Shift Parameter

Although it was originally developed for locating transition states, the EF algoritlnn is also efficient for minimization and usually perfonns as well as or better than the standard quasi-Newton algorithm. In this case, a single shift parameter is used, and the method is essentially identical to the augmented Hessian method. 

Step control (augmented Hessian, choice of shift parameter(s)). 

Near a first-order saddle point the NR step maximizes the energy in one direction (along the Hessian TS eigenvector) and minimizes the energy along all other directions. Such a step may be enforced by choosing suitable shift parameters in the augmented... 

In the Partitioned Rational Function Optimization (P-RFO), two shift parameters are employed. 

The QA method uses only one shift parameter, requiring that Ats = —A, and restricts the total step length to the trust radius (compare with eq. (14.9)). 

In conclusion therefore it may be stated that one must be able to distinguish between motional dispersion and motional homogeneity. Furthermore, a reconstruction of the chemical shift parameters from spectra with MAS at very low temperatures is needed to obtain quantitative motional information. Similar problems to the above also arise in other linear polymers containing interspaced soft and hard segments. 

NMR is an analytical technique that has been applied to the studies of chemical reactions with promising results. The chemical shift parameter may be used as a measure of the relative proportions of different species that are present in solution. These shifts are measured relative to a standard reference sample. 

Several methods have been developed to determine the chemical shift anisotropies in the presence of small and large quadrupolar broadenings, including lineshape analysis of CT or CT plus ST spectra measured under static, MAS, or high-resolution conditions [206-210]. These methods allow for determination of the quadrupolar parameters (Cq, i)q) and chemical shift parameters (dcs, //cs> <5CT), as well as the relative orientation of the quadrupolar and chemical shift tensors. In this context, the MQMAS experiment can be useful, as it scales the CSA by a factor of p in the isotropic dimension, allowing for determination of chemical shift parameters from the spinning sideband manifold [211],... 

The very simple idea that chemical shifts in binding energy can be accounted for in terms of changes in substituent groups is the basis of a predictive method involving additive group shift parameters. The method may be represented by the equation... 

The absolute and relative (to CH4) carbon 1 s binding energies for CH4, CF4, CC14, and CC1F3 are given in Table 1. From the data for CF4 and CC14 we can calculate group shift parameters of 2.76 and 1.38 eV for fluorine and chlorine atoms, respectively. 

C NMR spectroscopy of 1,7-dioxa- (314), l-oxa-7-thia- (315), and 1,7-dithiaspiro[5.5]undecane (316) and many of their derivatives, with special emphasis on stereoelectronic and steric effects governing the configurational and conformational properties of these compounds (484-486). This work showed that chemical-shift parameters developed for six-membered carbocyclic compounds in chair conformations (149) could be applied successfully only to sulfur and not to oxygen heterocycles (486). 

Accumulated NMR data support the proposal that the chemical shift for an olefinic carbon of monoenyl compounds can be calculated with ethylene as a reference [ 184]. A similar method was applied to the polyenyl Type I components with a conjugated system to estimate chemical shift parameters. Using 1,3-butadien for the base values (C 117.6 and 137.8 ppm), the chemical shift... 

From Table III, one can see that a common feature in both sets of shift parameters (that for 1,4-polyisoprene derivatives and that for 2-methylbutane derivatives) is a higher g effect for a methyl carbon (denoted g in Table III) than for a methylene carbon (denoted g in Table III). The difference between g and g effects is close to 4 ppm for the polymers whereas it is close to 3 ppm for the model compounds. On the other hand, one can see that there is no significant difference in the y effects whether the carbon under consideration is a methyl or methylene carbon. 

The empirical shift parameters calculated from the NMR data of the 1,4-polyisoprene derivatives will provide, hereafter, a basis for assigning the carbon resonances observed in the spectrum of hydrochlorinated 1,4-polydimethyl butadiene, which like hydro-chlorinated 1,4-polyisoprene has quaternary carbons substituted by one chlorine atom. 

The chemical shifts of the four methylene carbons depicted in Figure 8 have been calculated using the empirical shift parameters derived from the preceding study on hydrochlorinated... 

Pihlaja and Rossi [83ACSA(B)289] prepared l,3-dioxan-2-one and all of its methyl derivatives, recorded their C NMR spectra, and derived the methyl substituent shift parameters by a multiple linear regression analysis of the anancomeric and two equivalent chair conformers (Table X). With these values, the authors estimated the conformational equilibria for two unequally populated chair conformations (Nos. 2, 3, 9, 11, and 14 in Table X). A consistent picture of the predominance of the chair conformation and the corresponding chair chair equilibria in l,3-dioxan-2-ones was obtained in complete agreement with earlier H NMR results. 

The peak positions (the variables that determine the peak positions include the unit cell parameters and the zero-point shift parameter)... 

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