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Azobenzene

When the molecule is in LUMO potential surface (PS) the molecule will try to go to the lowest energy in that PS, during this process at each step using non-adiabatic molecular dynamics FIREBALL will calculate the probability of hop to other energy levels. In Azobenzene molecule the lowest energy level for LUMO is when the CNNC dihedral angle goes to angles close to 90 degrees depending on the functional groups. As this angle increses the energy level of HOMO increases too with makes the energy difference between LUMO and HOMO decrease. This will increase the probability of a hopping from LUMO to HOMO. Hence we would expect the highest number of transitions to occur around 90 degrees. So to analyze the isomerization time, angle and quantum yield it is good to plot the energy vs CNNC dihedral angle. If this plot is symmetric with respect to 90 degrees we can assume, the quantum yield from *cis* to *trans* is close to the quantum yield from *trans* to *cis*. In cases like azobenzene with organic linkers which the HOMO and LUMO energy levels get close to each other around 98 degree we can plot the difference between these two energy levels. In this plot if we choose an energy difference of 0.5ev and assume a probability of hoping for this energy difference, if we approach the conical intersection from *trans* isomer this energy difference happens at 110 degrees the molecule is already in *trans* isomer and this isomer is thermally stable so there is a higher possibility that the molecule does not isomerize and returns to *trans* while if we approach from *cis* isomer this energy difference happens at 88 degrees and this angle is close to isomerization angle(90 degrees) so there is a high possibility that the molecule isomerizes. And this energy difference does not change by a big amount for azobenzene molecules with asophtalic acid as their linkers and its derivatives. So in general we can expect a higher quantum yield for *cis* to *trans* than *trans* to *cis*. In order to plot Energy vs Dihedral angle, we start with CNNC angle equal to zero, fixed the CNNC atoms and optimize the molecule for 1000 steps equal to 250fs. Using a python script we rotate the dihedral angle by 0.3 degree and do the same optimization. This process will be repeated until the dihedral angle is equal to 180 degrees, from the optimizations we can read the energy levels of HOMO and LUMO.

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