1.3- Butadiene paired electron spins

The phenomenon of four singly-occupied active-space orbitals (AO or MO) arises in many seemingly-unrelated molecular situations. The singlet spin (S = 0) Rumer diagrams for these orbitals indicate that there are two linearly-independent or canonical spin-pairings schemes. These spin-pairings are well-exemplified by the 7i-electrons of butadiene, for which two canonical Lewis VB structures with different 7i-electron spin pairings are those of 1 and 2. 

Two of the TT molecular orbitals of 1,3-butadiene are bonding molecular orbitals. In the ground state these orbitals hold the four tt electrons with two spin-paired electrons in each. 

Since )3 is negative, the lowest energy is 0 + 1.62)3. The four n electrons in butadiene occupy the two lowest lying states with their spins paired, as shown in Figure 8.26. 

Figure 24.1 shows the molecular orbitals (MOs) for both ethene and 1,3-butadiene and identifies the highest occupied molecular orbitals (the HOMOs) and the lowest unoccupied molecular orbitals (the LUMOs) for both compounds. The MOs shown include the p-orbitals on each carbon atom. How are these molecular orbitals constructed First, only the p-orbitals of the diene and the alkene are used because these orbitals are involved in the Diels-Alder reaction. An alkene has two jt-electrons, so it will have two n-molecrdar orbitals. The two orbitals cannot be of the same energy, and the two electrons will reside, spin paired (see Chapter 3, Section 3.1.2), in the lowest energy orbital. 

The same analysis is done for the molecular orbitals of butadiene, with the lowest energy orbital having zero nodes. Butadiene has four n-electrons, so there will be four n-molecular orbitals, each one capable of containing two electrons. Therefore, the two lower energy MOs will contain the four electrons—two each and spin paired. The lowest energy MO will have a + + + + array so that all four colored lobes overlap and there are zero nodes. It is important to understand that the four lobes shown for the + + + + array constitute one molecular orbital, not four. There are four carbon atoms and each is sp hybridized, so there are four lobes, but it is one of four molecular orbitals. 

Let us consider the ultraviolet spectrum of butadiene (Table 11.1). Assuming two electrons loosely spin-paired in each orbital and neglecting the interaction between the electrons, we can fill two energy levels with four electrons. Then the lowest energy excitation will be firom the highest occupied molecular orbital (HOMO) n = 2 to the lowest unoccupied molecular orbital (LUMO) n = 3. We can estimate the wavelength of this transition as a one-electron jump from n = 2... 

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