The Complete Homogeneous Master Equation for a Heteronuclear Two-Spin System in the Basis of Cartesian Product Operators

Allard, Peter; Helgstrand, Magnus; Härd, Torleif

doi:10.1006/jmre.1998.1509

Cited by 66 publications

(61 citation statements)

References 26 publications

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“…The carrier of the 15 N channel was set to 147 ppm, the resonances of the investigated G4 donor nitrogen N 1 and of the C15 acceptor nitrogen N 3 were at 146.9 ppm and 196.3 ppm, respectively, so that the offset of the coupling partner was 1.5 kHz. The simulations and calculations were carried out by means of Mathematica, [15] using the propagator formalism of Allard et al [16] …”

Section: Methodsmentioning

confidence: 99%

Quenching Echo Modulations in NMR Spectroscopy

Dittmer¹,

Bodenhausen²

2006

ChemPhysChem

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In NMR spectroscopy, homonuclear scalar couplings normally lead to modulations of spin echoes that tend to interfere with the accurate determination of transverse relaxation rates by Carr-Purcell-Meiboom-Gill (CPMG) multiple refocusing experiments. Surprisingly, the echo modulations are largely cancelled when the refocusing pulses applied to the coupling partner deviate slightly from ideal pi rotations due to tilted effective radio-frequency (RF) fields, even at offsets that are much smaller than the radio-frequency amplitude. Experiments and simulations illustrate these effects for two-spin IS systems containing donor and acceptor (15)N nuclei I=N (D) and S=N(A) in RNA Watson-Crick base pairs with homonuclear scalar couplings J(IS)=(2h)J(N(D), N(A)) across the hydrogen bonds.

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Section: Methodsmentioning

confidence: 99%

Quenching Echo Modulations in NMR Spectroscopy

Dittmer¹,

Bodenhausen²

2006

ChemPhysChem

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“…The basis operators have the same form as in Eq. [33], but the factors multiplying them are different to make them normalized unit vectors in Liouville space. We keep the quantum numbers from Eq.…”

Section: The Quadrupolar Echo Againmentioning

confidence: 99%

“…Normally, we ignore the unit operator, as the total number of spins always remains constant. However, there are occasions, particularly when relaxation and exchange are involved, when its inclusion in the basis has advantages (33). It can turn an inhomogeneous differential equation into a homogeneous one.…”

Section: Roles Of Operatorsmentioning

confidence: 99%

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Operator formalisms: An overview

Bain

2006

Concepts Magnetic Resonance

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ABSTRACT:Operator formalisms are mathematical recipes for simplifying the manipulations of the density matrix. Because the density matrix is a vital tool in describing and analyzing magnetic resonance experiments, many approaches have been developed. This article gives an overview of a number of different methods: spherical tensors, fictitious spin-1/2, single-transition operators, product operators, superspin methods, and others. In principle, they all must give the same answer, because an exact description of magnetic resonance phenomena is usually within reach. The choice of the formalism for the user, therefore, depends on various personal decisions. Among these decisions is the choice between spherical and Cartesian tensors, between Hilbert space and Liouville space, between commutators and matrix elements, and so on. We do not go into the details of any of the formalisms but rather try to compare their approaches at a fairly general level. The quadrupolar echo pulse sequence is used as an example of the application of the formalisms. The aim of this overview is to give readers enough of a picture so that they can make an intelligent choice for themselves.

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“…In the analysis of CEST data, the number of coupled homogenous differential equations (n) is equal to 2 Â 4 m À 1, where m is the number of nuclear spins that are weakly coupled in an m-spin system [14,15]. For a 15 N-labeled sample each 15 N spin can be treated as a 1-spin system under 4-spin system in the 15 N CEST data analysis. Extraction of kinetics parameters from the CEST data is often time-consuming.…”

Section: Introductionmentioning

confidence: 99%