Electronic wave function butadiene

Hanson and Martin applied the same approach to investigate the rupture of isoprene and butadiene oligomers in order to investigate covalent bond rupture in rubber.Using density functional theory, they identified the point of rupture where the unrestricted solution to the Kohn-Sham electronic wave functions falls below the restricted solution. This implies that the rupture process should be heterolytic and so this concept can only be applied for instances in which radical species are formed in the initial rupture event. 

The next step up in complexity comes with four p orbitals conjugated together, with butadiene 1.5 as the parent member. There is a a framework 1.6 with 36 electrons and four p orbitals to house the remaining four. Using the electron in the box with four p orbitals, we can construct Fig. 1.31, which shows the four wave functions, inside which the p orbitals are placed at the appropriate regular intervals. We get a new set of orbitals, ipi, 3, and ip4, each described by Equation 1.11 with four terms. 

For jr—excitation energies the agreement between the calculated and experimentally observed data is more difficult to achieve. This is probably related to the intricacies of the correlation of a with Ji electrons in states with a highly zwitterionic character in the n part of the wave function. (Cf. Malmqvist and Roos, 1992.) Some of the difficulty is due to the limited availability of definitive and accurate experimental data. As an example, some data for butadiene are collected in Table 1.6. 

The butadiene molecule is the simplest conjugated diene in which electron delocalization occurs. As can be seen from Table 13.3, the major neutral Lewis structure of butadiene describes well the Hiickel reference wave function as it spans 90 % of the space. The description is gradually improved when including the diradical stmcture (case 2a t = 92 %) along with the two ionic structures (case 3 T = 95 %). The comparison of case 2a with case 2b (t = 92 %) tells us that the two ionic stmctures and the diradical contribute the same amount to the description of Pref, i.e. they overlap similarly with Wr. But they do not overlap with each other, so that the trust parameter increases when both are added. 

FIGURE 11.3 The PIB wave functions for butadiene spaced vertically approximately according to energy (ocn ). Note the number of nodes is (n — 1). (From Trindle, C. and Shillady, D., Electronic Structure Modeling Connections between Theory and Software, CRC Press, Boca Raton, FL, 2008. With permission.)... 

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