Diradicals cyclic orbital interactions

In 1982 the present author discovered cyclic orbital interactions in acyclic conjugation, and showed that the orbital phase continuity controls acyclic systems as well as the cyclic systems [23]. The orbital phase theory has thus far expanded and is still expanding the scope of its applications. Among some typical examples are included relative stabilities of cross vs linear polyenes and conjugated diradicals in the singlet and triplet states, spin preference of diradicals, regioselectivities, conformational stabilities, acute coordination angle in metal complexes, and so on. 

Scheme 9 Electron configuration and delocalization, cyclic orbital interaction, and orbital phase properties in the singlet diradicals...

Fig. 5a-c Through-bond interactions in the triplet state of 1,3-diradical, a Mechanism of electron delocalization and polarization of a-spin electrons, b Cyclic orbital interaction, c Orbital phase continuity... 

As mentioned above, the unpaired electrons of diradicals may interact with each other through bonds. The orbital phase relationships between the involved orbitals control the effectiveness of the cyclic orbital interactions underlying the through-bond coupling. 

Orbital phase continuity in triplet state. The orbital phase properties are depicted in Fig. 5c. For the triplet, the radical orbitals, p and q, and bonding n (a) orbital are donating orbitals (labeled by D in Fig. 5c) for a-spin electrons, while the antibonding jt (a ) orbital (marked by A) is electron-accepting. It can be seen from Fig. 5c that the electron-donating (D) radical orbitals, p and q, can be in phase with the accepting (a ) orbital (A), and out of phase with the donating orbital, Jt/a (D) at the same time for the triplet state. So the orbital phase is continuous, and the triplet state of 1,3-diradical (e.g., TMM and TM) is stabilized by the effective cyclic orbital interactions [29, 31]. 

Fig. 8a, b The cyclic orbital interaction (a) and orbital phase continuity (b) in the singlet state of O-type 1,3-diradical... 

Moreover, the radical orbitals, p(D) and q(A) are in phase. The direct through-space interaction between the radical centers, i.e., the p...q interaction, thermodynamically stabilizes the singlet 1,3-diradicals in addition to the cyclic orbital interactions through the bonds. However, the through-space interaction can also stabilize the transition states of the bond formation between the radical centers and kinetically destabilize the diradicals (which will be discussed in Sect. 3.4.2). 

In the singlet state of Jt-type 1,3-diradical (e.g., TM, 2), there may also exist the through-space interaction between radical centers, i.e., p...q interaction (Fig. 9), in addition to the previously addressed cyclic -p-o -q-o- orbital interactions (Fig. 6). The through-space interaction is indispensable for the bond formation between the radical centers. The corresponding delocalization of the a-spin electron is shown in Fig. 9a. Clearly, the involvement of the through-space p... q interaction gives rise to two cyclic orbital interactions, -p-o -q- and -p-o-q-. From Fig. 9, one can find that the cyclic -p-o -q- orbital interaction can satisfy the phase continuity requirements for the a-spin electron the electron-donating radical orbital, p (D) can... 

The cyclic orbital interaction of p and q with o or with o can significantly occur at the transition state of the ring closure of 1,3-diradicals. The continuous orbital phase for the cyclic orbital interaction with o implies effective stabilization of the transition states when the o bonds are electron acceptors. 

The introduction of heteroatoms into the hydrocarbon diradicals is a frequently applied strategy to tune the spin preference and relative stabilities of diradicals. The heteroatoms may change the energies of donor or acceptor orbitals, and consequently affect the donor-acceptor interaction involved in the cyclic orbital interaction. Take 2-oxopropane-l,3-diyl, or so-called oxyallyl (OXA, 18) as an example [29]. It is a hetero analog of TMM, as shown in Fig. 14. The replacement of CH with oxygen in the central fl unit leads to a decrease in energies of Jt and k orbitals. This may enhance the orbital interaction through one path (denoted by bold lines) and weaken that via the other (denoted by wavy lines) relative to the continuous cyclic orbital interaction in the parent species 1 (Fig. 14). As a result, the p-Jt -q... 

Most of the triplet diradicals have disrotatory conformations, in which the cyclic orbital interactions are favored by the phase continuity. 1,3-Diradicals with the second-row substituents, 25-28, prefer the conformer a with the central C-H bond in conjugation (except for the conrotatory conformation b in 27), whereas those substituted by the third-row groups, 29-32 favor the disrotatory conformations c... 

On the basis of the orbital phase continuity/discontinuity in the involved cyclic orbital interactions, some general rules were drawn for the Jt-conjugated and localized diradicals ... 

What is the o-type diradical Take a cyclic 1,3-diradical, with a four-membered-ring (4MR) structure as an example, the a-type radical orbitals interact with each other through the intervening chain of the a bonds, S, and (Fig. 4b). The cyclic interaction occurs among the radical orbitals, p and q, a, and o, and Oj and a orbitals. 

Singlet o-type diradical. Figure 8 shows the phase relationship between the electron donating and accepting orbitals in a o-type diradical (Scheme 4b). It can be seen that the cyclic -p-0j -02 -q-02-0j- orbital interaction satisfies the continuity requirements in the singlet state (Fig. 8) the neighboring orbitals in p(D)-Oj (A)-02 (A)-q(A)-02(D) are all in phase while those in the sequence p(D)-Oj(D)-02(p) are all out of phase. The phase is continuous for the cyclic interaction. 

T gap (cf. references collected in Table 1). This correlates well with a disfavored cyclic six-orbital interaction by the phase discontinuity in the triplet state of 7 [29] (shown in Fig. 11). In addition, TME is an important topological unit which appears frequently in many non-Kekule diradicals (as exemplified by 15-17 in Fig. 13). 

The orbital phase theory is applicable to the singlet diradicals [20]. The electron configuration of the singlet states of the cross- (TMM) and linear (BD) conjugate diradicals is shown in Scheme 9, where the mechanism of the delocalization of a and P spins between the radical centers through the double bond are separately illustrated by the arrows. The cyclic [-a-Tr-b-T -] interaction is readily seen to occur for the spin delocalizations. The p orbital a) in one radical center and the n orbital are occupied by a spins, and therefore, electron-donating orbitals. The p orbital (b) in the other radical center and the ii orbital are not occupied by a spins. 

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