\subsection{The modified Kempers model}
Using the the modified Kempers approach presented in Section \ref{sec:method_kempers_hs}, the Soret coefficient for several mixtures was predicted and compared to simulation data for Mie fluids. The SAFT-VR Mie EoS was used to compute the required thermodynamic properties, using the parameters indicated in Table \ref{tab:kempers_bad}. Computing the Soret coefficient for only a few mixtures, shown in Table \ref{tab:kempers_bad} quickly indicated that this approach did not give systematic improvement compared to Kempers 2001 model. 

Further investigation was made into how the discrepancy between model predictions and reported data varied with potential parameters, molecular masses and the state point. However the results were the same as those previously seen,\cite{prosjektoppgave} namely that the Kempers model varies between giving predictions in somewhat agreement with data to missing by orders of magnitude. Additionally, the disagreement did not clearly correlate with any meaningful property, other the fact that predictions improved in the low density regime in which the model reduces to the Enskog solutions. The modified Kempers approach was therefore quickly abandoned, and for the case of brevity only the values in Table \ref{tab:kempers_bad} are reported, as an illustrative example of the quality and consistency of the model predictions across the board.

\begin{table}[htb]
    \centering
    \caption{Soret coefficients of the first component in various equimolar mixtures at the reduced state point $T^* = 0.85$, $\rho^* = 0.81$. Reported values by Reith and Müller-Pathe.\cite{reith_muller} Predicted values using (a) the modified Kempers CoV model, (b) the Kempers 2001 CoV model. The state point has been reduced using the cross interaction parameters obtained via the LB mixing rules. All mixtures used the Lennard-Jones (12-6) exponents.}
    \begin{tabular}{c c c c}
    \toprule
        \multirow{2}{*}{Mixture}    &   Reported    &   Predicted (a) & Predicted (b) \\
        & $S_T$ [\si{\per\milli\kelvin}] & $S_T$ [\si{\per\milli\kelvin}] & $S_T$ [\si{\per\milli\kelvin}] \\
    \midrule
        Xe,Kr        & 5.1  & 10.3  & 8.2  \\
        Ar,\ce{CH4}  & 9.3  & 20.6   & 9.0  \\
        Xe,Ar        & 18.6 & 3.8  & 44.7 \\
        Kr,\ce{CH4}  & 22.3 & 25.5  & 6.4 \\
        Xe,\ce{CH4}  & 23.1 & 17.6  & 28.2 \\
    \midrule
    \midrule
    Component & $\sigma$ [Å] & $\varepsilon$ [$k_B$] & \\
    \midrule
    Ar & 3.405 & 120.27 & \\
    Kr & 3.633 & 167.18 & \\
    Xe & 3.975 & 206.87 & \\
    \ce{CH4} & 3.740 & 152.75 & \\
    \bottomrule
    \end{tabular}
    \label{tab:kempers_bad}
\end{table}