Equivalence between dynamical averaging methods of the Schrödinger equation: average Hamiltonian, secular averaging, and Van Vleck transformation

Llor, Antoine

doi:10.1016/0009-2614(92)80136-y

Cited by 47 publications

(34 citation statements)

References 24 publications

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“…Our design method neglects the off-resonance term generated by each rotating frame construction; however, in general corrections to lowest order in the resonance offset for counter-rotating waves (for example, the BlochSiegert shift 20 ) can be found using (e.g.) average Hamiltonian theory, 21,22 the Magnus expansion, 23,24 or the Floquet expansion, 25,26 and included in the effective Hamiltonian in each constructed frame. Note that with corrections for offresonance terms, (1) can be adjusted by adding the lowest order z-and x-component corrections to ω k−1 and u k−1 , respectively.…”

Section: A Pulse Design Using Four Nutating Framesmentioning

confidence: 99%

A new broadband homonuclear mixing pulse for NMR with low applied power

Coote

Leigh

et al. 2014

The Journal of Chemical Physics

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Broadband homonuclear mixing pulses with low radiofrequency power are essential for NMR spectroscopy of proteins and small molecules, especially for emerging applications in high field NMR. We have analytically designed a mixing pulse with high bandwidth-to-power ratio, using our recently developed multi-frame method. Here, we compare the new pulse, NF4 (mixing in the fourth nutating frame), to the best currently available sequence, focusing on the low-power regime. We use simulations and experiments to compare the two pulses' relaxation properties and bandwidth, and demonstrate that NF4 has approximately 1.35 times higher bandwidth, with similar effective relaxation. Therefore, NF4 is a good choice for broadband homonuclear mixing, particularly when the available radiofrequency power is limited.

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Section: A Pulse Design Using Four Nutating Framesmentioning

confidence: 99%

A new broadband homonuclear mixing pulse for NMR with low applied power

Coote

Leigh

et al. 2014

The Journal of Chemical Physics

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“…Some of the techniques are reviewed in Refs. [38,39,40]; a few of the difficulties are summarized here. It is not immediately clear to what order the perturbation expansion in Eq.…”

Section: The Hamiltonians Of Nmr 23mentioning

confidence: 99%

“…A rigorous quantum-mechanical derivation of the magnetic dipole-dipole coupling Hamiltonian without the contact term yields: 39) where ω 12 D = − µ 0 4π γ 1 γ 2 r −3 . Eq.…”

Section: The Hamiltonians Of Nmr 31mentioning

confidence: 99%

“…In general one must also consider the fact that the Zeeman eigenstates must receive corrections in higher-order perturbation treatments. It is appropriate to apply a tilting matrix transformation to include these effects [38,39,40,43]. A standard procedure [10, §4], [44] used to develop the second-order secular HamiltonianĤ Note that if more than one local interaction is involved, there can exist interference terms betweenĤ ξ andĤ ξ in the second-order secular Hamiltonian.…”

Section: The Hamiltonians Of Nmr 23mentioning

confidence: 99%

“…The secular dipolar Hamiltonian in the strong-coupling limit (also called the highfield homonuclear dipolar Hamiltonian) is: 40) where β is the angle between the internuclear vector and the z-axis andÎ ±j =Î xj ±iÎ yj . The orientation dependent term has a second-rank Legendre polynomial dependence: (3 cos 2 β − 1)/2 = P 2 (cos β).…”

Section: The Hamiltonians Of Nmr 31mentioning

confidence: 99%

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Nuclear magnetic resonance studies of quadrupolar nuclei and dipolar field effects

Urban

2004

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Experimental and theoretical research conducted in two areas in the field of nuclear magnetic resonance (NMR) spectroscopy is presented: (1) studies of the coherent quantummechanical control of the angular momentum dynamics of quadrupolar (spin I > 1/2) nuclei and its application to the determination of molecular structure; and (2) applications of the long-range nuclear dipolar field to novel NMR detection methodologies.The dissertation is organized into six chapters. The first two chapters and associated appendices are intended to be pedagogical and include an introduction to the quantum mechanical theory of pulsed NMR spectroscopy and the time dependent theory of quantum mechanics.The third chapter describes investigations of the solid-state multiple-quantum magic angle spinning (MQMAS) NMR experiment applied to I = 5/2 quadrupolar nu-2 clei. This work reports the use of rotary resonance-matched radiofrequency irradiation for sensitivity enhancement of the I = 5/2 MQMAS experiment. These experiments exhibited certain selective line narrowing effects which were investigated theoretically.The fourth chapter extends the discussion of multiple quantum spectroscopy of quadrupolar nuclei to a mostly theoretical study of the feasibility of enhancing the resolution of nitrogen-14 NMR of large biomolecules in solution via double-quantum spectroscopy.The fifth chapter continues to extend the principles of multiple quantum NMR spectroscopy of quadrupolar nuclei to make analogies between experiments in NMR/nuclear quadrupolar resonance (NQR) and experiments in atomic/molecular optics (AMO). These analogies are made through the Hamiltonian and density operator formalism of angular momentum dynamics in the presence of electric and magnetic fields.The sixth chapter investigates the use of the macroscopic nuclear dipolar field to encode the NMR spectrum of an analyte nucleus indirectly in the magnetization of a sensor nucleus. This technique could potentially serve as an encoding module for the recently developed NMR remote detection experiment. The feasibility of using hyperpolarized xenon-129 gas as a sensor is discussed. This work also reports the use of an optical atomic magnetometer to detect the nuclear magnetization of Xe-129 gas, which has potential applicability as a detection module for NMR remote detection experiments.

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Floquet Theory

Vega

2007

Encyclopedia of Magnetic Resonance

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Equivalence between dynamical averaging methods of the Schrödinger equation: average Hamiltonian, secular averaging, and Van Vleck transformation

Cited by 47 publications

References 24 publications

A new broadband homonuclear mixing pulse for NMR with low applied power

A new broadband homonuclear mixing pulse for NMR with low applied power

Nuclear magnetic resonance studies of quadrupolar nuclei and dipolar field effects

Floquet Theory

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