Increment systems

For illustration of the increment system, the 13C chemical shift of C-3 in 2-methylhexane is calculated below according to eq. (4.1) using the shift parameters listed in Tables 4.2 and 4.3 [85] ... 

The calculated shift of C-3 is 39.1 ppm as compared to an observed value of 39.45 ppm. Prediction of carbon chemical shifts using the Grant-Paul relation (4.1) is a practical aid in assigning the carbon signals of larger alkyl groups, e.g. in cholestane derivatives (Section 5.2.2). - Other increment systems have been proposed [201, 202], as well as an absolute scale for carbon shielding [203],... 

An increment system has been derived for methyldecalins [230] and methylated perhy-drophenanthrenes [231] by regressional analysis, because these compounds are steroid models and the increments, in fact, have proved to be of help in carbon-13 shift assignments of steroids (Section 5.2). Eq. (4.2) permits prediction of <5C using the increments A, of structural elements in position l to the carbon atom k to be considered (Table 4.9). These increments clearly indicate the configurational influence of the y substituent, decreasing for example from eclipsed via gauche to trans interactions (I , > Vq > Vt and... 

Similarly to alkanes, an increment system has been proposed in order to predict carbon-13 shifts of olefinic carbons from the reference value of ethene (122.1 ppm) [237] and the increments A, for a, f , y, and 6 alkylation, as well as multiple substitution corrections S (Table 4.11). Accuracy is about 1 ppm. 

Carbon-13 shifts of alkynes (Table 4.13) [246-250] are found between 60 and 95 ppm. To conclude, alkyne carbons are shielded relative to olefinic but deshielded relative to alkane carbons, also paralleling the behavior of protons in proton NMR. Shielding relative to alkenes is attributed to the higher electronic excitation energy of alkynes which decreases the paramagnetic term according to eq. (3.4), and to the anisotropic effect of the triple bond. An increment system can be used to predict carbon shieldings in alkynes... 

Two empirical increment systems (Table 4.22) derived from experimental data as collected in Table 4.23 permit prediction of alkanol carbon-13 shifts. One is related to the shift value B of the hydrocarbon R —H and involves, as usual, addition of the increments Z, = <5,(r oh) — r)(- R > according to eq. (4.8 a) [268]. The other employs a linear equation (4.8 b), correlating the shifts of an alkanol R — OH and the corresponding methyl-alkane R —CH3 by a constant bk and a slope ak, which is 0.7-0.8 for a and about 1 for ji and y positions [269]. Specific parameter sets characterize primary, secondary, and tertiary alcohols (Table 4.22). The magnitudes of Z) increments in eq. (4.8 a) decrease successively from primary to tertiary alcohols (Table 4.22), obviously as a result of reduced populations of conformers with yliauche interactions in the conformational equilibrium when the degree of alkylation increases. 

An empirical increment system permits prediction of charge distribution in a,/ -unsaturated carbonyl compounds, assuming additivity of electronic effects and neglecting the conformational dependence of carbon-13 chemical shifts [290]. Moreover, carbonyl and alkenyl carbon shifts of a, /3-unsaturatcd ketones may be used to differentiate between planar and twisted conjugated systems, as shown in Table 4.29 [291] and outlined for phenones in Section 3.1.3.8. 

Carbon-13 shift values of aliphatic amines [337-339] collected in Table 4.42 indicate that the y effect is about — 4.5 ppm for primary, secondary, and tertiary amines. The a effect, however, increases while the ft effect decreases with an increasing degree of alkylation at the amino nitrogen. Analogously to alkanols, two increment systems can be used to predict alkyl carbon shifts of amines according to eq. (4.12 a, b), based on the reference shifts of corresponding alkanes (R —H) or the methyl homologs (R —CH3) [337, 338] (Table 4.43). 

Carbon-13 shift values of parent heterocycloalkanes [408] collected in Table 4.61 are essentally determined by the heteroatom electronegativity, in analogy to the behavior of open-chain ethers, acetals, thioethers, thioacetals, secondary and tertiary amines. Similarly to cyclopropanes, three-membered heterocycloalkanes (oxirane, thiirane, and azirane derivatives) display outstandingly small carbon-13 shift values due to their particular bonding state. Empirical increment systems based on eq. (4.1) permit shift predictions of alkyl- and phenyl-substituted oxiranes [409] and of methyl-substituted tetrahydropyrans, tetrahydrothiapyrans, piperidines, 1,3-dithianes, and 1,3-oxathianes [408], respectively. Methyl increments of these heterocycloalkanes are closely related to those derived for cyclohexane (Table 4.7) due to common structural features of six-membered rings. 

