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Added Jastrow group and reorganize data

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Anthony Scemama 2023-01-02 16:00:57 +01:00
parent 932e403ad2
commit 23b6c9008a
3 changed files with 967 additions and 843 deletions
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1
ChangeLog
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@ -19,6 +19,7 @@ CHANGES
- Added OCaml binding - Added OCaml binding
- Added spin and energy in MOs - Added spin and energy in MOs
- Added CSF group - Added CSF group
- Added Jastrow group
- Added Cholesky-decomposed two-electron integrals - Added Cholesky-decomposed two-electron integrals
- Added Cholesky-decomposed RDMs for Gammcor - Added Cholesky-decomposed RDMs for Gammcor
- Added `trexio_flush` functionality - Added `trexio_flush` functionality

2
python/install_pytrexio.sh
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@ -73,7 +73,7 @@ python3 -m pip install dist/trexio-*.whl --force-reinstall
#python3 -m twine upload dist/trexio-*.tar.gz #python3 -m twine upload dist/trexio-*.tar.gz
# Cleaning # Cleaning
#rm -rf build dist trexio.egg-info rm -rf build dist trexio.egg-info
# Additional information related to the installation of the TREXIO Python API # Additional information related to the installation of the TREXIO Python API

685
trex.org
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@ -39,7 +39,7 @@ the [[./examples.html][examples]]. The ~sparse~ data representation implies the
[[https://en.wikipedia.org/wiki/Sparse_matrix#Coordinate_list_(COO)][coordinate list]] representation, namely the user has to write a list [[https://en.wikipedia.org/wiki/Sparse_matrix#Coordinate_list_(COO)][coordinate list]] representation, namely the user has to write a list
of indices and values. of indices and values.
For the Configuration Interfaction (CI) and Configuration State Function (CSF) For the Configuration Interaction (CI) and Configuration State Function (CSF)
groups, the ~buffered~ data type is introduced, which allows similar incremental groups, the ~buffered~ data type is introduced, which allows similar incremental
I/O as for ~sparse~ data but without the need to write indices of the sparse values. I/O as for ~sparse~ data but without the need to write indices of the sparse values.
@ -69,10 +69,12 @@ This means that the source code is not produced by the generator, but hand-writt
| ~description~ | ~str~ | | Text describing the content of file | | ~description~ | ~str~ | | Text describing the content of file |
| ~unsafe~ | ~int~ | | ~1~: true, ~0~: false | | ~unsafe~ | ~int~ | | ~1~: true, ~0~: false |
**Note:** ~unsafe~ attribute of the ~metadata~ group indicates whether the file has been previously opened with ~'u'~ mode. **Note:** ~unsafe~ attribute of the ~metadata~ group indicates
It is automatically written in the file upon the first unsafe opening. whether the file has been previously opened with ~'u'~ mode. It is
If the user has checked that the TREXIO file is valid (e.g. using ~trexio-tools~) after unsafe operations, automatically written in the file upon the first unsafe opening. If
then the ~unsafe~ attribute value can be manually overwritten (in unsafe mode) from ~1~ to ~0~. the user has checked that the TREXIO file is valid (e.g. using
~trexio-tools~) after unsafe operations, then the ~unsafe~ attribute
value can be manually overwritten (in unsafe mode) from ~1~ to ~0~.
#+CALL: json(data=metadata, title="metadata") #+CALL: json(data=metadata, title="metadata")
#+RESULTS: #+RESULTS:
@ -90,31 +92,8 @@ This means that the source code is not produced by the generator, but hand-writt
#+end_src #+end_src
:end: :end:
* Electron (electron group) * System
** Nucleus (nucleus group)
We consider wave functions expressed in the spin-free formalism, where
the number of \uparrow and \downarrow electrons is fixed.
#+NAME:electron
| Variable | Type | Dimensions | Description |
|----------+-------+------------+-------------------------------------|
| ~num~ | ~dim~ | | Number of electrons |
| ~up_num~ | ~int~ | | Number of \uparrow-spin electrons |
| ~dn_num~ | ~int~ | | Number of \downarrow-spin electrons |
#+CALL: json(data=electron, title="electron")
#+RESULTS:
:results:
#+begin_src python :tangle trex.json
"electron": {
"num" : [ "dim", [] ]
, "up_num" : [ "int", [] ]
, "dn_num" : [ "int", [] ]
} ,
#+end_src
:end:
* Nucleus (nucleus group)
The nuclei are considered as fixed point charges. Coordinates are The nuclei are considered as fixed point charges. Coordinates are
given in Cartesian $(x,y,z)$ format. given in Cartesian $(x,y,z)$ format.
