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\begin{document}
\section{Supplementary material}


\subsection{Impurity natural orbital occupancies obtained with CISD solver during the iterations of self-consistent cycle for cubic hydrogen at various lattice constants,  9 bath orbitals.}

\begin{table}[h!]
\caption{$a_{0}=1.4$ $\mathring{A}$}
\begin{tabular}{l cccccccc} 
\hline
\hline
iter/orb no. & 1-3 & 4 & 5 & 6 & 7 & 8 & 9-10 \\
\hline
1    &  2.000  &  1.999 &  1.908 &  0.091 &  0.001 &  0.001  &  0.000\\
2    &  2.000  &  1.999 &  1.886 &  0.113 &  0.001 &  0.001  &  0.000\\
3    &  2.000  &  1.999 &  1.906 &  0.094 &  0.001 &  0.000  &  0.000\\
4    &  2.000  &  1.999 &  1.902 &  0.098 &  0.001 &  0.000  &  0.000\\
5    &  2.000  &  1.999 &  1.898 &  0.101 &  0.001 &  0.001  &  0.000\\
6    &  2.000  &  1.999 &  1.905 &  0.094 &  0.001 &  0.001  &  0.000\\
7    &  2.000  &  1.999 &  1.905 &  0.094 &  0.001 &  0.001  &  0.000\\
8-20 &  2.000  &  1.999 &  1.905 &  0.095 &  0.001 &  0.000  &  0.000\\
\hline
\hline
\end{tabular}
\caption{$a_{0}=2.25$ $\mathring{A}$}
\begin{tabular}{l ccccccc }
\hline
\hline
iter/orb no. & 1-3 & 4 & 5 & 6 & 7 & 8-10 \\
\hline
1 &    2.000 &  1.999 &  1.801 &  0.199 &  0.002 &   0.000 \\
2 &    2.000 &  1.999 &  1.742 &  0.258 &  0.001 &   0.000 \\
3 &    2.000 &  1.999 &  1.725 &  0.275 &  0.001 &   0.000 \\
4 &    2.000 &  1.999 &  1.720 &  0.280 &  0.001 &   0.000 \\
5 &    2.000 &  1.999 &  1.720 &  0.280 &  0.001 &   0.000 \\
\hline
\hline
\end{tabular}
\caption{$a_{0}=6.0$ $\mathring{A}$}
\begin{tabular}{l ccccccc }
\hline
\hline
iter/orb no. & 1-3 & 4 & 5 & 6 & 7 & 8-10 \\
\hline
1 &    2.000 &  1.998 &  1.160 &  0.840 &  0.002 &  0.000 \\
2 &    2.000 &  2.000 &  1.000 &  1.000 &  0.000 &  0.000 \\
3 &    2.000 &  2.000 &  1.000 &  1.000 &  0.000 &  0.000 \\
4 &    2.000 &  2.000 &  1.000 &  1.000 &  0.000 &  0.000 \\
\hline
\hline
\end{tabular}
\end{table}


\subsection{Calculation details}
\begin{itemize} 
\item 5 bath dmft self-consistency using CISD solver was carried out for 200 imaginary frequencies and $\beta=100$, the used damping factor was $\alpha=0.4$, convergence threshold on self-energy $\tau=0.005$. 
\item 9 bath dmft self-consistency using both CISD and FCI solvers for all the lattice constants was carried out for 200 imaginary frequencies and $\beta=100$, the used damping factor was $\alpha=0.7$, convergence threshold on self-energy $\tau=0.005$. 
\item 19 bath dmft self-consistency using CISD solver was carried out for 200 imaginary frequencies and $\beta=100$, the used damping factor was $\alpha=0.8$, convergence threshold on self-energy $\tau=0.009$.  
\end{itemize}
\end{document}
