The algorithm developed in section II B relies on the low level calculations to detect potential electronic transitions. Whenever a low level transition is detected, it is double checked with a high level FS calculation such that the low level probabilities do not have to be quantitatively accurate. The transition probabilities in Fig. indicates that using LZ theory at the low level for the calculation of the transition probabilities is enough. In other words, the LZ probabilities can be used as a proxy during the low level steps of the MTS-TSH method.