The Ethylene Molecule

It is a property of linear, homogeneous differential equations, of which the Schroedinger equation is one. that a solution multiplied by a constant is a solution and a solution added to or subtracted from a solution is also a solution. If the solutions Pi and p2 in Eq. set (6-13) were exact molecular orbitals, id v would also be exact. Orbitals p[ and p2 are not exact molecular orbitals they are exact atomic orbitals therefore. j is not exact for the ethylene molecule. 

Fig. 22.1. (a) The ethylene molecule or monomer (b) the monomer in the activated state, ready to polymerise with others (<)-(f) the ethylene polymer ("polyethylene") the chain length is limited by the addition of terminators like —OH. The DP is the number of monomer units in the chain. 

The remaining AOs are the four H 1, two C 1, and four C 2p orbitals. All lie in the molecular plane. Only two combinations of the C 2s and H U orbitals meet the molecular symmetry requirements. One of these, nearest-neighbor atoms. No other combination corresponds to the symmetry of the ethylene molecule. 

In order to understand the physical properties and reactivity patterns of S-N compounds it is particularly instructive to compare their electronic structures with those of the analogous organic systems.On a qualitative level, the simplest comparison is that between the hypothetical HSNH radical and the ethylene molecule each of these units can be considered as the building blocks from which conjugated -S=N- or -CH=CH-systems can be constructed. To a first approximation the (j-framework of... 

Ethylene is sometimes known as the king of petrochemicals hecause more commercial chemicals are produced from ethylene than from any other intermediate. This unique position of ethylene among other hydrocarbon intermediates is due to some favorable properties inherent in the ethylene molecule as well as to technical and economical factors. These could be summarized in the following ... 

The shape of the ethylene molecule has been learned by a variety of types of experiments. Ethylene is a planar molecule—the four hydrogen and the two carbon atoms all lie in one plane. The implication of this experimental fact is that there is a rigidity of the double bond which prevents a twisting movement of one of the CHj groups relative to the other. Rotation of one CHt group relative to the other—with the C—C bond as an axis—must be energetically restricted or the molecule would not retain this flat form. 

Let us now apply these results to the ethylene molecule (Fig. 14), for which we attempt to build the bonding molecular orbitals. Clearly there are three symmetry planes. Two of these are of special interest... 

Unsaturated organic molecules, such as ethylene, can be chemisorbed on transition metal surfaces in two ways, namely in -coordination or di-o coordination. As shown in Fig. 2.24, the n type of bonding of ethylene involves donation of electron density from the doubly occupied n orbital (which is o-symmetric with respect to the normal to the surface) to the metal ds-hybrid orbitals. Electron density is also backdonated from the px and dM metal orbitals into the lowest unoccupied molecular orbital (LUMO) of the ethylene molecule, which is the empty asymmetric 71 orbital. The corresponding overall interaction is relatively weak, thus the sp2 hybridization of the carbon atoms involved in the ethylene double bond is retained. 

In the first investigation 20), ethylene in the collision chamber was bombarded with positive ions, and the intensities of the fragment ions, obtained after the charge exchange, were recorded. The mass spectra were thus not normalized. At low pressure only primary ions were observed that were formed from ethylene in the charge exchange, but at higher pressures also secondary and tertiary ions were obtained as a result of ion-molecule reactions between the primary ions and the ethylene molecules in the collision chamber. 

The accuracy of LDF calculations in the prediction of surface geometries not only holds for clean metal surfaces such as the W(001) surface discussed above, but is also found for adsorbates such as H (27), O (28), and S (29) on Ni(OOl) surfaces. Rather than going into detail on clean and adsorbate covered surfaces, we will now focus on the description of the C-C bond by LDF theory. To this end, we first discuss a layer of condensed benzene rings, i.e. a graphite monolayer, and then focus our attention on the ethylene molecule. 

Rotational Barrier in Ethylene. It is well known that the rotational barrier of the ethylene molecule cannot be adequately described by a single reference Hartree-Fock calculation SCF calculations on this level resulted in values of 126 kcal/mole (30) and 129 kcal/mole (31) whereas the experimental value is 65 kcal/mole (32). Open-shell ab initio calculations of double zeta+polarization quality give the more acceptable value of 48 kcal/mole (33). Inclusion of correlation such as in CEPA calculations yield theoretical results within the experimental error bar (34), albeit at a considerable computational cost. 

