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#+TITLE: TREX Configuration file
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#+STARTUP: latexpreview
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#+SETUPFILE: docs/theme.setup
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2021-12-16 00:11:36 +01:00
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This page contains information about the general structure of the
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TREXIO library. The source code of the library can be automatically
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generated based on the contents of the ~trex.json~ configuration file,
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which itself is compiled from different sections (groups) presented
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below.
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For more information about the automatic generation on the source code
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or regarding possible modifications, please contact the TREXIO
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developers.
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All quantities are saved in TREXIO file in atomic units. The
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dimensions of the arrays in the tables below are given in column-major
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order (as in Fortran), and the ordering of the dimensions is reversed
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in the produced ~trex.json~ configuration file as the library is
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written in C.
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TREXIO currently supports ~int~, ~float~ and ~str~ types for both
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single attributes and arrays. Note, that some attributes might have
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~dim~ type (e.g. ~num~ of the ~nucleus~ group). This type is treated
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exactly the same as ~int~ with the only difference that ~dim~
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variables cannot be negative. This additional constraint is required
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because ~dim~ attributes are used internally to allocate memory and to
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check array boundaries in the memory-safe API. Most of the times, the
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~dim~ variables contain the ~num~ suffix.
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In Fortran, the arrays are 1-based and in most other languages the
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arrays are 0-based. Hence, we introduce the ~index~ type which is an
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1-based ~int~ in the Fortran interface and 0-based otherwise.
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For sparse data structures such as electron replusion integrals,
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the data can be too large to fit in memory and the data needs to be
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fetched using multiple function calls to perform I/O on buffers.
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#+begin_src python :tangle trex.json :exports none
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{
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#+end_src
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* Metadata (metadata group)
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As we expect our files to be archived in open-data repositories, we
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need to give the possibility to the users to store some metadata
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inside the files. We propose to store the list of names of the codes
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which have participated to the creation of the file, a list of
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authors of the file, and a textual description.
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#+NAME: metadata
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| Variable | Type | Dimensions (for arrays) | Description |
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|-------------------+-------+-------------------------+------------------------------------------|
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| ~code_num~ | ~dim~ | | Number of codes used to produce the file |
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| ~code~ | ~str~ | ~(metadata.code_num)~ | Names of the codes used |
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| ~author_num~ | ~dim~ | | Number of authors of the file |
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| ~author~ | ~str~ | ~(metadata.author_num)~ | Names of the authors of the file |
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| ~package_version~ | ~str~ | | TREXIO version used to produce the file |
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| ~description~ | ~str~ | | Text describing the content of file |
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#+CALL: json(data=metadata, title="metadata")
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#+RESULTS:
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:RESULTS:
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#+begin_src python :tangle trex.json
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"metadata": {
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"code_num" : [ "dim", [] ]
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, "code" : [ "str", [ "metadata.code_num" ] ]
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, "author_num" : [ "dim", [] ]
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, "author" : [ "str", [ "metadata.author_num" ] ]
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, "package_version" : [ "str", [] ]
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, "description" : [ "str", [] ]
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} ,
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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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| ~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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"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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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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#+NAME: nucleus
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| Variable | Type | Dimensions | Description |
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|---------------+---------+-------------------+--------------------------|
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| ~num~ | ~dim~ | | Number of nuclei |
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| ~charge~ | ~float~ | ~(nucleus.num)~ | Charges of the nuclei |
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| ~coord~ | ~float~ | ~(3,nucleus.num)~ | Coordinates of the atoms |
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| ~label~ | ~str~ | ~(nucleus.num)~ | Atom labels |
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| ~point_group~ | ~str~ | | Symmetry point group |
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| ~repulsion~ | ~float~ | | Nuclear repulsion energy |
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#+CALL: json(data=nucleus, title="nucleus")
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"nucleus": {
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"num" : [ "dim" , [] ]
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, "charge" : [ "float", [ "nucleus.num" ] ]
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, "coord" : [ "float", [ "nucleus.num", "3" ] ]
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, "label" : [ "str" , [ "nucleus.num" ] ]
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, "point_group" : [ "str" , [] ]
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, "repulsion" : [ "float", [] ]
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} ,
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#+end_src
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:end:
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2021-09-15 14:58:02 +02:00
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* Effective core potentials (ecp 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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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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| 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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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 ~ang_mom~ in the TREXIO file.
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#+CALL: json(data=ecp, title="ecp")
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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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} ,
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#+end_src
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:END:
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** Example
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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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#+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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In TREXIO representation this would be:
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#+BEGIN_EXAMPLE
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num = 8
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# lmax+1 per atom
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max_ang_mom_plus_1 = [ 1, 1 ]
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# number of core electrons to remove per atom
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zcore = [ 0, 0 ]
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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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# 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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2021-10-19 15:47:13 +02:00
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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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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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|
|
|
2022-01-10 10:34:27 +01:00
|
|
|
power = [
|
|
|
|
-1, 1, 0, 0,
|
2021-10-18 16:53:17 +02:00
|
|
|
-1, 1, 0, 0
|
|
|
|
]
|
|
|
|
#+END_EXAMPLE
|
2021-10-18 16:23:07 +02:00
|
|
|
|
2021-06-25 11:52:53 +02:00
|
|
|
* Basis set (basis group)
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
We consider here basis functions centered on nuclei. Hence, we enable
|
2021-06-09 16:56:02 +02:00
|
|
|
the possibility to define /dummy atoms/ to place basis functions in
|
|
|
|
random positions.
