1. Use Multiwfn to calculate orbital composition of all unoccupied MOs of the combined system contributed by the dye fragment. See Section 4.8.3 for example on how to using Multiwfn to compute composition of a fragment in selected range of orbitals.

2. Check the MO compositions, find the range of MOs in which the sum of contributions by the dye fragment is nearly 100%. This step is somewhat tricky and not clearly described by the authors of the JCTC paper. I suggest you first check the MO of the combined system whose energy is closest to the LUMO energy of the dye in monomer state, and then identify the proper MO index range. (In fact the method employed in the JCTC paper doesn't work for all cases, it works only when energy separation between unoccupied MOs of the dye is evident, in other cases the range cannot be unambiguously determined)

3. Using MO energies of the combined system {e} as well as the contributions from the dye {p} in the MO range determined in the last step to calculate weighted average LUMO energy of the dye in the combined system (i.e. E_LUMO(ads)) via Eq. 4 of the JCTC paper. You can write a small code or simply use Excel to realize this process based on the {e} and {p} printed by Multiwfn.

4 Using {e}, {p} and E_LUMO(ads) to calculate h_bar * gamma_MD via Eq. 5, then substituting this into Eq. 9 to obtain the injection time.