Using local spin density functional (LSDF) theory, we obtain 70 kcal/mole for the rotational barrier of the ethylene molecule (35). In these calculations, we use the equivalent of a double-zeta+polarization basis set, i.e. for C two 2s functions. 

Table I. Bond lengths (in A) and bond angles (in degrees) for the ethylene molecule...

Ethylene, C2H4, can adsorb in two modes the weaker Jt-bonded ethylene, in which the C=C double bond is above a single metal atom, or the stronger di-cr bonded ethylene in which the two C-atoms of the ethylene molecule bind to two metal atoms (Fig. 6.37). We consider the (111) metal surface. Hydrogen adsorbs dis-sociatively and is believed to reside in the threefold hollow sites of the metal. 

Consider first the ethylene molecule. Its geometrical structure is shown in Fig. 5. The s, py and pz atomic orbitals of the carbon atoms are assumed to be hybridized. This sp2 hybridization implies H-C-H bond angles of 120°, approximately in agreement with experimental results. The remaining two px orbitals are thus available to contribute to a -electron system in the molecule. Here again, the two linear combinations of atomic orbitals yield bonding and... 

Fig. 5 The ethylene molecule showing only the single (o) bonds.

As the ethylene molecule contains a total of 16 electrons, there are but two that are available to occupy the n system. Two pairs of electrons are assumed to Ell the two Is atomic orbitals of the carbon atoms. Five pairs of electrons contribute to the a orbitals that represent single bonds in Fig. 5. Thus, the two... 

A more realistic use of free-electron simulation occurs with conjugated systems, assumed to be characterized by a number of electrons delocalized over the entire molecule. The simplest example is the ethylene molecule, C2H4. From the known planar structure... 

The first isolable alkenetitanium complex, the bis(pentamethylcyclopentadienyl)-titanium—ethylene complex 5, was prepared by Bercaw et al. by reduction of bis(penta-methylcyclopentadienyl)titanium dichloride in toluene with sodium amalgam under an atmosphere of ethylene (ca. 700 Torr) or from ( (n-C5Mc5)2Ti 2(fJ-N2)2 by treatment with ethylene [42], X-ray crystal structure analyses of 5 and of the ethylenebis(aryloxy)trimethyl-phosphanyltitanium complex 6 [53] revealed that the coordination of ethylene causes a substantial increase in the carbon—carbon double bond length from 1.337(2) A in free ethylene to 1.438(5) A and 1.425(3) A, respectively. Considerable bending of the hydrogen atoms out of the plane of the ethylene molecule is also observed. By comparison with structural data for other ethylene complexes and three-membered heterocyclic compounds, the structures of 5 and 6 would appear to be intermediate along the continuum between a Ti(11)-ethylene (4A) and a Ti(IV)-metallacyclopropane (4B) (Scheme 11.1) as... 

Four different experiments were realized by labeling either the methanol or the ethylene molecules (Figure 7). The reactions were studied in static conditions adsorbing either methanol (A and B) or ethylene (C and D) prior to the second reactants. The l C-NMR spectra of Figure 7 reveals that the order of adsorption of the reactants is very important for the reactivities at first, surface alkylation occurs and is followed by separated reaction pathways for CH3OH and C2H/. 

The ethylene- and catalyst-laden solvent is injected continuously into the reactor at 250-300°C and 1300 psi where the ethylene molecules react to create almost exclusively C4, Cg, Cs, and Cio, straight-chain alpha olefins in the proportions shown in Table 21-3. 

The bonding in ethylene is based initially on one C-C CT bond together with four C-H a bonds, much as we have seen in ethane. We are then left with a p orbital for each carbon, each carrying one electron, and these interact by side-to-side overlap to produce a IX bond (Figure 2.15). This makes the ethylene molecule planar, with bond angles of 120°, and the TX bond has its electron density above and below this plane. The combination of the C-C ct bond and the C-C Jt bond is what we refer to as a double bond note that we cannot have Jt bond formation... 

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