|
2021-05-21 14:04:19 +02:00
|
|
|
|
|
|
|
The atomic basis set is defined as a list of shells. Each shell $s$ is
|
|
|
|
centered on a center $A$, possesses a given angular momentum $l$ and a
|
|
|
|
radial function $R_s$. The radial function is a linear combination of
|
|
|
|
$N_{\text{prim}}$ /primitive/ functions that can be of type
|
|
|
|
Slater ($p=1$) or Gaussian ($p=2$),
|
|
|
|
parameterized by exponents $\gamma_{ks}$ and coefficients $a_{ks}$:
|
|
|
|
\[
|
|
|
|
R_s(\mathbf{r}) = \mathcal{N}_s \vert\mathbf{r}-\mathbf{R}_A\vert^{n_s}
|
2021-05-25 00:01:29 +02:00
|
|
|
\sum_{k=1}^{N_{\text{prim}}} a_{ks}\, f_{ks}(\gamma_{ks},p)\,
|
2021-05-21 14:04:19 +02:00
|
|
|
\exp \left( - \gamma_{ks}
|
2021-06-18 12:04:03 +02:00
|
|
|
\vert \mathbf{r}-\mathbf{R}_A \vert ^p \right).
|
2021-05-21 14:04:19 +02:00
|
|
|
\]
|
|
|
|
|
2021-05-25 00:01:29 +02:00
|
|
|
In the case of Gaussian functions, $n_s$ is always zero.
|
|
|
|
|
|
|
|
Different codes normalize functions at different levels. Computing
|
|
|
|
normalization factors requires the ability to compute overlap
|
|
|
|
integrals, so the normalization factors should be written in the
|
|
|
|
file to ensure that the file is self-contained and does not need the
|
|
|
|
client program to have the ability to compute such integrals.
|
|
|
|
|
|
|
|
Some codes assume that the contraction coefficients are for a linear
|
|
|
|
combination of /normalized/ primitives. This implies that a normalization
|
|
|
|
constant for the primitive $ks$ needs to be computed and stored. If
|
2021-06-09 16:56:02 +02:00
|
|
|
this normalization factor is not required, $f_{ks}=1$.
|
2021-06-18 12:04:03 +02:00
|
|
|
|
2021-05-25 00:01:29 +02:00
|
|
|
Some codes assume that the basis function are normalized. This
|
|
|
|
implies the computation of an extra normalization factor, $\mathcal{N}_s$.
|
2021-06-09 16:56:02 +02:00
|
|
|
If the the basis function is not considered normalized, $\mathcal{N}_s=1$.
|
2021-05-21 14:04:19 +02:00
|
|
|
|
|
|
|
|
2021-06-09 16:56:02 +02:00
|
|
|
All the basis set parameters are stored in one-dimensional arrays:
|
|
|
|
|
2021-05-21 12:10:29 +02:00
|
|
|
#+NAME: basis
|
2021-10-21 15:51:21 +02:00
|
|
|
| Variable | Type | Dimensions | Description |
|
|
|
|
|-----------------+---------+---------------------+--------------------------------------------------------------|
|
|
|
|
| ~type~ | ~str~ | | Type of basis set: "Gaussian" or "Slater" |
|
|
|
|
| ~prim_num~ | ~dim~ | | Total number of primitives |
|
|
|
|
| ~shell_num~ | ~dim~ | | Total number of shells |
|
|
|
|
| ~nucleus_index~ | ~index~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices |
|
2021-10-25 12:17:15 +02:00
|
|
|
| ~shell_ang_mom~ | ~int~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta |
|
2021-10-21 15:51:21 +02:00
|
|
|
| ~shell_factor~ | ~float~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$) |
|
|
|
|
| ~shell_index~ | ~index~ | ~(basis.prim_num)~ | One-to-one correspondence between primitives and shell index |
|
|
|
|
| ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) |
|
|
|
|
| ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) |
|
|
|
|
| ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) |
|
2021-06-18 12:04:03 +02:00
|
|
|
|
2021-05-21 12:10:29 +02:00
|
|
|
#+CALL: json(data=basis, title="basis")
|
|
|
|
|
|
|
|
#+RESULTS:
|
2021-09-22 10:56:25 +02:00
|
|
|
:RESULTS:
|
2021-05-21 12:10:29 +02:00
|
|
|
#+begin_src python :tangle trex.json
|
|
|
|
"basis": {
|
2021-10-21 15:51:21 +02:00
|
|
|
"type" : [ "str" , [] ]
|
|
|
|
, "prim_num" : [ "dim" , [] ]
|
|
|
|
, "shell_num" : [ "dim" , [] ]
|
|
|
|
, "nucleus_index" : [ "index", [ "basis.shell_num" ] ]
|
2021-10-25 13:28:18 +02:00
|
|
|
, "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ]
|
2021-10-21 15:51:21 +02:00
|
|
|
, "shell_factor" : [ "float", [ "basis.shell_num" ] ]
|
|
|
|
, "shell_index" : [ "index", [ "basis.prim_num" ] ]
|
|
|
|
, "exponent" : [ "float", [ "basis.prim_num" ] ]
