Field dependent isotropic shifts in solid state nuclear magnetic resonance: A Floquet treatment (original) (raw)

Advances in Theory of Solid-State Nuclear Magnetic Resonance

Journal of nature and science

Recent advances in theory of solid state nuclear magnetic resonance (NMR) such as Floquet-Magnus expansion and Fer expansion, address alternative methods for solving a time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state NMR in particular. The power and the salient features of these theoretical approaches that are helpful to describe the time evolution of the spin system at all times are presented. This review article presents a broad view of manipulations of spin systems in solid-state NMR, based on milestones theories including the average Hamiltonian theory and the Floquet theory, and the approaches currently developing such as the Floquet-Magnus expansion and the Fer expansion. All these approaches provide procedures to control and describe the spin dynamics in solid-state NMR. Applications of these theoretical methods to stroboscopic and synchronized manipulations, non-synchronized experiments, multiple incommensur...

Introduction of the Floquet-Magnus expansion in solid-state nuclear magnetic resonance spectroscopy

The Journal of Chemical Physics, 2011

In this article, we present an alternative expansion scheme called Floquet-Magnus expansion (FME) used to solve a time-dependent linear differential equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance (NMR) in particular. The commonly used methods to treat theoretical problems in solid-state NMR are the average Hamiltonian theory (AHT) and the Floquet theory (FT), which have been successful for designing sophisticated pulse sequences and understanding of different experiments. To the best of our knowledge, this is the first report of the FME scheme in the context of solid state NMR and we compare this approach with other series expansions. We present a modified FME scheme highlighting the importance of the (time-periodic) boundary conditions. This modified scheme greatly simplifies the calculation of higher order terms and shown to be equivalent to the Floquet theory (single or multimode time-dependence) but allows one to deri...

Magnetic field-induced effects on NMR properties

Journal of Magnetic Resonance, 2017

In principle, all the NMR observables, spin-spin coupling J, nuclear shielding s and quadrupole coupling q, are magnetic field-dependent. The field dependence may be classified into two categories: direct and indirect (apparent) dependence. The former arises from the magnetic field-induced deformation of the molecular electronic cloud, while the latter stems from a slightly anisotropic orientation distribution of molecules, due to the interaction between the anisotropy of the molecular susceptibility tensor and the external magnetic field. Here we use 1,3,5-D3-benzene as a model system to investigate the indirect effect on the one-bond 1 H-13 C and 2 H-13 C spin-spin couplings (J couplings) and the 2 H quadrupole coupling. Experiments carried out at four magnetic fields (4.7, 9.4, 14.1, and 18.8 Tesla) show that the indirect effect is significant already at the magnetic fields commonly used in NMR spectrometers. A joint fit of the data extracted at the different field strengths provides experimental results for the susceptibility anisotropy, 2 H quadrupole coupling constant and the related asymmetry parameter as well as the one-bond CH and CD coupling constants extrapolated to vanishing field strength. The field-induced contributions are found to exceed the commonly assumed error margins of the latter. The data also indicate a primary isotope effect on the one-bond CH coupling constant. There is a tendency to further increase the magnetic field of NMR spectrometers, which leads to more pronounced indirect contributions and eventually significant direct effects as well.

Direct magnetic-field dependence of NMR chemical shift†

Physical Chemistry Chemical Physics, 2020

Nuclear shielding and chemical shift are considered independent of the magnetic-field strength. Ramsey proposed on theoretical grounds in 1970 that this may not be valid for heavy nuclei. Here we present experimental evidence for the direct field dependence of shielding, using 59 Co shielding in Co(acac) 3 [tris(acetylacetonate)cobalt(III)] as an example. We carry out NMR experiments in four field strengths for this low-spin diamagnetic Co(III) complex, which features a very large and negative nuclear shielding constant of the central Co nucleus. This is due to a magnetically accessible, low-energy e g ' t 2g orbital excitation of the d 6 system. The experiments result in temperature-dependent magnetic-field dependence of À5.7 to À5.2 ppb T À2 of the 59 Co shielding constant, arising from the direct modification of the electron cloud of the complex by the field. First-principles multiconfigurational non-linear response theory calculations verify the sign and order of magnitude of the experimental results.

Recent Advances in Theoretical and Physical Aspects of NMR Chemical Shifts

Kimika, 2015

In the first part of this review, theoretical aspects of nuclear magnetic shielding include (a) general theory, for example, newly developed approaches in relativistic theory of nuclear shielding, the relation between the spin-rotation tensor and shielding in relativistic theory, ab initio methods for treating open shell systems and a complete theory of chemical shifts in paramagnetic systems, the link between the definitions of the elusive concepts aromaticity and anti-aromaticity and the magnetic properties: the magnetizability tensor and the nuclear magnetic shielding tensor via delocalized electron currents and electron current maps, (b) ab initio and DFT calculations, both relativistic and non-relativistic, for various nuclei in various molecular systems using various levels of theoretical treatment. Physical aspects include (a) anisotropy of the shielding tensor, usually from solid state measurements, and calculations to support these, (b) shielding surfaces and rovibrational averaging, paying special attention to the sensitive relationship between shielding and bond angles or torsion angles that makes shielding such a powerful tool for structural/conformational determination in macromolecules, (c) chemical shifts that arise from isotopic substitution of NMR nucleus or neighboring nuclei, (d) intermolecular effects on nuclear shielding, and (e) absolute shielding scales.

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

World Journal of Nuclear Science and Technology, 2015

This short review article presents theories used in solid-state nuclear magnetic resonance spectroscopy. Main theories used in NMR include the average Hamiltonian theory, the Floquet theory and the developing theories are the Fer expansion or the Floquet-Magnus expansion. These approaches provide solutions to the time-dependent Schrodinger equation which is a central problem in quantum physics in general and solid-state nuclear magnetic resonance in particular. Methods of these expansion schemes used as numerical integrators for solving the time dependent Schrodinger equation are presented. The action of their propagator operators is also presented. We highlight potential future theoretical and numerical directions such as the time propagation calculated by Chebychev expansion of the time evolution operators and an interesting transformation called the Cayley method.

Variable-angle correlation spectroscopy in solid-state nuclear magnetic resonancea)

The Journal of Chemical Physics, 1992

We describe here a new solid-state nuclear-magnetic-resonance (NMR) experiment for correlating anisotropic and isotropic chemical shifts of inequivalent nuclei in powdered samples. Spectra are obtained by processing signals arising from a spinning sample, acquired in independent experiments as a function of the angle between the axis of macroscopic rotation and the external magnetic field. This is in contrast to previously proposed techniques, which were based on sudden mechanical flippings or multiple-pulse sequences. We show that the time evolution of variable-angle-spinning signals is determined by a distribution relating the isotropic frequencies of the spins with their corresponding chemical shift anisotropies. Fourier transformation of these data therefore affords a twodimensional NMR spectrum, in which line shapes of isotropic and anisotropic interactions are correlated. Theoretical and experimental considerations involved in the extraction of this spectral information are discussed, and the technique is illustrated by an analysis of 13C NMR anisotropy in glycine, cysteine, and p-anisic acid. 4800