@ -144,140 +123,169 @@ This means that the source code is not produced by the generator, but hand-writt
#+end_src #+end_src
:end: :end:
* Effective core potentials (ecp group) ** Cell (cell group)
An effective core potential (ECP) $V_A^{\text{ECP}}$ replacing the 3 Lattice vectors to define a box containing the system, for example
core electrons of atom $A$ can be expressed as used in periodic calculations.
\[
V_A^{\text{ECP}} =
V_{A \ell_{\max}+1} +
\sum_{\ell=0}^{\ell_{\max}}
\sum_{m=-\ell}^{\ell} | Y_{\ell m} \rangle \left[
V_{A \ell} - V_{A \ell_{\max}+1} \right] \langle Y_{\ell m} |
\]
The first term in the equation above is sometimes attributed to the local channel, #+NAME: cell
while the remaining terms correspond to the non-local channel projections.
The functions $V_{A\ell}$ are parameterized as:
\[
V_{A \ell}(\mathbf{r}) =
\sum_{q=1}^{N_{q \ell}}
\beta_{A q \ell}\, |\mathbf{r}-\mathbf{R}_{A}|^{n_{A q \ell}}\,
e^{-\alpha_{A q \ell} |\mathbf{r}-\mathbf{R}_{A}|^2 }
\]
See http://dx.doi.org/10.1063/1.4984046 or https://doi.org/10.1063/1.5121006 for more info.
#+NAME: ecp
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|----------------------+---------+-----------------+----------------------------------------------------------------------------------------| |----------+---------+------------+-----------------------|
| ~max_ang_mom_plus_1~ | ~int~ | ~(nucleus.num)~ | $\ell_{\max}+1$, one higher than the max angular momentum in the removed core orbitals | | ~a~ | ~float~ | ~(3)~ | First lattice vector |
| ~z_core~ | ~int~ | ~(nucleus.num)~ | Number of core electrons to remove per atom | | ~b~ | ~float~ | ~(3)~ | Second lattice vector |
| ~num~ | ~dim~ | | Total number of ECP functions for all atoms and all values of $\ell$ | | ~c~ | ~float~ | ~(3)~ | Third lattice vector |
| ~ang_mom~ | ~int~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the angular momentum $\ell$ |
| ~nucleus_index~ | ~index~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the atom index |
| ~exponent~ | ~float~ | ~(ecp.num)~ | $\alpha_{A q \ell}$ all ECP exponents |
| ~coefficient~ | ~float~ | ~(ecp.num)~ | $\beta_{A q \ell}$ all ECP coefficients |
| ~power~ | ~int~ | ~(ecp.num)~ | $n_{A q \ell}$ all ECP powers |
#+CALL: json(data=cell, title="cell")
There might be some confusion in the meaning of the $\ell_{\max}$.
It can be attributed to the maximum angular momentum occupied
in the core orbitals, which are removed by the ECP.
On the other hand, it can be attributed to the maximum angular momentum of the
ECP that replaces the core electrons.
*Note*, that the latter $\ell_{\max}$ is always higher by 1 than the former.
*Note for developers*: avoid having variables with similar prefix in their name.
HDF5 back end might cause issues due to the way ~find_dataset~ function works.
For example, in the ECP group we use ~max_ang_mom~ and not ~ang_mom_max~.
The latter causes issues when written before the ~ang_mom~ array in the TREXIO file.
*Update*: in fact, the aforementioned issue has only been observed when using HDF5 version 1.10.4
installed via ~apt-get~. Installing the same version from the ~conda-forge~ channel and running it in
an isolated ~conda~ environment works just fine. Thus, it seems to be a bug in the ~apt~-provided package.
If you encounter the aforementioned issue, please report it to our [[https://github.com/TREX-CoE/trexio/issues][issue tracker on GitHub]].
#+CALL: json(data=ecp, title="ecp")
#+RESULTS: #+RESULTS:
:results: :results:
#+begin_src python :tangle trex.json #+begin_src python :tangle trex.json
"ecp": { "cell": {
"max_ang_mom_plus_1" : [ "int" , [ "nucleus.num" ] ] "a" : [ "float", [ "3" ] ]
, "z_core" : [ "int" , [ "nucleus.num" ] ] , "b" : [ "float", [ "3" ] ]
, "num" : [ "dim" , [] ] , "c" : [ "float", [ "3" ] ]
, "ang_mom" : [ "int" , [ "ecp.num" ] ]
, "nucleus_index" : [ "index", [ "ecp.num" ] ]
, "exponent" : [ "float", [ "ecp.num" ] ]
, "coefficient" : [ "float", [ "ecp.num" ] ]
, "power" : [ "int" , [ "ecp.num" ] ]
} , } ,
#+end_src #+end_src
:end: :end:
** Example ** Periodic boundary calculations (pbc group)
For example, consider H_2 molecule with the following A single $k$-point per TREXIO file can be stored. The $k$-point is
[[https://pseudopotentiallibrary.org/recipes/H/ccECP/H.ccECP.gamess][effective core potential]] defined in this group.
