Ethylene atom distances

The full ab-initio molecular dynamics simulation revealed the insertion of ethylene into the Zr-C bond, leading to propyl formation. The dynamics simulations showed that this first step in ethylene polymerisation is extremely fast. Figure 2 shows the distance between the carbon atoms in ethylene and between an ethylene carbon and the methyl carbon, from which it follows that the insertion time is only about 170 fs. This observation suggests the absence of any significant barrier of activation at this stage of the polymerisation process, and for this catalyst. The absence or very small value of a barrier for insertion of ethylene into a bis-cyclopentadienyl titanocene or zirconocene has also been confirmed by static quantum simulations reported independently... 

Fig. 2. Time-evolution of the methyl/ethyl C-C distances for both the zirconocene and the corresponding titanocene catalyst. The two curves starting at around 3.2 A represent the distance between the methyl carbon atom and the nearest-by ethylene carbon atom in the zirconocene-ethylene and the titanocene-ethylene complex, respectively. The two curves starting at around 1.35 A reflect the ethylene internal C-C bond lengths in the two complexes.

Fig. 3. Time evolution of the distance between the Zr atom and each of the three hydrogen atoms belonging to the methyl group (the original methyl group bonded to the Zr) in the zirconocene-ethylene complex. The time-evolution of one of the hydrogen atoms depicted by the dotted curve shows the development of an a-agostic interaction. Later on in the simulation (after about 450 fs) one of the other protons (broken curve) takes over the agostic interaction (which is then a 7-agostic interaction).

FIGURE 5 1 (a) The planar framework of u bonds in ethylene showing bond distances and angles (b) and (c) The p orbitals of two sp hybridized carbons overlap to produce a tt bond (d) The electrostatic potential map shows a region of high negative potential due to the tt elec trons above and below the plane of the atoms... 

In ethane it was possible to consider the C-H distance as a parameter and to evaluate it as 1.09 0.03 A. In the case of the other hydrocarbons studied in this investigation (aside from ethylene) there are so many structural parameters that the experimental evaluation of the C-H distance cannot be carried out conveniently. We have accordingly assumed values for this distance in these substances, namely, C-H = 1.09 A. for a carbon atom which forms four single bonds to... 

To monitor a possible influence of molecular products of photolysis of ethylene (acetylene, ethane, and butane) on the sensor, a second sensor was positioned at a distance of 50 cm from the photolysis zone. The second sensor was designed to introduce corrections into the readings of the movable sensor. The specified distance was chosen so that atoms and radicals produced in the lower part of the vessel could not reach the... 

The generalized Woodward-Hoffmann rule suggests that a synchronous addition of disulfonium dications at the double C=C bond of alkenes would be a thermally forbidden process and so would be hardly probable. Simulation of the frontal attack by ethylene on l,4-dithioniabicyclo[2.2.0]hexane 115 gave no optimal structure of an intermediate complex. On the other hand in the lateral approach of the reactants, orbital factors favor attack of the double bond by one of the sulfonium sulfur atoms of the dication. This pattern corresponds to SN2-like substitution at sulfur atom as depicted in Figure 5. Using such a reactant orientation, the structure of intermediate jc-complex was successfully optimized. The distances between the reaction centers in the complex, that is, between the carbon atoms of the ethylene fragment and the nearest sulfur atom of the dication, are 2.74 and 2.96 A, respectively. 

The results are insensitive to rotation of the molecule in its plane, as long as the molecular centre is kept fixed above the central Ni atom, at a distance of 2 A. The shift of the ethylene Tf-level is correctly calculated. 

The units by which crystallographers describe interatomic distances are Angstrom units (A = 10 8 cm.). Normal values for carbon-carbon interatomic distances are 1.34 A for a double bond (as in ethylene) and 1.54 A (as for-diamond) for a single bond. In a truly aromatic compound (such as benzene) the C-C bond length, as mentioned above, is 1.39 A. C-C-C angles are 109.5° for a tetrahedral carbon atom (sp3) and 120.0° for a trigonal carbon atom (sp2). 

Substituted ethylenes, with hydrogen atoms replaced by various alkyl groups, have a common feature in their electronic spectra, i.e. an absorption band at ca. 164 — 180 nm. This band is interpreted to show that the delocalization of the electron pair is largely confined to the vicinity of the unsaturated centre, commonly referred to as the C=C double bond. If the de-localization is assumed not to exceed a linear distance of one bond length on either side of the double bond, the electron pair remains in a linear potential box of width 3d, with allowed energy levels of... 

The electronic overlap populations in all three cases were calculated from the one electron Extended Hiickel MO s. For the photocyclizations of 1,2-difuryl ethylenes very similar results were obtained also from minimal basis set ab-initio wavefunctions l The possibility of obtaining useful reactivity analyses from wave-functions which are easily available even for large systems could prove to be an important practical consideration for further applications of this method. The dependence on Sri sj ill (5) ensures that electronic overlap populations show the desirable physical characteristics for their use as reactivity measures strong falling-off with increasing interatomic distance and proper directional dependence. This last point is of particular significance for bond formation in polyenes. Thus for two C 2 p atomic... 

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