Theoretical models of photoreactivity, correlation diagrams

The SOC operator contains the product of a term that acts on the spin part of a wavefunction, converting a triplet function to a singlet function and a term that acts on the space part of the wavefunction, changing one electronic configuration to another. Each component of the SOC vector, So /z so T , u = x, y or z, is a sum over all atoms and each atom contributes a sum over pairs of all basis set orbitals in the molecule. The terms in the sum are multiplied by numerical coefficients obtained from the Cl expansion and from the coefficients of the valence (primarily p-) orbitals in the two singly occupied MOs ofTj. The dominant contributors to the sum are those in which both basis set orbitals are located on the same atom ( one-centre terms ). Each term reflects the degree to which a 90° rotation around the axis u through the atom converts one member of the orbital pair into the other. If the space part of the wavefunctions differs only by the occupation number of two MOs ij/i and ij/j, we need to consider only the three matrix elements  

In Section 2.1, we developed rules of thumb to predict rate constants of photophysical processes for a given molecule (Table 2.1). These unavoidable energy-wasting processes limit the lifetime of a singlet state to nanoseconds or less and that of a triplet state to milliseconds or 200 ns in aerated solutions. For a photoreaction to compete efficiently, Arrhenius equation indicates that barriers on the excited state PES exceeding Ea = 30 kJ mol 1 for Sx and Ea = 60 kJ mol 1 for Tx will be prohibitive. 

Modem quantum mechanics can provide accurate excited-state PESs,14,16,17 but such calculations are demanding and in order to obtain useful answers one must ask the right questions. The chemist s intuition or knowledge from related reactions is instmmental in suggesting conceivable photoproducts of the initial reactant. Qualitative guidelines to 

Various approximations allow one to draw diabatic surfaces that connect the electronic states of the reactant with those of conceivable photoproducts and symmetry considerations (Section 4.4) are extremely helpful in this respect. We first consider state symmetry correlation diagrams.331 If the molecules of interest are symmetric (perhaps ignoring some substituents), we consider a reaction coordinate leading from reactant to 

Xas- sa °f the same symmetry aa (dashed lines). Configuration interaction between xo of symmetry, v,v and the doubly excited configuration of the same symmetry splits the two crossing states of symmetry ss apart (full lines), but a symmetry-imposed barrier remains, which classifies the reaction as forbidden in the ground state. 

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