Probing the validity of average Hamiltonian theory for spin I=1, 3/2 and 5/2 nuclei by analyzing a simple two-pulse sequence

Theories in Spin Dynamics of Solid-State Nuclear Magnetic Resonance Spectroscopy

“…This is satisfied only if ( ) H t is periodic ( ) c t and the observation is stroboscopic and synchronized with period ( ) c t . This technique set the stage for stroboscopic manipulations of spins and spin interactions by radio-frequency pulses and also explains how periodic pulses can be used to transform the symmetry of selected interactions in coupled, many-spin systems considering the average or effective Hamiltonian of the RF pulse train [27] [34] [35] [72]- [75]. Wilhelm Magnus recognizes in his seminal paper of 1954 that his work was stimulated by results on the theory of linear operators in quantum mechanics.…”

“…However, AHT is not applicable to Hamiltonians with multiple basic frequencies: MAS and radiofrequency irradiation must be synchronized or time-scale separated, multiple irradiations must be synchronized or time-scale separated [79] [80]. Our recent validation of the AHT method probed with quadrupolar nuclei showed that the AHT method becomes less efficient to predict the dynamics of the spin system as the quadrupolar spin nuclei dimension increase [75]. This is attributed to the Hilbert space becoming very large and leading to the contribution of non-negligible higher order terms in the Magnus expansion being truncated.…”

“…An important question to rise is the level of extension the FLT can be used in NMR without losing its conceptual framework. In other words, probing the validity of FLT for quadrupolar nuclei including those with spin I = 1, 3/2, 5/2, and 7/2 by analyzing for example a simple pulse sequence can be beneficial to the NMR community [75]. While the FLT scheme provides a more universal approach for the description of the full time dependence of the response of a periodically time-dependent system, it is most of the time impractical.…”

Applications of Floquet–Magnus expansion, average Hamiltonian theory and Fer expansion to study interactions in solid state NMR when irradiated with the magic-echo sequence

“…While the well-known theory of average Hamiltonian theory (AHT) 4 is a powerful analytical tool, it is not always applicable or sufficiently accurate. The technique of AHT is more appropriated for static experiments and stroboscopic observation, and has been used to study all types of interactions encountered in NMR, such as chemical shift anisotropy 9-11 , dipolar 9,10,12 , and quadrupolar 11,13,14 interactions. While this technique remains the most popular theoretical technique used so far in NMR because of its intuitive way of obtaining effective time-independent Hamiltonians, it is limited to a single time-dependent perturbation 15 .…”

Investigation of the effect of finite pulse errors on the BABA pulse sequence using the Floquet–Magnus expansion approach

“…The situation with quadrupolar nuclei is much worse, with resonances hundreds of kHz off-resonance. Therefore, accounting for finite pulse width is important due to the evolution of the spin system under the dipolar or quadrupolar interaction [4, 18, 19, 20, 21, 22]. Hence, a good understanding of the spin system behavior during the finite pulses and theory therein is important.…”