mirror of
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Added Jastrow group and reorganize data
This commit is contained in:
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@ -19,6 +19,7 @@ CHANGES
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- Added OCaml binding
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- Added spin and energy in MOs
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- Added CSF group
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- Added Jastrow group
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- Added Cholesky-decomposed two-electron integrals
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- Added Cholesky-decomposed RDMs for Gammcor
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- Added `trexio_flush` functionality
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@ -73,7 +73,7 @@ python3 -m pip install dist/trexio-*.whl --force-reinstall
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#python3 -m twine upload dist/trexio-*.tar.gz
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# Cleaning
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#rm -rf build dist trexio.egg-info
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rm -rf build dist trexio.egg-info
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# Additional information related to the installation of the TREXIO Python API
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685
trex.org
685
trex.org
@ -39,7 +39,7 @@ the [[./examples.html][examples]]. The ~sparse~ data representation implies the
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[[https://en.wikipedia.org/wiki/Sparse_matrix#Coordinate_list_(COO)][coordinate list]] representation, namely the user has to write a list
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of indices and values.
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For the Configuration Interfaction (CI) and Configuration State Function (CSF)
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For the Configuration Interaction (CI) and Configuration State Function (CSF)
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groups, the ~buffered~ data type is introduced, which allows similar incremental
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I/O as for ~sparse~ data but without the need to write indices of the sparse values.
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@ -69,10 +69,12 @@ This means that the source code is not produced by the generator, but hand-writt
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| ~description~ | ~str~ | | Text describing the content of file |
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| ~unsafe~ | ~int~ | | ~1~: true, ~0~: false |
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**Note:** ~unsafe~ attribute of the ~metadata~ group indicates whether the file has been previously opened with ~'u'~ mode.
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It is automatically written in the file upon the first unsafe opening.
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If the user has checked that the TREXIO file is valid (e.g. using ~trexio-tools~) after unsafe operations,
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then the ~unsafe~ attribute value can be manually overwritten (in unsafe mode) from ~1~ to ~0~.
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**Note:** ~unsafe~ attribute of the ~metadata~ group indicates
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whether the file has been previously opened with ~'u'~ mode. It is
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automatically written in the file upon the first unsafe opening. If
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the user has checked that the TREXIO file is valid (e.g. using
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~trexio-tools~) after unsafe operations, then the ~unsafe~ attribute
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value can be manually overwritten (in unsafe mode) from ~1~ to ~0~.
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#+CALL: json(data=metadata, title="metadata")
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#+RESULTS:
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@ -90,31 +92,8 @@ This means that the source code is not produced by the generator, but hand-writt
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#+end_src
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:end:
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* Electron (electron group)
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We consider wave functions expressed in the spin-free formalism, where
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the number of \uparrow and \downarrow electrons is fixed.
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#+NAME:electron
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| Variable | Type | Dimensions | Description |
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|----------+-------+------------+-------------------------------------|
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| ~num~ | ~dim~ | | Number of electrons |
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| ~up_num~ | ~int~ | | Number of \uparrow-spin electrons |
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| ~dn_num~ | ~int~ | | Number of \downarrow-spin electrons |
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#+CALL: json(data=electron, title="electron")
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"electron": {
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"num" : [ "dim", [] ]
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, "up_num" : [ "int", [] ]
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, "dn_num" : [ "int", [] ]
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} ,
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#+end_src
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:end:
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* Nucleus (nucleus group)
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* System
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** Nucleus (nucleus group)
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The nuclei are considered as fixed point charges. Coordinates are
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given in Cartesian $(x,y,z)$ format.
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@ -144,140 +123,169 @@ This means that the source code is not produced by the generator, but hand-writt
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#+end_src
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:end:
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* Effective core potentials (ecp group)
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** Cell (cell group)
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An effective core potential (ECP) $V_A^{\text{ECP}}$ replacing the
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core electrons of atom $A$ can be expressed as
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\[
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V_A^{\text{ECP}} =
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V_{A \ell_{\max}+1} +
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\sum_{\ell=0}^{\ell_{\max}}
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\sum_{m=-\ell}^{\ell} | Y_{\ell m} \rangle \left[
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V_{A \ell} - V_{A \ell_{\max}+1} \right] \langle Y_{\ell m} |
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\]
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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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The first term in the equation above is sometimes attributed to the local channel,
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while the remaining terms correspond to the non-local channel projections.