|
|
|
|
, "coefficient" : [ "float", [ "basis.prim_num" ] ]
|
|
|
|
, "prim_factor" : [ "float", [ "basis.prim_num" ] ]
|
2021-05-21 12:10:29 +02:00
|
|
|
} ,
|
|
|
|
#+end_src
|
2021-09-22 10:56:25 +02:00
|
|
|
:END:
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-10-18 17:40:53 +02:00
|
|
|
** Example
|
|
|
|
|
2021-06-09 16:56:02 +02:00
|
|
|
For example, consider H_2 with the following basis set (in GAMESS
|
|
|
|
format), where both the AOs and primitives are considered normalized:
|
|
|
|
|
|
|
|
#+BEGIN_EXAMPLE
|
|
|
|
HYDROGEN
|
|
|
|
S 5
|
|
|
|
1 3.387000E+01 6.068000E-03
|
|
|
|
2 5.095000E+00 4.530800E-02
|
|
|
|
3 1.159000E+00 2.028220E-01
|
|
|
|
4 3.258000E-01 5.039030E-01
|
|
|
|
5 1.027000E-01 3.834210E-01
|
|
|
|
S 1
|
|
|
|
1 3.258000E-01 1.000000E+00
|
|
|
|
S 1
|
|
|
|
1 1.027000E-01 1.000000E+00
|
|
|
|
P 1
|
|
|
|
1 1.407000E+00 1.000000E+00
|
|
|
|
P 1
|
|
|
|
1 3.880000E-01 1.000000E+00
|
|
|
|
D 1
|
2021-10-18 17:40:53 +02:00
|
|
|
1 1.057000E+00 1.000000E+00
|
2021-06-09 16:56:02 +02:00
|
|
|
#+END_EXAMPLE
|
|
|
|
|
2021-10-18 17:40:53 +02:00
|
|
|
In TREXIO representaion we have:
|
2021-06-09 16:56:02 +02:00
|
|
|
|
|
|
|
#+BEGIN_EXAMPLE
|
2021-10-18 17:40:53 +02:00
|
|
|
type = "Gaussian"
|
2021-10-21 15:51:21 +02:00
|
|
|
prim_num = 20
|
|
|
|
shell_num = 12
|
2021-10-18 17:40:53 +02:00
|
|
|
|
2021-10-21 15:51:21 +02:00
|
|
|
# 6 shells per H atom
|
2022-01-10 10:34:27 +01:00
|
|
|
nucleus_index =
|
|
|
|
[ 0, 0, 0, 0, 0, 0,
|
|
|
|
1, 1, 1, 1, 1, 1 ]
|
2021-10-18 17:40:53 +02:00
|
|
|
|
2021-10-21 15:51:21 +02:00
|
|
|
# 3 shells in S (l=0), 2 in P (l=1), 1 in D (l=2)
|
2021-10-25 13:28:18 +02:00
|
|
|
shell_ang_mom =
|
2022-01-10 10:34:27 +01:00
|
|
|
[ 0, 0, 0, 1, 1, 2,
|
2021-10-21 15:51:21 +02:00
|
|
|
0, 0, 0, 1, 1, 2 ]
|
2021-10-18 17:40:53 +02:00
|
|
|
|
2022-01-10 10:34:27 +01:00
|
|
|
# no need to renormalize shells
|
|
|
|
shell_factor =
|
|
|
|
[ 1., 1., 1., 1., 1., 1.,
|
|
|
|
1., 1., 1., 1., 1., 1. ]
|
2021-10-21 15:51:21 +02:00
|
|
|
|
|
|
|
# 5 primitives for the first S shell and then 1 primitive per remaining shells in each H atom
|
2022-01-10 10:34:27 +01:00
|
|
|
shell_index =
|
|
|
|
[ 0, 0, 0, 0, 0, 1, 2, 3, 4, 5,
|
2021-10-21 15:51:21 +02:00
|
|
|
6, 6, 6, 6, 6, 7, 8, 9, 10, 11 ]
|
2021-10-18 17:40:53 +02:00
|
|
|
|
2021-10-19 10:09:20 +02:00
|
|
|
# parameters of the primitives (10 per H atom)
|
2021-06-09 16:56:02 +02:00
|
|
|
exponent =
|
2022-01-10 10:34:27 +01:00
|
|
|
[ 33.87, 5.095, 1.159, 0.3258, 0.1027, 0.3258, 0.1027, 1.407, 0.388, 1.057,
|
2021-10-18 17:40:53 +02:00
|
|
|
33.87, 5.095, 1.159, 0.3258, 0.1027, 0.3258, 0.1027, 1.407, 0.388, 1.057 ]
|
2021-06-09 16:56:02 +02:00
|
|
|
|
|
|
|
coefficient =
|
2022-01-10 10:34:27 +01:00
|
|
|
[ 0.006068, 0.045308, 0.202822, 0.503903, 0.383421, 1.0, 1.0, 1.0, 1.0, 1.0,
|
2021-10-18 17:40:53 +02:00
|
|
|
0.006068, 0.045308, 0.202822, 0.503903, 0.383421, 1.0, 1.0, 1.0, 1.0, 1.0 ]
|
2021-06-09 16:56:02 +02:00
|
|
|
|
|
|
|
prim_factor =
|
|
|
|
[ 1.0006253235944540e+01, 2.4169531573445120e+00, 7.9610924849766440e-01
|
|
|
|
3.0734305383061117e-01, 1.2929684417481876e-01, 3.0734305383061117e-01,
|
|
|
|
1.2929684417481876e-01, 2.1842769845268308e+00, 4.3649547399719840e-01,
|
|
|
|
1.8135965626177861e+00, 1.0006253235944540e+01, 2.4169531573445120e+00,
|
|
|
|
7.9610924849766440e-01, 3.0734305383061117e-01, 1.2929684417481876e-01,
|
|
|
|
3.0734305383061117e-01, 1.2929684417481876e-01, 2.1842769845268308e+00,
|
|
|
|
4.3649547399719840e-01, 1.8135965626177861e+00 ]
|
|
|
|
#+END_EXAMPLE
|
|
|
|
|
2021-06-25 11:52:53 +02:00
|
|
|
* Atomic orbitals (ao group)
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
Going from the atomic basis set to AOs implies a systematic
|
|
|
|
construction of all the angular functions of each shell. We
|
|
|
|
consider two cases for the angular functions: the real-valued
|
|
|
|
spherical harmonics, and the polynomials in Cartesian coordinates.
