Configurational Splitting in Solution

For the methyl and methine carbons, the situation is essentially the same, and no new aspects occur. 

The ab initio IGLO calculations can be used to calculate the configurational splitting in solution by simply calculating the conformational average for a given configuration (xi,X2,X3). For the reader s convenience, the formula Eq. (3.17) derived in Sect. 3.3.3 is adopted to the special case of the methylene unit A of the model molecule 

The sum is over the geometries with given configuration (xi,X2,X3). In practice, only the conformations with significant probability are taken into account. As for the solid state NMR spectrum, symmetry is used to reduce the number of geometries to be calculated. The conformational statistics I is recomputed for the necessary tempera- 

At higher temperatures, the number of relevant conformations increases sharply because of the underlying Boltzmann statistics. The overall probability of the 90 geometries used in the quantum chemistry calculations is p 0.85 at T == 315 K compared with only p 0.75 at T = 391 K. Computer time considerations impede the ab initio treatment of many 

3 Method of ab initio Simulation of Solid State NMR Spectra 

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In the central part (Sect. 3), the simulation technique will be explained in detail and illustrated by the example of atactic poly(propylene) (Sects. 3.1-3.3). Special sections are devoted to the simulation of the solid state spectrum (Sect. 3.4), the correlation of chemical shift and geometry (Sect. 3.5), a molecular orbital (MO) analysis (Sect. 3.6), the configurational splitting in solution (Sect. 3.7) and the role of the anisotropy of the chemical shift as a source of structural information (Sect. 3.8). 

In the same spirit, the configurational splitting in solution can be calculated. The position of the configuration (xi,X2,X3) is simply the conforma-tionally averaged shift. 

In Eq. (3.17), the sum extends only over those geometries with the correct configuration (xi, X2, X3). It should be noted, that by Eq. (3.17), the configurational splitting in solution may be computed without special assumptions on the geometry dependence of the chemical shift. Only if a simple functional dependence for ok G ) is postulated, the phenomenological parametrisation of the YS uche effect is recovered (Sect. 2.5). 

For the simulation of the configurational splitting in solution, solvent effects must be virtually absent. This can easily be checked by recording the spectra with different solvents. 

Shortly, it will become clear, that the results for the configurational splitting in solution are in very good agreement with experiment. From this, we conclude that neither the single chain statistical model in itself nor the quantum chemistry calculations suffer from severe drawbacks, and that the discrepancy seen in Figs. 57, 58 indicates local conformational order in the glassy state and is not an artifact introduced by the calculation. In view of the numerous approximations and limitations of the PMMA calculation, more definite statements are not justified and must be deferred to the future, when faster computers will become available. 

Moreover, the configurational splitting in solution may be simulated as well. Quantum chemical calculations can thus provide a justification for the empirical y-gawc/ze method which uses a simple increment system to predict the chemical shift. In some systems (e.g. poly (methyl methacrylate)), where a breakdown of the empirical method is experienced, quantum chemistry may successfully predict the splitting as it does not rely on special assumptions. For routine analysis, the higher resolution and the much lower computation time favor the traditional phenomenological approach. In these cases, quantum-chemistry based simulations should be regarded as a complement rather than a replacement. 

The presence of various configurations in a sample gives rise to a configurational splitting in the solution NMR spectrum. This aspect will be discussed in some more detail in Sect. 3.7. 

Fig. 13. Experimental solid state spectrum of atactic poly(propylene) (top) and solution spectrum of configurational splitting in the methylene region (bottom). The broadening in the solid state spectrum is appreciably larger than the configurational splitting. Reprinted with minor changes from [63]...

The other mechanism is called the Fermi contact interaction and it produces the isotropic splittings observed in solution-phase EPR spectra. Electrons in spherically symmetric atomic orbitals (s orbitals) have finite probability in the nucleus. (Mossbauer spectroscopy is another technique that depends on this fact.) Of course, the strength of interaction will depend on the particular s orbital involved. Orbitals of lower-than-spherical symmetry, such as p or d orbitals, have zero probability at the nucleus. But an unpaired electron in such an orbital can acquire a fractional quantity of s character through hybridization or by polarization of adjacent orbitals (configuration interaction). Some simple cases are described later. 

Technetium(II) complexes are paramagnetic with the d5 low-spin configuration. A characteristic feature is the considerable number of mixed-valence halide clusters containing Tc in oxidation states of +1.5 to + 3. This area has been reviewed (42). For convenience, all complexes, except those of [Tc2]6+, are treated together here. EPR spectroscopy is particularly useful in both the detection of species in this oxidation state and the study of exchange reactions in solution. The nuclear spin of "Tc (1 = f) results in spectra of 10 lines with superimposed hyperfine splitting. The d5 low-spin system is treated as a d1 system in the hole formalism (40). 

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