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The functions $V_{A\ell}$ are parameterized as:
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\[
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V_{A \ell}(\mathbf{r}) =
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\sum_{q=1}^{N_{q \ell}}
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\beta_{A q \ell}\, |\mathbf{r}-\mathbf{R}_{A}|^{n_{A q \ell}}\,
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e^{-\alpha_{A q \ell} |\mathbf{r}-\mathbf{R}_{A}|^2 }
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\]
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See http://dx.doi.org/10.1063/1.4984046 or https://doi.org/10.1063/1.5121006 for more info.
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#+NAME: ecp
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#+NAME: cell
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| Variable | Type | Dimensions | Description |
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|----------------------+---------+-----------------+----------------------------------------------------------------------------------------|
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| ~max_ang_mom_plus_1~ | ~int~ | ~(nucleus.num)~ | $\ell_{\max}+1$, one higher than the max angular momentum in the removed core orbitals |
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| ~z_core~ | ~int~ | ~(nucleus.num)~ | Number of core electrons to remove per atom |
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| ~num~ | ~dim~ | | Total number of ECP functions for all atoms and all values of $\ell$ |
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| ~ang_mom~ | ~int~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the angular momentum $\ell$ |
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| ~nucleus_index~ | ~index~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the atom index |
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| ~exponent~ | ~float~ | ~(ecp.num)~ | $\alpha_{A q \ell}$ all ECP exponents |
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| ~coefficient~ | ~float~ | ~(ecp.num)~ | $\beta_{A q \ell}$ all ECP coefficients |
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| ~power~ | ~int~ | ~(ecp.num)~ | $n_{A q \ell}$ all ECP powers |
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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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There might be some confusion in the meaning of the $\ell_{\max}$.
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It can be attributed to the maximum angular momentum occupied
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in the core orbitals, which are removed by the ECP.
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On the other hand, it can be attributed to the maximum angular momentum of the
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ECP that replaces the core electrons.
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*Note*, that the latter $\ell_{\max}$ is always higher by 1 than the former.
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*Note for developers*: avoid having variables with similar prefix in their name.
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HDF5 back end might cause issues due to the way ~find_dataset~ function works.
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For example, in the ECP group we use ~max_ang_mom~ and not ~ang_mom_max~.
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The latter causes issues when written before the ~ang_mom~ array in the TREXIO file.
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*Update*: in fact, the aforementioned issue has only been observed when using HDF5 version 1.10.4
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installed via ~apt-get~. Installing the same version from the ~conda-forge~ channel and running it in
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an isolated ~conda~ environment works just fine. Thus, it seems to be a bug in the ~apt~-provided package.
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If you encounter the aforementioned issue, please report it to our [[https://github.com/TREX-CoE/trexio/issues][issue tracker on GitHub]].
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#+CALL: json(data=ecp, title="ecp")
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#+CALL: json(data=cell, title="cell")
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"ecp": {
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"max_ang_mom_plus_1" : [ "int" , [ "nucleus.num" ] ]
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, "z_core" : [ "int" , [ "nucleus.num" ] ]
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, "num" : [ "dim" , [] ]
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, "ang_mom" : [ "int" , [ "ecp.num" ] ]
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, "nucleus_index" : [ "index", [ "ecp.num" ] ]
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, "exponent" : [ "float", [ "ecp.num" ] ]
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, "coefficient" : [ "float", [ "ecp.num" ] ]
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, "power" : [ "int" , [ "ecp.num" ] ]
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"cell": {
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"a" : [ "float", [ "3" ] ]
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, "b" : [ "float", [ "3" ] ]
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, "c" : [ "float", [ "3" ] ]
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} ,
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#+end_src
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:end:
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** Example
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** Periodic boundary calculations (pbc group)
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For example, consider H_2 molecule with the following
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[[https://pseudopotentiallibrary.org/recipes/H/ccECP/H.ccECP.gamess][effective core potential]]
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(in GAMESS input format for the H atom):
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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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#+BEGIN_EXAMPLE
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H-ccECP GEN 0 1
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3
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1.00000000000000 1 21.24359508259891
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21.24359508259891 3 21.24359508259891
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-10.85192405303825 2 21.77696655044365
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1
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0.00000000000000 2 1.000000000000000
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#+END_EXAMPLE
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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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In TREXIO representation this would be:
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#+CALL: json(data=pbc, title="pbc")
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#+BEGIN_EXAMPLE
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num = 8
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"pbc": {
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"periodic" : [ "int" , [] ]
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, "k_point" : [ "float", [ "3" ] ]
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} ,
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#+end_src
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:end:
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# lmax+1 per atom
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max_ang_mom_plus_1 = [ 1, 1 ]
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** Numerical integration grid (grid group)
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# number of core electrons to remove per atom
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zcore = [ 0, 0 ]
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The molecular integrals have to be computed numerically on a grid in many applications.
