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Added plane waves

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Anthony Scemama 2022-12-26 13:15:16 +01:00
parent c98c4b4721
commit bab56408e1
2 changed files with 99 additions and 73 deletions
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@ -12,6 +12,7 @@ CHANGES
- Added `float buffered` type for vectors like CI/CSF coefficients - Added `float buffered` type for vectors like CI/CSF coefficients
- .git folder is no longer needed to activate TREXIO_DEVEL mode - .git folder is no longer needed to activate TREXIO_DEVEL mode
- Renamed debian folder into helpers-debian - Renamed debian folder into helpers-debian
- Added plane wave basis set
- Added trexio_to_bitfield_list functionality - Added trexio_to_bitfield_list functionality
- Added `trexio_has_group` functionality - Added `trexio_has_group` functionality
- Added OCaml binding - Added OCaml binding

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trex.org
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@ -276,78 +276,97 @@ power = [
* Basis set (basis group) * Basis set (basis group)
We consider here basis functions centered on nuclei. Hence, we enable
the possibility to define /dummy atoms/ to place basis functions in
random positions.
The atomic basis set is defined as a list of shells. Each shell $s$ is ** Gaussian and Slater-type orbitals
centered on a center $A$, possesses a given angular momentum $l$ and a
radial function $R_s$. The radial function is a linear combination of
$N_{\text{prim}}$ /primitive/ functions that can be of type
Slater ($p=1$) or Gaussian ($p=2$),
parameterized by exponents $\gamma_{ks}$ and coefficients $a_{ks}$:
\[
R_s(\mathbf{r}) = \mathcal{N}_s \vert\mathbf{r}-\mathbf{R}_A\vert^{n_s}
\sum_{k=1}^{N_{\text{prim}}} a_{ks}\, f_{ks}(\gamma_{ks},p)\,
\exp \left( - \gamma_{ks}
\vert \mathbf{r}-\mathbf{R}_A \vert ^p \right).
\]
In the case of Gaussian functions, $n_s$ is always zero. We consider here basis functions centered on nuclei. Hence, we enable
the possibility to define /dummy atoms/ to place basis functions in
random positions.
Different codes normalize functions at different levels. Computing The atomic basis set is defined as a list of shells. Each shell $s$ is
normalization factors requires the ability to compute overlap centered on a center $A$, possesses a given angular momentum $l$ and a
integrals, so the normalization factors should be written in the radial function $R_s$. The radial function is a linear combination of
file to ensure that the file is self-contained and does not need the $N_{\text{prim}}$ /primitive/ functions that can be of type
client program to have the ability to compute such integrals. Slater ($p=1$) or Gaussian ($p=2$),
parameterized by exponents $\gamma_{ks}$ and coefficients $a_{ks}$:
\[
R_s(\mathbf{r}) = \mathcal{N}_s \vert\mathbf{r}-\mathbf{R}_A\vert^{n_s}
\sum_{k=1}^{N_{\text{prim}}} a_{ks}\, f_{ks}(\gamma_{ks},p)\,
\exp \left( - \gamma_{ks}
\vert \mathbf{r}-\mathbf{R}_A \vert ^p \right).
\]
Some codes assume that the contraction coefficients are for a linear In the case of Gaussian functions, $n_s$ is always zero.
combination of /normalized/ primitives. This implies that a normalization
constant for the primitive $ks$ needs to be computed and stored. If
this normalization factor is not required, $f_{ks}=1$.
Some codes assume that the basis function are normalized. This Different codes normalize functions at different levels. Computing
implies the computation of an extra normalization factor, $\mathcal{N}_s$. normalization factors requires the ability to compute overlap
If the the basis function is not considered normalized, $\mathcal{N}_s=1$. integrals, so the normalization factors should be written in the
file to ensure that the file is self-contained and does not need the
client program to have the ability to compute such integrals.
Some codes assume that the contraction coefficients are for a linear
combination of /normalized/ primitives. This implies that a normalization
constant for the primitive $ks$ needs to be computed and stored. If
this normalization factor is not required, $f_{ks}=1$.
Some codes assume that the basis function are normalized. This
implies the computation of an extra normalization factor, $\mathcal{N}_s$.
If the the basis function is not considered normalized, $\mathcal{N}_s=1$.
All the basis set parameters are stored in one-dimensional arrays.
** Plane waves
A plane wave is defined as
\[
\chi_j(r) = \exp \left( -i \mathbf{k}_j \mathbf{r} \right)
\]
The basis set is defined as the array of $k$-points in the
reciprocal space, defined in the ~pbc~ group. The kinetic energy
cutoff ~e_cut~ is the only input data relevant to plane waves.
