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Anthony Scemama 2023-01-04 18:26:03 +01:00
parent f829036f0e
commit 52a00468c0
1 changed files with 9 additions and 15 deletions
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@ -154,14 +154,14 @@ with the same name suffixed by ~_im~.
** Periodic boundary calculations (pbc group) ** 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. defined in this group.
#+NAME: pbc #+NAME: pbc
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|------------+---------+------------+-------------------------| |------------+---------+------------+-------------------------|
| ~periodic~ | ~int~ | | ~1~: true or ~0~: false | | ~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") #+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) \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 reciprocal space, defined in the ~pbc~ group. The kinetic energy
cutoff ~e_cut~ is the only input data relevant to plane waves. 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}) \chi_i (\mathbf{r}) = \mathcal{N}_i\, P_{\eta(i)}(\mathbf{r})\, R_{\theta(i)} (\mathbf{r})
\] \]
where $i$ is the atomic orbital index, where $i$ is the atomic orbital index, $P$ refers to either the
$P$ encodes for either the
polynomials or the spherical harmonics, $\theta(i)$ returns the polynomials or the spherical harmonics, $\theta(i)$ returns the
shell on which the AO is expanded, and $\eta(i)$ denotes which shell on which the AO is expanded, and $\eta(i)$ denotes which
angular function is chosen. angular function is chosen.
@ -1130,7 +1129,7 @@ power = [
* Correlation factors * Correlation factors
** Jastrow factor (jastrow group) ** 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: $\Psi = \Phi \times \exp(J)$, expansion is multiplied: $\Psi = \Phi \times \exp(J)$,
where where
@ -1190,14 +1189,14 @@ power = [
The terms $J_{\text{ee}}^\infty$ and $J_{\text{eN}}^\infty$ are shifts to ensure that 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. $J_{\text{ee}}$ 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
\[ \[
f(r) = \frac{1-e^{-\kappa\, r}}{\kappa} \text{ and } f(r) = \frac{1-e^{-\kappa\, r}}{\kappa} \text{ and }
g_\alpha(r) = e^{-\kappa_\alpha\, r}. g_\alpha(r) = e^{-\kappa_\alpha\, r}.
\] \]
*** mu *** Mu
The "mu" Jastrow factor has only a single parameter $\mu$ for the The "mu" Jastrow factor has only a single parameter $\mu$ for the
[[https://doi.org/10.1063/5.0044683][electron-electron term]]: [[https://doi.org/10.1063/5.0044683][electron-electron term]]:
@ -1209,19 +1208,14 @@ power = [
e^{-(\mu\,r_{ij})^2} e^{-(\mu\,r_{ij})^2}
\] \]
# It was then updated for frozen-core calculations by introducing a *** Mu with frozen core
# set of electron-electron-nucleus terms with one parameter per nucleus:
# \[
# J_{\text{eeN}}(\mathbf{r}) =
# \]
*** Table of values *** Table of values
#+name: jastrow #+name: jastrow
| Variable | Type | Dimensions | Description | | 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 | | ~ee_num~ | ~dim~ | | Number of Electron-electron parameters |
| ~en_num~ | ~dim~ | | Number of Electron-nucleus parameters | | ~en_num~ | ~dim~ | | Number of Electron-nucleus parameters |
| ~een_num~ | ~dim~ | | Number of Electron-electron-nucleus parameters | | ~een_num~ | ~dim~ | | Number of Electron-electron-nucleus parameters |