Hiickel theory ethylene

The regioselectivity in radical addition reactions to alkenes in general has successfully been interpreted by a combination of steric and electronic effects1815,47. In the absence of steric effects, regiochemical preferences can readily be explained with FMO theory. The most relevant polyene orbital for the addition of nucleophilic radicals to polyenes will be the LUMO for the addition of electrophilic orbitals it will be the HOMO. Table 10 lists the HOMO and LUMO coefficients (without the phase sign) for the first three members of the polyene family together with those for ethylene as calculated from Hiickel theory and with the AMI semiempirical method48. 

The HOMO-LUMO based reactivity theories are at the heart of mechanistic pictures in organic chemistry /110/ and the simplest prototypical representative with well established pictures of HOMO and LUMO is the ethylene molecule for which Hiickel theory calculations are routine in characterizing its frontier orbitals. While qualitative correlations abound /18,19/, a rigorous quantitative investigation of this simple prototypical polyatomic molecule is specially significant /45,46/ and results from our own calculations are discussed below. 

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. ... 

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. 

There is no set of fundamentally sound values for a and ft to use in Hiickel calculations with heteroatoms. Everything is relative and approximate. The values for energies and coefficients that come from simple calculations on molecules with heteroatoms must be taken only as a guide and not as gospel. In simple Hiickel theory, the value of a to use in a calculation is adjusted for the element in question X from the reference value for carbon a0 by Equation 1.15. Likewise, the ft value for the C=C bond in ethylene ft0 is adjusted for C=X by Equation 1.16. 

That is a quantity, by no means negligible, which Hiickel theory neglects. In order to give an order-of-magnitude to this neglect, let us consider a simple example, that of ethylene, in which there is a transition which transforms the normal ground-state of the molecule (N) to the triplet state (T) ... 

The bent bond picture, later restated in terms of localized molecular orbitals, extends the model presented by Pauling and Slater for ethylene to a stem with three centers. Walsh s model parallels that of Mulliken for the a, w model of the double bond widely used in Hiickel theory. Since the canonical orbitals are good models for the interpretation of photoelectron spectra (see Introduction) we will discuss the Walsh model briefly. 

Dithiosquarate Dithiopheno-tetrathiafulvalene Ethylene-1,2-dithiolate Ethylenedithiotetrathiafulvalene Extended Hiickel Theory... 

Ethylene 1 displays a single sharp line in its p.m.r. spectrum (S = 2-32 p.p.m., external TMS), indicating that rotation about the central C—bonds is rapid on the n.m.r, time scale. The requirement of a center of symmetry imposed by the lack of C=C stretching absorption in the infrared spectrum of 1 (strong Raman band at 1630 cm ) ° is, of course, consistent with a propeller-like structure as well as a planar one, and the steric barrier to coplanarity is considerable. Bond-order calculations, from Hiickel theory and vibrational spectra, indicate that nearly all of the twist in a non-planar structure would involve the C—N bonds rather than the G—G bond. ... 

FIGURE 15.20 Hiickel theory predicts the above arrangement for the two tt electrons in ethylene. 

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. 

Hiickel molecular orbital theory and its application to ethylene and butadiene... 

Hiickel molecular orbital theory benzene, 174 butadiene, 171-173 computational resources, 174 ethylene, 173... 

We have seen so far that MOs resulting from the LCAO approximation are delocalized among the various nuclei in the polyatomic molecule even for the so-called saturated a bonds. The effect of delocalization is even more important when looking to the n electron systems of conjugated and aromatic hydrocarbons, the systems for which the theory was originally developed by Hiickel (1930, 1931, 1932). In the following, we shall consider four typical systems with N n electrons, two linear hydrocarbon chains, the allyl radical (N = 3) and the butadiene molecule (N = 4), and two closed hydrocarbon chains (rings), cyclobutadiene (N = 4) and the benzene molecule (N = 6). The case of the ethylene molecule, considered as a two n electron system, will however be considered first since it is the reference basis for the n bond in the theory. 

A theoretical study of the interaction of sulfur atoms with ethylene within the framework of the Extended Hiickel MO theory has been reported by HoflFmann and co-workers (19). Potential surface calculations revealed two minima for the 8( 02) + C2H4 system. The higher corresponds to vinyl mercaptan formation via C-H bond insertion, and the lower, lying about 20 kcal below the former, to the least-motion, symmetry-allowed addition of sulfur across the double bond. The two are viewed as competing concerted processes. Similar calculations for the... 

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