** Data definitions
#+NAME: basis
| Variable | Type | Dimensions | Description |
|-----------------+---------+---------------------+-----------------------------------------------------------------|
| ~type~ | ~str~ | | Type of basis set: "Gaussian", "Slater" or "PW" for plane waves |
| ~prim_num~ | ~dim~ | | Total number of primitives |
| ~shell_num~ | ~dim~ | | Total number of shells |
| ~nucleus_index~ | ~index~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices |
| ~shell_ang_mom~ | ~int~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta |
| ~shell_factor~ | ~float~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$) |
| ~r_power~ | ~int~ | ~(basis.shell_num)~ | Power to which $r$ is raised ($n_s$) |
| ~shell_index~ | ~index~ | ~(basis.prim_num)~ | One-to-one correspondence between primitives and shell index |
| ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) |
| ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) |
| ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) |
| ~e_cut~ | ~float~ | | Energy cut-off for plane-wave calculations |
All the basis set parameters are stored in one-dimensional arrays: #+CALL: json(data=basis, title="basis")
#+NAME: basis #+RESULTS:
| Variable | Type | Dimensions | Description | :results:
|-----------------+---------+---------------------+--------------------------------------------------------------| #+begin_src python :tangle trex.json
| ~type~ | ~str~ | | Type of basis set: "Gaussian" or "Slater" | "basis": {
| ~prim_num~ | ~dim~ | | Total number of primitives | "type" : [ "str" , [] ]
| ~shell_num~ | ~dim~ | | Total number of shells | , "prim_num" : [ "dim" , [] ]
| ~nucleus_index~ | ~index~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices | , "shell_num" : [ "dim" , [] ]
| ~shell_ang_mom~ | ~int~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta | , "nucleus_index" : [ "index", [ "basis.shell_num" ] ]
| ~shell_factor~ | ~float~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$) | , "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ]
| ~r_power~ | ~int~ | ~(basis.shell_num)~ | Power to which $r$ is raised ($n_s$) | , "shell_factor" : [ "float", [ "basis.shell_num" ] ]
| ~shell_index~ | ~index~ | ~(basis.prim_num)~ | One-to-one correspondence between primitives and shell index | , "r_power" : [ "int" , [ "basis.shell_num" ] ]
| ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) | , "shell_index" : [ "index", [ "basis.prim_num" ] ]
| ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) | , "exponent" : [ "float", [ "basis.prim_num" ] ]
| ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) | , "coefficient" : [ "float", [ "basis.prim_num" ] ]
, "prim_factor" : [ "float", [ "basis.prim_num" ] ]
#+CALL: json(data=basis, title="basis") , "e_cut" : [ "float", [] ]
} ,
#+RESULTS: #+end_src
:results: :end:
#+begin_src python :tangle trex.json
"basis": {
"type" : [ "str" , [] ]
, "prim_num" : [ "dim" , [] ]
, "shell_num" : [ "dim" , [] ]
, "nucleus_index" : [ "index", [ "basis.shell_num" ] ]
, "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ]
, "shell_factor" : [ "float", [ "basis.shell_num" ] ]
, "r_power" : [ "int" , [ "basis.shell_num" ] ]
, "shell_index" : [ "index", [ "basis.prim_num" ] ]
, "exponent" : [ "float", [ "basis.prim_num" ] ]
, "coefficient" : [ "float", [ "basis.prim_num" ] ]
, "prim_factor" : [ "float", [ "basis.prim_num" ] ]
} ,
#+end_src
:end:
** Example ** Example
@ -917,12 +936,15 @@ prim_factor =
* Cell (cell group) * Cell (cell group)
3 Lattice vectors to define a box containing the system, for example
used in periodic calculations.
#+NAME: cell #+NAME: cell
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|----------+---------+------------+-------------------------| |----------+---------+------------+-----------------------|
| ~a~ | ~float~ | ~(3)~ | First unit cell vector | | ~a~ | ~float~ | ~(3)~ | First lattice vector |
| ~b~ | ~float~ | ~(3)~ | Second unit cell vector | | ~b~ | ~float~ | ~(3)~ | Second lattice vector |
| ~c~ | ~float~ | ~(3)~ | Third unit cell vector | | ~c~ | ~float~ | ~(3)~ | Third lattice vector |
#+CALL: json(data=cell, title="cell") #+CALL: json(data=cell, title="cell")
@ -939,11 +961,14 @@ prim_factor =
* Periodic boundary calculations (pbc group) * Periodic boundary calculations (pbc group)
A single $k$-point per TREXIO file can be stored. The $k$-point is
defined in this group.
#+NAME: pbc #+NAME: pbc
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|------------+---------+------------+-------------------------| |---------------+---------+------------+-------------------------|
| ~periodic~ | ~int~ | | ~1~: true or ~0~: false | | ~is_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")