\subsection{Quantum yield determinations}
\label{quantumyield}

The absorption factor is a function of $\lambda$ that represents the fraction of the incident radiation absorbed by the sample \cite{Braslavsky2007} and is defined as follows:

\begin{equation}
\label{eq:factor}
f_{\lambda}=1-T_{\lambda}=1-10^{-A_{\lambda}}
\end{equation}

where $T_{\lambda}$ is the solution transmittance when the reflection and scattering are negligible, and $A_{\lambda}$ is the absorbance spectrum. Therefore, the absorbed spectral photon irradiance of a sample exposed to sunlight is given by:

\begin{equation}
\label{eq:Ea}
E^{a}_{n,p,\lambda}= f_{\lambda} \cdot \left(\frac{E^{S}_{\lambda}}{{N_{A}h\nu}}\right)  
\end{equation}

As an example, Figure \ref{overlap} shows the functions $f_{\lambda}$ and $E^{S}_{n,p,\lambda}$, as well as their product $E^{a}_{n,p,\lambda}$, for an experiment carried out with a H$_{2}$Bip solution in a clear sky day. The absorbed photon irradiance of the sample ($E^{a}_{n,p}$) is obtained by integration of $E^{a}_{n,p,\lambda}$ (grey area in Figure \ref{overlap}) and mathematically can be expressed by:

\begin{equation}
\label{eq:Elamb}
E^{a}_{n,p}=\int_{\lambda_{1}}^{\lambda_{2}}E^{a}_{n,p,\lambda}d\lambda
\end{equation}

Finally, the absorbed photon flux density ($q^{a,V}_{n,p}$) of a given aqueous solutions during the solar exposure can be calculated from the $E^{a}_{n,p}$ as follows:

\begin{equation}
\label{eq:qaVnp}
q^{a,V}_{n,p}= \frac{S}{V} \cdot E^{a}_{n,p} 
\end{equation}

where V and S are the volume and the area of the cell containing the sample exposed to the irradiation, respectively.

Therefore combining Equations \ref{eq:factor} to \ref{eq:qaVnp}, the complete equation to calculate $q^{a,V}_{n,p}$ is obtained:

\begin{equation}
\label{eq:Ip}
q^{a,V}_{n,p}=\frac{S}{V}\int_{\lambda_{1}}^{\lambda_{2}} \left(1-10^{-A_{\lambda}}\right)\frac{E^{S}_{\lambda}}{{N_{A}h\nu}} d\lambda
\end{equation}

The quantum yields of reactant disappearance ($\Phi_{R}$) can be calculated as follows:

\begin{equation}
\label{eq:rendimiento}
\Phi_{R}=-\frac{\left(d\left[R\right]/dt\right)_{0}}{q^{a,V}_{n,p}}
\end{equation}

where $\left(d\left[R\right]/dt\right)_{0}$ is the initial rate of reactant consumption. For determining the initial rates, the experiments were carried out during periods of time within which the change of $q^{a,V}_{n,p}$ was lower than 20 $\%$. In our experiments, this condition was fulfilled at exposure times lower than 60 s. The initial rates were obtained from the slope of the corresponding plots of concentration vs. irradiation time within such time windows, where the time evolution of the concentrations of reactants and products followed a zero-order rate. $\Phi_{R}$ values of 0.05$\pm$0.01 and 0.037$\pm$0.004 were obtained for H$_{2}$Bip and Bip, respectively. These values are equal, within experimental error, to those reported in literature, calculated using a lamp \citep{Vignoni2009, Vignoni2010}.

 