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@ -366,7 +366,7 @@ energy is obtained as
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E_0= \mel{\Psi^{\mu}}{\hat{T}+\hat{W}_\text{{ee}}^{\text{lr},\mu}+\hat{V}_{\text{ne}}}{\Psi^{\mu}}+\bar{E}^{\text{sr},\mu}_{\text{Hxc}}[n_{\Psi^\mu}].
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E_0= \mel{\Psi^{\mu}}{\hat{T}+\hat{W}_\text{{ee}}^{\text{lr},\mu}+\hat{V}_{\text{ne}}}{\Psi^{\mu}}+\bar{E}^{\text{sr},\mu}_{\text{Hxc}}[n_{\Psi^\mu}].
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\end{equation}
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\end{equation}
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Note that for $\mu=0$ the long-range interaction vanishes, \ie,
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Note that, for $\mu=0$, the long-range interaction vanishes, \ie,
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$w_{\text{ee}}^{\text{lr},\mu=0}(r) = 0$, and thus RS-DFT reduces to standard
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$w_{\text{ee}}^{\text{lr},\mu=0}(r) = 0$, and thus RS-DFT reduces to standard
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KS-DFT and $\Psi^\mu$ is the KS determinant. For $\mu = \infty$, the long-range
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KS-DFT and $\Psi^\mu$ is the KS determinant. For $\mu = \infty$, the long-range
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interaction becomes the standard Coulomb interaction, \ie,
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interaction becomes the standard Coulomb interaction, \ie,
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@ -404,7 +404,7 @@ In the outer (macro-iteration) loop (red), at the $k$th iteration, a CIPSI selec
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to obtain $\Psi^{\mu\,(k)}$ with the RS-DFT Hamiltonian $\hat{H}^{\mu\,(k)}$
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to obtain $\Psi^{\mu\,(k)}$ with the RS-DFT Hamiltonian $\hat{H}^{\mu\,(k)}$
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parameterized using the current one-electron density $n^{(k)}$.
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parameterized using the current one-electron density $n^{(k)}$.
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At each iteration, the number of determinants in $\Psi^{\mu\,(k)}$ increases.
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At each iteration, the number of determinants in $\Psi^{\mu\,(k)}$ increases.
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One exits the outer loop when the absolute energy difference between two successive macro-iterations $\Delta E^{(k)}$ is below a threshold $\tau_1$ that has been set to $10^{-3}$ \hartree{} in the present study which is consistent with the CIPSI threshold (see Sec.~\ref{sec:comp-details}).
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One exits the outer loop when the absolute energy difference between two successive macro-iterations $\Delta E^{(k)}$ is below a threshold $\tau_1$ that has been set to $10^{-3}$ \hartree{} in the present study and which is consistent with the CIPSI threshold (see Sec.~\ref{sec:comp-details}).
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An inner (micro-iteration) loop (blue) is introduced to accelerate the
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An inner (micro-iteration) loop (blue) is introduced to accelerate the
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convergence of the self-consistent calculation, in which the set of
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convergence of the self-consistent calculation, in which the set of
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determinants in $\Psi^{\mu\,(k,l)}$ is kept fixed, and only the diagonalization of
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determinants in $\Psi^{\mu\,(k,l)}$ is kept fixed, and only the diagonalization of
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@ -453,7 +453,7 @@ QMC calculations have been performed with \textit{QMC=Chem},\cite{Scemama_2013}
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in the determinant localization approximation (DLA),\cite{Zen_2019}
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in the determinant localization approximation (DLA),\cite{Zen_2019}
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where only the determinantal component of the trial wave
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where only the determinantal component of the trial wave
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function is present in the expression of the wave function on which
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function is present in the expression of the wave function on which
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the pseudopotential is localized. Hence, in the DLA the fixed-node
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the pseudopotential is localized. Hence, in the DLA, the fixed-node
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energy is independent of the Jastrow factor, as in all-electron
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energy is independent of the Jastrow factor, as in all-electron
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calculations. Simple Jastrow factors were used to reduce the
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calculations. Simple Jastrow factors were used to reduce the
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fluctuations of the local energy (see Sec.~\ref{sec:rsdft-j} for their explicit expression).
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fluctuations of the local energy (see Sec.~\ref{sec:rsdft-j} for their explicit expression).
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