scemama/RSDFT-CIPSI-QMC
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Anthony Scemama 2020-08-16 15:26:52 +02:00
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Manuscript/rsdft-cipsi-qmc.tex
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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: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