Ethylene, atomic orbital model

The effectiveness of the second type of overlap presumably determines the extent of oMnic character of tho epoxide. That ethylene oxides are less unaaturated in character than the corresponding cyclopropane derivatives is then attributable to a less favorable oxygen atomic-orbital orientation. The Walsh model is a satisfactory one in that it predicts accurately the C—H bond force constants... 

Information corresponding to the k populations of the orbital model is recovered in the quadrupole polarization of the atomic charge densities, a property of the total charge density. A quadrupolar polarization of the density along the z-axis, eqn (6.48), has the form of a d i orbital, a removal of charge from a plane and its concentration in an axial direction perpendicular to the plane (Fig. 6.1) for < 0. In benzene and ethylene, with the z-axis perpendicular to the plane containing the nuclei, Qjj(C) = — 3.34 and =... 

The interaction of atomic orbitals giving rise to molecular orbitals is the simplest type of conjugation. Thus in ethylene the two p orbitals can be described as being conjugated with each other to make the n bond. The simplest extension to make longer conjugated systems is to add one p orbital at a time to the n bond to make successively the n components of the allyl system with three carbon atoms, of butadiene with four, of the pentadienyl system with five, and so on. Hiickel theory applies, because in each case we separate completely the n system from the a framework, and we can continue to use the electron-in-the-box model. 

A possible explanation for the calculated trend in the metal ion binding energies to ethylene, which will be discussed for the triply bonded substrates, could lie in a consideration of the Dewar-Chatt-Duncanson donor-acceptor model for bridging-type metal-olefin complexes. Their proposed two-way interaction involves mixing of the olefin n electrons with a metal (n + l)sp a hybrid atomic orbital (L —> M, for short) and simultaneous back donation (M L) of metal nd electrons of appropriate symmetry into the olefin k molecular orbital MO. For the monocation metal ions the latter-type interaction should be less favourable due to stabilizaion of the nd electrons by the charge on the metal. L M should be favoured for the same reason stabilization of the (n + l)s and (n+ l)p orbitals by the + 1 charge. 

The Linear Combination of Atomic Orbitals (LCAO) approximation is fundamental to many of our current models of chemistry. Both the vast majority of the calculational programs that we use, be they ab initioy density functional, semiempirical molecular orbital, or even some sophisticated force-fields, and our qualitative understanding of chemistry are based on the concept that the orbitals of a given molecule can be built from the orbitals of the constituent atoms. We feel comfortable with the Ji-HOMO (Highest Occupied Molecular Orbital) of ethylene depicted as a combination of two carbon p-orbitals, as shown in Fig. 2.1, although this is not a very accurate description of the electron density of this Molecular Orbital (MO). The use of the Jt-Atomic Orbitals (AOs), however, makes it easier to understand both the characteristics of the MO itself and the transformations that it can undergo during reactions. 

According to the orbital overlap model, a carbon-carbon double bond consists of one sigma bond formed by the overlap of sp hybrid orbitals and one pi bond formed by the overlap of parallel 2p atomic orbitals. It takes approximately 264 kJ/mol (63 kcal/mol) to break the pi bond in ethylene. 

In contrast to VBT, "full-blown" MOT considers the electrons in molecules to occupy molecular orbitals that are formed by linear combinations (addition and subtraction) of all the atomic orbitals on all the atoms in the structure. In MOT, electrons are not confined to an individual atom plus the bonding region with another atom. Instead, electrons are contained in MOs that are highly delocalized—spread across the entire molecule. MOT does not create discrete and localized bonds between neighboring atoms. An immediate benefit of MOT over VBT is its treatment of conjugated tt systems. We don t need a "patch" like resonance to explain the structure of a carboxylate anion or of benzene it falls naturally out of the delocalized nature of the MOs. The MO models of simple molecules like ethylene or formaldehyde also lead to bonding concepts that are pervasive in organic chemistry. 

In the case of ethylene the a framework is formed by the carbon sp -orbitals and the rr-bond is formed by the sideways overlap of the remaining two p-orbitals. The two 7r-orbitals have the same symmetry as the ir 2p and 7T 2p orbitals of a homonuclear diatomic molecule (Fig. 1.6), and the sequence of energy levels of these two orbitals is the same (Fig. 1.7). We need to know how such information may be deduced for ethylene and larger conjugated hydrocarbons. In most cases the information required does not provide a searching test of a molecular orbital approximation. Indeed for 7r-orbitals the information can usually be provided by the simple Huckel (1931) molecular orbital method (HMO) which uses the linear combination of atomic orbitals (LCAO), or even by the free electron model (FEM). These methods and the results they give are outlined in the remainder of this chapter. 

The n molecular orbitals described so far involve two atoms, so the orbital pictures look the same for the localized bonding model applied to ethylene and the MO approach applied to molecular oxygen. In the organic molecules described in the introduction to this chapter, however, orbitals spread over three or more atoms. Such delocalized n orbitals can form when more than two p orbitals overlap in the appropriate geometry. In this section, we develop a molecular orbital description for three-atom n systems. In the following sections, we apply the results to larger molecules. 

It turns out, in fact, that the electron distribution and bonding in ethylene can be equally well described by assuming no hybridization at all. The "bent bond" model depicted at the right requires only that the directions of some of the atomic-p orbitals be distorted sufficiently to provide the overlap needed for bonding. So one could well argue that hybrid orbitals are not real they do turn out to be convenient for understanding the bonding of simple molecules at the elementary level, and this is why we use them. 

Recall that in the VSEPR model a double bond acts as one effective pair. Thus in the ethylene molecule each carbon is surrounded by three effective pairs. This model requires a trigonal planar arrangement with bond angles of 120 degrees. What orbitals do the carbon atoms use in this molecule The molecular geometry requires a planar set of orbitals at angles of 120 degrees. Since... 

However, better results are obtained if specific values Kpq are taken, i.e. different proportionality factors for different pairs of atoms and orbitals, and a special formula is used for one-center off-diagonal elements (for details, see 58>). The K factors are not fitted on empirical data but obtained by trial and error after ab initio SCF calculations on model compounds (for ethylene, KCc — 1.0 for valence-shell orbitals, Xhh = 1.18, Ka,n = 1.05, K p,H = 0.98). 

Figure 4.8 illustrates how these differences influence available orbitals. In the [100] plane, e, orbitals emerge perpendicular and parallel to the surface, orbitals at 4S Empty or partially htled Cg orbitals overlap the l5 orbital of hydrogen in two locations, with one g orbital at the on top position or with hve at the position one half of an atomic layer into the surface. Similar situations prevail for other surface planes. With this model, it is now possible to visualize interactions of molecules such as hydrogen and ethylene with the nickel surface. Figure 4.9 shows the possibilities. Currently these models are only qualitative and much more... 

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