Molecular orbital calculations ethylene molecules

HMO theory is named after its developer, Erich Huckel (1896-1980), who published his theory in 1930 [9] partly in order to explain the unusual stability of benzene and other aromatic compounds. Given that digital computers had not yet been invented and that all Hiickel s calculations had to be done by hand, HMO theory necessarily includes many approximations. The first is that only the jr-molecular orbitals of the molecule are considered. This implies that the entire molecular structure is planar (because then a plane of symmetry separates the r-orbitals, which are antisymmetric with respect to this plane, from all others). It also means that only one atomic orbital must be considered for each atom in the r-system (the p-orbital that is antisymmetric with respect to the plane of the molecule) and none at all for atoms (such as hydrogen) that are not involved in the r-system. Huckel then used the technique known as linear combination of atomic orbitals (LCAO) to build these atomic orbitals up into molecular orbitals. This is illustrated in Figure 7-18 for ethylene. 

Ultra high vacuum studies of nickel and platinum with simple organic molecules like olefins and arenes are described. These surface chemistry studies were done as a function of surface crystallography and surface composition. The discussion is limited to the chemistry of methyl isocyanide, acetonitrile, benzene and toluene, pyridine, trimethylphosphine, ethylene, acetylene and saturated hydrocarbons. Molecular orbital calculations are presented that support the experimental identification of the importance of C-H-M metal bonding for metal surfaces. 

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. 

Figures 1.18-1.20 are another type of representation of the ethylene molecule derived from molecular orbital calculations. Figure 1.18 is a log scale plot of the <7-electron density. It shows the highest density around the nuclear positions as indicated by the pronounced peaks corresponding to the atomic positions but also indicates the continuous nature of the cr-electron distribution. A representation of the TT-electron density is given in Fig, 1.19. This represents the density in a plane...

In the crystal the atoms of this molecule are found to be distributed in three planes Hie two tolyl rings are rotated by 24° (trans to Br) and 68° (cis to Br) with respect to the ethylene plane. Semiempirical Huckel molecular orbital (MO)-type calculations give essentially the same angles in the crystal, but predict 35° and 45° for these angles in the Bee molecule. 

To take a concrete example, any MO calculation of the electronic structure of the ethene (ethylene) molecule wiU generate two lowest MOs (almost degenerate) which are just the in-phase and out-of-phase linear combinations of the basis functions used to describe the Is shells of the carbon atoms. The fact that they occur as molecular orbitals rather than remaining actually unchanged as atomic orbitals is simply an artifact of the symmetry of ethene the MOs are computed as symmetric or antisymmetric with respect to the operations of the point group which in this case includes reflection in a plane perpendicular to the C—C axis. If a calculation is carried through on the isoelectronic methanal (formaldehyde) molecule the oxygen Is AO and the carbon Is AO survive the calculation almost unscathed as the lowest MOs . 

Table 7 summarizes several predictions of mid-sized aromatic molecules from the study of Matsuzawa and Dixon. The p value for a molecule with the inversion symmetry operation (benzene) is zero from symmetry arguments. Note that there are sizeable deviations among the experimental observations of p and Y values, as they are also properties difficult to measure. Agreement in Table 7 should be considered reasonably good. Matsuzawa and Dixon have also compared their calculated y values of ethylene, frans-butadiene, and trans-hexatriene with those obtained from ab initio molecular orbital methods the results from their study show that B-LYP calculations are more accurate than those at the Hartree-Fock level and are of comparable accuracy to MP2 results. 

---