Chemical shift correlation equation

Consequently, more recent conformational studies have utilized the Karplus equation only as a guide to conformation and have not attempted the precise calculation of dihedral angles. In addition, various chemical-shift correlations have been shown to be of value in providing conformational information. 

As the proton chemical shifts of the methylene group protons are related to the C chemical shifts 8cy (Equation 41), also the H4 proton chemical shifts of monosubstituted allenes correlate with the group electronegativities (10). 

Carbon-13 chemical shifts of the a- and (8-carbon atoms of various unsubstituted and 3-substituted thietane oxides and dioxides have been recorded and correlated by the equations S = ay + bx and Sf = ax + by where a and b are parameters characteristic of the sulfoxide or sulfone (y) and the substituent (x)216. The values of the substituent parameters were found to parallel those which determine the effect on the 13C chemical shifts when hydrogen is replaced by a substituent224. 

The only physical property which has been studied for substituted vinylidene sets is the nmr chemical shift of the vinylidene proton in substituted ethylenes and in tra s-l,2-disubstituted ethylenes. The first attempt at correlating chemical shift data for substituted ethylenes with the Hammett equation appears to be the work of Banwell and Sheppard (53), who reported a correlation of A2 values with the or constants, the A2 values being defined by the equation... 

Chemical shifts of cis protons in substituted ethylenes and in trans-1,2-disubstituted ethylenes have been correlated with the Hammett equation in... 

Three sets of nmr chemical shifts for the ethynyl proton have been correlated with eq. (2). Of these sets, two gave significant correlations with eq. (2). Nevertheless, as the most extensive collection of substituents is included in the set which did not give significant correlation, it seems likely that chemical shifts of ethynyl protons are not correlated by the extended Hammett equation. This behavior contrasts with that of chemical shifts for trans- and c/s-vinyl protons and is in agreement with the behavior of geminal vinyl protons. 

The behavior of D2 in the Raman experiments is strongly correlated with the Q4 chemical shift, 6, in the NMR spectra. 6 equals about -110 to -111 ppm when D2 is absent or when it exhibits low relative intensities comparable to those in conventional vitreous silica, for example the 50 and 1050°C sample spectra and the rehydrated 600°C sample spectrum. From the regression equation cited above -110 to -111 ppm corresponds to - 147 to 149°, values quite close to the average in conventional v-Si02, 151° (4 ). The average 64 is shifted downfield to about -107 ppm in the 600°C sample in which D2 is observed to be quite intense. Deconvolution of this peak reveals two Q4 resonances at -110 and -105 ppm. -105 ppm corresponds to - 138°, which is very near the equilibrium 4> calculated for the isolated cyclic trisiloxane molecule, HgSi303, ( = 136.7°) (46). The positions of the Q2 and Q3 resonances, however, appear to be totally unaffected by the presence or absence of D2 (as shown in the 600°C CP MASS sample spectrum). 

Figure 5. Correlation between calculated (S29Sfa,c) and experimental29Si NMR chemical shift (S29Sfxp) for the cations 8-10. The correlation is given by the following equation 829Si

Figure 6 shows a good correlation between torsional angle and 170 chemical shift. The empirical equation 7 has been established by Boykin and Balakrishnan110, between nitro group torsion angles (q in degrees) and the chemical shifts of the 170 resonance of the... 

Correlations between substituent-induced chemical shift differences and reactivity parameters have been examined. Good linear correlations have been obtained using the Swain-Lupton two-parameter equation ... 

A linear correlation between 13C chemical shifts and local n electron densities has been reported for monocyclic (4n + 2) n electron systems such as benzene and nonbenzenoid aromatic ions [76] (Section 3.1.3, Fig. 3.2). In contrast to theoretical predictions (86.7 ppm per n electron [75]), the experimental slope is 160 ppm per it electron (Fig. 3.2), so that additional parameters such as o electron density and bond order have to be taken into account [381]. Another semiempirical approach based on perturbational MO theory predicts alkyl-induced 13C chemical shifts in aromatic hydrocarbons by means of a two-parameter equation parameters are the atom-atom polarizability nijt obtained from HMO calculations, and an empirically determined substituent constant [382]. 

Several approaches have been made to calculate 13C chemical shifts of coumarins by MO methods. Good correlations were found between the 13C chemical shift values of coumarin (also protonated) and the n charge densities calculated by the CNDO/2 method [962], and of coumarins with it charge densities calculated by the Hiickel MO method (which, however, fails for methoxylated coumarins) [965]. Chemical shifts of mono- and dimethoxycoumarins have been correlated with parameters determined by refined INDO MO calculations, in which n bond orders, atom-atom polarizabilities, excitation energies and electron-nucleus distances were taken into consideration [966], In 3-substituted 4-hydroxy and 4-hydroxy-7-methoxycoumarins chemical shifts were found to be related to Swain and Lupton s parameters iF and M [388], according to equation 5.4 (SE = Substitution Effect) ... 

This NMR titration method was subsequently applied to equilibrium IEs on acidity.30 33 Like the previous methods, it too benefits from the high sensitivity of 13C and 19F chemical shifts, and even 111 chemical shifts, to both isotopic substitution and state of protonation. Figure 1 shows the NMR titration of a mixture of tri(methyl-d)amine and tri(methyl-t/2)amine in D20, plotted according to Equation (19). The slope is 1.1618 0.0004. The intercept is -0.0061 0.0046, properly zero. The correlation coefficient is an impressive 0.999999, which is an indication of the accuracy achievable. Another remarkable result was the measurement of the relative basicity of the two exceedingly similar isotopomers of 1 -benzyl-4-methylpiperidine-2,2,6-t/3 (6). These are truly isotopomers (here stereoisomers), which bear the same number of isotopic substitutions and differ only in the position of the isotope, which is either axial or equatorial. 

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