## 3 Results and Discussions
### Density Functional Theory Calculations  
To simplify the polymer models and exclude complicated configuration effects, we used a single PCzPO and PNoFPO D-A moiety for DFT calculations. We analysed their electron density distribution of molecular orbitals, their free energy of proton binding and their free energy of activation for both intramolecular and intermolecular H\({}_{2}\) formation, demonstrated in previous studies [10; 17; 26]. We computed the difference between the energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) to predict the capability of the polymer to absorb photons as photocatalysts. The DFT calculated HOMO-LUMO gaps (Figure 2) for PCzPO (2.48 eV) and PNoFPO (2.42 eV) are inconsistent from the measured experimental optical gaps listed in Table 1. In general, the experimental optical gap, which is a better indicator of photon absorption efficiency normally differs from the HOMO-LUMO gap by an amount called the exciton binding energy [31]. In addition, realistic extended chains of polymers might affect HOMO-LUMO gaps due to extended \(\pi\) conjugation and interchain stacking or clustering, which were not taken into consideration in our simulation model. In the donor-acceptor type conjugated polymer, the photoexcitation of the electron in the orbital (HOMO) involves an intramolecular charge transfer from the donor group to the acceptor group. To demonstrate this, the electron density distributions of the frontier orbitals of both polymers were analysed and shown in Figure 2. For both PCzPO and PNoFPO, the electron density for high-lying occupied molecular orbitals is concentrated on the donor group while that of the low-lying unoccupied molecular orbitals is concentrated on the acceptor group. Thus, when the electrons in the HOMO is excited to the LUMO, the electron is indeed transferred from the donor group to the acceptor group. Photocatalytic HER involves (i) the photoexcitation of the neutral polymer catalyst (P), (ii) the electron transfer from a sacrificial donor to P, (iii) the proton (H\({}^{+}\)) binding to P and (iv) the reduction of the H\({}^{+}\) and the formation of hydrogen (H\({}_{2}\)) and recovery of P. Although the actual order of the first three steps is not very clear, we assume herein that the first two steps happen before the proton binding. Figure 3 shows the schematic representation of the first two steps culminating in the formation of an anion radical intermediate form (P\({}^{\bullet}\)) of the polymer catalyst. To justify this assumption, we compared the binding free energy of a proton (\(\Delta\)G\({}_{\text{H}+}\)) to the phosphorous oxide of the neutral catalysts and the reduced catalysts. Predictably so, the binding free energies of H\({}^{+}\) to the reduced polymers (2.96 and 3.02 eV) were almost twice as thermodynamically favourable than those to the neutral polymers (5.93 and 5.95 eV) for PCZPO and PNoFPO D-A moiety, respectively (in Table 2). This makes it reasonable to assume that the formation of the unstable P\({}^{\bullet}\) precedes the binding of H\({}^{+}\) and may be the driving \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Polymer** & **Absorption Peaks** & **HOMO/LUMO** & **Optical Gap [eV] \({}^{\circ}\)** & **HER Rate** \\  & **[nm]** & **[eV] \({}^{\circ,\text{b}}\)** & **[\(\mu\)mol h\({}^{-1}\) g\({}^{-1}\)] \({}^{\text{d}}\)** \\ \hline PCzPO & 334, 357 & \(-5.59/-2.85\) & 2.74 & 34.23 \\ \hline PNoFPO & 342, 368 & \(-5.87/-2.84\) & 3.03 & 7.34 \\ \hline \hline \end{tabular}  
* HOMO was measured by a photoelectron spectrometer (model AC-2). \({}^{\text{b}}\) LUMO was calculated by HOMO + Optical gap. \({}^{\circ}\) calculated from UV-vis absorption. \({}^{\text{d}}\) 3 mg polymer in 10 mL mixture (water, triethylamine, and methanol (1:1:1)). 3 wt\(\%\) H\({}_{2}\)PtCl\({}_{6}\) was added.  
\end{table} 
Table 1: UV-vis absorption peaks, HOMO/LUMO energy levels, optical gap and hydrogen evolution rate (HER rate) using PCzPO and PNoFPO D-A polymers.