|
2022-01-07 15:37:02 +01:00
|
|
|
In the case of spherical harmonics, the AOs are ordered as
|
|
|
|
$0, +1, -1, +2, -2, \dots, +m, -m$ and in the case of polynomials we
|
|
|
|
impose the canonical (or alphabetical) ordering), i.e
|
2021-05-21 14:04:19 +02:00
|
|
|
|
|
|
|
\begin{eqnarray}
|
|
|
|
p & : & p_x, p_y, p_z \nonumber \\
|
|
|
|
d & : & d_{xx}, d_{xy}, d_{xz}, d_{yy}, d_{yz}, d_{zz} \nonumber \\
|
|
|
|
f & : & f_{xxx}, f_{xxy}, f_{xxz}, f_{xyy}, f_{xyz}, f_{xzz}, f_{yyy}, f_{yyz}, f_{yzz}, …f_{zzz} \nonumber \\
|
|
|
|
{\rm etc.} \nonumber
|
|
|
|
\end{eqnarray}
|
|
|
|
|
2022-01-07 15:37:02 +01:00
|
|
|
Note that there is no exception for $p$ orbitals in spherical
|
|
|
|
coordinates: the ordering is $0,+1,-1$ which corresponds $p_z, p_x, p_y$.
|
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
AOs are defined as
|
|
|
|
|
|
|
|
\[
|
|
|
|
\chi_i (\mathbf{r}) = \mathcal{N}_i\, P_{\eta(i)}(\mathbf{r})\, R_{\theta(i)} (\mathbf{r})
|
|
|
|
\]
|
|
|
|
|
|
|
|
where $i$ is the atomic orbital index,
|
|
|
|
$P$ encodes for either the
|
|
|
|
polynomials or the spherical harmonics, $\theta(i)$ returns the
|
|
|
|
shell on which the AO is expanded, and $\eta(i)$ denotes which
|
|
|
|
angular function is chosen.
|
|
|
|
$\mathcal{N}_i$ is a normalization factor that enables the
|
|
|
|
possibility to have different normalization coefficients within a
|
|
|
|
shell, as in the GAMESS convention where
|
|
|
|
$\mathcal{N}_{x^2} \ne \mathcal{N}_{xy}$ because
|
|
|
|
\[ \left[ \iiint \left(x-X_A \right)^2 R_{\theta(i)}
|
2021-06-18 12:04:03 +02:00
|
|
|
(\mathbf{r}) dx\, dy\, dz \right]^{-1/2} \ne
|
2021-05-21 14:04:19 +02:00
|
|
|
\left[ \iiint \left( x-X_A \right) \left( y-Y_A \right) R_{\theta(i)}
|
2021-06-18 12:04:03 +02:00
|
|
|
(\mathbf{r}) dx\, dy\, dz \right]^{-1/2}. \]
|
2021-05-21 14:04:19 +02:00
|
|
|
|
|
|
|
In such a case, one should set the normalization of the shell (in
|
2021-06-25 14:15:50 +02:00
|
|
|
the [[Basis set (basis group)][Basis set]] section) to $\mathcal{N}_{z^2}$, which is the
|
2021-05-21 14:04:19 +02:00
|
|
|
normalization factor of the atomic orbitals in spherical coordinates.
|
|
|
|
The normalization factor of the $xy$ function which should be
|
|
|
|
introduced here should be $\frac{\mathcal{N}_{xy}}{\mathcal{N}_{z^2}}$.
|
|
|
|
|
2021-05-21 12:10:29 +02:00
|
|
|
#+NAME: ao
|
2021-06-25 11:52:53 +02:00
|
|
|
| Variable | Type | Dimensions | Description |
|
|
|
|
|-----------------+---------+------------+---------------------------------|
|
2021-05-24 15:45:30 +02:00
|
|
|
| ~cartesian~ | ~int~ | | ~1~: true, ~0~: false |
|
2021-09-22 10:56:25 +02:00
|
|
|
| ~num~ | ~dim~ | | Total number of atomic orbitals |
|
2021-06-04 14:43:27 +02:00
|
|
|
| ~shell~ | ~index~ | ~(ao.num)~ | basis set shell for each AO |
|
2021-05-24 15:01:04 +02:00
|
|
|
| ~normalization~ | ~float~ | ~(ao.num)~ | Normalization factors |
|
2021-05-21 12:10:29 +02:00
|
|
|
|
|
|
|
#+CALL: json(data=ao, title="ao")
|
|
|
|
|
|
|
|
#+RESULTS:
|
2021-09-22 10:56:25 +02:00
|
|
|
:RESULTS:
|
2021-05-21 12:10:29 +02:00
|
|
|
#+begin_src python :tangle trex.json
|
2021-05-24 15:01:04 +02:00
|
|
|
"ao": {
|
2021-09-22 10:56:25 +02:00
|
|
|
"cartesian" : [ "int" , [] ]
|
|
|
|
, "num" : [ "dim" , [] ]
|
|
|
|
, "shell" : [ "index", [ "ao.num" ] ]
|
|
|
|
, "normalization" : [ "float", [ "ao.num" ] ]
|
2021-05-24 15:01:04 +02:00
|
|
|
} ,
|
2021-05-21 12:10:29 +02:00
|
|
|
#+end_src
|
2021-09-22 10:56:25 +02:00
|
|
|
:END:
|
2021-06-18 12:04:03 +02:00
|
|
|
|
2021-06-25 14:15:50 +02:00
|
|
|
** One-electron integrals (~ao_1e_int~ group)
|
2021-05-24 15:01:04 +02:00
|
|
|
:PROPERTIES:
|
|
|
|
:CUSTOM_ID: ao_one_e
|
|
|
|
:END:
|
2022-01-10 10:34:27 +01:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
- \[ \hat{V}_{\text{ne}} = \sum_{A=1}^{N_\text{nucl}}
|
|
|
|
\sum_{i=1}^{N_\text{elec}} \frac{-Z_A }{\vert \mathbf{R}_A -
|
|
|
|
\mathbf{r}_i \vert} \] : electron-nucleus attractive potential,
|
2021-06-18 12:04:03 +02:00
|
|
|
- \[ \hat{T}_{\text{e}} =
|
2021-05-21 14:04:19 +02:00
|
|
|
\sum_{i=1}^{N_\text{elec}} -\frac{1}{2}\hat{\Delta}_i \] : electronic kinetic energy
|
|
|
|
- $\hat{h} = \hat{T}_\text{e} + \hat{V}_\text{ne} +
|
|
|
|
\hat{V}_\text{ecp,l} + \hat{V}_\text{ecp,nl}$ : core electronic Hamiltonian
|
|
|
|
|
|
|
|
The one-electron integrals for a one-electron operator $\hat{O}$ are
|
|
|
|
\[ \langle p \vert \hat{O} \vert q \rangle \], returned as a matrix
|
|
|
|
over atomic orbitals.