Fig. 4.17 illustrates the potential of carbon-13 NMR to detect the presence of isotactic (a), syndiotactic (b), and atatactic (c) vinyl polymers with polypropylene as sample [521], The spectrum of atactic polypropylene (Fig. 4.17(c)) displays the signals of all possible stereosequences including iso- and syndiotactic ones. Using the empirical increment systems for alkane carbon shift prediction [85, 201, 202] and including y effects of Zy = — 5 ppm specifically obtained by analysis of stereoisomeric polypropylene partial sequences between 3,5-dimethylheptane and 3,5,7,9,11,13,15-heptamethylheptadecane as a heptad model, the methyl carbon-13 shifts of all 36 possible heptads can be calculated... 

Keller (1982) developed an additive increment system for the calculation of the 13C chemical shift in polymers as a function of the substitution of the (neighbouring) C atoms. 

The decreasing aromaticity in the anion is also manifested in a smaller magnetic sus-ceptibihty exaltation (A) , which is defined as the difference between the bulk magnetic susceptibility (xm) of a compound and the susceptibility (xm ) estimated from an increment system for the same structure without cyclic conjugation (A = xm — Xm in units of ppm cgs). Thus, the value A = —9.1 for PhO is equal to only 59% of the A = —15.5 for phenol. The computed values for the diamagnetic susceptibility anisotropy (Xanis) follow the same trend, indicating that PhO has actually about 60% of the aromaticity of PhOH352. 

Basicity or acidity are estimated by using topology-based increment systems. No software package is available so far that is able to predict basicity precisely for arbitrary structures. Basicity is a very important drug property, and therefore also a very rough estimation of pJ A values is useful in describing a library. 

If the diamagnetic behavior of matter could be completely explained by local currents around the nuclei, and if the diamagnetic susceptibility of the different nuclei of the periodic table were known, the susceptibility of molecular compounds consisting of different elements would be the sum of the individual contributions, and could be easily predicted. As early as 1919, Pascal [23], and later Pacault [24] and Haberditzl [25], published simple increment systems to calculate diamagnetic susceptibilities of molecules. The increment system is quite accurate for most organic and inorganic compounds, with a few exceptions. 

Dauben suggested using the magnetic exaltation as a measure of aromaticity [32-34]. According to this criterion a conjugated molecule is aromatic if A > 0, nonaromatic if A 0, and anti-aromatic if A <0. Practically, is either determined by experiment, or more conveniently calculated by quantum chemical calculations. Increments are available from Haberditzel [25]. The latter increment system also includes local contributions from binding electrons. The following calculation for benzene may serve as an example (susceptibiUty increments in —10 cm mol ) ... 

The relative contributions of the paramagnetic shielding and the diamagnetic shielding constants within this increment system have been discussed Empirical systems of this kind allow an estimation of chemical shifts with a mean deviation of less than one ppm. Modern data bank systems, e.g. SPECINFO or CSEARCH, are able to reproduce the chemical shifts of any given alkane even more accurately within a few seconds. In a slightly different approach, a substituent constant for 34 different alkyl groups was defined, and it was shown that the chemical shift of a nucleus X in a compound XR4 obeys equation 1, where m and b are constants. 

TABLE 2. Increment system for NMR chemical shifts of alkanes ... 

A special increment system for methyl-substituted cycloalkanes requires for each substituent a positional parameter which is different for axial and equatorial substitution. Furthermore, correction factors for vicinal methyl pairs have to be included . This increment system is presented in Table 5 along with an example of its use. Conformational... 

TABLE 5. Increment system for CNMR chemical shifts of methyl-substituted cycloalkanes c(fc) = 26.5 -I- i ki... 

Methyldecalins, perhydrophenanthrenes and perhydroanthracenes are models for steroids. Therefore an incremental system was developed which includes several features inherent in these ring systems and from which the chemical shifts of similar compounds can be calculated This system is given in Table 7 along with an example of its use. 

Determined by polarizing microscopy, heating rate 10 C min d-values were calculated by the increment system given in [55]. 

Pascal increment system for diamagnetic susceptibility aromatic exaltation M... 

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