(in GAMESS input format for the H atom):
#+BEGIN_EXAMPLE #+NAME: pbc
H-ccECP GEN 0 1 | Variable | Type | Dimensions | Description |
3 |------------+---------+------------+-------------------------|
1.00000000000000 1 21.24359508259891 | ~periodic~ | ~int~ | | ~1~: true or ~0~: false |
21.24359508259891 3 21.24359508259891 | ~k_point~ | ~float~ | ~(3)~ | $k$-point sampling |
-10.85192405303825 2 21.77696655044365
1
0.00000000000000 2 1.000000000000000
#+END_EXAMPLE
In TREXIO representation this would be: #+CALL: json(data=pbc, title="pbc")
#+BEGIN_EXAMPLE #+RESULTS:
num = 8 :results:
#+begin_src python :tangle trex.json
"pbc": {
"periodic" : [ "int" , [] ]
, "k_point" : [ "float", [ "3" ] ]
} ,
#+end_src
:end:
# lmax+1 per atom ** Numerical integration grid (grid group)
max_ang_mom_plus_1 = [ 1, 1 ]
# number of core electrons to remove per atom The molecular integrals have to be computed numerically on a grid in many applications.
zcore = [ 0, 0 ] A common choice for the angular grid is the one proposed by Lebedev and Laikov
[Russian Academy of Sciences Doklady Mathematics, Volume 59, Number 3, 1999, pages 477-481].
For the radial grids, many approaches have been developed over the years.
# first 4 ECP elements correspond to the first H atom ; the remaining 4 elements are for the second H atom The structure of this group is adapted for the [[https://github.com/dftlibs/numgrid][numgrid]] library.
nucleus_index = [ Feel free to submit a PR if you find missing options/functionalities.
0, 0, 0, 0,
1, 1, 1, 1
]
# 3 first ECP elements correspond to potential of the P orbital (l=1), then 1 element for the S orbital (l=0) ; similar for the second H atom #+name: grid
ang_mom = [ | Variable | Type | Dimensions | Description |
1, 1, 1, 0, |-----------------+---------+------------------+-------------------------------------------------------------------------|
1, 1, 1, 0 | ~description~ | ~str~ | | Details about the used quadratures can go here |
] | ~rad_precision~ | ~float~ | | Radial precision parameter (not used in some schemes like Krack-Köster) |
| ~num~ | ~dim~ | | Number of grid points |
| ~max_ang_num~ | ~int~ | | Maximum number of angular grid points (for pruning) |
| ~min_ang_num~ | ~int~ | | Minimum number of angular grid points (for pruning) |
| ~coord~ | ~float~ | ~(grid.num)~ | Discretized coordinate space |
| ~weight~ | ~float~ | ~(grid.num)~ | Grid weights according to a given partitioning (e.g. Becke) |
| ~ang_num~ | ~dim~ | | Number of angular integration points (if used) |
| ~ang_coord~ | ~float~ | ~(grid.ang_num)~ | Discretized angular space (if used) |
| ~ang_weight~ | ~float~ | ~(grid.ang_num)~ | Angular grid weights (if used) |
| ~rad_num~ | ~dim~ | | Number of radial integration points (if used) |
| ~rad_coord~ | ~float~ | ~(grid.rad_num)~ | Discretized radial space (if used) |
| ~rad_weight~ | ~float~ | ~(grid.rad_num)~ | Radial grid weights (if used) |
# ECP quantities that can be attributed to atoms and/or angular momenta based on the aforementioned ecp_nucleus and ecp_ang_mom arrays #+CALL: json(data=grid, title="grid")
coefficient = [
1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000,
1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000
]
exponent = [ #+RESULTS:
21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000, :results:
21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000 #+begin_src python :tangle trex.json
] "grid": {
"description" : [ "str" , [] ]
, "rad_precision" : [ "float", [] ]
, "num" : [ "dim" , [] ]
, "max_ang_num" : [ "int" , [] ]
, "min_ang_num" : [ "int" , [] ]
, "coord" : [ "float", [ "grid.num" ] ]
, "weight" : [ "float", [ "grid.num" ] ]
, "ang_num" : [ "dim" , [] ]
, "ang_coord" : [ "float", [ "grid.ang_num" ] ]
, "ang_weight" : [ "float", [ "grid.ang_num" ] ]
, "rad_num" : [ "dim" , [] ]
, "rad_coord" : [ "float", [ "grid.rad_num" ] ]
, "rad_weight" : [ "float", [ "grid.rad_num" ] ]
} ,
#+end_src
:end:
power = [ ** Electron (electron group)
-1, 1, 0, 0,
-1, 1, 0, 0
]
#+END_EXAMPLE
* Basis set (basis group) We consider wave functions expressed in the spin-free formalism, where
the number of \uparrow and \downarrow electrons is fixed.
