Line-shape analysis

In solution, rate constants and activation parameters for dynamic processes can be estimated by direct analysis of the change of the NMR signal shape as a function of temperature. This technique is called line shape analysis (LSA) and it is best suited vhen the rate of exchange ranges from ca. 10 to 10 s [142, 159]. 

If the exchange rate, k, is much smaller than the frequency difference between the signals for the exchanging sites, then the NMR spectrum will exhibit well separated peaks for these resonances. Based on the Bloch equation [146], it is possible to find relationships connecting the shape of the NMR signal, Avii2, the lifetime, T, for a nucleus in different positions of a molecule and the rate constant, k. The lifetime is related to the rate constant by Eq. (4). 

At values where k equals the difference in resonance frequencies, the peaks coalesce. The rate of interchange at coalescence, kmai. can be determined via Eq. (5) [155], for exchange between two equally populated sites that do not exhibit scalar coupling [160]. 

Although this equation only applies when the coalescence point is reached, rate constants for the exchange between two or more exchanging sites are accessible by analysis of line widths at half height, Avip, and shift differences, Ar, in Hz. The comparison between the experimental spectrum and the spectrum calculated by use of a simulation package for line shapes provides the mechanism for determining the rate constant of exchange [161, 162]. 

Casey et al. have studied complex 98 as a model for intermediates in metallocene catalyzed alkene polymerization, by means of LSA [166]. 

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Chemical shift anisotropy 5.5,5 xxr yy zz Line-shape analysis MAS-sidebands Coordination symmetry... 

Nuclear electric quadrupole QCC (quadrupole coupling constant), (asymmetry parameter) Line-shape analysis, nutation NMR Coordination symmetry... 

Another example is the proton exchange between H2O and HDO at low water concentrations in organic solvents. t values were obtained by line shape analysis ... 

Weis [85AHC(38)1, pp. 70-73] has also studied the kinetics of 1,4-dihydro to 1,6-dihydro transformation quantitatively using H NMR line-shape analysis. The results indicated that two mechanisms (monomolecular and bimolecular reactions) are involved in the process, for which all the kinetic parameters were calculated. 

After the completion of this manuscript a paper concerning conformational analyses of 1,1, 3,3 -tetra-r< H-alkylmctallocene of iron and ruthenium including 6 based on thorough NMR spectroscopic measurements (line-shape analysis) has appeared in which the nature of the transition states has conclusively been discussed in detail [164]. 

NMR line shape analysis, 260-263 Negative activation enthalpy, 162 Noncompetitive inhibitor, 93 Nucleophilic catalysis, 237-238 Numerical simulations, 112-119... 

Solid state materials have been studied by nuclear magnetic resonance methods over 30 years. In 1953 Wilson and Pake ) carried out a line shape analysis of a partially crystalline polymer. They noted a spectrum consisting of superimposed broad and narrow lines which they ascribed to rigid crystalline and amorphous material respectively. More recently several books and large articles have reviewed the tremendous developments in this field, particularly including those of McBrierty and Douglas 2) and the Faraday Symposium (1978)3) —on which this introduction is largely based. 

In Fig. 7 actual numbers for the correlation times of the motion are included that apply for 2H NMR of deuterons in C—H bonds. It is evident that the line shape analysis of deuteron spectra should, in principle, provide a means to determine accurate values for the correlation times in a range of at least three orders of magnitude, the limits... 

Fig. 10. Correlation times for the tetrahedral jump motion in solid HMT obtained from 2H line shape analysis and 2H spin alignment...

Bodor, G. X-ray Line Shape Analysis. A. Means for the Characterization of Crystalline Polymers. Vol. 67, pp. 165-194. 

A Simple Example of Line Shape Analysis Spin-State Relaxation in the Nitrosyl... 

Rates of Spin-State Transition for Solid Metal Complexes Based on the Line Shape Analysis of Mosshauer Spectra... 

For iron(III) eomplexes, uic venues /vlh [Fe(aepa)2]BPh4 H2O and k = 6.7 x 10 s for [Fe(mim)2(salacen)]PF6 have been obtained [156, 166]. The rate constants derived from the line shape analysis of Mossbauer spectra thus vary between 2.1 x 10 and 2.3 x 10 s at room temperature, no significant difference between iron(II) and iron(III) being apparent. In addition, it is evident that the rates of spin-state conversion in solution and in the crystalline solid are almost the same. For iron(II) eomplexes, for example, the solution rates vary between /cjjl = 5 x 10 and 2 x 10 s , whereas in solid compounds values between kjjL = 6.6 x 10 and 2.3 x 10 s have been obtained. Rates resulting from the relaxation of thermally quenched spin transition systems are considerably slower, since they have been measured only over a small range of relatively low temperatures. Extrapolation of the kinetic data to room temperature is, however, of uncertain validity. 

