Singlet-Triplet Probabilities

In the simulation it is necessary to extract the singlet character of the wavefunction to determine whether reaction can take place (for the purpose of this work the triplet state is unreactive). This can readily be achieved by converting from the Zeeman basis to the ST-basis using the transformation matrix (P), which for a fixed nuclear spin state is 

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Following a cross recombination, it is important to verify that the wavefunction for the newly correlated pair has the correct singlet-triplet probability. For this reason, a separate simulation in which V tot is simulated at all times was also adopted to... 

Goodman, L., Laurenzi, B. J. Probability of singlet-triplet transitions. In Advances in quantum chemistry, Vol. 4 (ed. by Per-Olov Lowdin). New York—London Academic Press 1968. 

It is highly probable that most of the conformational exploration of the BR s occurs while they are triplets. Ultimately, the triplets will convert to singlets which probably react (by cyclization, fragmentation, or reverse hydrogen transfer to the parent molecule) before significant conformational change occurs. 

Recently, the response theory formalism was applied for the calculation of singlet-triplet spectra in polyenes and aromatic hydrocarbons [83,133,134,132]. In this section we shall discuss mainly the vertical Tn <— So transitions probability in polyenes. The minimum level of accuracy includes CAS calculations of the ground state correlating all x electrons followed by linear and quadratic multi-configuration response calculations. Because the ethene molecule is the simplest representative of unsaturated hydrocarbons, different types of active spaces and AO basis sets were tested more thoroughly for this molecule in order to study the convergence of the S-T transition probability with respect to the level of accuracy. 

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