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Added plane waves
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@ -12,6 +12,7 @@ CHANGES
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- Added `float buffered` type for vectors like CI/CSF coefficients
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- .git folder is no longer needed to activate TREXIO_DEVEL mode
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- Renamed debian folder into helpers-debian
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- Added plane wave basis set
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- Added trexio_to_bitfield_list functionality
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- Added `trexio_has_group` functionality
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- Added OCaml binding
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171
trex.org
171
trex.org
@ -276,78 +276,97 @@ power = [
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* Basis set (basis group)
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We consider here basis functions centered on nuclei. Hence, we enable
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the possibility to define /dummy atoms/ to place basis functions in
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random positions.
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The atomic basis set is defined as a list of shells. Each shell $s$ is
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centered on a center $A$, possesses a given angular momentum $l$ and a
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radial function $R_s$. The radial function is a linear combination of
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$N_{\text{prim}}$ /primitive/ functions that can be of type
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Slater ($p=1$) or Gaussian ($p=2$),
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parameterized by exponents $\gamma_{ks}$ and coefficients $a_{ks}$:
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\[
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R_s(\mathbf{r}) = \mathcal{N}_s \vert\mathbf{r}-\mathbf{R}_A\vert^{n_s}
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\sum_{k=1}^{N_{\text{prim}}} a_{ks}\, f_{ks}(\gamma_{ks},p)\,
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\exp \left( - \gamma_{ks}
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\vert \mathbf{r}-\mathbf{R}_A \vert ^p \right).
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\]
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** Gaussian and Slater-type orbitals
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In the case of Gaussian functions, $n_s$ is always zero.
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We consider here basis functions centered on nuclei. Hence, we enable
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the possibility to define /dummy atoms/ to place basis functions in
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random positions.
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Different codes normalize functions at different levels. Computing
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normalization factors requires the ability to compute overlap
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integrals, so the normalization factors should be written in the
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file to ensure that the file is self-contained and does not need the
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client program to have the ability to compute such integrals.
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The atomic basis set is defined as a list of shells. Each shell $s$ is
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centered on a center $A$, possesses a given angular momentum $l$ and a
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radial function $R_s$. The radial function is a linear combination of
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$N_{\text{prim}}$ /primitive/ functions that can be of type
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Slater ($p=1$) or Gaussian ($p=2$),
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parameterized by exponents $\gamma_{ks}$ and coefficients $a_{ks}$:
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\[
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R_s(\mathbf{r}) = \mathcal{N}_s \vert\mathbf{r}-\mathbf{R}_A\vert^{n_s}
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\sum_{k=1}^{N_{\text{prim}}} a_{ks}\, f_{ks}(\gamma_{ks},p)\,
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\exp \left( - \gamma_{ks}
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\vert \mathbf{r}-\mathbf{R}_A \vert ^p \right).
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\]
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Some codes assume that the contraction coefficients are for a linear
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combination of /normalized/ primitives. This implies that a normalization
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constant for the primitive $ks$ needs to be computed and stored. If
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this normalization factor is not required, $f_{ks}=1$.
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In the case of Gaussian functions, $n_s$ is always zero.
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Some codes assume that the basis function are normalized. This
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implies the computation of an extra normalization factor, $\mathcal{N}_s$.
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If the the basis function is not considered normalized, $\mathcal{N}_s=1$.
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Different codes normalize functions at different levels. Computing
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normalization factors requires the ability to compute overlap
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integrals, so the normalization factors should be written in the
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file to ensure that the file is self-contained and does not need the
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client program to have the ability to compute such integrals.
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Some codes assume that the contraction coefficients are for a linear
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combination of /normalized/ primitives. This implies that a normalization
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constant for the primitive $ks$ needs to be computed and stored. If
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this normalization factor is not required, $f_{ks}=1$.
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Some codes assume that the basis function are normalized. This
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implies the computation of an extra normalization factor, $\mathcal{N}_s$.
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If the the basis function is not considered normalized, $\mathcal{N}_s=1$.
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All the basis set parameters are stored in one-dimensional arrays.
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** Plane waves
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A plane wave is defined as
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\[
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\chi_j(r) = \exp \left( -i \mathbf{k}_j \mathbf{r} \right)
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\]
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The basis set is defined as the array of $k$-points in the
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reciprocal space, defined in the ~pbc~ group. The kinetic energy
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cutoff ~e_cut~ is the only input data relevant to plane waves.
