From 5ca4f1247c1495f7809b037d1eb6bf148b12c9b5 Mon Sep 17 00:00:00 2001 From: Anthony Scemama Date: Sun, 16 Aug 2020 15:26:52 +0200 Subject: [PATCH] Minor change --- Manuscript/rsdft-cipsi-qmc.tex | 10 +++++++--- 1 file changed, 7 insertions(+), 3 deletions(-) diff --git a/Manuscript/rsdft-cipsi-qmc.tex b/Manuscript/rsdft-cipsi-qmc.tex index dc26882..e679fa6 100644 --- a/Manuscript/rsdft-cipsi-qmc.tex +++ b/Manuscript/rsdft-cipsi-qmc.tex @@ -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:ci-j} \end{equation} -but also the non-Hermitian \manu{transcorrelated eigenvalue problem \cite{many_things} MANU:CITATIONS} +but also the non-Hermitian \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 non-Hermiticity. Of course, the FN-DMC energy of $\Phi$ depends therefore only on the nodes of $\Psi^J$. @@ -574,8 +578,8 @@ a simple one- and two-body Jastrow factor \toto{$e^J$ of the form $\exp(J_{eN} + \end{eqnarray} $J_\text{eN}$ contains the electron-nucleus terms with a single parameter $\alpha_A$ per atom, and $J_\text{ee}$ contains the electron-electron 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