OK up to results

Manuscript/rsdft-cipsi-qmc.tex

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