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** Data definitions
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#+NAME: basis
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| Variable | Type | Dimensions | Description |
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|-----------------+---------+---------------------+-----------------------------------------------------------------|
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| ~type~ | ~str~ | | Type of basis set: "Gaussian", "Slater" or "PW" for plane waves |
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| ~prim_num~ | ~dim~ | | Total number of primitives |
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| ~shell_num~ | ~dim~ | | Total number of shells |
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| ~nucleus_index~ | ~index~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices |
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| ~shell_ang_mom~ | ~int~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta |
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| ~shell_factor~ | ~float~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$) |
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| ~r_power~ | ~int~ | ~(basis.shell_num)~ | Power to which $r$ is raised ($n_s$) |
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| ~shell_index~ | ~index~ | ~(basis.prim_num)~ | One-to-one correspondence between primitives and shell index |
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| ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) |
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| ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) |
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| ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) |
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| ~e_cut~ | ~float~ | | Energy cut-off for plane-wave calculations |
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All the basis set parameters are stored in one-dimensional arrays:
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#+CALL: json(data=basis, title="basis")
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#+NAME: basis
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| Variable | Type | Dimensions | Description |
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|-----------------+---------+---------------------+--------------------------------------------------------------|
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| ~type~ | ~str~ | | Type of basis set: "Gaussian" or "Slater" |
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| ~prim_num~ | ~dim~ | | Total number of primitives |
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| ~shell_num~ | ~dim~ | | Total number of shells |
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| ~nucleus_index~ | ~index~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices |
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| ~shell_ang_mom~ | ~int~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta |
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| ~shell_factor~ | ~float~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$) |
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| ~r_power~ | ~int~ | ~(basis.shell_num)~ | Power to which $r$ is raised ($n_s$) |
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| ~shell_index~ | ~index~ | ~(basis.prim_num)~ | One-to-one correspondence between primitives and shell index |
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| ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) |
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| ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) |
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| ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) |
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#+CALL: json(data=basis, title="basis")
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"basis": {
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"type" : [ "str" , [] ]
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, "prim_num" : [ "dim" , [] ]
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, "shell_num" : [ "dim" , [] ]
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, "nucleus_index" : [ "index", [ "basis.shell_num" ] ]
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, "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ]
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, "shell_factor" : [ "float", [ "basis.shell_num" ] ]
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, "r_power" : [ "int" , [ "basis.shell_num" ] ]
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, "shell_index" : [ "index", [ "basis.prim_num" ] ]
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, "exponent" : [ "float", [ "basis.prim_num" ] ]
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, "coefficient" : [ "float", [ "basis.prim_num" ] ]
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, "prim_factor" : [ "float", [ "basis.prim_num" ] ]
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} ,
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#+end_src
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:end:
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"basis": {
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"type" : [ "str" , [] ]
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, "prim_num" : [ "dim" , [] ]
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, "shell_num" : [ "dim" , [] ]
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, "nucleus_index" : [ "index", [ "basis.shell_num" ] ]
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, "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ]
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, "shell_factor" : [ "float", [ "basis.shell_num" ] ]
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, "r_power" : [ "int" , [ "basis.shell_num" ] ]
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, "shell_index" : [ "index", [ "basis.prim_num" ] ]
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, "exponent" : [ "float", [ "basis.prim_num" ] ]
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, "coefficient" : [ "float", [ "basis.prim_num" ] ]
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, "prim_factor" : [ "float", [ "basis.prim_num" ] ]
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, "e_cut" : [ "float", [] ]
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} ,
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#+end_src
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:end:
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** Example
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@ -917,12 +936,15 @@ prim_factor =
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* Cell (cell group)
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3 Lattice vectors to define a box containing the system, for example
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used in periodic calculations.
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#+NAME: cell
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| Variable | Type | Dimensions | Description |
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|----------+---------+------------+-------------------------|
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| ~a~ | ~float~ | ~(3)~ | First unit cell vector |
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| ~b~ | ~float~ | ~(3)~ | Second unit cell vector |
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| ~c~ | ~float~ | ~(3)~ | Third unit cell vector |
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| Variable | Type | Dimensions | Description |
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|----------+---------+------------+-----------------------|
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| ~a~ | ~float~ | ~(3)~ | First lattice vector |
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| ~b~ | ~float~ | ~(3)~ | Second lattice vector |
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| ~c~ | ~float~ | ~(3)~ | Third lattice vector |
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#+CALL: json(data=cell, title="cell")
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@ -939,11 +961,14 @@ prim_factor =
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* Periodic boundary calculations (pbc group)
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A single $k$-point per TREXIO file can be stored. The $k$-point is
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defined in this group.
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#+NAME: pbc
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| Variable | Type | Dimensions | Description |
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|------------+---------+------------+-------------------------|
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| ~periodic~ | ~int~ | | ~1~: true or ~0~: false |
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| ~k_point~ | ~float~ | ~(3)~ | k-point sampling |
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| Variable | Type | Dimensions | Description |
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|---------------+---------+------------+-------------------------|
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| ~is_periodic~ | ~int~ | | ~1~: true or ~0~: false |
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| ~k_point~ | ~float~ | ~(3)~ | $k$-point sampling |
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#+CALL: json(data=pbc, title="pbc")
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