Spin preferences

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 10 Spin preference and degree of the discontinuity of orbital phase...

Stability of diradicals is important for photochemical reactions. Spin multiplicity of the ground states is critical for the molecular magnetic materials. The relative stability of singlet (triplet) isomers and the spin multiplicity of the ground states (spin preference) [48] has been described to introduce the orbital phase theory in Sects. 2.1.5 and 2.1.6. Applications for the design of diradicals are reviewed by Ma and Inagaki elsewhere in this volume. Here, we briefly summarize the applications. 

Substituent effects on spin preference and kinetic stabilities... 

Scheme 28 Spin preference of designed or observed diradicals...

Keywords Diradical, Kinetic stability. Orbital phase theory. Spin preference... 

To summarize, the properties of triplet and singlet diradicals are closely related to the effectiveness of through-bond and through-space interactions, which are governed by the orbital phase continuity/discontinuity properties. In the next two sections, we will utilize this simple model to predict the spin preference and intramolecular reactivity for a broad range of diradicals. 

Table 1 Spin preference of ground state and the calculated singlet-triplet energy separation of some selected Jt-conjugated diradicals...

Among the non-Kekule diradicals, tetramethyleneethane (TME, 7) has evoked lasting attention during the last two decades due to the controversy over its spin preference in the ground state between experiments and theoretical predictions [48-59], Now TME is known to be a slightly favored singlet diradical with a negligible... 

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... 

The classification into Kekule and non-Kekule diradicals is mainly based on the difference in their resonance structures. From the proceeding discussions, however, such a classification does not closely relate to the relative stabilities and spin preference of TT-conjugated diradicals. For example, some non-Kekule diradicals, such as 1 and 8, prefer a triplet ground state, but some others (like 7) have a singlet ground... 

An alternative stream came from the valence bond (VB) theory. Ovchinnikov judged the ground-state spin for the alternant diradicals by half the difference between the number of starred and unstarred ir-sites, i.e., S = (n -n)l2 [72]. It is the simplest way to predict the spin preference of ground states just on the basis of the molecular graph theory, and in many cases its results are parallel to those obtained from the NBMO analysis and from the sophisticated MO or DFT (density functional theory) calculations. However, this simple VB rule cannot be applied to the non-alternate diradicals. The exact solutions of semi-empirical VB, Hubbard, and PPP models shed light on the nature of spin correlation [37, 73-77]. 

In this chapter, the orbital phase theory was applied to develop a theoretical model of diradicals, to predict the substituent effects on the spin preference and S-T gaps, and to design some new 1,3-diradicals. 

The substituents and heteroatoms can be used to tune the spin preference of the acyclic diradicals by changing the energy levels of electron-donating and -accepting orbitals and hence the donor-acceptor interaction. 

Fig. 11 Phenoxyl-based conjugated multispin model systems used to test high spin versus low spin preference as a function of degrees of oligomerization.

A number of diradicals (also called biradicals) are known,and the thermodynamic stability of diradicals has been examined. Orbital phase theory has been applied to the development of a theoretical model of localized 1,3-diradicals, and used to predict the substitution effects on the spin preference and S-T gaps, and to design stable localized carbon-centered 1,3-diradicals. When the unpaired electrons of a diradical are widely separated, for example, as in CH2CH2CH2CH2, ... 

Prototypical spin preferences. A. At all separations, r, molecular hydrogen shows a singlet ground state. B. Atomic carbon shows a triplet ground state because of a cancellation of regions of positive and negative overlap of the 2p atomic orbitals. C. Possible spin states for the two-electron system. 

Closer consideration of the NBMOs of these systems explains the differing spin preferences. For a degenerate pair, any linear combination of the MOs is acceptable. For CBD, we can make a linear combination of the NBMOs such that they have no atoms in common (Figure 14.32 A). One NBMO is confined to atoms 1 and 3, while the other is confined to atoms 2 and 4. Such orbitals are said to be disjoint they occupy different sets of atoms. In contrast, it is not possible to find a linear combination of the NBMOs of TMM that are disjoint (Figure 14.32 B). No matter what you do, there will always be atoms in common, and the NBMOsare termed non-disjoint. 

Earlier in this chapter we introduced the concept of alternate hydrocarbons (AH). TMM and CBD are both even AHs, but there is a significant difference. While CBD has two and two non- atoms, TMM has three and one non-. It is not a coincidence that these two systems with differing spin preferences also appear different in the /non- analysis. The / non- rule is basically a topology rule—it reflects the connectivity of the system. The topology of the system also influences the nature of the NBMOs. In fact, it can be shown that a system with an excess of over non- atoms will in general have non-disjoint NBMOs, while a system with equal numbers of and non- atoms will have disjoint NBMOs. 

While methylene (CH2) is a ground state triplet (T), substituents can have a large effect on the spin preference. Aminometh-y lene CH N H2, for example, prefers the singlet (S) ground state by 42 kcal / mol ... 

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