Chemical shifts systems

Figure B2.4.1 shows the lineshape for intennediate chemical exchange between two equally populated sites without scalar coupling. For more complicated spin systems, the lineshapes are more complicated as well, since a spin may retain its coupling infonnation even though its chemical shift changes in the exchange.

For a coupled spin system, the matrix of the Liouvillian must be calculated in the basis set for the spin system. Usually this is a simple product basis, often called product operators, since the vectors in Liouville space are spm operators. The matrix elements can be calculated in various ways. The Liouvillian is the conmuitator with the Hamiltonian, so matrix elements can be calculated from the commutation rules of spin operators. Alternatively, the angular momentum properties of Liouville space can be used. In either case, the chemical shift temis are easily calculated, but the coupling temis (since they are products of operators) are more complex. In section B2.4.2.7. the Liouville matrix for the single-quantum transitions for an AB spin system is presented. 

Figure B2.4.5. Simulated lineshapes for an intennolecular exchange reaction in which the bond joining two strongly coupled nuclei breaks and re-fomis at a series of rates, given beside tlie lineshape. In slow exchange, the typical spectrum of an AB spin system is shown. In the limit of fast exchange, the spectrum consists of two lines at tlie two chemical shifts and all the coupling has disappeared.

A useful empirical method for the prediction of chemical shifts and coupling constants relies on the information contained in databases of structures with the corresponding NMR data. Large databases with hundred-thousands of chemical shifts are commercially available and are linked to predictive systems, which basically rely on database searching [35], Protons are internally represented by their structural environments, usually their HOSE codes [9]. When a query structure is submitted, a search is performed to find the protons belonging to similar (overlapping) substructures. These are the protons with the same HOSE codes as the protons in the query molecule. The prediction of the chemical shift is calculated as the average chemical shift of the retrieved protons. 

A proton can be (numerically) represented by a series of topological and physicochemical descriptors, which account for the influence of the neighborhood on its chemical shift. Fast empirical procedures for the calculation of physicochemical descriptors are now easily accessible [45. Geometric descriptors were added in the case of some rigid substructures, as well as for rr-systems, to account for stereochemistry and 3D effects. 

Ah initio methods are applicable to the widest variety of property calculations. Many typical organic molecules can now be modeled with ah initio methods, such as Flartree-Fock, density functional theory, and Moller Plesset perturbation theory. Organic molecule calculations are made easier by the fact that most organic molecules have singlet spin ground states. Organics are the systems for which sophisticated properties, such as NMR chemical shifts and nonlinear optical properties, can be calculated most accurately. 

LORG (localized orbital-local origin) technique for removing dependence on the coordinate system when computing NMR chemical shifts LSDA (local spin-density approximation) approximation used in more approximate DFT methods for open-shell systems LSER (linear solvent energy relationships) method for computing solvation energy... 

Katritzky and Topsom have reviewed the information available, largely from infrared and n.m.r. studies, concerning the distortion of the tt-electron system in the benzene ring brought about in the ground state by substituents. Of particular interest is the observation that both n.m.r. studies (of m- F and chemical shifts) and infrared investigations (of the intensities of bands due to certain skeletal vibrations) suggest that the value of Taft s [Pg.226]

The proton chemical shifts of the protons directly attached to the basic three carbon skeleton are found between 5.0 and 6.8 ppm. The J(H,H) between these protons is about -5 Hz. The shift region is similar to the region for similarly substituted alkenes, although the spread in shifts is smaller and the allene proton resonances are slightly upfield from the alkene resonances. We could not establish a reliable additivity rule for the allene proton shifts as we could for the shifts (vide infra) and therefore we found the proton shifts much less valuable for the structural analysis of the allene moiety than the NMR data on the basic three-carbon system. 

Over the past decade it has been established that for various substituents the i C chemical shift increment is a constitutive property. This applies to many systems e.g. benzenes, alkanes and alkenes. The availability of over 200 allenes, randomly substituted with groups of different nature, enabled us to prove that in the case of allenes the chemical shift increment is a constitutive property too, thus establishing a convenient method for estimating i ( C) values for allenes. 

