Ethylene, molecular orbitals

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. 

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. 

These absorptions are ascribed to n-n transitions, that is, transitions of an electron from the highest occupied n molecular orbital (HOMO) to the lowest unoccupied n molecular orbital (LUMO). One can decide which orbitals are the HOMO and LUMO by filling electrons into the molecular energy level diagram from the bottom up, two electrons to each molecular orbital. The number of electrons is the number of sp carbon atoms contributing to the n system of a neuhal polyalkene, two for each double bond. In ethylene, there is only one occupied MO and one unoccupied MO. The occupied orbital in ethylene is p below the energy level represented by ot, and the unoccupied orbital is p above it. The separation between the only possibilities for the HOMO and LUMO is 2.00p. 

As is true for all orbitals a ti orbital may contain a maximum of two electrons Ethylene has two ti electrons and these occupy the bonding ti molecular orbital which is the HOMO The antibondmg ti molecular orbital is vacant and is the LUMO... 

Which molecular orbital of ethylene (tt or tt ) is the most impor 1 tant one to look at in a reaction in which ethylene is attacked by an electrophile J... 

Let us now examine the Diels-Alder cycloaddition from a molecular orbital perspective Chemical experience such as the observation that the substituents that increase the reac tivity of a dienophile tend to be those that attract electrons suggests that electrons flow from the diene to the dienophile during the reaction Thus the orbitals to be considered are the HOMO of the diene and the LUMO of the dienophile As shown m Figure 10 11 for the case of ethylene and 1 3 butadiene the symmetry properties of the HOMO of the diene and the LUMO of the dienophile permit bond formation between the ends of the diene system and the two carbons of the dienophile double bond because the necessary orbitals overlap m phase with each other Cycloaddition of a diene and an alkene is said to be a symmetry allowed reaction... 

Refer to the molecular orbital diagrams of allyl cation (Figure 10 13) and those presented earlier in this chapter for ethylene and 1 3 butadiene (Figures 10 9 and 10 10) to decide which of the following cycloaddition reactions are allowed and which are forbidden according to the Woodward-Floffmann rules... 

This displays the LUMO of ethylene This IS an unoccupied antibonding molecular orbital... 

Structure. The straiued configuration of ethylene oxide has been a subject for bonding and molecular orbital studies. Valence bond and early molecular orbital studies have been reviewed (28). Intermediate neglect of differential overlap (INDO) and localized molecular orbital (LMO) calculations have also been performed (29—31). The LMO bond density maps show that the bond density is strongly polarized toward the oxygen atom (30). Maximum bond density hes outside of the CCO triangle, as suggested by the bent bonds of valence—bond theory (32). The H-nmr spectmm of ethylene oxide is consistent with these calculations (33). 

Fig. 1.23. Rcprcacntation of the molecular orbitals of ethylene. (From W. L. Jorgensen and L. Salem, The Organic Chemist s Book of Orbitals, Academic Press, New York, 1973. Reproduced with permission.)...

This displays the HOMO of ethylene. This is an occupied bonding molecular orbital. 

Lowest unoccupied molecular orbital (or formaldehyde (tapi and ethylene... 

Highest occupied molecular orbital for formaldehyde (tapI and ethylene... 

In ethylene, both the HOMO and LUMO are formed primarily from p orbitals from the two carbons. The carbons lie in the YZ-plane, and so the p,j orbitals lie above and below the C-C bond. In the HOMO, the orbitals have like signs, and so they combine to form a bonding n molecular orbital. In contrast, in the LUMO, they have opposite signs, indicating that they combine to form an antibonding Tt molecular orbital. 

Figure 1.18 A molecular orbital description of the C=C tt bond in ethylene. The lower-energy, tt bonding MO results from a combination of p orbital lobes with the same algebraic sign and is filled. The higher-energy, -tt antibonding MO results from a combination of p orbital lobes with the opposite algebraic signs and is unfilled.

What is wrong with the following sentence "The it bonding molecular orbital in ethylene results from sideways overlap of two p atomic orbitals."... 

Problem 30.1 Look at Figure 30.1, and tell which molecular orbital is the HOMO and which is the LUMO for both ground and excited states of ethylene and 1,3-butadiene. 

Parr, R. G., and Crawford, B. L., Jr., J. Chem. Phys. 16, 526, Molecular orbital calculations of vibrational force constants. I. Ethylene."... 

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