Au metal Thick absorber line-shape analysis and interference effects... 

The transition from single- to many-chain behavior already becomes obvious qualitatively from a line shape analysis of the NSE spectra (see Fig. 60) [116]. For dilute solutions (c = 0.05) the line shape parameter (3 is equal to about 0.7 for all Q-values, which is characteristic of the Zimm relaxation. In contrast, in semi-dilute solutions (e.g. c = 0.18), ft-values of 0.7 are only found at larger Q-values, whereas P-values of about 1.0, as predicted for collective diffusion [see Eq. (128)] are obtained at small Q-values. A similar observation was reported by [163]. 

Figure 64 presents the results of the line-shape analysis for c = 0.18 and c = 0.45. In the first case the polymer relaxation is still determined by the Zimm modes at larger Q-values, while at smaller Q the Rouse modes become dominant. Qualitatively, this behavior is expected for the crossover from unscreened Zimm to enhanced Rouse relaxation. At c = 0.45 the Q-dependence P is... 

Dynamic parameters for heterogeneous systems have been explored in the liquid, liquid like, solid like, and solid states, based on analyses of the longitudinal or transverse relaxation times, chemical exchange based on line-shape analysis and separated local field (SLF), time domain 1H NMR, etc., as summarized in Figure 3. It is therefore possible to utilize these most appropriate dynamic parameters, to explore the dynamic features of our concern, depending upon the systems we study. 

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... 

The dynamic NMR (DNMR) spectroscopy has been used in studies of stereomutations of non-symmetrical di-Schiff bases [18].39 It was shown that the hindered Schiff bases exist in DMSO in two chiral conformations. The presence of a pair of conformers being in equilibrium was explained by the existence of two stereogenic axes a g (aligned to Cl—N8 bond) and a 7 (aligned to C6—N7 bond) due to restricted rotation around two Ar—N bonds. The trans to cis interconversion as well as enantio- or diastereoisomerisation barriers for the compounds studied have been established using line shape analysis. 

Similarly, 39K nmr line-shape analysis has been applied to the study of the interaction of K+ with 18-crown-6 in a range of solvent mixtures (Schmidt Popov, 1983). In most instances, the cation exchange proceeds via a normal dissociative process (as found in water) however, in 1,3-dioxolane, metal exchange switches to a bimolecular exchange mechanism. 

At higher temperatures kinetic line broadening and coalescence is observed (Fig. 8). Upon warming above the coalescence temperature of about 110 °C four lines for the aromatic methine carbons with decreasing line width are observable until decomposition takes place at about -70 °C (Fig. 8). From line shape analysis the energy barrier for the isomerization process is obtained as AG11 — 7.5kcal/mol.101... 

The kinetic information for NMR experiments is contained in the line broadening observed for a nucleus that resides in two different magnetic environments, and values for rate constants can be obtained using line-shape analysis.28,68,69 Line broadening experiments obtained using ID NMR is the method of choice when analyzing the kinetics of a molecule in two sites. 2D NMR techniques, such as 2D EXYS are employed when the kinetics are sequential, i.e. more than one step, or multiple sites are analyzed.69 For example in the case of supramolecular systems this technique was employed to measure the exchange kinetics in capsules.70... 

Line shape analysis was performed for the binding of some dihydroxycholate ions to /1-cyclodextrin.205 The dihydroxycholates show different 18-CH3 signals for the complexed and free dihydroxycholate ions. To extract exchange rate constants from the NMR spectra, a complete line-shape simulation was performed. The simulation requires input of the chemical shift difference between the two sites, the line width in the absence of exchange, the residence time in each site (thg and Tg), and the relative population (fHG and fG) of each site (Equation (11)). The values were varied until the simulated and experimental spectra could be superimposed. The dissociation rate... 

This reaction has been reexamined using optical, IR and NMR spectroscopic methods to probe NO reactions with Fe(TPP)(NO) and the more soluble Fe(TmTP)(NO) (92). These studies confirmed the formation of Fe(Por)(NO)2 in toluene-dg at low temperature (Eq. (43)). NMR line shape analysis was used to calculate K43 = 23 M-1 at 253 K (3100 M-1 at 179 K, AH° = —28kJmol 1) (92). The failure of the Fen(Por) complexes to promote NO disproportionation, in contrast to the behavior of the respective Ru(II) and Os(II) analogs, may find its origin partly in the relatively low stability of the dinitrosyl intermediate (K52 estimated to be 2.8 M-1 at 298 K) and unfavorable kinetics of subsequent reaction of this species with NO. 

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