From intermolecular dipolar contributions

Fig. 7 PELDOR signal analysis, (a) Time domain PELDOR signal as a function of the delay time T of the pump pulse. The dashed line shows the exponentially decaying intermolecular dipolar contribution to the signal, (b) Time domain PELDOR signal after division of the original PELDOR time domain data by the fit-function representing the intermolecular decay, (c) Fourier transform of the PELDOR time trace (b) representing the dipolar Pake-pattem. (d) Distance distribution function obtained from the PELDOR time traces (b) by Tikhonov regularization. From the last representation the distances for spin pairs A-B can be the most easily extracted...

Jonas et al. measured the proton rotating frame spin-lattice relaxation time (Tip) at pressures from 1 bar to 5000 bar and at temperatures of 50 to 70 °C for DPPC and at 5 to 35 °C for POPC. If intermolecular dipolar interactions modulated by translational motion contribute significantly to the proton relaxation, the rotating frame spin-lattice relaxation rate (1/Tip) is a function of the square root of the spin-locking field angular frequency... 

NOE as n is changed from 0 to 4, The slower moving molecules demonstrate an increased importance of the dipolar contribution. In diphenyldichlorosilane (234) DD and SR relaxation mechanisms contribute about equally to the Si T[ value, providing a probable upper limit for a long range intermolecular contribution of dipolar relaxation from phenyl protons in phenylsilanes. 

The relaxivity induced by gadolinium chelates due to inner-sphere water molecules, riIS, is well understood on the microscopic scale as can be seen from the above discussion. The contribution to the overall relaxation enhancement due to all other water molecules is normally summed up in the term r, generally called the outer-sphere contribution. The interaction between the water proton nuclear spin I and the gadolinium electron spin S is supposed to be a dipolar intermolecular interaction whose fluctuations are governed by random translational motion. The corresponding relaxation rate, l/Tly for unlike spins is given by Eq. (23) [88-90]... 

A wide variety models have been proposed to evaluate these intermolecular contributions to the relaxation energy, including ab initio models for hydrated electrons (33) and hydrated ions (34), microscopic models based on dipolar lattices (35), and dielectric models ranging from the classic Bom model of solvation to its more modern extensions ( , ). The model which... 

Localized orbitals have also been used as a tool to extract the infrared spectrum of a solute in solution [194,195,202] or to decompose the IR spetrum in intramolecular and intermolecular contributions [202]. Model electrostatics of solute molecules was also based on localized orbitals [242, 243], not only at the dipolar level [244]. As an extension we also defined molecular states from localized orbitals to study the electronic states of liquid water [245], or of solvated ions [47]. It is also possible to perform CP-MD propagating the Wannier orbitals, by constraining the Kohn-Sham orbitals to stay in a Wannier gauge [246]. 

THz-TDS was also used to study the benchmark of molecular nanomagnetism, Mni2Ac [102-104], but has not been employed to study MNM since. These early studies demonstrated that the ZES of MNMs can be obtained by THz-TDS. Parks et al. then investigated the linewidth in some detail, where they considered contributions from hyperfine interactions and intermolecular magneto-dipolar interactions on the linewidth and concluded that, in addition to these, there must also be a distribution in the Z)-parameter. These investigations also made use of the fact that both amplitude and phase of the THz electric field are obtained, which can be converted to the real and imaginary parts of the index of refraction. 

This chapter concludes by pointing out that relaxation of multispin proton systems played a major role in the early days of NMR relaxation measurements on liquid crystals [5.34]. In particular, the detection of director fluctuations [5.35] by means of its characteristic frequency dependence in proton Ti [5.36-5.39] started intensive NMR research on liquid crystals. Since there are many inequivalent proton species in a liquid crystalline molecule, it is impossible to distinguish various atomic sites from a broad proton lineshape, which is a result of strong dipolar couplings. Moreover, translation self-diffusion also modulates the intermolecular dipole-dipole interactions and contributes to proton relaxation in liquid crystals [5.40, 5.41]. Partially deuterated liquid crystals may be used to reduce the number of inequivalent proton species. Proton spin relaxation studies remain as a possible method of probing intermolecular interactions or translational motions in liquid crystals. 

The direct NMR method for determining translational difiFusion constants in liquid crystals was described previously. The indirect NMR methods involve measurements of spin-lattice relaxation times (Ti,Ti ),Tip) [7.45]. Prom their temperature and frequency dependences, it is hoped to gain information on the self-diflPusion. In favorable cases, where detailed theories of spin relaxation exist, difiFusion constants may be calculated. Such theories, in principle, can be developed [7.16] for translational difiFusion. However, until recently, only a relaxation theory of translational difiFusion in isotropic hquids or cubic solids was available [7.66-7.68]. This has been used to obtain the difiFusion correlation times in nematic and smectic phases [7.69-7.71]. Further, an average translational difiFusion constant may be estimated if the mean square displacement is known. However, accurate determination of the difiFusion correlation times is possible in liquid crystals provided that a proper theory of translational difiFusion is available for liquid crystals, and the contribution of this difiFusion to the overall relaxation rate is known. In practice, all of the other relaxation mechanisms must first be identified and their contributions subtracted from the observed spin relaxation rate so as to isolate the contribution from translational difiFusion. This often requires careful measurements of proton Ti over a very wide frequency range [7.72]. For spin - nuclei, dipolar interactions may be modulated by intramolecular (e.g., collective motion, reorientation) and/or intermolecular (e.g., self-diffusion) processes. Because the intramolecular (Ti ) and intermolecular... 

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