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A common choice for the angular grid is the one proposed by Lebedev and Laikov
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[Russian Academy of Sciences Doklady Mathematics, Volume 59, Number 3, 1999, pages 477-481].
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For the radial grids, many approaches have been developed over the years.
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# first 4 ECP elements correspond to the first H atom ; the remaining 4 elements are for the second H atom
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nucleus_index = [
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0, 0, 0, 0,
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1, 1, 1, 1
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]
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The structure of this group is adapted for the [[https://github.com/dftlibs/numgrid][numgrid]] library.
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Feel free to submit a PR if you find missing options/functionalities.
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# 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
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ang_mom = [
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1, 1, 1, 0,
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1, 1, 1, 0
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]
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#+name: grid
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| Variable | Type | Dimensions | Description |
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|-----------------+---------+------------------+-------------------------------------------------------------------------|
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| ~description~ | ~str~ | | Details about the used quadratures can go here |
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| ~rad_precision~ | ~float~ | | Radial precision parameter (not used in some schemes like Krack-Köster) |
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| ~num~ | ~dim~ | | Number of grid points |
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| ~max_ang_num~ | ~int~ | | Maximum number of angular grid points (for pruning) |
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| ~min_ang_num~ | ~int~ | | Minimum number of angular grid points (for pruning) |
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| ~coord~ | ~float~ | ~(grid.num)~ | Discretized coordinate space |
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| ~weight~ | ~float~ | ~(grid.num)~ | Grid weights according to a given partitioning (e.g. Becke) |
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| ~ang_num~ | ~dim~ | | Number of angular integration points (if used) |
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| ~ang_coord~ | ~float~ | ~(grid.ang_num)~ | Discretized angular space (if used) |
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| ~ang_weight~ | ~float~ | ~(grid.ang_num)~ | Angular grid weights (if used) |
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| ~rad_num~ | ~dim~ | | Number of radial integration points (if used) |
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| ~rad_coord~ | ~float~ | ~(grid.rad_num)~ | Discretized radial space (if used) |
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| ~rad_weight~ | ~float~ | ~(grid.rad_num)~ | Radial grid weights (if used) |
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# ECP quantities that can be attributed to atoms and/or angular momenta based on the aforementioned ecp_nucleus and ecp_ang_mom arrays
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coefficient = [
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1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000,
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1.00000000000000, 21.24359508259891, -10.85192405303825, 0.00000000000000
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]
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#+CALL: json(data=grid, title="grid")
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exponent = [
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21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000,
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21.24359508259891, 21.24359508259891, 21.77696655044365, 1.000000000000000
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]
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"grid": {
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"description" : [ "str" , [] ]
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, "rad_precision" : [ "float", [] ]
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, "num" : [ "dim" , [] ]
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, "max_ang_num" : [ "int" , [] ]
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, "min_ang_num" : [ "int" , [] ]
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, "coord" : [ "float", [ "grid.num" ] ]
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, "weight" : [ "float", [ "grid.num" ] ]
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, "ang_num" : [ "dim" , [] ]
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, "ang_coord" : [ "float", [ "grid.ang_num" ] ]
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, "ang_weight" : [ "float", [ "grid.ang_num" ] ]
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, "rad_num" : [ "dim" , [] ]
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, "rad_coord" : [ "float", [ "grid.rad_num" ] ]
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, "rad_weight" : [ "float", [ "grid.rad_num" ] ]
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} ,
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#+end_src
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:end:
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power = [
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-1, 1, 0, 0,
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-1, 1, 0, 0
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]
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#+END_EXAMPLE
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** Electron (electron group)
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* Basis set (basis group)
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We consider wave functions expressed in the spin-free formalism, where
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the number of \uparrow and \downarrow electrons is fixed.
