Comparison and Use of Vector and Quantum Representations of J-Coupled Spin Evolution in an IS Spin System during RF Irradiation of One Spin

Bendall, M.Robin; Skinner, Thomas E.

doi:10.1006/jmre.1999.1981

Cited by 10 publications

(28 citation statements)

References 35 publications

(128 reference statements)

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“…Inspection of the equivalent off-resonance term (24) shows the well-known residual splitting of the centerband when ϩ Ϫ (16). Since there is no such splitting of the centerband on resonance at any decoupling power for an IS system (for example, 13 Clabeled formate) the centerband S-spin signal will always increase in intensity (by as much as a factor of two on resonance compared to far off-resonance), as CW decoupling applied to the I spins passes through zero resonance offset, independent of decoupling power.…”

Section: Efficient Characterization Of An Insensitive I-spin Decouplementioning

confidence: 98%

“…(24). One application of these exact general equations is to provide a rigorous vector picture of the evolution of measurable magnetizations from the combined effects of RF irradiation and J-coupling.…”

Section: Applicationsmentioning

confidence: 99%

“…[38] have no obvious classical analog in the sense of the I-spin components rotating at a constant rate about a fixed axis, although a vector description of the evolution of these components is still possible (24). Nonetheless, a judicious choice of coordinate system enables the classical rotations underlying these nonclassical transformations to be determined, resulting in a classical vector model for the evolution of weakly coupled IS spin systems during RF irradiation of one of the spin species.…”

Section: Coupling Evolution During Rf Irradiationmentioning

confidence: 99%

“…The time evolution of the spin system is most generally a function of ϩ Ϯ Ϫ and ͉ ϩ ͉ Ϯ ͉ Ϫ ͉, which can be seen by expanding the results in Table 1-3, as worked out in detail in Ref. (24).…”

Section: Coupling Evolution During Rf Irradiationmentioning

confidence: 99%

“…Alternatively, we can interchange the rows and columns to form the transpose matrix ⍀ T and write ⍀ T (0) ϭ (t), as in Ref. (24). Coefficients ␣ defined in Eq.…”

Section: M S N Systemsmentioning

confidence: 99%

See 4 more Smart Citations

J‐coupling and chemical‐shift evolution during I‐spin irradiation of I_mS_n systems: Product operator solutions and applications

Skinner

Bendall

2002

Concepts Magn. Reson.

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ABSTRACT:We previously obtained exact solutions for the time dependence of the density operator in weakly coupled spin-1 2 I m S n systems during arbitrary RF irradiation of the I spins. The solutions for the density operator were written as explicit linear combinations of its product operator components (i.e., the operator basis set consisting of direct products of the I-and S-spin operators). Other solutions for the product-operator evolution of the density matrix have considered either evolution in the absence of RF irradiation or the case where the RF is sufficiently strong that J-coupling effects can be ignored. The present solutions therefore extend the range of applications that are accessible to the product-operator formalism and vector pictures of nuclear spin evolution. Here, we derive the solutions for an IS system in detail to illustrate the simplicity of the formalism and supplement our previous, but more general, abstract treatment of the subject. We then outline how the formalism is applied to the I m S n case. We also briefly discuss the rigorous vector picture that can be associated with the states of the system at each time. The solutions provide new insight into the combined effects of RF irradiation and J-coupling. Applications include (1) novel methods for calibrating an RF channel for insensitive I spins by observing large signals from multiple quantum coherences with the S-spin channel, and (2) new RF pulses for achieving selective coherence transfer.

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Section: Efficient Characterization Of An Insensitive I-spin Decouplementioning

confidence: 98%

Section: Applicationsmentioning

confidence: 99%

Section: Coupling Evolution During Rf Irradiationmentioning

confidence: 99%

Section: Coupling Evolution During Rf Irradiationmentioning

confidence: 99%

“…Alternatively, we can interchange the rows and columns to form the transpose matrix ⍀ T and write ⍀ T (0) ϭ (t), as in Ref. (24). Coefficients ␣ defined in Eq.…”

Section: M S N Systemsmentioning

confidence: 99%

See 3 more Smart Citations

J‐coupling and chemical‐shift evolution during I‐spin irradiation of I_mS_n systems: Product operator solutions and applications

Skinner

Bendall

2002

Concepts Magn. Reson.

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New Perspectives on Heteronuclear Decoupling: Classical Rotational Dynamics Applied to NMR Systems

Skinner

2016

eMagRes

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Matrix method for analysis of selective NMR pulses

Tesiram

Separovic

2005

Concepts Magn. Reson.

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ABSTRACT:The evolution of a single nuclear magnetic spin during the application of radiofrequency (RF) pulses is followed using the 3 ϫ 3 matrix solution to the Bloch equations. The effect of different pulses on the magnetization of spin-1/2 nuclei is described using this 3 ϫ 3 matrix. Simulations of the magnetization following a simple square pulse, amplitude and amplitude/frequency modulated pulses are represented as unit vectors in the rotating reference frame, and evolution of the magnetization can be followed at any time during the application of the pulse. Projection of these vectors onto the transverse plane of the rotating frame of reference is the magnitude of the various components of detectable magnetization. From these simulations, the peak amplitude required to drive the RF power output of linear amplifiers can be calculated accurately and directly related to experiment. In addition, the magnitude of magnetization for a range of frequency offsets within an NMR spectrum can be simulated with or without phase cycling. The simulations of shaped and adiabatic pulses are described. The accuracy of these simulations were readily verified by experiment so that implementation of new pulses into pulse sequences could be assessed by simulation prior to application and reduce the use of spectrometer time for optimization of RF pulses in NMR pulse sequences.

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Comparison and Use of Vector and Quantum Representations of J-Coupled Spin Evolution in an IS Spin System during RF Irradiation of One Spin

Cited by 10 publications

References 35 publications

J‐coupling and chemical‐shift evolution during I‐spin irradiation of I_mS_n systems: Product operator solutions and applications

J‐coupling and chemical‐shift evolution during I‐spin irradiation of I_mS_n systems: Product operator solutions and applications

New Perspectives on Heteronuclear Decoupling: Classical Rotational Dynamics Applied to NMR Systems

Matrix method for analysis of selective NMR pulses

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Comparison and Use of Vector and Quantum Representations of J-Coupled Spin Evolution in an IS Spin System during RF Irradiation of One Spin

Cited by 10 publications

References 35 publications

J‐coupling and chemical‐shift evolution during I‐spin irradiation of ImSn systems: Product operator solutions and applications

J‐coupling and chemical‐shift evolution during I‐spin irradiation of ImSn systems: Product operator solutions and applications

New Perspectives on Heteronuclear Decoupling: Classical Rotational Dynamics Applied to NMR Systems

Matrix method for analysis of selective NMR pulses

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Product

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J‐coupling and chemical‐shift evolution during I‐spin irradiation of I_mS_n systems: Product operator solutions and applications

J‐coupling and chemical‐shift evolution during I‐spin irradiation of I_mS_n systems: Product operator solutions and applications