Computed indications

Model computations indicate that for short times, polydispersity is inversely proportional to average size... 

In order to exemplify how the various computed indices can be used in testing the predictions of OEMO theory within the framework of the dynamic model we shall consider once again the problems of conformational isomerism of 1,3-butadiene and geometrical isomerism of 1,2-difluoroethylene. We first consider the cis and tram conformers of 1,3 butadiene. 

The problems facing the static model can be best understood by reference to the various computed indices for difluoromethane at various FCF angles. Comparing the two structures shown above, we note that the total pi overlap population increases as the angle shrinks. Thus, according to the dynamic model, there is F—F pi nonbonded attraction since the difference in the total pi overlap populations is... 

Optimized SCF computations indicate that for the carbon atoms of samrated hydrocarbons any gain in electronic charge, with respect to the ethane carbon, occurs at the 2s level [44]. Further, (9s 5p 6s) [5i 3p 3i] calculations of methane... 

The coefficients (8.38) are still not in a form suitable for computations indices are required to be positive integers in most versions of Fortran. We can get around this easily enough by defining Gn = Dn x (n = 1,2,. .. ), which satisfies the recurrence relation... 

We shall explore how the orbital symmetries and energies of these small molecular fragments contribute to the observed properties of these compounds by using semiempirical electronic structure calculations. Our tools for analysis include an arsenal of computational indices, e.g. overlap populations and Mulliken populations.4 The remainder of this introduction... 

Similar computations indicate that non-bonded H. .. H, H. .. F,or F. .. F distances for eclipsed forms of the ethane series are not seriously in conflict with... 

The experimental and selected computed r(Ln-X) bond lengths are presented in fig. 32. The most important trend that is obvious from the figure is the gradual decrease of r(Ln-X) along the lanthanide row as a result of the well known lanthanide contraction . Although the computations indicate the same trend, they consistently overestimate the bond distances. The best probable values for the equilibrium geometrical parameters are given in tables 16 and 17. They take into account the opposite effects of dimer formation and the harmonic... 

The high metal atom surface-to-volume ratio observed in nanostructured materials not only has importance to the number of active sites in a catalyst, but also can influence the oxygen and other anion-defect chemistry and the observation of metastable phases. Siegel s (1991, 1994) computations indicated that the percentage of metal atoms on the surface of a crystallite increased from a few percent in a 100-nm particle to about 90% in a... 

Various computations indicate that triplet type II 1,4-biradicals exist as a mixture of several conformers with geometries disposed toward product formation, as shown in Sch. 5. The initial biradical rotates such that the p orbital on the hydroxy-substituted site is aligned nearly parallel to the 2,3 C-C bond as required for cyclization and cleavage. The computed percent population of four conformers are shown for valerophenone (R = CH3), but they do not correlate with the product distribution as listed in Table 1. 

The large lead atom might also be hepta- or octa-coordinated, but computations indicate that PbNa7 and PbNas clusters are only weakly bound, with dissociation energies to MX i + X of only 7.9 and 6.7 kcalmol-1, respectively (26.3 kcalmol-1 in PbNag)165. 

Computation indicated that Z is always less than unity, signifying the fact that the congregation of particles in fluidization reduces the rate of fall of the particles, thus prolonging their residence time. At the point for minimum cross-sectional area A the corresponding bed height is... 

The pulsation amplitude for different pump speeds have been computed at three testpoints (TP 1, TP 2, TP 3). The computation indicates, that nearly over the whole speed range the pressure pulsations remain below 3 %. At a speed of 45 rpm the pulsation amplitudes pass a maximum which indicates an acoustical resonance (Fig. 6)... 

Our computations indicate that there is a large activation barrier for this reaction27. Both MINDO/3 and ab initio STO-3G calculations were used in preliminary investigations, and the results of a surface scan by the former in which D3h sym-... 

We cannot, then, expect this approach to understanding chemical reactivity to explain everything. Most attempts to check the validity of frontier orbital theory computationally indicate that the sum of all the interactions of the filled with the unfilled orbitals swamp the contribution from the frontier orbitals alone. Even though the frontier orbitals make a weighted contribution to the third term of the Salem-Klopman equation, they do not account quantitatively for the many features of chemical reactions for which they seem to provide such an uncannily compelling explanation. Organic chemists, with a theory that they can handle easily, have fallen on frontier orbital theory with relief, and comfort themselves with the suspicion that something deep in the patterns of molecular orbitals must be reflected in the frontier orbitals in some disproportionate way. 

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