#+NAME:electron
| Variable | Type | Dimensions | Description |
|----------+-------+------------+-------------------------------------|
| ~num~ | ~dim~ | | Number of electrons |
| ~up_num~ | ~int~ | | Number of \uparrow-spin electrons |
| ~dn_num~ | ~int~ | | Number of \downarrow-spin electrons |
** Gaussian and Slater-type orbitals #+CALL: json(data=electron, title="electron")
#+RESULTS:
:results:
#+begin_src python :tangle trex.json
"electron": {
"num" : [ "dim", [] ]
, "up_num" : [ "int", [] ]
, "dn_num" : [ "int", [] ]
} ,
#+end_src
:end:
** Ground or excited states (state group)
This group contains information about excited states. Since only a
single state can be stored in a TREXIO file, it is possible to store
in the main TREXIO file the names of auxiliary files containing the
information of the other states.
The ~file_name~ and ~label~ arrays have to be written only for the
main file, e.g. the one containing the ground state wave function
together with the basis set parameters, molecular orbitals,
integrals, etc.
The ~id~ and ~current_label~ attributes need to be specified for each file.
#+NAME: state
| Variable | Type | Dimensions | Description |
|-----------------+-------+---------------+---------------------------------------------------------------------------------------------|
| ~num~ | ~dim~ | | Number of states (including the ground state) |
| ~id~ | ~int~ | | Index of the current state (0 is ground state) |
| ~current_label~ | ~str~ | | Label of the current state |
| ~label~ | ~str~ | ~(state.num)~ | Labels of all states |
| ~file_name~ | ~str~ | ~(state.num)~ | Names of the TREXIO files linked to the current one (i.e. containing data for other states) |
#+CALL: json(data=state, title="state")
#+RESULTS:
:results:
#+begin_src python :tangle trex.json
"state": {
"num" : [ "dim", [] ]
, "id" : [ "int", [] ]
, "current_label" : [ "str", [] ]
, "label" : [ "str", [ "state.num" ] ]
, "file_name" : [ "str", [ "state.num" ] ]
} ,
#+end_src
:end:
* One-electron basis
** Basis set (basis group)
*** Gaussian and Slater-type orbitals
We consider here basis functions centered on nuclei. Hence, we enable We consider here basis functions centered on nuclei. Hence, we enable
the possibility to define /dummy atoms/ to place basis functions in the possibility to define /dummy atoms/ to place basis functions in
@ -315,7 +323,7 @@ power = [
All the basis set parameters are stored in one-dimensional arrays. All the basis set parameters are stored in one-dimensional arrays.
** Plane waves *** Plane waves
A plane wave is defined as A plane wave is defined as
@ -327,7 +335,7 @@ power = [
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.
** Data definitions *** Data definitions
#+NAME: basis #+NAME: basis
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
@ -368,7 +376,7 @@ power = [
#+end_src #+end_src
:end: :end:
** Example *** Example
For example, consider H_2 with the following basis set (in GAMESS For example, consider H_2 with the following basis set (in GAMESS
format), where both the AOs and primitives are considered normalized: format), where both the AOs and primitives are considered normalized:
@ -439,7 +447,137 @@ prim_factor =
4.3649547399719840e-01, 1.8135965626177861e+00 ] 4.3649547399719840e-01, 1.8135965626177861e+00 ]
#+END_EXAMPLE #+END_EXAMPLE
* Atomic orbitals (ao group) ** Effective core potentials (ecp group)
An effective core potential (ECP) $V_A^{\text{ECP}}$ replacing the
core electrons of atom $A$ can be expressed as
\[
V_A^{\text{ECP}} =
V_{A \ell_{\max}+1} +
\sum_{\ell=0}^{\ell_{\max}}
\sum_{m=-\ell}^{\ell} | Y_{\ell m} \rangle \left[
V_{A \ell} - V_{A \ell_{\max}+1} \right] \langle Y_{\ell m} |
\]
The first term in the equation above is sometimes attributed to the local channel,
while the remaining terms correspond to the non-local channel projections.
The functions $V_{A\ell}$ are parameterized as:
\[
V_{A \ell}(\mathbf{r}) =
\sum_{q=1}^{N_{q \ell}}
\beta_{A q \ell}\, |\mathbf{r}-\mathbf{R}_{A}|^{n_{A q \ell}}\,
e^{-\alpha_{A q \ell} |\mathbf{r}-\mathbf{R}_{A}|^2 }
\]
See http://dx.doi.org/10.1063/1.4984046 or https://doi.org/10.1063/1.5121006 for more info.