|
|
|
|
|
|
|
|
#+NAME: ao_1e_int
|
2021-06-25 11:52:53 +02:00
|
|
|
| Variable | Type | Dimensions | Description |
|
|
|
|
|--------------------+---------+--------------------+-----------------------------------------------------------|
|
|
|
|
| ~overlap~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ |
|
|
|
|
| ~kinetic~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ |
|
|
|
|
| ~potential_n_e~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ |
|
|
|
|
| ~ecp_local~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp,l}} \vert q \rangle$ |
|
|
|
|
| ~ecp_non_local~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp,nl}} \vert q \rangle$ |
|
|
|
|
| ~core_hamiltonian~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ |
|
2021-05-21 14:04:19 +02:00
|
|
|
|
|
|
|
#+CALL: json(data=ao_1e_int, title="ao_1e_int")
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
#+RESULTS:
|
|
|
|
:results:
|
|
|
|
#+begin_src python :tangle trex.json
|
2021-05-24 15:45:30 +02:00
|
|
|
"ao_1e_int": {
|
|
|
|
"overlap" : [ "float", [ "ao.num", "ao.num" ] ]
|
|
|
|
, "kinetic" : [ "float", [ "ao.num", "ao.num" ] ]
|
|
|
|
, "potential_n_e" : [ "float", [ "ao.num", "ao.num" ] ]
|
|
|
|
, "ecp_local" : [ "float", [ "ao.num", "ao.num" ] ]
|
|
|
|
, "ecp_non_local" : [ "float", [ "ao.num", "ao.num" ] ]
|
|
|
|
, "core_hamiltonian" : [ "float", [ "ao.num", "ao.num" ] ]
|
|
|
|
} ,
|
2021-05-21 14:04:19 +02:00
|
|
|
#+end_src
|
|
|
|
:end:
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-06-25 14:15:50 +02:00
|
|
|
** Two-electron integrals (~ao_2e_int~ group)
|
2021-05-24 15:01:04 +02:00
|
|
|
:PROPERTIES:
|
|
|
|
:CUSTOM_ID: ao_two_e
|
|
|
|
:END:
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
The two-electron integrals for a two-electron operator $\hat{O}$ are
|
|
|
|
\[ \langle p q \vert \hat{O} \vert r s \rangle \] in physicists
|
|
|
|
notation or \[ ( pr \vert \hat{O} \vert qs ) \] in chemists
|
|
|
|
notation, where $p,q,r,s$ are indices over atomic orbitals.
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
Functions are provided to get the indices in physicists or chemists
|
|
|
|
notation.
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
# TODO: Physicist / Chemist functions
|
2021-06-18 12:04:03 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
- \[ \hat{W}_{\text{ee}} = \sum_{i=2}^{N_\text{elec}} \sum_{j=1}^{i-1} \frac{1}{\vert \mathbf{r}_i - \mathbf{r}_j \vert} \] : electron-electron repulsive potential operator.
