Greetings,

I am working with a system in which an oxygen molecule (triplet ground-state) is incorporated into an organic molecule to produce a singlet product. Throughout the reaction, there is a MECP (minimum energy crossing point) between the triplet and the singlet, and in principle, the free energy of reaction is calculated as usual in TST (adding entropy terms to the electronic energy), to then add a deltaG term caused by the hopping probability between triplet and singlet surfaces, which will be between 0 and 1 (so there will be an increase of 1-4 kcal/mol in free energy barrier).

To carry out this study, I am trying to follow the publication of Lykhin et al. [1], together with other previous publications that develop and review the theoretical basis of spin-orbit coupling and spin-forbidden reactions [2,3,4]. In this publication, they work with the coupling matrices between the two surfaces (what I understand to be a state-interaction calculation), so they obtain some elements of the coupling matrix, denoted as z and b). These elements are then used to calculate the zero-field splitting energy (H_so), which is the final parameter that is plugged in the hopping probability formula (Fig. 1).

On the other hand, there are some programs, such as Molpro or Molcas, which provide an output with the elements of the spin-orbit coupling as shown in Fig. 2. In this way, we have obtained a graph with the spin-orbit coupling calculated for each point of our reaction trajectory, between the triplet and the singlet in question (Fig. 3). The red line is a calculation in Molcas with CASPT2 method and the blue line is a calculation in Molpro with MRCI method.

The doubt comes mainly from the confusion between the terms, the use of different terminology between different publications and books, and the lack of information on the exact technical procedure carried out by some of the publications when calculating the spin-orbit coupling. If, on the one hand, I use the values provided in the output of Fig. 2 to obtain the spin-orbit coupling, I obtain the plot shown in Fig. 3. If, on the other hand, I consider that the spin-orbit coupling used in the Landau-Zenner hopping probability formula should actually be the zero-field splitting, as in Ref. [1], that zero-field splitting will be the energy difference between the three spin-states triplets, and a plot appears with values close to zero all the way, except in the MECP which rises to a maximum of 3 cm^(-1).

To summarise, what I am really looking for is a clear protocol that allows me to obtain an unambiguous H_so value, to put it into the Landau-Zenner formula and to be able to calculate the hopping probability and the associated increase in free energy. If you need more information or a clearer explanation, please do not hesitate to ask.

Thanks in advance,

Pablo

References:

[1] A. O. Lykhin, D. S. Kaliakin, G. E. dePolo, A. A. Kuzubov and S. A. Varganov, Int. J. Quantum Chem., 2016, 116, 750–761.

[2] J. N. Harvey, Phys. Chem. Chem. Phys., 2007, 9, 331–343.

[3] C. M. Marian, Wiley Interdiscip. Rev. Comput. Mol. Sci., 2012, 2, 187–203.

[4] J. N. Harvey, Wiley Interdiscip. Rev. Comput. Mol. Sci., 2014, 4, 1–14.