mirror of https://github.com/TREX-CoE/trexio.git
Merge pull request #143 from TREX-CoE/row-major
Added both row-major and column-major representations in documentation.
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trex.org
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@ -13,6 +13,13 @@
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{
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#+end_src
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Dimensions are given both in row-major ~[]~ and column-major ~()~
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formats. Pick the one adapted to the programming language in which
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you use TREXIO (Numpy is by default row-major, and Fortran is column-major).
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In the column-major representation, ~A(i,j)~ and ~A(i+1,j)~ are
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contiguous in memory. In the row-major representation, ~A[i,j]~ and
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~A[i,j+1]~ are contiguous.
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* Metadata (metadata group)
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As we expect TREXIO files to be archived in open-data repositories,
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@ -22,15 +29,15 @@
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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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| ~unsafe~ | ~int~ | | ~1~: true, ~0~: false |
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| Variable | Type | Row-major Dimensions | Column-major Dimensions | 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]~ | ~(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]~ | ~(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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| ~unsafe~ | ~int~ | | | ~1~: true, ~0~: false |
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**Note:** The ~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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@ -62,14 +69,14 @@
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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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| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description | |
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|---------------+---------+----------------------+-------------------------+--------------------------+---|
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| ~num~ | ~dim~ | | | Number of nuclei | |
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| ~charge~ | ~float~ | ~[nucleus.num]~ | ~(nucleus.num)~ | Charges of the nuclei | |
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| ~coord~ | ~float~ | ~[nucleus.num, 3]~ | ~(3, nucleus.num)~ | Coordinates of the atoms | |
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| ~label~ | ~str~ | ~[nucleus.num]~ | ~(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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@ -92,15 +99,15 @@
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used in periodic calculations.
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#+NAME: cell
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| Variable | Type | Dimensions | Description |
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|----------+---------+------------+--------------------------------------------------------------------------|
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| ~a~ | ~float~ | ~(3)~ | First real space lattice vector |
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| ~b~ | ~float~ | ~(3)~ | Second real space lattice vector |
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| ~c~ | ~float~ | ~(3)~ | Third real space lattice vector |
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| ~G_a~ | ~float~ | ~(3)~ | First reciprocal space lattice vector |
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| ~G_b~ | ~float~ | ~(3)~ | Second reciprocal space lattice vector |
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| ~G_c~ | ~float~ | ~(3)~ | Third reciprocal space lattice vector |
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| ~two_pi~ | ~int~ | | ~0~ or ~1~. If ~two_pi=1~, $2\pi$ is included in the reciprocal vectors. |
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| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
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|----------+---------+----------------------+-------------------------+--------------------------------------------------------------------------|
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| ~a~ | ~float~ | ~[3]~ | ~(3)~ | First real space lattice vector |
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| ~b~ | ~float~ | ~[3]~ | ~(3)~ | Second real space lattice vector |
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| ~c~ | ~float~ | ~[3]~ | ~(3)~ | Third real space lattice vector |
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| ~G_a~ | ~float~ | ~[3]~ | ~(3)~ | First reciprocal space lattice vector |
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| ~G_b~ | ~float~ | ~[3]~ | ~(3)~ | Second reciprocal space lattice vector |
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| ~G_c~ | ~float~ | ~[3]~ | ~(3)~ | Third reciprocal space lattice vector |
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| ~two_pi~ | ~int~ | | | ~0~ or ~1~. If ~two_pi=1~, $2\pi$ is included in the reciprocal vectors. |
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#+CALL: json(data=cell, title="cell")
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@ -125,10 +132,10 @@
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defined in this group.
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#+NAME: pbc
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| Variable | Type | Dimensions | Description |
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|------------+---------+------------+-------------------------|
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| ~periodic~ | ~int~ | | ~1~: true or ~0~: false |
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| ~k_point~ | ~float~ | ~(3)~ | $k$-point sampling |
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| Variable | Type | Row-major Dimensions | Column-major 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]~ | ~(3)~ | $k$-point sampling |
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#+CALL: json(data=pbc, title="pbc")
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@ -158,11 +165,11 @@
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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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| Variable | Type | Row-major Dimensions | Column-major 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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@ -190,14 +197,14 @@
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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~ | ~index~ | | Index of the current state (0 is ground state) |
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| ~energy~ | ~float~ | | Energy of the current 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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| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
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|-----------------+---------+----------------------+-------------------------+---------------------------------------------------------------------------------------------|
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| ~num~ | ~dim~ | | | Number of states (including the ground state) |
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| ~id~ | ~index~ | | | Index of the current state (0 is ground state) |
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| ~energy~ | ~float~ | | | Energy of the current state |
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| ~current_label~ | ~str~ | | | Label of the current state |
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| ~label~ | ~str~ | ~[state.num]~ | ~(state.num)~ | Labels of all states |
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| ~file_name~ | ~str~ | ~[state.num]~ | ~(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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@ -220,7 +227,7 @@
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*** Gaussian and Slater-type orbitals
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We consider here basis functions centered on nuclei. Hence, it is
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We consider here basis functions centered on nuclei. Hence, it is
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possibile to define /dummy atoms/ to place basis functions in
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arbitrary positions.