|
|
|
|
- \[ \hat{W}^{lr}_{\text{ee}} = \sum_{i=2}^{N_\text{elec}}
|
|
|
|
\sum_{j=1}^{i-1} \frac{\text{erf}(\vert \mathbf{r}_i -
|
|
|
|
\mathbf{r}_j \vert)}{\vert \mathbf{r}_i - \mathbf{r}_j \vert} \] : electron-electron long range potential
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
#+NAME: ao_2e_int
|
2021-06-25 11:52:53 +02:00
|
|
|
| Variable | Type | Dimensions | Description |
|
|
|
|
|----------+----------------+------------------------------------+-----------------------------------------|
|
|
|
|
| ~eri~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Electron repulsion integrals |
|
|
|
|
| ~eri_lr~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Long-range Electron repulsion integrals |
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
#+CALL: json(data=ao_2e_int, title="ao_2e_int")
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-21 14:04:19 +02:00
|
|
|
#+RESULTS:
|
|
|
|
:results:
|
|
|
|
#+begin_src python :tangle trex.json
|
2021-05-24 15:45:30 +02:00
|
|
|
"ao_2e_int": {
|
|
|
|
"eri" : [ "float sparse", [ "ao.num", "ao.num", "ao.num", "ao.num" ] ]
|
|
|
|
, "eri_lr" : [ "float sparse", [ "ao.num", "ao.num", "ao.num", "ao.num" ] ]
|
|
|
|
} ,
|
2021-05-21 14:04:19 +02:00
|
|
|
#+end_src
|
|
|
|
:end:
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-06-25 11:52:53 +02:00
|
|
|
* Molecular orbitals (mo group)
|
2021-05-21 12:10:29 +02:00
|
|
|
|
|
|
|
#+NAME: mo
|
2021-09-15 15:03:20 +02:00
|
|
|
| Variable | Type | Dimensions | Description |
|
|
|
|
|---------------+---------+--------------------+--------------------------------------------------------------------------|
|
2021-09-15 14:58:02 +02:00
|
|
|
| ~type~ | ~str~ | | Free text to identify the set of MOs (HF, Natural, Local, CASSCF, /etc/) |
|
2021-09-22 10:56:25 +02:00
|
|
|
| ~num~ | ~dim~ | | Number of MOs |
|
2021-09-15 15:03:20 +02:00
|
|
|
| ~coefficient~ | ~float~ | ~(ao.num, mo.num)~ | MO coefficients |
|
|
|
|
| ~class~ | ~str~ | ~(mo.num)~ | Choose among: Core, Inactive, Active, Virtual, Deleted |
|
|
|
|
| ~symmetry~ | ~str~ | ~(mo.num)~ | Symmetry in the point group |
|
|
|
|
| ~occupation~ | ~float~ | ~(mo.num)~ | Occupation number |
|
2021-05-21 12:10:29 +02:00
|
|
|
|
|
|
|
#+CALL: json(data=mo, title="mo")
|
|
|
|
|
|
|
|
#+RESULTS:
|
2021-09-22 10:56:25 +02:00
|
|
|
:RESULTS:
|
2021-05-21 12:10:29 +02:00
|
|
|
#+begin_src python :tangle trex.json
|
|
|
|
"mo": {
|
2021-09-22 10:56:25 +02:00
|
|
|
"type" : [ "str" , [] ]
|
|
|
|
, "num" : [ "dim" , [] ]
|
|
|
|
, "coefficient" : [ "float", [ "mo.num", "ao.num" ] ]
|
|
|
|
, "class" : [ "str" , [ "mo.num" ] ]
|
|
|
|
, "symmetry" : [ "str" , [ "mo.num" ] ]
|
|
|
|
, "occupation" : [ "float", [ "mo.num" ] ]
|
2021-05-21 12:10:29 +02:00
|
|
|
} ,
|
|
|
|
#+end_src
|
2021-09-22 10:56:25 +02:00
|
|
|
:END:
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-06-25 14:15:50 +02:00
|
|
|
** One-electron integrals (~mo_1e_int~ group)
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-24 15:01:04 +02:00
|
|
|
The operators as the same as those defined in the
|
2021-06-18 12:04:03 +02:00
|
|
|
[[#ao_one_e][AO one-electron integrals section]]. Here, the integrals are given in
|
2021-05-24 15:01:04 +02:00
|
|
|
the basis of molecular orbitals.
|
2021-06-18 12:04:03 +02:00
|
|
|
|
2021-05-21 12:10:29 +02:00
|
|
|
#+NAME: mo_1e_int
|
2021-06-25 11:52:53 +02:00
|
|
|
| Variable | Type | Dimensions | Description |
|
|
|
|
|--------------------+---------+--------------------+-----------------------------------------------------------|
|
|
|
|
| ~overlap~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert j \rangle$ |
|
|
|
|
| ~kinetic~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{T}_e \vert j \rangle$ |
|
|
|
|
| ~potential_n_e~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ne}} \vert j \rangle$ |
|
|
|
|
| ~ecp_local~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ecp,l}} \vert j \rangle$ |
|
|
|
|
| ~ecp_non_local~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ecp,nl}} \vert j \rangle$ |
|
|
|
|
| ~core_hamiltonian~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{h} \vert j \rangle$ |
|
2021-05-21 12:10:29 +02:00
|
|
|
|
|
|
|
#+CALL: json(data=mo_1e_int, title="mo_1e_int")
|
|
|
|
|
|
|
|
#+RESULTS:
|
|
|
|
:results:
|
|
|
|
#+begin_src python :tangle trex.json
|
|
|
|
"mo_1e_int": {
|
|
|
|
"overlap" : [ "float", [ "mo.num", "mo.num" ] ]
|
|
|
|
, "kinetic" : [ "float", [ "mo.num", "mo.num" ] ]
|
|
|
|
, "potential_n_e" : [ "float", [ "mo.num", "mo.num" ] ]
|
|
|
|
, "ecp_local" : [ "float", [ "mo.num", "mo.num" ] ]
|
|
|
|
, "ecp_non_local" : [ "float", [ "mo.num", "mo.num" ] ]
|
|
|
|
, "core_hamiltonian" : [ "float", [ "mo.num", "mo.num" ] ]
|
|
|
|
} ,
|
|
|
|
#+end_src
|
|
|
|
:end:
|
|
|
|
|
2021-06-25 14:15:50 +02:00
|
|
|
** Two-electron integrals (~mo_2e_int~ group)
|
2021-05-21 12:10:29 +02:00
|
|
|
|
2021-05-24 15:01:04 +02:00
|
|
|
The operators as the same as those defined in the
|
2021-06-25 14:15:50 +02:00
|
|
|
[[#ao_two_e][AO two-electron integrals section]]. Here, the integrals are given in
|
2021-05-24 15:01:04 +02:00
|
|
|
the basis of molecular orbitals.
