The butadiene molecule

The Hiickel secular equation for the linear chain with N = 4 is  

33For the definition of alternant hydrocarbons, see Magnasco (Magnasco, 2007, 2009a). 

Proceeding as we did for the allyl radical, it is easily seen that the electron charge distribution is uniform (one n electron onto each carbon atom, alternant hydrocarbon) and the spin density is zero, as expected for a state with S = Ms = 0 since the two bonding MOs are fully occupied by electrons with opposite spin. The delocalization (or conjugation) energy for linear butadiene is  

This description is in agreement with the classical formula 

Problem 9.7 Relate the structures of the isoelectronic molecules acetylene and nitrogen including a comparison of the corresponding molecular orbital description. 

The a framework is a clear extension of what was considered for ethylene. Let us then consider the four tt m.o.s as linear combinations of the four 2p carbon orbitals having axes perpendicular to the plane of the nuclei (the xy plane)  

It is clear that there is overlap not only in each pair zj, Z2 and Z3, Z4 but also between Z2 and Z3. Recalling the study of a linear H3 molecule (page 141), we can relate the successive energies of the four tt m.o.s to the number of nodes (besides the angular nodes of the p orbitals) in various combinations. Thus, the 7T orbital of minimum energy must be bonding for each pair of adjacent atoms (no new nodes)  

The next linear combination (next in energy) must have one node. The symmetry of the system then requires that this m.o. will be bonding in C(l)-C(2) and in C(3)-C(4) and anti-bonding in C(2)-C(3)  

---

Fain, J., and Matsen, F. A., J. Chem. Phys. 26, 376, Complete -electron treatment of the butadiene molecule and ion." Complete VB. Results in agreement with SCF with superposition of configurations. 

The tris-allyl complex, in each case, produced a 1.2 growth step of the butadiene molecule. With the more anionic (or less cationic) cobalt salt, the growth occured to only the dimer before it underwent anionic hydride chain transfer. With less anionic chromium the 1.2 chain growth continued on the produce polymer. 

The results of the particle in a one-dimensional box problem can be used to describe the delocalized n electrons in (linear) conjugated polyenes. Such an approximation is called the free-electron model. Take the butadiene molecule CH2=CH-CH=CH2 as an example. The four n electrons of this system would fill up the [Pg.16]

Similar oxidative additions involving the inner carbon atoms of the butadiene molecules can generate complexes having the formal structures 7.26 and 7.27. These may also be formed from 7.25 through tautomerization. Regeneration of 7.24 from these species involves elimination of vinyl cyclohexene and divinyl cyclobutane, respectively. 

Removal of one electron should make no difference to the relative stabilities of polyene molecule ions or even electron polyene fragments as compared to their neutral counterparts, e.g. butadiene and the allyl radical should have the same relative stabihties as the butadiene molecule ion, and the allyl cation. Removal of one electron will, however, alter the stabihties, and thus the reactivities of cychc polyenes. The molecule ions of aromatic hydrocarbons will be substantially less aromatic then their neutral counterparts. Correspondingly the molecule ions of antiaromatic hydrocarbons will not be as antiaromatic as their neutral analogs, e.g. cyclobutadiene + should be relatively more stable than cyclobutadiene. The largest charge effects in hydrocarbons will be observed in nonaltemant ) monocychc hydrocarbons. The cyclopropenium ion 7 and the tropillium ion 2 are both strongly aromatic as compared to their neutral analogs. Consequently CsHs is a very common ion in the mass spectra of hydrocarbons while cyclopropene is not a common product of hydrocarbon pyrolysis or photo-... 

Formation of the relatively unstable complexes (olefin)M(C0)5 and (olefin)2M(C0)4 (M = Mo or W) with propylene and butadiene has been accomplished (559) by UV irradiation of M(CO)o with olefin in w-hexane. From W(CO)e, the complexes (cis-2-butene)W(CO)6, (fmws-2-butene)-W(CO)5, and (cis-2-butene)2W(CO)4 have been produced similarly. As with the corresponding ethylene complexes, the olefin ligands in the bis-olefin complexes are in trans positions. Although, in these complexes, the butadiene molecule is coordinated at only one double bond, upon lengthy irradiation of (butadiene)2Mo(CO)4 (559), the previously reported (268) complex (butadiene)2Mo(CO)2 involving chelated butadiene molecules is produced. 

Because of the similarities between the infrared spectra of free 1,3-butadiene, Zeise s salt, and the complex K2[(C4Ha)Pt2Cle], Grogan and Nakamoto (260) have concluded that the complex has the structure (209) in which the butadiene molecule has the trans configuration which... 

The second structure will have a higher energy than the first because of the much reduced interaction between the electrons of atoms / and 4, and therefore contributes less to the final state of the butadiene molecule than... 

Consider the four tt electrons of the butadiene molecule. There are two possible bond localizations given by the canonical structures a — b a— ... 

TT-Complex formation between butadiene molecules and the transition metal of the catalysts, preformation of the ring and activation of the butadiene molecules in this complex. 

The difference 0.48 is negative which means an additional stabilization of the butadiene molecule associated with the non-localization of the tt molecular orbitals. This is a consequence of an interaction between the 2pz a.o.s of atoms C(2) and C(3) which prevents the mere existence of two independent tt bonds localized in C(1)C(2) and C(3)C(4). In this and similar situations one refers to conjugation of double bonds, a phenomenon clearly related to the molecular topology, that is to the sequence and geometric arrangement of atoms in the molecule. 

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. 

In reaction (7.1), one of the butadiene molecules is reacting across its ends, so the HOMO and LUMO are for the whole conjugated system, but the other molecule is only reacting across one of the double bonds. The second double bond is unchanged in the reaction, so plays no part in... 

It can be seen in Figure 7.6 that there is favourable (same phase) overlap between both ends of the HOMO of the butadiene molecule with the LUMO of the ethene molecule, and vice versa. Accordingly, as the molecules approach, there is a favourable energy change and the reaction takes place readily. 

A mechanism is proposed for the polymerization that involves two metal alkyl units associated with a Co atom differing in Lewis acidity such as AICIR2 + AICI2R. The second growth steps involve 1,4-addition of the coordinated butadiene to a butadienyl Co. The Co atom acts as carrier of the cw-coordinated butadiene and confers increased polarizability on the butadiene molecule. 

---