For Abdallah

trex.org

@@ -154,14 +154,14 @@ with the same name suffixed by ~_im~.
 
 ** Periodic boundary calculations (pbc group)
 
-   A single $k$-point per TREXIO file can be stored. The $k$-point is
+   A single k-point per TREXIO file can be stored. The k-point is
    defined in this group.
 
    #+NAME: pbc
    | Variable   | Type    | Dimensions | Description             |
    |------------+---------+------------+-------------------------|
    | ~periodic~ | ~int~   |            | ~1~: true or ~0~: false |
-   | ~k_point~  | ~float~ | ~(3)~      | $k$-point sampling      |
+   | ~k_point~  | ~float~ | ~(3)~      | k-point sampling        |
 
    #+CALL: json(data=pbc, title="pbc")
 
@@ -285,7 +285,7 @@ with the same name suffixed by ~_im~.
        \chi_j(r) = \exp \left( -i \mathbf{k}_j \mathbf{r} \right)
     \]
 
-    The basis set is defined as the array of $k$-points in the
+    The basis set is defined as the array of k-points in the
     reciprocal space, defined in the ~pbc~ group. The kinetic energy
     cutoff ~e_cut~ is the only input data relevant to plane waves.
 
@@ -612,8 +612,7 @@ power = [
    \chi_i (\mathbf{r}) = \mathcal{N}_i\, P_{\eta(i)}(\mathbf{r})\, R_{\theta(i)} (\mathbf{r})
    \]
 
-   where $i$ is the atomic orbital index,
-   $P$ encodes for either the
+   where $i$ is the atomic orbital index, $P$ refers to either the
    polynomials or the spherical harmonics, $\theta(i)$ returns the
    shell on which the AO is expanded, and $\eta(i)$ denotes which
    angular function is chosen.
@@ -1130,7 +1129,7 @@ power = [
 * Correlation factors
 ** Jastrow factor (jastrow group)
 
-   The Jastrow factor is an $N$-electron function to which the CI
+   The Jastrow factor is an N-electron function to which the CI
    expansion is multiplied: $\Psi = \Phi \times \exp(J)$,
    where
 
@@ -1190,14 +1189,14 @@ power = [
    The terms $J_{\text{ee}}^\infty$ and $J_{\text{eN}}^\infty$ are shifts to ensure that
    $J_{\text{ee}}$ and $J_{\text{eN}}$ have an asymptotic value of zero.
 
-   $f$ and $g$ are scaling function defined as
+   $f$ and $g$ are scaling functions defined as
 
    \[
    f(r) = \frac{1-e^{-\kappa\, r}}{\kappa} \text{ and }
    g_\alpha(r) = e^{-\kappa_\alpha\, r}.
    \]
 
-*** mu
+*** Mu
 
     The "mu" Jastrow factor has only a single parameter $\mu$ for the
  [[https://doi.org/10.1063/5.0044683][electron-electron term]]: 
@@ -1209,19 +1208,14 @@ power = [
    e^{-(\mu\,r_{ij})^2}
    \]
 
-#  It was then updated for frozen-core calculations by introducing a
-#  set of electron-electron-nucleus terms with one parameter per nucleus:
-
-#  \[
-#  J_{\text{eeN}}(\mathbf{r}) =
-#  \]
+*** Mu with frozen core
 
 *** Table of values
    
    #+name: jastrow
   | Variable      | Type     | Dimensions          | Description                                                     |
   |---------------+----------+---------------------+-----------------------------------------------------------------|
-  | ~type~        | ~string~ |                     | Type of Jastrow factor: ~CHAMP~ or ~Mu~                         |
+  | ~type~        | ~string~ |                     | Type of Jastrow factor: ~CHAMP~, ~Mu~ or ~MuFC~                 |
   | ~ee_num~      | ~dim~    |                     | Number of Electron-electron parameters                          |
   | ~en_num~      | ~dim~    |                     | Number of Electron-nucleus parameters                           |
   | ~een_num~     | ~dim~    |                     | Number of Electron-electron-nucleus parameters                  |