|
2021-05-21 12:10:29 +02:00
|
|
|
|
|
|
|
#+NAME: mo_2e_int
|
2021-06-25 11:52:53 +02:00
|
|
|
| Variable | Type | Dimensions | Description |
|
|
|
|
|----------+----------------+------------------------------------+-----------------------------------------|
|
|
|
|
| ~eri~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Electron repulsion integrals |
|
|
|
|
| ~eri_lr~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Long-range Electron repulsion integrals |
|
2021-05-21 12:10:29 +02:00
|
|
|
|
|
|
|
#+CALL: json(data=mo_2e_int, title="mo_2e_int")
|
|
|
|
|
|
|
|
#+RESULTS:
|
|
|
|
: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" ] ]
|
|
|
|
} ,
|
|
|
|
#+end_src
|
|
|
|
:end:
|
|
|
|
|
|
|
|
* TODO Slater determinants
|
2021-12-08 12:03:14 +01:00
|
|
|
* Reduced density matrices (rdm group)
|
2021-06-18 12:04:03 +02:00
|
|
|
|
2022-01-10 10:25:18 +01:00
|
|
|
The reduced density matrices are defined in the basis of molecular
|
|
|
|
orbitals.
|
|
|
|
|
|
|
|
The $\uparrow$-spin and $\downarrow$-spin components of the one-body
|
|
|
|
density matrix are given by
|
|
|
|
\begin{eqnarray*}
|
2022-01-10 10:34:27 +01:00
|
|
|
\gamma_{ij}^{\uparrow} &=& \langle \Psi | \hat{a}^{\dagger}_{j\alpha}\, \hat{a}_{i\alpha} | \Psi \rangle \\
|
|
|
|
\gamma_{ij}^{\downarrow} &=& \langle \Psi | \hat{a}^{\dagger}_{j\beta} \, \hat{a}_{i\beta} | \Psi \rangle
|
2022-01-10 10:25:18 +01:00
|
|
|
\end{eqnarray*}
|
|
|
|
and the spin-summed one-body density matrix is
|
|
|
|
\[
|
2022-01-10 10:34:27 +01:00
|
|
|
\gamma_{ij} = \gamma^{\uparrow}_{ij} + \gamma^{\downarrow}_{ij}
|
2022-01-10 10:25:18 +01:00
|
|
|
\]
|
|
|
|
|
|
|
|
The $\uparrow \uparrow$, $\downarrow \downarrow$, $\uparrow \downarrow$, $\downarrow \uparrow$
|
|
|
|
components of the two-body density matrix are given by
|
|
|
|
\begin{eqnarray*}
|
|
|
|
\Gamma_{ijkl}^{\uparrow \uparrow} &=&
|
2022-01-10 10:34:27 +01:00
|
|
|
\langle \Psi | \hat{a}^{\dagger}_{k\alpha}\, \hat{a}^{\dagger}_{l\alpha} \hat{a}_{j\alpha}\, \hat{a}_{i\alpha} | \Psi \rangle \\
|
2022-01-10 10:25:18 +01:00
|
|
|
\Gamma_{ijkl}^{\downarrow \downarrow} &=&
|
2022-01-10 10:34:27 +01:00
|
|
|
\langle \Psi | \hat{a}^{\dagger}_{k\beta}\, \hat{a}^{\dagger}_{l\beta} \hat{a}_{j\beta}\, \hat{a}_{i\beta} | \Psi \rangle \\
|
2022-01-10 10:25:18 +01:00
|
|
|
\Gamma_{ijkl}^{\uparrow \downarrow} &=&
|
2022-01-10 10:34:27 +01:00
|
|
|
\langle \Psi | \hat{a}^{\dagger}_{k\alpha}\, \hat{a}^{\dagger}_{l\beta} \hat{a}_{j\beta}\, \hat{a}_{i\alpha} | \Psi \rangle \\
|
2022-01-10 10:25:18 +01:00
|
|
|
\Gamma_{ijkl}^{\downarrow \uparrow} &=&
|
2022-01-10 10:34:27 +01:00
|
|
|
\langle \Psi | \hat{a}^{\dagger}_{k\beta}\, \hat{a}^{\dagger}_{l\alpha} \hat{a}_{j\alpha}\, \hat{a}_{i\beta} | \Psi \rangle \\
|
2022-01-10 10:25:18 +01:00
|
|
|
\end{eqnarray*}
|
|
|
|
and the spin-summed one-body density matrix is
|
|
|
|
\[
|
|
|
|
\Gamma_{ijkl} = \Gamma_{ijkl}^{\uparrow \uparrow} +
|
2022-01-10 10:34:27 +01:00
|
|
|
\Gamma_{ijkl}^{\downarrow \downarrow} + \Gamma_{ijkl}^{\uparrow \downarrow}
|
2022-01-10 10:25:18 +01:00
|
|
|
\Gamma_{ijkl}^{\downarrow \uparrow}
|
|
|
|
\]
|
2022-01-10 10:34:27 +01:00
|
|
|
|
2022-01-10 10:25:18 +01:00
|
|
|
The total energy can be computed as:
|
|
|
|
\[
|
|
|
|
E = E_{\text{NN}} + \sum_{ij} \gamma_{ij} \langle j|h|i \rangle +
|
|
|
|
\frac{1}{2} \sum_{ijlk} \Gamma_{ijkl} \langle k l | i j \rangle
|
|
|
|
\]
|
2022-01-10 10:34:27 +01:00
|
|
|
|
2021-05-21 12:10:29 +02:00
|
|
|
#+NAME: rdm
|
2021-12-08 12:03:14 +01:00
|
|
|
| Variable | Type | Dimensions | Description |
|
|
|
|
|-----------+----------------+------------------------------------+-----------------------------------------------------------------------|
|
|
|
|
| ~1e~ | ~float~ | ~(mo.num, mo.num)~ | One body density matrix |
