\begin{table}[]
    \tiny{
    \centering
    \begin{tabular}{l|c|c|c|c|c|c|c|c|c|c|c|c|}
        \hline
        Cu(111)                                     &\multicolumn{3}{c|}{MAD (eV) H$_2$}& \multicolumn{3}{c|}{MSD (eV) H$_2$} &\multicolumn{3}{c|}{MAD (eV) D$_2$}& \multicolumn{3}{c|}{MSD (eV) D$_2$}  \\
                                                    & total  & $\nu=0$ & $\nu=1$ & total     & $\nu=0$   & $\nu=1$     & total  & $\nu=0$ & $\nu=1$   & total     & $\nu=0$   & $\nu=1$      \\
        \hline
        SRP48\cite{diaz2009chemically}              & 0.0434 & 0.0522 & 0.0301   & 0.0373    & 0.0522    & 0.0151      & 0.0254 & 0.0243 & 0.0272     & -0.0066 & -0.0008 & -0.0152       \\
        MS-B86bl\cite{smeets2019mgga}               & 0.0274 & 0.0165 & 0.0438   & -0.0149   & 0.0044    & -0.0438     & 0.0551 & 0.0440 & 0.0717     & -0.0551 & -0.0440 & -0.0717      \\
        B86SRP68-DF2                                & 0.0209 & 0.0142 & 0.0308   & -0.0176   & -0.0089   & -0.0308     & 0.0663 & 0.0640 & 0.0698     & -0.0663 & -0.0640 & -0.0698      \\
        PBE$\alpha$57-DF2                           & 0.0140 & 0.0117 & 0.0174   & 0.0040    & 0.0054    & 0.0018      & 0.0573 & 0.0615 & 0.0509     & -0.0573 & -0.0616 & -0.0509      \\
        SRPsol63-DF2                                & 0.0153 & 0.0136 & 0.0177   & -0.0025   & 0.0064    & -0.0158     & 0.0510 & 0.0487 & 0.0545     & -0.0511 & -0.0487 & -0.0545      \\
        optPBE-DF2\cite{wijzenbroek2015vdw}         & 0.0146 & 0.0147 & 0.0143   & 0.0054    & 0.0111    & -0.0032     & 0.0480 & 0.0481 & 0.0478     & -0.0480 & -0.0615 & -0.0478      \\
        \hline
        \multicolumn{13}{c}{} \\
        \hline
        Au(111)                                     &\multicolumn{3}{c|}{MAD (eV) H$_2$}& \multicolumn{3}{c|}{MSD (eV) H$_2$}&\multicolumn{3}{c|}{MAD (eV) D$_2$}&\multicolumn{3}{c|}{MSD (eV) D$_2$}  \\
                                                    & total     & $\nu=0$   & $\nu=1$   & total     & $\nu=0$   & $\nu=1$    & total     & $\nu=0$   & $\nu=1$   & total     & $\nu=0$   & $\nu=1$     \\
        \hline
        PBE                                         & 0.1025    & 0.1333    & 0.0718    & 0.1025    & 0.1333    &  0.0718    & 0.0955    & 0.1178    & 0.0734    & 0.0955    & 0.1176    & 0.0733 \\
        SRP48\cite{wijzenbroek2016dynamics}         & 0.0309    & 0.0468    & 0.0151    & 0.0158    & 0.0468    & -0.0151    & 0.0229    & 0.0325    & 0.0133    & 0.0094    & 0.0321    & -0.0131\\
        PBE$\alpha$57-DF2                           & 0.0189    & 0.0241    & 0.0136    & 0.0026    & 0.0177    & -0.0125    & 0.0187    & 0.0246    & 0.0127    & 0.0125    & 0.0246    & 0.0005  \\
        B86SRP68-DF2                                & 0.0270    & 0.0457    & 0.0083    & 0.0217    & 0.0457    & -0.0022    & 0.0190    & 0.0275    & 0.0105    & 0.0113    & 0.0275    & -0.0050  \\
        optPBE-DF2\cite{wijzenbroek2016dynamics}    & 0.0260    & 0.0225    & 0.0259    & -0.0044   & 0.0206    & -0.0296    & 0.0212    & 0.0116    & 0.0309    & -0.0143   & 0.0023    & -0.0307\\
        MS-PBEl\cite{smeets2019mgga}                & 0.0329    & 0.0393    & 0.0264    & 0.0028    & 0.0320    & -0.0264    & 0.0270    & 0.0116    & 0.0105    &  0.0212   & 0.0435    & -0.0009 \\
        \hline
    \end{tabular}
    \caption{Mean absolute and mean signed deviations for the theoretical $E_0(\nu,J)$ parameters compared to experimental values for Cu(111)\cite{kaufmannCu211} and Au(111)\cite{shuai2017evidence}.}
    \label{tab:E0}
    }
\end{table}