Application of NMR spectroscopy to heterocyclic chemistry has developed very rapidly during the past 15 years, and the technique is now used almost as routinely as H NMR spectroscopy. There are four main areas of application of interest to the heterocyclic chemist (i) elucidation of structure, where the method can be particularly valuable for complex natural products such as alkaloids and carbohydrate antibiotics (ii) stereochemical studies, especially conformational analysis of saturated heterocyclic systems (iii) the correlation of various theoretical aspects of structure and electronic distribution with chemical shifts, coupling constants and other NMR derived parameters and (iv) the unravelling of biosynthetic pathways to natural products, where, in contrast to related studies with " C-labelled precursors, stepwise degradation of the secondary metabolite is usually unnecessary. 

Work on indazoles has the drawback of having to employ computer procedures to analyze the ABCDX system of C-unsubstituted indazoles. The first five examples in Table 9 correspond to LAOCOON-analyzed spectra and the last two to simpler systems for which the first-order analysis gives acceptable chemical shifts. 

Aromatic character in isoxazoles has been studied from a number of viewpoints, and these studies indicate that although isoxazole may be formally considered an aromatic system, the disposition of the ring heteroatoms modifies this character to an appreciable extent. From a qualitative viewpoint, thermal stability and electrophilic attack at the 4-position may be considered consistent with an aromatic character. Furthermore, NMR chemical shifts of the ring protons are consistent with those of an aromatic compound. References related to these studies may be found in Section 4.16.2.3.4. 

Representative chemical shifts from the large amount of available data on isothiazoles are included in Table 4. The chemical shifts of the ring hydrogens depend on electron density, ring currents and substituent anisotropies, and substituent effects can usually be predicted, at least qualitatively, by comparison with other aromatic systems. The resonance of H(5) is usually at a lower field than that of H(3) but in some cases this order is reversed. As is discussed later (Section 4.17.3.4) the chemical shift of H(5) is more sensitive to substitution in the 4-position than is that of H(3), and it is also worth noting that the resonance of H(5) is shifted downfield (typically 0.5 p.p.m.) when DMSO is used as solvent, a reflection of the ability of this hydrogen atom to interact with proton acceptors. This matter is discussed again in Section 4.17.3.7. 

The stability of isothiazole derives from the fact that it has an aromatic delocalized ir-electron system. The NMR chemical shifts, which depend, inter alia, on ring currents, and the high stability of the molecular ions in mass spectrometry, are typical of aromatic compounds, and X-ray measurements confirm the partial double bond character of all the bonds of the ring. 

First-order spectra (mulliplels) are observed when the eoupling constant is small compared with the frequency difference of chemical shifts between the coupling nuclei This is referred to as an A n spin system, where nucleus A has the smaller and nucleus X has the considerably larger chemical shift. An AX system (Fig. 1.4) consists of an T doublet and an X doublet with the common coupling constant J x The chemical shifts are measured from the centres of eaeh doublet to the reference resonance. 

Figure 1.4. Two-spin system of type AX with a chemical shift difference which is large compared with the coupling constants (schematic)...

Figure 2.22, HH ROESY diagram of a-pinene (1) with H NMR spectrum [CDCI3, 10% v/v, 25 °C, 500 MHz, section from Sh = 0.84 to 2.34]. Deviations of chemical shifts from those in other experiments (Figs, 2.14, 2.16) arise from solvent effects the methylene protons collapsing in Fig, 2.21 at Sh = 2.19 (200 MHz) display in this experiment an AB system with Sa = 2,17 and Sb = 2.21 (500 MHz)...

The chemical shift of a nucleus depends in part on its spatial position in relation to a bond or a bonding system. The knowledge of such anisotropic effects is useful in structure elucidation. An example of the anisotropic effect would be the fact that axial nuclei in cyclohexane almost always show smaller H shifts than equatorial nuclei on the same C atom (illustrated in the solutions to problems 37, 47, 48, 50 and 51). The y-effect also contributes to the corresponding behaviour of C nuclei (see Section 2.3.4). 

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