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#+NAME:electron
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| Variable | Type | Dimensions | Description |
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|----------+-------+------------+-------------------------------------|
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| ~num~ | ~dim~ | | Number of electrons |
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| ~up_num~ | ~int~ | | Number of \uparrow-spin electrons |
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| ~dn_num~ | ~int~ | | Number of \downarrow-spin electrons |
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** Gaussian and Slater-type orbitals
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#+CALL: json(data=electron, title="electron")
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"electron": {
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"num" : [ "dim", [] ]
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, "up_num" : [ "int", [] ]
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, "dn_num" : [ "int", [] ]
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} ,
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#+end_src
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:end:
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** Ground or excited states (state group)
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This group contains information about excited states. Since only a
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single state can be stored in a TREXIO file, it is possible to store
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in the main TREXIO file the names of auxiliary files containing the
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information of the other states.
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The ~file_name~ and ~label~ arrays have to be written only for the
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main file, e.g. the one containing the ground state wave function
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together with the basis set parameters, molecular orbitals,
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integrals, etc.
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The ~id~ and ~current_label~ attributes need to be specified for each file.
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#+NAME: state
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| Variable | Type | Dimensions | Description |
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|-----------------+-------+---------------+---------------------------------------------------------------------------------------------|
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| ~num~ | ~dim~ | | Number of states (including the ground state) |
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| ~id~ | ~int~ | | Index of the current state (0 is ground state) |
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| ~current_label~ | ~str~ | | Label of the current state |
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| ~label~ | ~str~ | ~(state.num)~ | Labels of all states |
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| ~file_name~ | ~str~ | ~(state.num)~ | Names of the TREXIO files linked to the current one (i.e. containing data for other states) |
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#+CALL: json(data=state, title="state")
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"state": {
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"num" : [ "dim", [] ]
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, "id" : [ "int", [] ]
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, "current_label" : [ "str", [] ]
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, "label" : [ "str", [ "state.num" ] ]
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, "file_name" : [ "str", [ "state.num" ] ]
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} ,
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#+end_src
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:end:
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* One-electron basis
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** Basis set (basis group)
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*** Gaussian and Slater-type orbitals
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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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@ -315,7 +323,7 @@ power = [
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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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*** Plane waves
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A plane wave is defined as
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@ -327,7 +335,7 @@ power = [
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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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*** Data definitions
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#+NAME: basis
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| Variable | Type | Dimensions | Description |
|
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@ -368,7 +376,7 @@ power = [
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#+end_src
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:end:
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** Example
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*** Example
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For example, consider H_2 with the following basis set (in GAMESS
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format), where both the AOs and primitives are considered normalized:
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@ -439,7 +447,137 @@ prim_factor =
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4.3649547399719840e-01, 1.8135965626177861e+00 ]
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#+END_EXAMPLE
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* Atomic orbitals (ao group)
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** Effective core potentials (ecp group)
|
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|
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An effective core potential (ECP) $V_A^{\text{ECP}}$ replacing the
|
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core electrons of atom $A$ can be expressed as
|
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\[
|
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V_A^{\text{ECP}} =
|
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V_{A \ell_{\max}+1} +
|
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\sum_{\ell=0}^{\ell_{\max}}
|
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\sum_{m=-\ell}^{\ell} | Y_{\ell m} \rangle \left[
|
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V_{A \ell} - V_{A \ell_{\max}+1} \right] \langle Y_{\ell m} |
|
||||
\]
|
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|
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The first term in the equation above is sometimes attributed to the local channel,
|
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while the remaining terms correspond to the non-local channel projections.