#+NAME: ecp
| Variable | Type | Dimensions | Description |
|----------------------+---------+-----------------+----------------------------------------------------------------------------------------|
| ~max_ang_mom_plus_1~ | ~int~ | ~(nucleus.num)~ | $\ell_{\max}+1$, one higher than the max angular momentum in the removed core orbitals |
| ~z_core~ | ~int~ | ~(nucleus.num)~ | Number of core electrons to remove per atom |
| ~num~ | ~dim~ | | Total number of ECP functions for all atoms and all values of $\ell$ |
| ~ang_mom~ | ~int~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the angular momentum $\ell$ |
| ~nucleus_index~ | ~index~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the atom index |
| ~exponent~ | ~float~ | ~(ecp.num)~ | $\alpha_{A q \ell}$ all ECP exponents |
| ~coefficient~ | ~float~ | ~(ecp.num)~ | $\beta_{A q \ell}$ all ECP coefficients |
| ~power~ | ~int~ | ~(ecp.num)~ | $n_{A q \ell}$ all ECP powers |
There might be some confusion in the meaning of the $\ell_{\max}$.
It can be attributed to the maximum angular momentum occupied
in the core orbitals, which are removed by the ECP.
On the other hand, it can be attributed to the maximum angular momentum of the
ECP that replaces the core electrons.
*Note*, that the latter $\ell_{\max}$ is always higher by 1 than the former.
*Note for developers*: avoid having variables with similar prefix in their name.
HDF5 back end might cause issues due to the way ~find_dataset~ function works.
For example, in the ECP group we use ~max_ang_mom~ and not ~ang_mom_max~.
The latter causes issues when written before the ~ang_mom~ array in the TREXIO file.
*Update*: in fact, the aforementioned issue has only been observed when using HDF5 version 1.10.4
installed via ~apt-get~. Installing the same version from the ~conda-forge~ channel and running it in
an isolated ~conda~ environment works just fine. Thus, it seems to be a bug in the ~apt~-provided package.
If you encounter the aforementioned issue, please report it to our [[https://github.com/TREX-CoE/trexio/issues][issue tracker on GitHub]].
#+CALL: json(data=ecp, title="ecp")
#+RESULTS:
:results:
#+begin_src python :tangle trex.json
"ecp": {
"max_ang_mom_plus_1" : [ "int" , [ "nucleus.num" ] ]
, "z_core" : [ "int" , [ "nucleus.num" ] ]
, "num" : [ "dim" , [] ]
, "ang_mom" : [ "int" , [ "ecp.num" ] ]
, "nucleus_index" : [ "index", [ "ecp.num" ] ]
, "exponent" : [ "float", [ "ecp.num" ] ]
, "coefficient" : [ "float", [ "ecp.num" ] ]
, "power" : [ "int" , [ "ecp.num" ] ]
} ,
#+end_src
:end:
*** Example
For example, consider H_2 molecule with the following
[[https://pseudopotentiallibrary.org/recipes/H/ccECP/H.ccECP.gamess][effective core potential]]
(in GAMESS input format for the H atom):
#+BEGIN_EXAMPLE
H-ccECP GEN 0 1
3
1.00000000000000 1 21.24359508259891
21.24359508259891 3 21.24359508259891
-10.85192405303825 2 21.77696655044365
1
0.00000000000000 2 1.000000000000000
#+END_EXAMPLE
In TREXIO representation this would be:
#+BEGIN_EXAMPLE
num = 8
# lmax+1 per atom
max_ang_mom_plus_1 = [ 1, 1 ]
# number of core electrons to remove per atom
zcore = [ 0, 0 ]
# first 4 ECP elements correspond to the first H atom ; the remaining 4 elements are for the second H atom
nucleus_index = [
0, 0, 0, 0,
1, 1, 1, 1
]
# 3 first ECP elements correspond to potential of the P orbital (l=1), then 1 element for the S orbital (l=0) ; similar for the second H atom
ang_mom = [
1, 1, 1, 0,
1, 1, 1, 0
]
# ECP quantities that can be attributed to atoms and/or angular momenta based on the aforementioned ecp_nucleus and ecp_ang_mom arrays
coefficient = [
1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000,
1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000
]
exponent = [
21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000,
21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000
]
power = [
-1, 1, 0, 0,
-1, 1, 0, 0
]
#+END_EXAMPLE
** Atomic orbitals (ao group)
Going from the atomic basis set to AOs implies a systematic Going from the atomic basis set to AOs implies a systematic
construction of all the angular functions of each shell. We construction of all the angular functions of each shell. We
@ -508,7 +646,7 @@ prim_factor =
#+end_src #+end_src
:end: :end:
** One-electron integrals (~ao_1e_int~ group) *** One-electron integrals (~ao_1e_int~ group)
:PROPERTIES: :PROPERTIES:
:CUSTOM_ID: ao_one_e :CUSTOM_ID: ao_one_e
:END: :END:
@ -558,7 +696,7 @@ prim_factor =
