Radical orbital

There is a degree in the continuity and discontinuity of the orbital phase [20]. 2-Oxopropane-l,3-diyl (Scheme 10) is a hetero analog of trimethylenemethane (TMM) where the orbital phase is continuous in the triplet diradical (Sect. 2.1.5) and discontinuous in the singlet diradical (Sect. 2.1.6). The n and orbitals of carbonyl bonds are lower in energy than those of C=C bonds. The lowering strengthens the interaction of the radical orbitals (a, b) with and weakens that... 

Fig. 4a, b General models for (a) Jt-type and (b) o-type diradicals, in which the radical orbitals are mainly of the p-character and sp hybrid, respectively... 

If the radical orbitals are mainly of the p-character (e.g., a p-orbital of carbon in TMM), they interact with each other through the n bond, labeled fl (Fig. 4a). This kind of ir-conjugated diradicals with p-type radical orbitals is classified as the ir-type diradicals. Interestingly, in the language of orbital phase theory, the simplest 1,3-localized diradical, TM (2) also belongs to the ir-type family provided its radical orbitals are dominated by the p-character. The only difference between the TMM (Fig. 4a, left) and TM (Fig. 4a, right) lies in the fact that the radical orbitals of TM interact with each other through the a bond (labeled X) instead of the n bond in TMM. 

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. 

The delocalization of excessive a- (or P-) spins and the bond polarization can take place among radical orbitals, p and q, and the central n (or o) and n (or o ) orbitals, resulting in the electron transferred configurations (T) and locally excited configurations (E), respectively (Fig. 5a). The delocalization-polarization mechanisms are different between singlet and triplet states, as addressed in the following subsections. 

The delocalization-polarization mechanism in the singlet state is more complicated than that in triplet. Similar to the triplet state, there also exists a cyclic - G- T - E- T - configuration or -7t-p-7t -q- (-o-p-o -q-) orbital interaction in the singlet (Fig. 6). In the singlet state, however, the radical orbital q is an electron-accepting orbital (A) for the a-spin electron (rather than the donating orbital in triplet). Thus, there is an additional path of a-spin electron delocalization, - G- T - Tj- T - or... 

Let us return to the phase relationship of a triplet state. Both of the radical orbitals, p and q, are donating (D) orbitals for a-spin electrons. The bonding n and antibonding 71 orbitals are electron-denoting (D) and -accepting (A), respectively. If all the continuity conditions are satisfied in a triplet state, i.e., D-A in phase s(p, tt ) > 0... 

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]. 

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... 

As shown in Fig. 23, the radical orbitals interact with each other through a bond chain, and in 1,3-o-diradicals (60), while delocalization in 1,4-a-diradicals (61) involves Z, Z, and Z bonds. From the phase properties depicted in Fig. 23,... 

Figure 3.54 shows the form of two singly occupied spin-NBOs in the vinylamine triplet excited state the 7tCN 1 half-bond of the (3 spin set (Fig. 3.54(a)) and the terminal nc radical orbital of the a spin set (Fig. 3.54(b)). Neither of these orbitals has a true counterpart in the MOs or NBOs of the ground-state molecule. These results emphasize that hyperconjugative reorganization is a strong feature of the excited-state orbitals, and the oversimplified HOMO-LUMO (Koopmans-like)... 

Figure 3.54 Singly occupied spin-NBOs of the lowest triplet 7t 7t+ excited state of vinylamine (X = NH2) (a) The 7TCn half-bond, (3 spin and (b) the ncf radical orbital of the terminal C atom, a spin.

Nevertheless, the more direct test (3.168b) of the Koopmans assumption demonstrates the failure of this assumption for a wide range of torsional angles. Specifically, the form of the ionized radical orbital rad is found to closely resemble 4>+ for all torsion angles shown in Figs. 3.72(a) and (b). Particularly striking is... 

Consequently, in the vicinity of the TS the highest occupied in-plane MO (HOMO-1) is destabilized to the extent that it becomes the new HOMO, whereas the unoccupied in-plane MO is stabilized to become the LUMO. In other words, in the reactant both HOMO and LUMO correspond to out-of-plane orbitals but, at shorter C1-C6 or C1-C5 distances, the frontier MOs are localized at in-plane non-bonding (radical) orbitals. 

The formed anomeric radical adopts both a form (equatorial radical) [I] and (3 form (axial radical) [II], and these are in equilibrium state. However, the (3 form radical is more reactive and nucleophilic, because of its orbital interaction between the singly occupied radical orbital and the axial lone-pair on the neighboring ring-oxygen atom (like aftfi-periplanar effect) [20-22]. Therefore, the (3 form radical (axial radical) [II] predominantly reacted with a hydrogen donor to generate p-O-glycoside. 

When a chemist sees a molecular structure that contains several free radicals, orbitals with unpaired electrons, his or her inclination is to predict that such a structure will undergo a geometric change in which electrons will... 

Consider the interaction of methyl, CH3, with a surface, in on-top and bridging sites, 110.78 Let s assume low coverage. The important methyl orbital is obviously its nonbonding or radical orbital n, a hybrid pointing away from the CH3 group. It will have the greatest overlap with any surface orbitals. The position of the n orbital in energy is probably just below the bottom of the metal d band. How to analyze the interactions of metal and methyl ... 

The methyl radical orbital (it s really a band, but the band is narrow for low coverage) interacts with the entire z2 and xz bands of the metal, except at a few special symmetry-determined points where the overlap is zero. But it s easy to rank the magnitude of the overlaps, as I ve done in 112 for on-top adsorption. 

Kass argued that 2r is stabilized by an interaction between the radical orbital on Cx and ct(C2-C3) orbital. This allows the radical to delocalize, especially onto C3. As listed in Scheme 3.2, the spin densities at Cj and C3 are quite similar, 0.59 and 0.34, respectively. A further manifestation of this delocalization is the short Cl -C3 distance (1.493 A) in 2r compared to that in 2 (1.512 A). This orbital interaction is negligible in the anion 2cb because it is a filled-filled interaction. The charge density is much more localized onto Cj for 2a than is the spin density for 2r. Consequently, 2r is more stable than expected, leading 2 to have a smaller BDE than anticipated. 2 thus has the acidity of an acetylene but the bond energy of methane. ... 

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