|
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|
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The functions $V_{A\ell}$ are parameterized as:
|
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\[
|
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V_{A \ell}(\mathbf{r}) =
|
||||
\sum_{q=1}^{N_{q \ell}}
|
||||
\beta_{A q \ell}\, |\mathbf{r}-\mathbf{R}_{A}|^{n_{A q \ell}}\,
|
||||
e^{-\alpha_{A q \ell} |\mathbf{r}-\mathbf{R}_{A}|^2 }
|
||||
\]
|
||||
|
||||
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
|
||||
construction of all the angular functions of each shell. We
|
||||
@ -508,7 +646,7 @@ prim_factor =
|
||||
#+end_src
|
||||
:end:
|
||||
|
||||
** One-electron integrals (~ao_1e_int~ group)
|
||||
*** One-electron integrals (~ao_1e_int~ group)
|
||||
:PROPERTIES:
|
||||
:CUSTOM_ID: ao_one_e
|
||||
:END:
|
||||
@ -558,7 +696,7 @@ prim_factor =
|
||||
#+end_src
|
||||
:end:
|
||||
|
||||
** Two-electron integrals (~ao_2e_int~ group)
|
||||
*** Two-electron integrals (~ao_2e_int~ group)
|
||||
:PROPERTIES:
|
||||
:CUSTOM_ID: ao_two_e
|
||||
:END:
|
||||
@ -596,7 +734,7 @@ prim_factor =
|
||||
#+end_src
|
||||
:end:
|
||||
|
||||
* Molecular orbitals (mo group)
|
||||
** Molecular orbitals (mo group)
|
||||
|
||||
#+NAME: mo
|
||||
| Variable | Type | Dimensions | Description |
|
||||
@ -630,7 +768,7 @@ prim_factor =
|
||||
#+end_src
|
||||
: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
|
||||
[[#ao_one_e][AO one-electron integrals section]]. Here, the integrals are given in
|
||||
@ -670,7 +808,7 @@ prim_factor =
|
||||
#+end_src
|
||||
: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
|
||||
[[#ao_two_e][AO two-electron integrals section]]. Here, the integrals are given in
|
||||
@ -707,8 +845,21 @@ prim_factor =
|
||||
} ,
|
||||
#+end_src
|
||||
: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 $\Psi$
|
||||
can be expanded in the basis of Slater determinants $D_I$ as follows
|
||||
@ -756,7 +907,7 @@ prim_factor =
|
||||
#+end_src
|
||||
:end:
|
||||
|
||||
* Configuration state functions (csf group)
|
||||
** Configuration state functions (csf group)
|
||||
|
||||
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)
|
||||
@ -792,44 +943,7 @@ prim_factor =
|
||||
#+end_src
|
||||
:end:
|
||||
|
||||
* 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:
|
||||
|
||||
* Reduced density matrices (rdm group)
|
||||
** Reduced density matrices (rdm group)
|
||||
|
||||
The reduced density matrices are defined in the basis of molecular
|
||||
orbitals.
|
||||
@ -936,103 +1050,112 @@ prim_factor =
|
||||
#+end_src
|
||||
:end:
|
||||
|
||||
* Cell (cell group)
|
||||
* Correlation factors
|
||||
** Jastrow factor (jastrow group)
|
||||
|
||||
3 Lattice vectors to define a box containing the system, for example
|
||||
used in periodic calculations.
|
||||
The Jastrow factor is an $N$-electron function to which the CI
|
||||
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 |
|
||||
|----------+---------+------------+-----------------------|
|
||||
| ~a~ | ~float~ | ~(3)~ | First lattice vector |
|
||||
| ~b~ | ~float~ | ~(3)~ | Second lattice vector |
|
||||
| ~c~ | ~float~ | ~(3)~ | Third lattice vector |
|
||||
|
||||
#+CALL: json(data=cell, title="cell")
|
||||
|
||||
#+RESULTS:
|
||||
:results:
|
||||
#+begin_src python :tangle trex.json
|
||||
"cell": {
|
||||
"a" : [ "float", [ "3" ] ]
|
||||
, "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:
|
||||
|---------------+----------+---------------------+-----------------------------------------------------------------|
|
||||
| ~type~ | ~string~ | | Type of Jastrow factor: ~champ~ or ~mu~ |
|
||||
| ~ee_num~ | ~dim~ | | Number of Electron-electron parameters |
|
||||
| ~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 |
|
||||
| ~ee~ | ~float~ | ~(jastrow.ee_num)~ | Electron-electron parameters |
|
||||
| ~en~ | ~float~ | ~(jastrow.en_num)~ | Electron-nucleus parameters |
|
||||
| ~een~ | ~float~ | ~(jastrow.een_num)~ | Electron-electron-nucleus parameters |
|
||||
| ~en_nucleus~ | ~index~ | ~(jastrow.en_num)~ | Nucleus relative to the eN parameter |
|
||||
| ~een_nucleus~ | ~index~ | ~(jastrow.een_num)~ | Nucleus relative to the eeN parameter |
|
||||
| ~ee_scaling~ | ~float~ | | $\kappa$ value in CHAMP Jastrow for electron-electron distances |
|
||||
| ~eN_scaling~ | ~float~ | ~(nucleus.num)~ | $\kappa$ value in CHAMP Jastrow for electron-nucleus distances |
|
||||
|
||||
* Quantum Monte Carlo data (qmc group)
|
||||
|
||||
|
||||
Loading…
Reference in New Issue
Block a user