#+end_src #+end_src
:end: :end:
** Two-electron integrals (~ao_2e_int~ group) *** Two-electron integrals (~ao_2e_int~ group)
:PROPERTIES: :PROPERTIES:
:CUSTOM_ID: ao_two_e :CUSTOM_ID: ao_two_e
:END: :END:
@ -596,7 +734,7 @@ prim_factor =
#+end_src #+end_src
:end: :end:
* Molecular orbitals (mo group) ** Molecular orbitals (mo group)
#+NAME: mo #+NAME: mo
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
@ -630,7 +768,7 @@ prim_factor =
#+end_src #+end_src
:end: :end:
** One-electron integrals (~mo_1e_int~ group) *** One-electron integrals (~mo_1e_int~ group)
The operators as the same as those defined in the The operators as the same as those defined in the
[[#ao_one_e][AO one-electron integrals section]]. Here, the integrals are given in [[#ao_one_e][AO one-electron integrals section]]. Here, the integrals are given in
@ -670,7 +808,7 @@ prim_factor =
#+end_src #+end_src
:end: :end:
** Two-electron integrals (~mo_2e_int~ group) *** Two-electron integrals (~mo_2e_int~ group)
The operators are the same as those defined in the The operators are the same as those defined in the
[[#ao_two_e][AO two-electron integrals section]]. Here, the integrals are given in [[#ao_two_e][AO two-electron integrals section]]. Here, the integrals are given in
@ -707,8 +845,21 @@ prim_factor =
} , } ,
#+end_src #+end_src
:end: :end:
:results:
#+begin_src python :tangle trex.json
"mo_2e_int": {
"eri" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
, "eri_lr" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
, "eri_cholesky_num" : [ "dim" , [] ]
, "eri_cholesky" : [ "float sparse", [ "mo_2e_int.eri_cholesky_num", "mo.num", "mo.num" ] ]
, "eri_lr_cholesky_num" : [ "dim" , [] ]
, "eri_lr_cholesky" : [ "float sparse", [ "mo_2e_int.eri_lr_cholesky_num", "mo.num", "mo.num" ] ]
} ,
#+end_src
:
* Slater determinants (determinant group) * N-electron basis
** Slater determinants (determinant group)
The configuration interaction (CI) wave function $\Psi$ The configuration interaction (CI) wave function $\Psi$
can be expanded in the basis of Slater determinants $D_I$ as follows can be expanded in the basis of Slater determinants $D_I$ as follows
@ -756,7 +907,7 @@ prim_factor =
#+end_src #+end_src
:end: :end:
* Configuration state functions (csf group) ** Configuration state functions (csf group)
The configuration interaction (CI) wave function $\Psi$ can be The configuration interaction (CI) wave function $\Psi$ can be
expanded in the basis of [[https://en.wikipedia.org/wiki/Configuration_state_function][configuration state functions]] (CSFs) expanded in the basis of [[https://en.wikipedia.org/wiki/Configuration_state_function][configuration state functions]] (CSFs)
@ -792,44 +943,7 @@ prim_factor =
#+end_src #+end_src
:end: :end:
* Excited states (state group) ** Reduced density matrices (rdm group)
This group contains information about excited states. Since only a
single state can be stored in a TREXIO file, it is possible to store
in the main TREXIO file the names of auxiliary files containing the
information of the other states.
The ~file_name~ and ~label~ arrays have to be written only for the
main file, e.g. the one containing the ground state wave function
together with the basis set parameters, molecular orbitals,
integrals, etc.
The ~id~ and ~current_label~ attributes need to be specified for each file.
#+NAME: state
| Variable | Type | Dimensions | Description |
|-----------------+-------+---------------+---------------------------------------------------------------------------------------------|
| ~num~ | ~dim~ | | Number of states (including the ground state) |
| ~id~ | ~int~ | | Index of the current state (0 is ground state) |
| ~current_label~ | ~str~ | | Label of the current state |
| ~label~ | ~str~ | ~(state.num)~ | Labels of all states |
| ~file_name~ | ~str~ | ~(state.num)~ | Names of the TREXIO files linked to the current one (i.e. containing data for other states) |
#+CALL: json(data=state, title="state")
#+RESULTS:
:results:
#+begin_src python :tangle trex.json
"state": {
"num" : [ "dim", [] ]
, "id" : [ "int", [] ]
, "current_label" : [ "str", [] ]
, "label" : [ "str", [ "state.num" ] ]
, "file_name" : [ "str", [ "state.num" ] ]
} ,
#+end_src
:end:
* Reduced density matrices (rdm group)
The reduced density matrices are defined in the basis of molecular The reduced density matrices are defined in the basis of molecular
orbitals. orbitals.
