Minor changes

Manuscript/rsdft-cipsi-qmc.tex

@@ -701,7 +701,7 @@ former can vary by about 10$\%$ in some regions.
 In the high-density region of the \ce{O-H} bond, the value of the on-top
 pair density obtained from $\Psi^J$ is superimposed with
 $\Psi^{\mu=0.5}$, and at a large distance the on-top pair density of $\Psi^J$ is
-the closest to $\mu=\infty$. The integrated on-top pair density
+the closest to that of $\Psi^{\mu=\infty}$. The integrated on-top pair density
 obtained with $\Psi^J$ is $\expval{P}=1.404$, which nestles between the values obtained at
 $\mu=0.5$ and $\mu=1$~bohr$^{-1}$, consistently with the FN-DMC energies
 and the overlap curve depicted in Fig.~\ref{fig:overlap}.
@@ -723,7 +723,7 @@ Regarding now the transcorrelated Hamiltonian $e^{-J}He^J$, as pointed out by Te
 the effective two-body interaction induced by the presence of a Jastrow factor
 can be non-divergent when a proper two-body Jastrow factor $J_\text{ee}$ is chosen, \ie, the Jastrow factor must fulfill the so-called electron-electron cusp conditions. \cite{Kato_1957,Pack_1966}
 There is therefore a clear parallel between $\hat{W}_{\text{ee}}^{\text{lr},\mu}$ in RS-DFT and $J_\text{ee}$ in FN-DMC.
-Moreover, the one-body Jastrow term $J_\text{eN}$ ensures that the one-body density remain unchanged when the CI coefficients are re-optmized in the presence of $J_\text{ee}$.
+Moreover, the one-body Jastrow term $J_\text{eN}$ ensures that the one-body density remains unchanged when the CI coefficients are re-optmized in the presence of $J_\text{ee}$.
 There is then a second clear parallel between $\hat{\bar{V}}_{\text{Hxc}}^{\text{sr},\mu}[n]$ in RS-DFT and $J_\text{eN}$ in FN-DMC.
 Thus, one can understand the similarity between the eigenfunctions of $H^\mu$ and the optimization of the Slater-Jastrow wave function:
 they both deal with an effective non-divergent interaction but still