Htickel orbital systems

Figure 4.16. The n MOs and jt energy levels for an acyclic three-p-orbital system in the simple Htickel method. The MOs are composed of the basis functions (three p AOs) and the eigenvectors (the c s), while the energies of the MOs follow from the eigenvalues (Eq. (4.68)), In the drawings of the MOs, the relative sizes of the AOs in each MO suggest the relative contribution of each AO to that MO. This diagram is for the propenyl radical. The paired arrows represent a pair of electrons of opposite spin, in the fully-occupied lowest MO,, and the single arrow represents an unpaired electron in the nonbonding MO, 4 2> tlie highest n MO, fs, is empty in the radical.

Cycloadditions of Carbenes and Ketens.—Carbenes in which the empty p-orbital is part of a Htickel aromatic system show nucleophilic properties and react with electron-poor alkenes. Diphenylcyclopropenylidene adds 1,4 to tetracyclone, giving, after CO loss, the spiro-system (315). The reaction of cycloheptatrienylidene is more complex. The initial adduct is not isolated but behaves as if it were (316) and loses CO to give an interconverting set of isomeric hydrocarbons which terminate in (317) and (318) in the ratio 1 2. The same set can be produced photochemically but not thermally from the spiro-hydrocarbon (319). ... 

This method is called Extended Htickel because it is in fact an extension, including all the a valence orbitals, of a much earlier method that considers only ir-electron systems in which each atom is represented by one electron in one pz orbital. Matrix elements are obtained as = a and = p, where a and P are empirical parameters for each atomic species. In the simple Htickel formulation butadiene is a four-orbital system and the secular equation can be solved by hand. 

The benzene molecule in its equilibrium configuration is planar. Its symmetry is described by the point group as shown in Fig. 8-l(c). The delocalized n system is represented there by dotted lines. The six pz orbitals contribute to tbe jt system, as simply described by the Htickel approximation. The reduction r, = B2g Hjg E2u can be found as in the previous examples. 

Consider initially the cyclopentadienyl ring system. In the Htickel approximation the one-electron energies of the molecular orbitals are related in a very simple way to the ring size and the symmetry of the particular level thus one finds... 

In contrast to the useful conceptual framework provided by the approximate approach just described, the results of more detailed molecular orbital calculations have on the whole been rather disappointing. Thus, although some semi-empirical SCF treatments were attempted, most of the earlier MO calculations for metallocene systems (18, 161, 162, 163, 164,165) suffered from such deficiencies as the neglect of the a-framework, or the use of various one-electron Hamiltonians, for example the various Wolfsberg-Helmholz techniques. Of late, Drago and his coworkers have carried out further Extended Htickel type computations for a wide range of both metallocene and bis-arene species (153, 154), and similar... 

In 1931, Erich Htickel postulated that monocyclic (single ring) planar compounds that contained carbon atoms with unhybridized atomic p orbitals would possess a closed bond shell of delocalized n electrons if the number of n electrons in the molecule fit a value of 4 + 2 where n equaled any whole number. Because a closed bond shell of n electrons defines an aromatic system, you can use Hiickel s Rule to predict the aromaticity of a compound. For example, the benzene molecule, which has 3 n bonds or 6 n electrons, is aromatic. 

Cyclooctatetraene would be antiaromatic if Htickel s rule applied, so the conjugation of its double bonds is energetically unfavorable. Remember that Htickel s rule applies to a compound only if there is a continuous ring of overlapping p orbitals, usually in a planar system. Cyclooctatetraene is more flexible than cyclobutadiene, and it assumes a nonplanar tub conformation that avoids most of the overlap between adjacent pi bonds. Hiickel s rule simply does not apply. 

We can draw a five-membered ring of sp2 hybrid carbon atoms with all the unhybridized p orbitals lined up to form a continuous ring. With five pi electrons, this system would be neutral, but it would be a radical because an odd number of electrons cannot all be paired. With four pi electrons (a cation), Htickel s rule predicts this system to be antiaromatic. With six pi electrons (an anion), Htickel s rule predicts aromaticity. 

As expected, the Mobius-Htickel method leads to the same predictions. Here, we look at the basis set of orbitals shown in F and G for [1,3]- and [1,5]-rearrangements, respectively. A [1,3]-shift involves four electrons, so an allowed thermal pericyclic reaction must be a Mobius system (p. 1210) with one or an odd number... 

W. Htickel, also provided a basis for a rational description of molecular orbitals in these systems. An extended Htickel theory allowed a study of molecular orbitals throughout chemistry at a certain level of approximation. 

If the ring were sufficiently large that the twist between individual orbitals was small, such a system would not necessarily be less stable than the normal array of atomic orbitals. This same analysis points out that in such an array the Htickel rule is reversed and aromaticity is predicted for the An rr-electron systems. 

The selection rules for [tt4 + tt2 ] and other cycloaddition reactions can also be derived from consideration of the aromaticity of the TS3 In this approach, the basis set p orbitals are aligned to correspond with the orbital overlaps that occur in the TS. The number of nodes in the array of orbitals is counted. If the number is zero or even, the system is classified as a Htickel system. If the number is odd, it is a Mobius system. Just as was the case for ground state molecules (see p. 716), Htickel systems are stabilized with 4 + 2 electrons, whereas Mobius systems are stabilized with 4n electrons. For the [tt4 + tt2] suprafacial-suprafacial cycloaddition the transition state is aromatic. 

Basis set orbital analysis of the hexatriene-cyclohexadiene system leads to the conclusion that the disrotatory process will be favored. The basis set orbitals for the conrotatory and disrotatory transition states are shown below. Here, with six electrons involved, it is the disrotatory mode (Htickel system) that gives a stabilized TS. 

The Woodward-Hoffmann orbital symmetry rules are not limited in application to the neutral polyene systems that have been discussed up to this point. They also apply to charged systems, just as the Htickel aromaticity rule can be applied to charged ring systems. The conversion of a cyclopropyl cation to an allyl cation is the simplest... 

An alternative analysis of sigmatropic reactions involves drawing the basis set atomic orbitals and classifying the resulting system as Htickel or Mobius in character. When this classification has been done, the electrons involved in the process are counted to determine if the TS is aromatic or antiaromatic. The conclusions reached are the same as for the frontier orbital approach. The suprafacial 1,3-shift of hydrogen is forbidden but the suprafacial 1,5-shift is allowed. Analysis of a 1,7-shift of hydrogen shows that the antarafacial shift is allowed. This analysis is illustrated in Figure 10.31. These conclusions based on orbital symmetry considerations are supported by HF/6-31G calculations, which conclude that 1,5-shifts should be suprafacial, whereas... 

In the simple Htickel model the approximations are taken to the limit. Only planar conjugated systems are considered. The o-orbitals, which are symmetric with respect to a reflection in the molecular plane, are neglected. Only the Ji-electrons (antisymmetric with respect to the molecular mirror plane) are considered. The overlap matrix... 

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