## 3 Results and Discussions
### Density Functional Theory Calculations
force for faster H+ binding and overall HER. Thus, in contrast to previous theoretical calculations that bind H+ to the neutral catalyst, P [10; 26], the proceeding calculations in this work goes with the assumption that H+ binds to P+. Furthermore, due to the accumulation of electrons in the acceptor group, as explained above, H+ will most probably bind to the negatively charged acceptor group atoms due to electrostatic interaction. In addition, the similar proton binding free energies to P or P+ correlate with the similar LUMO levels of PCZPO and PNoFPO D-A moieties. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Polymer Catalyst**} & \multicolumn{2}{c}{**Proton Binding Free Energy (eV)**} \\ \cline{2-3}  & **P + H+** \(\rightarrow\) PH+ & **P\({}^{\bullet}\) + H+** \(\rightarrow\) PH \\ \hline PCzPO & 5.93 & 2.96 \\ \hline PNoFPO & 5.95 & 3.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Proton binding free energy (\(\Delta\)G\({}_{\text{H}}\)) for neutral and negative PCZPO and PNoFPO D-A moieties with H bound to the O atoms of PO groups of acceptor groups, computed by density functional theory (DFT). Figure 3: Schematic representation of the formation of P+. Figure 2: 3D electron density distribution of the frontier orbitals of PCzPO and PNoFPO D-A moieties, computed at the B3 LYP/6-311G(d,p) level of theory. Energy levels (eV) of each orbital is shown in green, and the HOMO-LUMO gaps are shown at the bottom of each column. The frontier molecular orbitals (in Figure 2) show that H\({}^{+}\) might bind to acceptor atoms where photoexcited electrons are localised. Since PCzPO performed better in the experiment, we began with the PCzPO for a detailed exploration of H\({}^{+}\) binding and H\({}_{2}\) formation mechanisms. First, the frontier molecular orbitals of the PCzPO\({}^{\bullet}\) before and after protonation were analysed and depicted in Figure 4. The HOMO of PCzPO\({}^{\bullet}\) was similar to the LUMO of the neutral PCzPO (first column in Figure 2), except for the increased energy levels brought by spin and charge destabilisation and the new HOMO containing the radical corresponds to the LUMO of the neutral PCzPO. The H\({}^{+}\) binding neutralises the excess charge, which makes the molecular orbital energy levels of H-PCzPO\({}^{\bullet}\) lower compared to PCzPO\({}^{\bullet}\). In addition, the frontier molecular orbitals of neutral PCzPO and H-PCzPO\({}^{\bullet}\) were similar, apart from the HOMO-2 molecular orbital. For H-PCzPO\({}^{\bullet}\), the electron density was concentrated on the phosphindole group to which the proton was bound. This was a new orbital formed through the interaction with the bound H\({}^{+}\). Figure 5 shows the simplified molecular orbital diagram, which summarises the transfer of electron observed in Figure 4. The incoming H\({}^{+}\) interacted with the HOMO of PCzPO\({}^{\bullet}\) to form H-PCzPO\({}^{\bullet}\), where a new bonding orbital contributed by the H atom was formed. This is a simplified interpretation since it is possible for orbitals to mix and many different molecular orbitals to interact with H\({}^{+}\). But what is important is that H\({}^{+}\) gained electron density while the LUMO of PCzPO (HOMO of PCzPO\({}^{\bullet}\)) became empty again. Thus, there is a clear electron transfer from the donor group atoms to the bound H\({}^{+}\). The Mulliken charge of PCzPO\({}^{\bullet}\) was analysed to explore the various possible H\({}^{+}\) binding sites. The most negatively charged atoms of PCzPO were labelled accordingly in Figure 1 and listed in Table 3. In a previous DFT study of D-A polymers [10], electronegative heteroatoms were assumed as binding sites due to charge considerations. However, as seen in Table 3, even though N1 was one of the most negatively charged atoms, the H\({}^{+}\) binding to this site is the least favourable. This is because N1 is part of the donor PO group where the HOMO of PCzPO\({}^{\bullet}\) intermediate has no electron density.