Cross orbital interaction

Because the spin-orbit interaction is anisotropic (there is a directional dependence of the view each electron has of the relevant orbitals), the intersystem crossing rates from. S to each triplet level are different. 

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. 

The electron delocalizations in the linear and cross-conjugated hexatrienes serve as good models to show cyclic orbital interaction in non-cyclic conjugation (Schemes 2 and 3), to derive the orbital phase continuity conditions (Scheme 4), and to understand the relative stabilities (Scheme 5) [15]. 

Interactions polarize bonds. Trimethylenemethane (TMM) and 2-buten-l,4-diyl (BD) dianions (Scheme 6a, b) are chosen as models for hnear and cross-conjngated dianions. The bond polarization (Scheme 7) is shown to contain cyclic orbital interaction (Scheme 6c) even in non-cyclic conjugation [15]. The orbital phase continnity-discon-tinnity properties (Scheme 6d, e) control the relative thermodynamic stabihties. 

Similar arguments lead to the prediction that the cross conjugate TMM dication should be more stable than the linear conjugate BD dication. The cyclic orbital interaction is favored by the continuity of orbital phase in the TMM dication, but the orbital phase is discontinuous in the BD dication. 

Frosch(84,133) have explained the external heavy-atom effect in intersystem crossing by postulating that the singlet and triplet states of the solute, which cannot interact directly, couple with the solvent singlet and triplet states, which themselves are strongly coupled through spin-orbit interaction. Thus the transition integral becomes<134)... 

Resultant energy curves in H2 and H2. u, Burrau s curve for H2 . b, Curve for H2 for non-interacting electrons, c, Approximate curve for H2 with interacting electrons. The small circle in the crook of curve b, represents the equilibrium position and energy on Hutchisson s classical crossed-orbit model of H2. Units same as figure 1 (note different scales of ordinates for Ha and H2+). 

The rate determining step in intersystem crossing is the transfer from the thermally relaxed singlet state to the vibronically excited triplet state S/ >7 (j > k). This is followed by vibrational relaxation. The spin-orbital interaction modifies the transition rates. A prohibition factor of 10 — 10 is introduced and the values of kiSc lie between 101 and 107 s-1. The reverse transfer from the relaxed triplet to vibronically excited singlet is also possible. 

Apart from the selection rules for the electronic coupling matrix element, spin-forbidden and spin-allowed nonradiative transitions are treated completely analogously. Nonradiative transitions caused by spin-orbit interaction are mostly calculated in the basis of pure spin Born-Oppenheimer states. With respect to spin-orbit coupling, this implies a diabatic behavior, meaning that curve crossings may occur in this approach. The nuclear Schrodinger equation is first solved separately for each electronic state, and the rovibronic states are spin-orbit coupled then in a second step. 

Rates for nonradiative spin-forbidden transitions depend on the electronic spin-orbit interaction matrix element as well as on the overlap between the vibrational wave functions of the molecule. Close to intersections between potential energy surfaces of different space or spin symmetries, the overlap requirement is mostly fulfilled, and the intersystem crossing is effective. Interaction with vibrationally unbound states may lead to predissociation. 

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