Bond error statistics

Another example for error statistics is given in Tables 2 and 3 for elements of the second row. Complete statistics for all second-row elements Na-Cl have so far only been published for two methods, MSINDO and MNDO/d. Both methods perform similar for the calculation of heats of formation. The agreement with experimental bond lengths seems to be slightly better with MSINDO than with MNDO/d, but as for... 

The value of the torsional energy increment has been variously estimated, but TORS = 0.42 kcal mol was settled on for the bond contribution method in MM3, In the full statistical method (see below), low-frequency torsional motion should be calculated along with all the others so the empirical TORS inererneut should be zero. In fact, TORS is not zero (Allinger, 1996). It appears that the TORS inererneut is a repository for an energy eiror or errors in the method that are as yet unknown. 

Computer simulation is an experimental science to the extent that calculated dynamic properties are subject to systematic and statistical errors. Sources of systematic error consist of size dependence, poor equilibration, non-bond interaction cutoff, etc. These should, of course, be estimated and eliminated where possible. It is also essential to obtain an estimate of the statistical significance of the results. Simulation averages are taken over runs of finite length, and this is the main cause of statistical imprecision in the mean values so obtained. 

Heats of formation, molecular geometries, ionization potentials and dipole moments are calculated by the MNDO method for a large number of molecules. The MNDO results are compared with the corresponding MINDO/3 results on a statistical basis. For the properties investigated, the mean absolute errors in MNDO are uniformly smaller than those in MINDO/3 by a factor of about 2. Major improvements of MNDO over MINDO/3 are found for the heats of formation of unsaturated systems and molecules with NN bonds, for bond angles, for higher ionization potentials, and for dipole moments of compounds with heteroatoms. 

In this contribution, we report equilibrium modulus and sol fraction measurements on diepoxidet-monoepoxide-diamine networks and polyoxypropylene triol-diisocyanate networks and a comparison with calculated values. A practically zero (epoxides) or low (polyurethanes) Mooney-Rivlin constant C and a low and accounted for wastage of bonds in elastically inactive cycles are the advantages of the systems. Plots of reduced modulus against the gel fraction have been used, because they have been found to minimize the effect of EIC, incompleteness of the reaction, or possible errors in analytical characteristics (16-20). A full account of the work on epoxy and polyurethane networks including the statistical derivation of various structural parameters will be published separately elsewhere. 

Fig.20. Order parameter profiles m(z)=([pA(z)-pB(z)])/([pA(z)+pB(z)]), where pA(z), pB(z) are densities of A-monomers or B-monomers at distance z from the left wall, for LxLx20 films confining a symmetric polymer mixture, polymers being described by the bond fluctuation model with N=32, ab=- aa=- bb=8 and interaction range 6. Four inverse temperatures are shown as indicated. In each case two choices of the linear dimension L parallel to the film are included. While for e/kBT>0.02 differences between L=48 and L=80 are small and only due to statistical errors (which typically are estimated to be of the size of the symbols), data for e/kBT=0.018 clearly suffer from finite size effects. Broken straight lines indicate the values of the bulk order parameters mb in each case [280]. Arrows show the gyration radius and its smallest component in the eigencoordinate system of the gyration tensor [215]. Average volume fraction of occupied sites was chosen as 0.5. From Rouault et al. [56].

Head-to-Head and Head-to-Tail Linkages. Errors in the linkages between successive monomeric units of the poljrmers are possible (and always statistically present). The effect of head-to-head (HH) and head-to-tail (HT) bonds in the XPS core levels spectra of substituted polymers have been computed and found at the limit of the sensitivity of the technique (e.g. ). The control of these linkages during the synthesis is difficult and the number of polymers that can be prepared with 100% of HH or HT linkages is small (43). 

Zambelli et al. reported on the mechanism of styrene polymerization [36]. They showed that the main chain of the syndiotactic polymer has a statistically trans-trans conformation. It was established then the double-bond opening mechanism in the syndiospecific polymerization of styrene involves a cis opening. The details in the control of the monomer coordination for this polymerization mechanism were examined by Newman and Malanga using detailed, 3C NMR. It was shown through the analysis of tacticity error (rmrr) that the tacticity in the polymer is chain-end controlled and that the last monomer added directs the orientation and coordination of the incoming monomer unit prior to insertion [37]. 

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