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add headers to tables and group names
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@ -2,22 +2,29 @@
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#+STARTUP: latexpreview
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#+SETUPFILE: docs/theme.setup
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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~ file, which is
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compiled from different sections (groups) presented below.
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All the quantities are saved in atomic units.
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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 developers.
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All quantities are saved in TREXIO file in atomic units.
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The dimensions of the arrays in the tables below are given in
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column-major order (as in Fortran), and the ordering of the dimensions
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is reversed in the produces JSON configuration file as the library is
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is reversed in the produced JSON configuration file as the library is
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written in C.
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In Fortran, the arrays are 1-based and in most other languages the
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arrays are 0-base. Hence, we introduce the ~index~ type which is an
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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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#+begin_src python :tangle trex.json
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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
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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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@ -26,6 +33,8 @@ arrays are 0-base. Hence, we introduce the ~index~ type which is an
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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~ | ~int~ | | 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~ | ~int~ | | Number of authors of the file |
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@ -46,14 +55,16 @@ arrays are 0-base. Hence, we introduce the ~index~ type which is an
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#+end_src
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:end:
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* Electron
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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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| ~up_num~ | ~int~ | | Number of \uparrow-spin electrons |
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| ~dn_num~ | ~int~ | | Number of \downarrow-spin electrons |
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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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@ -66,12 +77,14 @@ arrays are 0-base. Hence, we introduce the ~index~ type which is an
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#+end_src
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:end:
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* Nucleus
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* Nucleus (nucleus group)i
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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~ | ~int~ | | 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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@ -92,7 +105,7 @@ arrays are 0-base. Hence, we introduce the ~index~ type which is an
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#+end_src
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:end:
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* TODO Effective core potentials
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* TODO Effective core potentials (ecp group)
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An effective core potential (ECP) $V_A^{\text{pp}}$ replacing the
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core electrons of atom $A$ is the sum of a local component
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@ -126,6 +139,8 @@ arrays are 0-base. Hence, we introduce the ~index~ type which is an
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- $\hat{V}_\text{ecp,nl} = \sum_A \hat{V}_A^{\text{nl}}$ : non-local component
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#+NAME: ecp
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| Variable | Type | Dimensions | Description |
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|-----------------------+---------+------------------------------------------+----------------------------|
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| ~lmax_plus_1~ | ~int~ | ~(nucleus.num)~ | $l_{\max} + 1$ |
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| ~z_core~ | ~float~ | ~(nucleus.num)~ | Charges to remove |
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| ~local_n~ | ~int~ | ~(nucleus.num)~ | Number of local function |
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@ -161,7 +176,7 @@ arrays are 0-base. Hence, we introduce the ~index~ type which is an
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#+end_src
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:end:
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* Basis set
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* Basis set (basis group)
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We consider here basis functions centered on nuclei. Hence, we enable
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the possibility to define /dummy atoms/ to place basis functions in
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@ -201,6 +216,8 @@ arrays are 0-base. Hence, we introduce the ~index~ type which is an
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All the basis set parameters are stored in one-dimensional arrays:
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#+NAME: basis
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| Variable | Type | Dimensions | Description |
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|---------------------+---------+--------------------+----------------------------------------------------------|
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| ~type~ | ~str~ | | Type of basis set: "Gaussian" or "Slater" |
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| ~num~ | ~int~ | | Total Number of shells |
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| ~prim_num~ | ~int~ | | Total number of primitives |
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@ -210,7 +227,7 @@ arrays are 0-base. Hence, we introduce the ~index~ type which is an
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| ~shell_prim_num~ | ~int~ | ~(basis.num)~ | Number of primitives in the shell ($N_{\text{prim}}$) |
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| ~shell_factor~ | ~float~ | ~(basis.num)~ | Normalization factor of the shell ($\mathcal{N}_s$) |
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| ~shell_prim_index~ | ~index~ | ~(basis.num)~ | Index of the first primitive in the complete list |
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| ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) |
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| ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) |
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| ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) |
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| ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) |
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@ -292,7 +309,7 @@ prim_factor =
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4.3649547399719840e-01, 1.8135965626177861e+00 ]
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#+END_EXAMPLE
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* Atomic orbitals
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* Atomic orbitals (ao group)
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Going from the atomic basis set to AOs implies a systematic
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construction of all the angular functions of each shell. We
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@ -337,6 +354,8 @@ prim_factor =
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introduced here should be $\frac{\mathcal{N}_{xy}}{\mathcal{N}_{z^2}}$.
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#+NAME: ao
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| Variable | Type | Dimensions | Description |
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|-----------------+---------+------------+---------------------------------|
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| ~cartesian~ | ~int~ | | ~1~: true, ~0~: false |
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| ~num~ | ~int~ | | Total number of atomic orbitals |
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| ~shell~ | ~index~ | ~(ao.num)~ | basis set shell for each AO |
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@ -356,7 +375,7 @@ prim_factor =
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#+end_src
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:end:
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** One-electron integrals
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** One-electron integrals (ao_1e_int group)
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:PROPERTIES:
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:CUSTOM_ID: ao_one_e
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:END:
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@ -374,12 +393,14 @@ prim_factor =
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over atomic orbitals.
