Pair-wise coupling

This process does not necessarily have to be simultaneous, but the two atoms of the dihydrogen molecule must retain a spin-spin coupling throughout the whole process. Conversely, if they are not transferred pair-wise (i. e., if the transferred hydrogen atoms stem from different dihydrogen molecules or if they lose their coupling in the course of the process), no polarization can be detected. 

It has been pointed out that any relationship between the exchange integral and the Weiss field is only valid at 0 K, since the former considers magnetic coupling in a pair-wise manner and the latter results from a mean-field theory (Goodenough, 1966). Finally, it is also essential to understand that Eq. 8.43 is strictly valid only for localized moments (in the context of the Heitler-London model). One might wonder then whether the Weiss model is applicable to the ferromagnetic metals, in which the electrons are in delocalized Bloch states, for example, Fe, Co, and Ni. This will be taken up later. 

The continuum electrostatic approach has been considered also appropriate for studying biomolecular systems when electronic polarisation effects, typically neglected by the additive pair-wise potentials commonly use in MD and MC, are dominant in relation to the conformational flexibility, and when changes in protonation states of tritable sites [193-198] or electron-proton coupling phenomena [199-204] occur. 

CH3CH=CHCH=CHC00H)][CF3S03] is shown in a iH-PHIP experiment (see Fig. 21.10). The spectrum reveals the characteristic PFIIP polarization pattern of adsorptive and emissive lines. This polarization pattern proves the pair-wise transfer of the para-hydrogen to the substrate. The observed anti-phase coupling constant of... 

The cross-photodimerization reaction represents a great challenge because it requires D to selectively recognize two different olefins in a pair-wise fashion prior to irradiation, whereas the cross-coupling reaction under standard conditions shows no preference over the homo-coupling. The cross-photodimerization of acenaphthylene with substituted naphthoquinones within D resulted in exclusive formation of the cross syn-dimer only... 

The principle purpose of correlation experiments is to establish a one-to-one mapping from the signal to its source i.e. to the particular atomic nucleus in the molecule. This assignment task involves identification of the members in the coupling network, referred to as the spin system. In addition, correlation experiments, as such or with modifications, are suitable for measurements of scalar and dipolar couplings. Correlation in the two dimensions is the most natural dimensionality because the spin-spin interactions are pair wise. Three-dimensional or experiments of higher dimensionality are constructed from concatenated two-dimensional experiments. Homonuclear three-dimensional experiments, such as TOCSY-NOESY, are not considered here because in many cases the multidimensional heteronuclear experiments are superior. 

The step wise reduction procedure described above can been automated by the use of the Directed Relation Graph method (Lu and Law, 2005) (Lu and Law, 2006). This procedure quantifies the coupling between species, and assigns an "pair wise" error which contains the information of how much error is introduced to a species A by elimination of a species B ... 

The BO description is in principle well adapted to incorporate the zero-frequency ionic polarisability and account for the coupling between charges, fixed and induced dipoles. A polarisable particle (solvent or ion) responds to the applied electric field exerted by its neighbours with an induced dipole, which will then exert a new field in the neighbourhood, and so on. The problem of the polarisable systems is that the interaction is no more pair-wise additive. The 2 -body problem can be explicitly treated in numerical simulation (with difficult and rather time-consuming iterative procedure at each configuration) but is not adapted to integral equations... 

In the solid, dynamics occurring within the kHz frequency scale can be examined by line-shape analysis of 2H or 13C (or 15N) NMR spectra by respective quadrupolar and CSA interactions, isotropic peaks16,59-62 or dipolar couplings based on dipolar chemical shift correlation experiments.63-65 In the former, tyrosine or phenylalanine dynamics of Leu-enkephalin are examined at frequencies of 103-104 Hz by 2H NMR of deuterated samples and at 1.3 x 102 Hz by 13C CPMAS, respectively.60-62 In the latter, dipolar interactions between the 1H-1H and 1H-13C (or 3H-15N) pairs are determined by a 2D-MAS SLF technique such as wide-line separation (WISE)63 and dipolar chemical shift separation (DIP-SHIFT)64,65 or Lee-Goldburg CP (LGCP) NMR,66 respectively. In the WISE experiment, the XH wide-line spectrum of the blend polymers consists of a rather featureless superposition of components with different dipolar widths which can be separated in the second frequency dimension and related to structural units according to their 13C chemical shifts.63... 

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