Electronic wave function ethylene

For some systems a single determinant (SCFcalculation) is insufficient to describe the electronic wave function. For example, square cyclobutadiene and twisted ethylene require at least two configurations to describe their ground states. To allow several configurations to be used, a multi-electron configuration interaction technique has been implemented in HyperChem. 

Then, the electronic wave function of the ar-electron system is constructed from ethylene-like MOs. For example, for structure A of naphthalene the wave functions is ... 

A quantitative treatment of tt complex formation is, however, more complicated, since it is generally recognized that all three wave functions are necessary for an accurate description of the bond. For instance, it has been pointed out by Orgel (27) that n complex stability cannot solely be the result of n electron donation into empty metal d orbitals, since d and ions (Cu+, Ag+, Ni , Rh+, Pt , Pd++) form some of the strongest complexes with poor bases such as ethylene, tt Complex stability would thus appear to involve the significant back-donation of metal d electrons into vacant antibonding orbitals of the olefin. Because of the additional complication of back-donation plus the uncertainty of metal surface orbitals, it is only possible to give a qualitative treatment of this interaction at the present time. 

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... 

The wave function is an extension of the one we used for the dissociation of ethylene. We now have 18 electrons in nine core orbitals, and six electrons in the three a and three tt orbitals that will make up the C—C bonds. As before, the valence orbitals are allowed to breathe (see Eqs. (16.1) and (16.2) for the linear combinations) as the system changes. According to the Weyl dimension formula... 

The key to get a diabatic electronic state is a strict constraint i.e. keep local symmetry elements invariant. For ethylene, let us start from the cis con-former case. The nuclear geometry of the attractor must be on the (y,z)-plane according to Fig.l. The reaction coordinate must be the dis-rotatory displacement. Due to the nature of the LCAO-MO model in quantum computing chemistry, the closed shell filling of the HOMO must change into a closed shell of the LUMO beyond 0=n/4. The symmetry of the diabatic wave function is hence respected. Mutatis mutandis, the trans conformer wave function before n/4 corresponds to a double filling of the LUMO beyond the n/4 point on fills the HOMO twice. At n/4 there is the diradical singlet and triplet base wavefunctions. 

The main result that emerges from the discussions of particular eases is that it has proved possible to give a description of a molecule in terms of equivalent orbitals which are approximately localised, but which can be-transformed into delocalised molecular orbitals without any change in the value of the total wave function. The equivalent orbitals are closely associated with the interpretation of a chemical bond in the theory, for, in a saturated molecule, the equivalent orbitals are mainly localised about two atoms, or correspond to lone-pair electrons. Double and triple bonds in molecules such as ethylene and acetylene are represented as bent single bonds, although the rather less localised o-n description is equally valid. 

A ghost orbital pt is imagined as being attached to each atom of the metal. This orbital represents that part of the wave function of the atom which is antisymmetric with respect to the plane of the ethylene molecule. It is supposed also that each atom contributes one electron. 

Fig. 18. Wave functions of the bonding electrons in the molecule of ethylene, G2H4.

This separation of the cr framework and the re bond is the essence of Hiickel theory. Because the re bond in ethylene in this treatment is self-contained, we may treat the electrons in it in the same way as we do for the fundamental quantum mechanical picture of an electron in a box. We look at each molecular wave function as one of a series of sine waves, with the limits of the box one bond length out from the atoms at the end of the conjugated system, and then inscribe sine waves so that a node always comes at the edge of the box. With two orbitals to consider for the re bond of ethylene, we only need the 180° sine curve for re and the 360° sine curve for re. These curves can be inscribed over the orbitals as they are on the left of Fig. 1.23, and we can see on the right how the vertical lines above and below the atoms duplicate the pattern of the coefficients, with both c and c2 positive in the re orbital, and c positive and c2 negative in re. ... 

Ethylene has the well-known classical >2/1 structure with a barrier to rotation. The next in complexity of the simple hydrides is the methyl radical CH3. The obvious (sp2) planar arrangement can only accommodate six of the seven valence electrons. The electronic configuration of this molecule can therefore not be described in terms of either atomic wave functions or hybrid orbitals. An alternative approach is to view the structure of the methyl radical as a reduced-symmetry form, derived from the structure of methane, to be considered next. 

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