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@ -547,13 +547,17 @@ Let us call $\Psi^J$ the linear combination of Slater determinant minimizing the
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\end{equation}
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\end{equation}
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Such a wave function $\Psi^J$ satisfies the generalized Hermitian eigenvalue equation
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Such a wave function $\Psi^J$ satisfies the generalized Hermitian eigenvalue equation
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\begin{equation}
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\begin{equation}
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\toto{
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e^{J} \hat{H} \qty( e^{J} \Psi^J ) = E e^{2J} \Psi^J,
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e^{J} \hat{H} \qty( e^{J} \Psi^J ) = E e^{2J} \Psi^J,
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}
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\label{eq:ci-j}
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\label{eq:ci-j}
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\end{equation}
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\end{equation}
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but also the non-Hermitian \manu{transcorrelated eigenvalue problem \cite{many_things} MANU:CITATIONS}
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but also the non-Hermitian \toto{transcorrelated eigenvalue problem \cite{many_things} MANU:CITATIONS}
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\begin{equation}
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\begin{equation}
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\label{eq:transcor}
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\label{eq:transcor}
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\toto{
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e^{-J} \hat{H} \qty( e^{J} \Psi^J) = E \Psi^J,
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e^{-J} \hat{H} \qty( e^{J} \Psi^J) = E \Psi^J,
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}
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\end{equation}
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\end{equation}
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which is much easier to handle despite its non-Hermiticity.
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which is much easier to handle despite its non-Hermiticity.
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Of course, the FN-DMC energy of $\Phi$ depends therefore only on the nodes of $\Psi^J$.
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Of course, the FN-DMC energy of $\Phi$ depends therefore only on the nodes of $\Psi^J$.
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@ -574,8 +578,8 @@ a simple one- and two-body Jastrow factor \toto{$e^J$ of the form $\exp(J_{eN} +
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\end{eqnarray}
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\end{eqnarray}
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$J_\text{eN}$ contains the electron-nucleus terms with a single parameter
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$J_\text{eN}$ contains the electron-nucleus terms with a single parameter
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$\alpha_A$ per atom, and $J_\text{ee}$ contains the electron-electron terms
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$\alpha_A$ per atom, and $J_\text{ee}$ contains the electron-electron terms
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where the indices $i$ and $j$ loop over all electrons. The parameters $a=1/2$
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where the indices $i$ and $j$ loop over all electron pairs. The parameters $a=1/2$
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and $b=0.89$ were fixed, and the parameters $\gamma_O=1.15$ and $\gamma_H=0.35$
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and $b=0.89$ were fixed, and the parameters $\gamma_{\text{O}}=1.15$ and $\gamma_{\text{H}}=0.35$
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were obtained by energy minimization with a single determinant.
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were obtained by energy minimization with a single determinant.
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The optimal CI expansion $\Psi^J$ is obtained by sampling the matrix elements
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The optimal CI expansion $\Psi^J$ is obtained by sampling the matrix elements
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of the Hamiltonian ($\mathbf{H}$) and the overlap ($\mathbf{S}$), in the
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of the Hamiltonian ($\mathbf{H}$) and the overlap ($\mathbf{S}$), in the
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