|
|
|
|
| ~1e_up~ | ~float~ | ~(mo.num, mo.num)~ | \uparrow-spin component of the one body density matrix |
|
|
|
|
| ~1e_dn~ | ~float~ | ~(mo.num, mo.num)~ | \downarrow-spin component of the one body density matrix |
|
|
|
|
| ~2e~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Two-body reduced density matrix (spin trace) |
|
|
|
|
| ~2e_upup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\uparrow component of the two-body reduced density matrix |
|
|
|
|
| ~2e_dndn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\downarrow component of the two-body reduced density matrix |
|
|
|
|
| ~2e_updn~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\downarrow component of the two-body reduced density matrix |
|
2022-01-10 10:25:18 +01:00
|
|
|
| ~2e_dnup~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \downarrow\uparrow component of the two-body reduced density matrix |
|
2021-05-21 12:10:29 +02:00
|
|
|
|
|
|
|
#+CALL: json(data=rdm, title="rdm", last=1)
|
|
|
|
|
|
|
|
#+RESULTS:
|
|
|
|
:results:
|
|
|
|
#+begin_src python :tangle trex.json
|
|
|
|
"rdm": {
|
2021-12-08 12:03:14 +01:00
|
|
|
"1e" : [ "float" , [ "mo.num", "mo.num" ] ]
|
|
|
|
, "1e_up" : [ "float" , [ "mo.num", "mo.num" ] ]
|
|
|
|
, "1e_dn" : [ "float" , [ "mo.num", "mo.num" ] ]
|
|
|
|
, "2e" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
|
|
|
|
, "2e_upup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
|
|
|
|
, "2e_dndn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
|
|
|
|
, "2e_updn" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
|
2022-01-10 10:25:18 +01:00
|
|
|
, "2e_dnup" : [ "float sparse", [ "mo.num", "mo.num", "mo.num", "mo.num" ] ]
|
2021-05-21 12:10:29 +02:00
|
|
|
}
|
|
|
|
#+end_src
|
|
|
|
:end:
|
|
|
|
|
2021-10-07 12:53:52 +02:00
|
|
|
* Appendix :noexport:
|
2021-05-21 12:10:29 +02:00
|
|
|
** Python script from table to json
|
|
|
|
|
|
|
|
#+NAME: json
|
2021-06-18 12:04:03 +02:00
|
|
|
#+begin_src python :var data=nucleus title="nucleus" last=0 :results output drawer
|
|
|
|
print("""#+begin_src python :tangle trex.json""")
|
2021-05-21 12:10:29 +02:00
|
|
|
print(""" "%s": {"""%(title))
|
|
|
|
indent = " "
|
|
|
|
f1 = 0 ; f2 = 0 ; f3 = 0
|
|
|
|
for line in data:
|
|
|
|
line = [ x.replace("~","") for x in line ]
|
|
|
|
name = '"'+line[0]+'"'
|
|
|
|
typ = '"'+line[1]+'"'
|
|
|
|
dims = line[2]
|
|
|
|
if '(' in dims:
|
|
|
|
dims = dims.strip()[1:-1]
|
|
|
|
dims = [ '"'+x.strip()+'"' for x in dims.split(',') ]
|
|
|
|
dims = "[ " + ", ".join(dims) + " ]"
|
|
|
|
else:
|
|
|
|
dims = "[ ]"
|
|
|
|
f1 = max(f1, len(name))
|
|
|
|
f2 = max(f2, len(typ))
|
|
|
|
f3 = max(f3, len(dims))
|
|
|
|
|
|
|
|
fmt = "%%s%%%ds : [ %%%ds, %%%ds ]" % (f1, f2, f3)
|
|
|
|
for line in data:
|
|
|
|
line = [ x.replace("~","") for x in line ]
|
|
|
|
name = '"'+line[0]+'"'
|
|
|
|
typ = '"'+line[1]+'"'
|
|
|
|
dims = line[2]
|
|
|
|
if '(' in dims:
|
|
|
|
dims = dims.strip()[1:-1]
|
|
|
|
dims = [ '"'+x.strip()+'"' for x in dims.split(',') ]
|
2021-05-21 14:04:19 +02:00
|
|
|
dims.reverse()
|
2021-05-21 12:10:29 +02:00
|
|
|
dims = "[ " + ", ".join(dims) + " ]"
|
|
|
|
else:
|
2021-05-24 15:01:04 +02:00
|
|
|
if dims.strip() != "":
|
|
|
|
dims = "ERROR"
|
|
|
|
else:
|
|
|
|
dims = "[]"
|
2021-05-21 12:10:29 +02:00
|
|
|
buffer = fmt % (indent, name, typ.ljust(f2), dims.ljust(f3))
|
|
|
|
indent = " , "
|
|
|
|
print(buffer)
|
|
|
|
|
|
|
|
if last == 0:
|
|
|
|
print(" } ,")
|
|
|
|
else:
|
|
|
|
print(" }")
|
|
|
|
print("""#+end_src""")
|
|
|
|
|
|
|
|
#+end_src
|
|
|
|
|
|
|
|
|
2021-06-25 11:52:53 +02:00
|
|
|
#+begin_src python :tangle trex.json :results output drawer :exports none
|
2021-05-21 12:10:29 +02:00
|
|
|
}
|
|
|
|
#+end_src
|