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@ 547,13 +547,17 @@ Let us call $\Psi^J$ the linear combination of Slater determinant minimizing the


\end{equation}


Such a wave function $\Psi^J$ satisfies the generalized Hermitian eigenvalue equation


\begin{equation}


\toto{


e^{J} \hat{H} \qty( e^{J} \Psi^J ) = E e^{2J} \Psi^J,


}


\label{eq:cij}


\end{equation}


but also the nonHermitian \manu{transcorrelated eigenvalue problem \cite{many_things} MANU:CITATIONS}


but also the nonHermitian \toto{transcorrelated eigenvalue problem \cite{many_things} MANU:CITATIONS}


\begin{equation}


\label{eq:transcor}


\toto{


e^{J} \hat{H} \qty( e^{J} \Psi^J) = E \Psi^J,


}


\end{equation}


which is much easier to handle despite its nonHermiticity.


Of course, the FNDMC energy of $\Phi$ depends therefore only on the nodes of $\Psi^J$.


@ 574,8 +578,8 @@ a simple one and twobody Jastrow factor \toto{$e^J$ of the form $\exp(J_{eN} +


\end{eqnarray}


$J_\text{eN}$ contains the electronnucleus terms with a single parameter


$\alpha_A$ per atom, and $J_\text{ee}$ contains the electronelectron terms


where the indices $i$ and $j$ loop over all electrons. The parameters $a=1/2$


and $b=0.89$ were fixed, and the parameters $\gamma_O=1.15$ and $\gamma_H=0.35$


where the indices $i$ and $j$ loop over all electron pairs. The parameters $a=1/2$


and $b=0.89$ were fixed, and the parameters $\gamma_{\text{O}}=1.15$ and $\gamma_{\text{H}}=0.35$


were obtained by energy minimization with a single determinant.


The optimal CI expansion $\Psi^J$ is obtained by sampling the matrix elements


of the Hamiltonian ($\mathbf{H}$) and the overlap ($\mathbf{S}$), in the



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