Hiickel theory butadiene

To illustrate the latter point, consider the butadiene radical cation (BD+ ). On the basis of Hiickel theory (or any single-determinant Hartree-Fock model) one would expect this cation to show two closely spaced absorption bands of very similar intensity, due to 7i i -> ji2 and ji2 —> JI3 excitation (denoted by subscripts a and v in Figure 28), which are associated with transition moments /xa and /xv of similar magnitude and orientation. Using the approximation fiwm) —3 eV288 the expected spacing amounts to about 0.7 eV. 

The opposite conclusion that correlation increases the dimerization reached in PPP valence bond (VB) theory [36] holds only in comparison to Hiickel theory which is not the semiempirical equivalent to ab initio HF. In fact Hiickel theory would correspond to diagonalization of the one-electron part of the ab initio Fock matrix rather than to HF itself although in Hiickel theory correlation may appear implicitely via the parameters. And indeed, if one considers only the one-electron part of the ab initio Fock matrix (core diagonalization) in a 6-31G basis set the equidistant geometry for trans-butadiene is favored. Inclusion of electron-electron interactions on one-particle level (HF), which corresponds to PPP theory yields an increase of the bond-alternation beyond its experimental value. The inclusion of Jt-n correlations (CCD-level) decreases this value again to the experimental one [16]. 

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. 

The key assumptions in the Hiickel theory involve the integrals in (17.10). The integral 7/ / is assumed to have the same value for every carbon atom in the molecule. (For benzene the six carbons are equivalent, and this is no assnmption. For 1,3-butadiene, CH2CHCHCH2, one would expect for an end carbon and a middle carbon to differ slightly.) Moreover, is assumed to be the same for carbon atoms in different planar hydrocarbons. The integral is assumed to have the same value for any two carbon atoms bonded to each other and to vanish for two nonbonded carbons. The integral Srr is... 

It is possible to treat electrocyclic reactions in another way, namely, via a two-sided correlation diagram approach. This was first worked out by Longuet-Higgins and Abrahamson [14]. Only orbitals (occupied and unoccupied) that are involved in bonds being made or broken during the course of the reaction are included in the diagram. For butadiene, these are the four n MOs already familiar from simple Hiickel theory. For cyclobutene, they are the two n MOs associated with the isolated 2-center n bond and the two a MOs associated with the new C-C a bond. These orbitals and their energies are shown in Fig. 14-20. 

FIGURE 15.19 Hiickel theory predicts this arrangement for the four it electrons in butadiene. A comparison (see text) suggests that this molecule is more stable than expected due to the conjugation of the TT electrons. 

Use the energy level expressions for benzene and for 1,3-butadiene to obtain two different values for the parameter p in the Hiickel theory, using the fact that the strongest ultraviolet absorption in benzene is at a wavelength 180 nm, while the strongest ultraviolet absorption in 1,3-butadiene is at 217 nm. Conpare these values with an accepted value of = —2.71 eV and explain why the values do not agree. 

Such cross-conjugation (where two of the vinyls are conjugated with each other through boron but not simultaneously with the third vinyl35) always lowers the total delocalization energy (DE) of the conjugated atomic set In simple Hiickel MO theory, for example, ( )-l,3,5-hexatriene (37) has a DE of 0.988/3, while 2-vinyl-1,3-butadiene (38) yields a DE of 0.900/3. 

The resulting LBOs are fairly localized, one on Ci — C2 the other on C3—C4. Elowever, the delocalization tails are significant even though we used Hiickel orbitals. These large localization tails reflect the fact that butadiene has some conjugation between the n-bonds and in terms of VB theory is describable by a linear combination of the major Kekule structure and the minor long bond structure. 

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

An analysis of reaction possibilities in the Hiickel-Mobius theory requires us to construct a fully interacting basis set, which is simply a sketch of the transition state, drawn with the maximum possible bonding character (the fewest nodes possible). Next, draw a line to connect the reactant orbitals as they would be connected by conrotatory and disrotatory processes. This gives a complete model of the transition state for butadiene as shown in Fig. 8.49. 

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. 

Calculate the energy levels and coefficients for 1,3-butadiene using Hiickel MO theory. 

Figure 15.17 B shows the aromatic transition state analysis of these reactions. We draw a picture of an opening pathway with the minimum number of phase changes and examine the number of nodes. The four-electron butadiene-cyclobutene system should follow the Mobius/conrotatory path, and the six-electron hexatriene-cyclohexadiene system should follow the Hiickel/disrotatory path. As such, aromatic transition state theory provides a simple analysis of electrocyclic reactions. The disrotatory motion is always of Hiickel topology, and the conrotatory motion is always of Mobius topology.

---