@ -936,103 +1050,112 @@ prim_factor =
#+end_src #+end_src
:end: :end:
* Cell (cell group) * Correlation factors
** Jastrow factor (jastrow group)
3 Lattice vectors to define a box containing the system, for example The Jastrow factor is an $N$-electron function to which the CI
used in periodic calculations. expansion is multiplied: $\Psi = \Phi \times \exp(J)$,
where
#+NAME: cell \[
J(\mathbf{r},\mathbf{R}) = J_{\text{eN}}(\mathbf{r},\mathbf{R}) + J_{\text{ee}}(\mathbf{r}) + J_{\text{eeN}}(\mathbf{r},\mathbf{R})
\]
In the following, we use the notations $r_{ij} = |\mathbf{r}_i - \mathbf{r}_j|$ and
$R_{i\alpha} = |\mathbf{r}_i - \mathbf{R}_\alpha|$, where indices
$i$ and $j$ correspond to electrons and $\alpha$ to nuclei.
Parameters for multiple forms of Jastrow factors can be saved in
TREXIO files, and are described in the following sections. These
are identified by the ~type~ attribute. The type can be one of the
following:
- ~champ~
- ~mu~
*** CHAMP
The first form of Jastrow factor is the one used in
the [[https://trex-coe.eu/trex-quantum-chemistry-codes/champ][CHAMP]] program.
$J_{\text{eN}}$ contains electron-nucleus terms:
\[
J_{\text{eN}}(\mathbf{r},\mathbf{R}) = \sum_{i=1}^{N_\text{elec}} \sum_{\alpha=1}^{N_\text{nucl}}
\frac{a_{1,\alpha}\, g_\alpha(R_{i\alpha})}{1+a_{2,\alpha}\, g_\alpha(R_{i\alpha})} +
\sum_{p=2}^{N_\text{ord}^a} a_{p+1,\alpha}\, [g_\alpha(R_{i\alpha})]^p - J_{eN}^\infty
\]
$J_{\text{ee}}$ contains electron-electron terms:
\[
J_{\text{ee}}(\mathbf{r}) =
\sum_{i=1}^{N_\text{elec}} \sum_{j=1}^{i-1}
\frac{b_1\, f(r_{ij})}{1+b_2\, f(r_{ij})} +
\sum_{p=2}^{N_\text{ord}^b} a_{p+1}\, [f(r_{ij})]^p - J_{ee}^\infty
\]
and $J_{\text{eeN}}$ contains electron-electron-Nucleus terms:
\[
J_{\text{eeN}}(\mathbf{r},\mathbf{R}) =
\sum_{\alpha=1}^{N_{\text{nucl}}}
\sum_{i=1}^{N_{\text{elec}}}
\sum_{j=1}^{i-1}
\sum_{p=2}^{N_{\text{ord}}}
\sum_{k=0}^{p-1}
\sum_{l=0}^{p-k-2\delta_{k,0}}
c_{lkp\alpha} \left[ f({r}_{ij}) \right]^k
\left[ \left[ g_\alpha({R}_{i\alpha}) \right]^l + \left[ g_\alpha({R}_{j\alpha}) \right]^l \right]
\left[ g_\alpha({R}_{i\,\alpha}) \, g_\alpha({R}_{j\alpha}) \right]^{(p-k-l)/2}
\]
$c_{lkp\alpha}$ are non-zero only when $p-k-l$ is even.
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
\[
f(r) = \frac{1-e^{-\kappa\, r}}{\kappa} \text{ and }
g_\alpha(r) = e^{-\kappa_\alpha\, r}.
