Coupled spin systems detection

The detectable signal in the time intervals between the moments of exchanges can be determined by solving the time-dependent Schrodinger equation for the specific conformer however, in this case, the Hamiltonian is independent of time.18 The advantage of this method is its smaller memory requirement its disadvantage is the longer computational time because of the Monte Carlo simulation and that it was not possible to apply it to coupled spin systems so far. 

The vector model cannot be interpreted in such a simple way in the case of a spin system with more than one nucleus. For weakly coupled spin systems, the single spin vector model may be applied for each nucleus, one after the other. Thus the coupling with the other nuclei can be incorporated into its precession frequency, since the definition of the weak coupling (J -C vM v,/1) means that the transitions of a nucleus only depend on the spin states of the other nuclei in the first order. The detected signal is the sum of the sine curves provided by the individual environment of the nuclei. 

The calculation method presented here also provides a possible extension of the single spin vector model. This extension is performed in two steps first to weakly coupled spin systems, then to strongly coupled ones. In the first case, the introduction of the well-known product basis functions and their coherences is sufficient while in the latter one the solution is not so trivial. The crucial point is the interpretation of the linear transformation between the basis functions and the eigenfunctions (or coherences) during the detection and exchange processes. These two processes can be described by the population changes of single quantum... 

The most straightforward way to understand the origin of ESEEM and the physical chemistry behind its detection and analysis is to step back ft om this Cu(II) center and focns on an 5 = 1 /2, 7 = 1/2 coupled spin system. The spin Hamiltonian for this system consists of electronic Zeeman, nuclear Zeeman, and electron-nnclear hyperfine interaction terms. For the case of an isotropic electron -matrix and an axial hyperfine interaction, this Hamiltonian can be conveniently written in the laboratory reference Ifame,... 

S = 312 coupled spin system. The lineshape reflects an axially symmetric zero field splitting (ZFS) interaction with its principal axis directed along and the Fe(n)NO bond. Identical ESE-detected EPR spectra were obtained for Fe(II)NO-TauD treated with aKG and deuterated taurines. 

NMR spectrometers of the late 1960s did not permit the detection of higher spin orders for sensitivity reasons, so no new name was coined for them the term used today is "higher multiplet effects". More importantly, with the cw instruments ubiquitous at that time a separation of different spin orders n was principally impossible. The advent of pulsed and Fourier transform spectrometers reduced that to a trivial task Because for a weakly coupled spin system the amplitude of the detectable signal is proportional to sim cos i , one simply has to acquire spectra with different flip angles i9 and form suitable linear combinations (e.g. one- and two-spin orders are separated by adding and subtracting two spectra acquired with = 45° and = 135°). ... 

W.P. RothweU, J.S. Waugh, Transverse relaxation of dipolar coupled spin systems under rf irradiation detecting motions in solids, J. Chem. Phys. 74 (1981) 2721-2732. 

Canet D 1989 Construction, evolution and detection of magnetization modes designed for treating longitudinal relaxation of weakly coupled spin 1/2 systems with magnetic equivalence Prog. NMR Spectrosc. 21 237-91... 

The experiment just discussed represents a heteronuclear spin system. In a homonuclear case, the separate 90° C pulse necessary in the heteronuclear system is not required, since the second 90° H pulse affects the coupled partner H nucleus as well. The nucleus detected therefore has its two transitions antiphase with respect to each other, corresponding to the states represented in Fig. 2.7, Ilg, Ilh, etc. at detection. 

A 90° Gaussian pulse is employed as an excitation pulse. In the case of a simple AX spin system, the delay t between the first, soft 90° excitation pulse and the final, hard 90° detection pulse is adjusted to correspond to the coupling constant JJ x (Fig- 7.2). If the excitation frequency corresponds to the chemical shift frequency of nucleus A, then the doublet of nucleus A will disappear and the total transfer of magnetization to nucleus X will produce an antiphase doublet (Fig. 7.3). The antiphase structure of the multiplets can be removed by employing a refocused ID COSY experiment (Hore, 1983). 

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