rotation NMR Relaxation-allowed nuclear magnetic resonance transitions by interference between the quadrupolar coupling and the paramagnetic interaction A general theoretical description of the effect of the second-order dipolar coupling between spin-1/2 and quadrupole nuclei is presented based on the density operator formalism rather than the Shrödinger equation as in previous publications. The main task of this formalism is to diagonalize the evolution operator which can be performed analytically when the quadrupole nucleus is spin-1 or spin-3/2; no approximations such as the adiabatic assumption, perturbation expansion and the average Hamiltonian treatment are assumed. Therefore, it is general and can be used for all nuclear spins and any value of quadrupole coupling constant and in the case of magic-angle spinning ͑MAS͒ for any rotor spinning speed; it can also include the case when more than one species of spin-1/2 nuclei is coupled to the quadrupole nucleus. The effects of indirect dipolar coupling, chemical shift anisotropy and sample spinning speeds on Nuclear Magnetic Resonance ͑NMR͒ lineshapes can be uniformly incorporated in the formalism. Lineshape simulations based on this formalism can yield structural and electronic parameters of compounds and materials with high accuracy. Experimental results for several typical compounds of different complexities are demonstrated and are shown to be in good agreement with the theoretical spectral simulations.

Decoupling residual dipolar coupling between 13C and14N spin pairs in CPMAS NMR

“…This effect is often referred to as a residual dipolar coupling. Various types of theoretical formulations to analyse this effect under MAS have been reported, including an adiabatic model [4], perturbation treatment [5], and an analytical density operator approach [6]. An average Hamiltonian approach leads to a first-order dipolar coupling contribution to nuclear spin Hamiltonian, which has its usual form, and a second-order dipolar-quadrupolar cross-term that leads to the asymmetric splitting under MAS [8].…”

“…In solid-state 13 C magic-angle spinning (MAS) NMR spectra, the asymmetric splitting observed for signals arising from carbon nuclei of 13 C-14 N spin pairs has been well documented [1][2][3][4][5][6][7][8]. In general, a modulation of the lineshape is seen in the spectra of spin-1/2 nuclei that are dipolar coupled to a quadrupolar nucleus [1,3].…”

Differential broadening caused by dipolar interaction with1H in13C MAS NMR signals split by residual dipolar interaction with14N

“…Similarly to the 13 C signals, the signals of 1 H bonded to 14 N are split and broadened by the residual dipolar interaction with 14 N, and consequently off-resonance 1 H irradiation might be a cause of the 13 C differential broadening. This mechanism is effective in the CH-NH 3 C signal of the L-alanine single crystal. 15 However, this possibility was excluded by measuring 13 C CP/MAS spectra under 1 H CW decoupling with various frequencies.…”

“…Figure 4 shows the spinning rate dependence of the broadening factors in the C-NH 2 signals together with those in the aromatic C-H, CH 3 and C Ł -CH 3 signals. The m s D š1 C-NH 2 signal shows a gradual increase in the broadening factor with increase in the spinning rate, which is similar to the aromatic C-H signal.…”

“…The high-frequency peak corresponds to 13 C bonded to 14 N with m s D š1 and should have twice the intensity of the lowfrequency peak corresponding to m s D 0. We simulated the signal of 2-methyl-4-nitroaniline (II) assuming that the Euler angles areˇD 0°and˛D 0°1 3 and that the asymmetric factor of the electric field gradient is Á Q D 0.29 from the value for p-nitroaniline. The TPPM and CW decouplings show almost the same spectral pattern.…”