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#+NAME: ao_1e_int
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| ~overlap~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ |
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| ~kinetic~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ |
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| ~potential_n_e~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ |
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| ~ecp_local~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp,l}} \vert q \rangle$ |
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| ~ecp_non_local~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp,nl}} \vert q \rangle$ |
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| ~core_hamiltonian~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ |
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| Variable | Type | Dimensions | Description |
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|--------------------+---------+--------------------+-----------------------------------------------------------|
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| ~overlap~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ |
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| ~kinetic~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ |
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| ~potential_n_e~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ |
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| ~ecp_local~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp,l}} \vert q \rangle$ |
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| ~ecp_non_local~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp,nl}} \vert q \rangle$ |
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| ~core_hamiltonian~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ |
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#+CALL: json(data=ao_1e_int, title="ao_1e_int")
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@ -397,7 +418,7 @@ prim_factor =
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#+end_src
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:end:
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** Two-electron integrals
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** Two-electron integrals (ao_2e_int group)
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:PROPERTIES:
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:CUSTOM_ID: ao_two_e
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:END:
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@ -418,8 +439,10 @@ prim_factor =
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\mathbf{r}_j \vert)}{\vert \mathbf{r}_i - \mathbf{r}_j \vert} \] : electron-electron long range potential
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#+NAME: ao_2e_int
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| ~eri~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Electron repulsion integrals |
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| ~eri_lr~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Long-range Electron repulsion integrals |
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| Variable | Type | Dimensions | Description |
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|----------+----------------+------------------------------------+-----------------------------------------|
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| ~eri~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Electron repulsion integrals |
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| ~eri_lr~ | ~float sparse~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Long-range Electron repulsion integrals |
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#+CALL: json(data=ao_2e_int, title="ao_2e_int")
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@ -433,9 +456,11 @@ prim_factor =
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#+end_src
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:end:
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* Molecular orbitals
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* Molecular orbitals (mo group)
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#+NAME: mo
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| Variable | Type | Dimensions | Description |
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|---------------+---------+--------------------+------------------------------------------|
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| ~type~ | ~str~ | | String identify the set of MOs |
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| ~num~ | ~int~ | | Number of MOs |
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| ~coefficient~ | ~float~ | ~(ao.num, mo.num)~ | MO coefficients |
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@ -459,19 +484,21 @@ prim_factor =
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#+end_src
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:end:
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** One-electron integrals
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** One-electron integrals (mo_1e_int group)
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The operators as the same as those defined in the
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[[#ao_one_e][AO one-electron integrals section]]. Here, the integrals are given in
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the basis of molecular orbitals.
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#+NAME: mo_1e_int
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| ~overlap~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert j \rangle$ |
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| ~kinetic~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{T}_e \vert j \rangle$ |
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| ~potential_n_e~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ne}} \vert j \rangle$ |
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| ~ecp_local~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ecp,l}} \vert j \rangle$ |
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| ~ecp_non_local~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ecp,nl}} \vert j \rangle$ |
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| ~core_hamiltonian~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{h} \vert j \rangle$ |
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| Variable | Type | Dimensions | Description |
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|--------------------+---------+--------------------+-----------------------------------------------------------|
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| ~overlap~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert j \rangle$ |
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| ~kinetic~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{T}_e \vert j \rangle$ |
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| ~potential_n_e~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ne}} \vert j \rangle$ |
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| ~ecp_local~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ecp,l}} \vert j \rangle$ |
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| ~ecp_non_local~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ecp,nl}} \vert j \rangle$ |
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| ~core_hamiltonian~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{h} \vert j \rangle$ |
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#+CALL: json(data=mo_1e_int, title="mo_1e_int")
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@ -489,15 +516,17 @@ prim_factor =
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#+end_src
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:end:
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** Two-electron integrals
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** Two-electron integrals (mo_2e_int group)
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The operators as the same as those defined in the
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[[#ao_one_e][AO one-electron integrals section]]. Here, the integrals are given in
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the basis of molecular orbitals.
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#+NAME: mo_2e_int
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| ~eri~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Electron repulsion integrals |
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| ~eri_lr~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Long-range Electron repulsion integrals |
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| Variable | Type | Dimensions | Description |
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|----------+----------------+------------------------------------+-----------------------------------------|
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| ~eri~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Electron repulsion integrals |
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| ~eri_lr~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Long-range Electron repulsion integrals |
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#+CALL: json(data=mo_2e_int, title="mo_2e_int")
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@ -512,13 +541,15 @@ prim_factor =
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:end:
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* TODO Slater determinants
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* TODO Reduced density matrices
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* TODO Reduced density matrices (rdm group)
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#+NAME: rdm
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| ~one_e~ | ~float~ | ~(mo.num, mo.num)~ |
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| ~one_e_up~ | ~float~ | ~(mo.num, mo.num)~ |
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| ~one_e_dn~ | ~float~ | ~(mo.num, mo.num)~ |
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| ~two_e~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ |
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| Variable | Type | Dimensions | Description |
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|------------+----------------+------------------------------------+-------------|
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| ~one_e~ | ~float~ | ~(mo.num, mo.num)~ | |
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| ~one_e_up~ | ~float~ | ~(mo.num, mo.num)~ | |
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| ~one_e_dn~ | ~float~ | ~(mo.num, mo.num)~ | |
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| ~two_e~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num)~ | |
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#+CALL: json(data=rdm, title="rdm", last=1)
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@ -587,6 +618,6 @@ print("""#+end_src""")
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#+end_src
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#+begin_src python :tangle trex.json :results output drawer
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#+begin_src python :tangle trex.json :results output drawer :exports none
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}
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#+end_src
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