Simulated Spectrum as a Combination of Statistical Model and ab initio Quantum Chemistry

Simulated Spectrum as a Combination of Statistical Model and ab initio Quantum Chemistry 

The statistics of the long polymer chain (that is inaccessible to explicit quantum chemistry calculations) is now transferred to the small model molecule (that can be conveniently treated on a workstation). Then the simulated line shape for the nucleus K is 

In this formula, pconfig is the experimental configurational statistics of the sample to be simulated it is fully determined by the synthetic conditions and is not subject to change. For ideally atactic poly (propylene), the configurational statistics is easily calculated, pco yig( i 2 3) = ( ) = 0.125, Xi 6 m, r. I x ) is the conditional conforma- 

To allow for deviations from the ideal RIS dihedral values, we replace the d-function in Eq. (3.15) by a Gaussian function Sb(x) = exp(—x /2b ). 

Note that only the nuclei K = A, Bi, B2, Ci, C2 in the central part of the model molecule can be considered representative of an extended polymer chain, as only here the geometry is well defined and the end-group effects can be neglected. As already mentioned, the positions of the y-neighbors of the methine groups Bi, B2 are not fully determined (lacking a definite value for i9 o and i s), so the simulation for these tertiary carbons will be only indicative of a trend. 

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