\]
*** mu
The "mu" Jastrow factor has only a single parameter $\mu$ for the
[[https://doi.org/10.1063/5.0044683][electron-electron term]]:
\[
J_{\text{ee}}(\mathbf{r}) =
\sum_{i=1}^{N_\text{elec}} \sum_{j=1}^{i-1} r_{ij}
\left( 1 - \text{erf}(\mu\, r_{ij})\right) - \frac{1}{\mu\sqrt{\pi}}
e^{-(\mu\,r_{ij})^2}
\]
# It was then updated for frozen-core calculations by introducing a
# set of electron-electron-nucleus terms with one parameter per nucleus:
# \[
# J_{\text{eeN}}(\mathbf{r}) =
# \]
*** Table of values
#+name: jastrow
| Variable | Type | Dimensions | Description | | Variable | Type | Dimensions | Description |
|----------+---------+------------+-----------------------| |---------------+----------+---------------------+-----------------------------------------------------------------|
| ~a~ | ~float~ | ~(3)~ | First lattice vector | | ~type~ | ~string~ | | Type of Jastrow factor: ~champ~ or ~mu~ |
| ~b~ | ~float~ | ~(3)~ | Second lattice vector | | ~ee_num~ | ~dim~ | | Number of Electron-electron parameters |
| ~c~ | ~float~ | ~(3)~ | Third lattice vector | | ~en_num~ | ~dim~ | ~(nucleus.num)~ | Number of Electron-nucleus parameters, per nucleus |
| ~een_num~ | ~dim~ | ~(nucleus.num)~ | Number of Electron-electron-nucleus parameters, per nucleus |
#+CALL: json(data=cell, title="cell") | ~ee~ | ~float~ | ~(jastrow.ee_num)~ | Electron-electron parameters |
| ~en~ | ~float~ | ~(jastrow.en_num)~ | Electron-nucleus parameters |
#+RESULTS: | ~een~ | ~float~ | ~(jastrow.een_num)~ | Electron-electron-nucleus parameters |
:results: | ~en_nucleus~ | ~index~ | ~(jastrow.en_num)~ | Nucleus relative to the eN parameter |
#+begin_src python :tangle trex.json | ~een_nucleus~ | ~index~ | ~(jastrow.een_num)~ | Nucleus relative to the eeN parameter |
"cell": { | ~ee_scaling~ | ~float~ | | $\kappa$ value in CHAMP Jastrow for electron-electron distances |
"a" : [ "float", [ "3" ] ] | ~eN_scaling~ | ~float~ | ~(nucleus.num)~ | $\kappa$ value in CHAMP Jastrow for electron-nucleus distances |
, "b" : [ "float", [ "3" ] ]
, "c" : [ "float", [ "3" ] ]
} ,
#+end_src
:end:
* 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
| Variable | Type | Dimensions | Description |
|---------------+---------+------------+-------------------------|
| ~periodic~ | ~int~ | | ~1~: true or ~0~: false |
| ~k_point~ | ~float~ | ~(3)~ | $k$-point sampling |
#+CALL: json(data=pbc, title="pbc")
#+RESULTS:
:results:
#+begin_src python :tangle trex.json
"pbc": {
"periodic" : [ "int" , [] ]
, "k_point" : [ "float", [ "3" ] ]
} ,
#+end_src
:end:
* Numerical integration grid (grid group)
The molecular integrals have to be computed numerically on a grid in many applications.
A common choice for the angular grid is the one proposed by Lebedev and Laikov
[Russian Academy of Sciences Doklady Mathematics, Volume 59, Number 3, 1999, pages 477-481].
For the radial grids, many approaches have been developed over the years.
The structure of this group is adapted for the [[https://github.com/dftlibs/numgrid][numgrid]] library.
Feel free to submit a PR if you find missing options/functionalities.
#+name: grid
| Variable | Type | Dimensions | Description |
|-----------------+---------+------------------+-------------------------------------------------------------------------|
| ~description~ | ~str~ | | Details about the used quadratures can go here |
| ~rad_precision~ | ~float~ | | Radial precision parameter (not used in some schemes like Krack-Köster) |
| ~num~ | ~dim~ | | Number of grid points |
| ~max_ang_num~ | ~int~ | | Maximum number of angular grid points (for pruning) |
| ~min_ang_num~ | ~int~ | | Minimum number of angular grid points (for pruning) |
| ~coord~ | ~float~ | ~(grid.num)~ | Discretized coordinate space |
| ~weight~ | ~float~ | ~(grid.num)~ | Grid weights according to a given partitioning (e.g. Becke) |
| ~ang_num~ | ~dim~ | | Number of angular integration points (if used) |
| ~ang_coord~ | ~float~ | ~(grid.ang_num)~ | Discretized angular space (if used) |
| ~ang_weight~ | ~float~ | ~(grid.ang_num)~ | Angular grid weights (if used) |
| ~rad_num~ | ~dim~ | | Number of radial integration points (if used) |
| ~rad_coord~ | ~float~ | ~(grid.rad_num)~ | Discretized radial space (if used) |
| ~rad_weight~ | ~float~ | ~(grid.rad_num)~ | Radial grid weights (if used) |
#+CALL: json(data=grid, title="grid")
#+RESULTS:
:results:
#+begin_src python :tangle trex.json
"grid": {
"description" : [ "str" , [] ]
, "rad_precision" : [ "float", [] ]
, "num" : [ "dim" , [] ]
, "max_ang_num" : [ "int" , [] ]
, "min_ang_num" : [ "int" , [] ]
, "coord" : [ "float", [ "grid.num" ] ]
, "weight" : [ "float", [ "grid.num" ] ]
, "ang_num" : [ "dim" , [] ]
, "ang_coord" : [ "float", [ "grid.ang_num" ] ]
, "ang_weight" : [ "float", [ "grid.ang_num" ] ]
, "rad_num" : [ "dim" , [] ]
, "rad_coord" : [ "float", [ "grid.rad_num" ] ]
, "rad_weight" : [ "float", [ "grid.rad_num" ] ]
} ,
#+end_src
:end:
* Quantum Monte Carlo data (qmc group) * Quantum Monte Carlo data (qmc group)