## 3 Results and Discussions
### Density Functional Theory Calculations
Thus, we posit that besides overall electron density, the electron density of the HOMO is crucial in  
Figure 4: 3D electron density distribution of the frontier orbitals of PCzPO\({}^{\bullet}\) and H-PCzPO\({}^{\bullet}\) calculated under DFT-B3 LYP/6-311G(d,p) level of theory. predicting H\({}^{+}\) binding sites and further support the deduction of H\({}^{+}\) being expected to bind to atoms of the acceptor group in a donor-acceptor type conjugated polymer. Since phosphorous is the least electronegative atom for the polymer catalyst, atoms directly bonded to it become negatively charged due to induction, making them preferred sites for H\({}^{+}\) binding. As depicted in Figure 1, the phosphorous atom of the P = O group is bonded to 3 carbon atoms (C1 to C3) and an oxygen atom (O). C1 and C2 are the carbons of the phosphindole group with C2 being close to the acceptor group while C3 is the carbon of the phenyl group. Table 3 shows that H\({}^{+}\) bound more strongly to C1 and C2 than to O. The binding of H\({}^{+}\) to C1 and C2 led to various possible configurations, as shown in Figure 6. The more stable configurations, C1a and C2a, were generated when H\({}^{+}\) binds from the top, along the plane of the phosphhole ring. In this configuration, the bond of C1 or C2 to the phosphorous was broken to open up the phosphhole ring. This allows the C1 or C2 to maintain sp\({}^{2}\) hybridisation and maintain the extended \(\pi\) conjugation of the molecule. But H\({}^{+}\) may also bind perpendicular to the plane of the phosphhole ring (C1b and C2b in Figure 6). This does not break the bond to phosphorous but is less stable because it converts the carbon binding site to an sp\({}^{3}\) hybridised tetrahedral centre, thus, breaking the planar configuration of the ring and interrupting the \(\pi\) conjugation. We note that the difference in H\({}^{+}\) binding energies for proton binding onto the three C and the O site was very small (<0.2 eV) as seen in Table 3. This means that the H\({}^{+}\) may realistically bind to any of these sites to form H-PCZPO\({}^{\bullet}\). In fact, H\({}^{+}\) may very well bind to sites other than the ones discussed here since the charges of the C atoms along the P = O acceptor group (not shown here) did not differ significantly. However, for practicality, we proceeded with the assumption that these sites are the most probable H\({}^{+}\) binding sites. Figure 5: Molecular orbital diagram of the binding of a proton to PCzPO\({}^{\bullet}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Site** & **Configuration** & **Mulliken Charge** & \(\Delta\)**G\({}_{\text{H+}}\) (eV)** \\ \hline \multirow{2}{*}{C1} & a & \(-\)0.417 & 2.83 \\ \cline{2-4}  & b & & 2.98 \\ \hline \multirow{2}{*}{C2} & a & \multirow{2}{*}{\(-\)0.412} & 2.90 \\ \cline{2-4}  & b & & 2.99 \\ \hline \multirow{2}{*}{C3} & C3 & \(-\)0.382 & 3.07 \\ \cline{2-4}  & O & \(-\)0.593 & 2.97 \\ \hline \multirow{2}{*}{N1} & N1 & \(-\)0.593 & 4.37 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mulliken charge analysis and H\({}^{+}\) binding free energy (\(\Delta\)G\({}_{\text{H+}}\)) of different binding sites and configurations on PCZPO\({}^{\bullet}\) moiety, computed by DFT. To study the last step of the hydrogen evolution reaction where H\({}_{2}\) is finally formed and the initial neutral polymer is recovered, two possible reaction mechanisms were considered. In an intramolecular reaction mechanism, a single P-H\({}^{\bullet}\) will undergo the above-described protonation process again and bind another proton in a different site to form an H2-PCzPO intermediate before releasing the product: P-H\({}_{2}\rightarrow\) P + H\({}_{2}\). In an intermolecular mechanism, two H-PCZPO\({}^{\bullet}\) molecules will react to form the hydrogen molecule: 2 P-H \(\rightarrow\) 2 P + H\({}_{2}\). The minimum energy paths (MEP) of these two reaction mechanisms were calculated.