Molecular orbital diradicals

The fragmentation/cyclization ratio is determined by the relative orientation of the respective molecular orbitals, and thus by the conformation of diradical species 2. The quantum yield with respect to formation of the above products is generally low the photochemically initiated 1,5-hydrogen shift from the y-carbon to the carbonyl oxygen is a reversible process, and may as well proceed back to the starting material. This has been shown to be the case with optically active ketones 7, containing a chiral y-carbon center an optically active ketone 7 racemizes upon irradiation to a mixture of 7 and 9 ... 

Fig. 1 A schematic illustration of the in-phase and out-of-phase combinations of the atomic orbitals into the bonding and antibonding molecular orbitals, respectively. The dissociation limit of a H molecule corresponds to a pure diradical with degenerate singlet and triplet states...

It is well known that Hund s rule is applicable to atoms, but hardly so to the exchange coupling between two singly occupied molecular orbitals (SOMOs) of a diradical with small overlap integrals. Several MO-based approaches were then developed. Diradicals were featured by a pair of non-bonding molecular orbitals (NBMOs), which are occupied by two electrons [65-67]. Within the framework of Hiickel MO approximation, the relationship between the number of NBMOs,... 

Following Salem (77), we define diradicals as molecules with two electrons occupying two (near)-degenerate molecular orbitals. More loosely, Salem considers molecules with a broken bond as diradicals. 

The mechanism of the reaction has generally been discussed in terms of a thermally allowed concerted 1,3-dipoIar cycloaddition process, in which control is realized by interaction between the highest occupied molecular orbital (HOMO) of the dipole (diazoalkane) and the lowest unoccupied molecular orbital (LUMO) of the dipolarophile (alkyne).76 In some cases unequal bond formation has been indicated in the transition state, giving a degree of charge separation. Compelling evidence has also been presented for a two-step diradical mechanism for the cycloaddition77 but this issue has yet to be resolved. 

The anion diradical (BQNN)- has two nondegenerated single occupied molecular orbitals (SOMOs). One is delocalized over the entire molecule and the other (SOMO ) is localized within the NN group. 

Some molecular species are not calculated properly by straightforward model chemistries these include singlet diradicals and some excited state species. For these the standard method is the complete active space approach, CAS (CASSCF, complete active space SCF). This is a limited version of configuration interaction, in which electrons are promoted from and to a carefully chosen set of molecular orbitals. 

Fig. 8.12 The molecular orbitals of 1,5-pentanediyl and cyclopentane, relevant to the C-C cleavage of the cycloalkane that leads to the acyclic diradical. Calculated with the HF/STO-3G wavefunction and localized by the NBO method. The cyclopentane C-C bonding orbital, MO 10, relevant to this reaction, must be switched with MO 20, a pure C-H bonding MO with no relevance here, to move the C-C MO into the active space. Note that these molecules have 40 electrons...

As predicted by molecular orbital theory dioxygen has two unpaired electrons and some of its chemistry shows diradical characteristics in particular, it reacts readily with other radicals. Singlet oxygen is an excited state in which the two electrons in the p anti-bonding orbitals have paired spins. It produced in some chemical reactions and has different chemical reactivity. 

The electronic configuration in Figure 16-7 indicates that cyclobutadiene should be unstable. Its highest-lying electrons are in nonbonding orbitals (ir2 and ir3) and are therefore very reactive. According to Hund s rule, the compound exists as a diradical (two unpaired electrons) in its ground state. Such a diradical is expected to be extremely reactive. Thus, molecular orbital theory successfully predicts the dramatic stability difference between benzene and cyclobutadiene. 

The present chapter is dedicated to the cycloaddition reactions of enamines, which include transformations that, independently of the mechanism, create a new ring1. The cycloadditions may proceed via a concerted mechanism (following Woodward-Hoff-mann rules) or a two-step mechanism which may involve zwitterionic or diradical intermediates. Due to their low ionization potentials and asymmetric molecular orbital... 

In this chapter, we focus on the class of reactive intermediates that bear at least two unpaired electrons diradicals and carbenes. The exact definition of a diradical is somewhat in the eye of the beholder. Salem and Rowland provided perhaps the most general, yet effective, definition—a diradical is a molecule that has two degenerate or nearly degenerate orbitals occupied by two electrons. With this definition, carbenes can be considered as a subcategory of diradicals. In a carbene, the two degenerate molecular orbitals are localized about a single carbon atom. 

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