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@ -257,10 +264,10 @@
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All the basis set parameters are stored in one-dimensional arrays.
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*** Numerical orbitals
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Trexio supports numerical atom centered orbitals. The implementation is
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based on the approach of FHI-aims [Blum, V. et al; Ab initio molecular
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simulations with numeric atom-centered orbitals; Computer Physics
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based on the approach of FHI-aims [Blum, V. et al; Ab initio molecular
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simulations with numeric atom-centered orbitals; Computer Physics
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Communications 2009]. These orbitals are
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defined by the atom they are centered on, their angular momentum and a
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radial function $R_s$, which is of the form
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@ -271,7 +278,7 @@
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grid. It is constructed to vanish for any $\mathbf{r}$
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outside of the grid. The reference points are stored in ~nao_grid_r~
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and ~nao_grid_phi~. Additionaly, a separate spline for the first and second
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derivative of $u(\mathbf{r})$ can be stored in ~nao_grid_grad~ and ~nao_grid_lap~.
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derivative of $u(\mathbf{r})$ can be stored in ~nao_grid_grad~ and ~nao_grid_lap~.
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Storing them in this form allows to calculate the actual first and
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second derivatives easily as follows:
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@ -307,7 +314,7 @@
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\]
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For convenience, this conversion and functions to evaluate the splines
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are provided with trexio. Since these implementations are not adapted to
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a specific software architecture, a programm using these orbitals should
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a specific software architecture, a programm using these orbitals should
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reimplement them with consideration for its specific needs.
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*** Plane waves
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@ -326,32 +333,32 @@
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*** Data definitions
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#+NAME: basis
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| Variable | Type | Dimensions | Description | |
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|---------------------+---------+-----------------------------------------------+------------------------------------------------------------------------------+---|
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| ~type~ | ~str~ | | Type of basis set: "Gaussian", "Slater", "Numerical" or "PW" for plane waves | |
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| ~prim_num~ | ~dim~ | | Total number of primitives | |
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| ~shell_num~ | ~dim~ | | Total number of shells | |
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| ~nao_grid_num~ | ~dim~ | | Total number of grid points for numerical orbitals | |
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| ~interp_coeff_cnt~ | ~dim~ | | Number of coefficients for the numerical orbital interpolator | |
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| ~nucleus_index~ | ~index~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices | |
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| ~shell_ang_mom~ | ~int~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta | |
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| ~shell_factor~ | ~float~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$) | |
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| ~r_power~ | ~int~ | ~(basis.shell_num)~ | Power to which $r$ is raised ($n_s$) | |
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| ~nao_grid_start~ | ~index~ | ~(basis.shell_num)~ | Index of the first data point for a given numerical orbital | |
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| ~nao_grid_size~ | ~dim~ | ~(basis.shell_num)~ | Number of data points per numerical orbital | |
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| ~shell_index~ | ~index~ | ~(basis.prim_num)~ | One-to-one correspondence between primitives and shell index | |
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| ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) | |
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| ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) | |
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| ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) | |
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| ~e_cut~ | ~float~ | | Energy cut-off for plane-wave calculations | |
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| ~nao_grid_radius~ | ~float~ | ~(basis.nao_grid_num)~ | Radii of grid points for numerical orbitals | |
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| ~nao_grid_phi~ | ~float~ | ~(basis.nao_grid_num)~ | Wave function values for numerical orbitals | |
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| ~nao_grid_grad~ | ~float~ | ~(basis.nao_grid_num)~ | Radial gradient of numerical orbitals | |
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| ~nao_grid_lap~ | ~float~ | ~(basis.nao_grid_num)~ | Laplacian of numerical orbitals | |
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| ~interpolator_kind~ | ~str~ | | Kind of spline, e.g. "Polynomial" | |
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| ~interpolator_phi~ | ~float~ | ~(basis.interp_coeff_cnt,basis.nao_grid_num)~ | Coefficients for numerical orbital interpolation function | |
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| ~interpolator_grad~ | ~float~ | ~(basis.interp_coeff_cnt,basis.nao_grid_num)~ | Coefficients for numerical orbital gradient interpolation function | |
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| ~interpolator_lap~ | ~float~ | ~(basis.interp_coeff_cnt,basis.nao_grid_num)~ | Coefficients for numerical orbital laplacian interpolation function | |
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| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
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|---------------------+---------+------------------------------------------------+------------------------------------------------+------------------------------------------------------------------------------|
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| ~type~ | ~str~ | | | Type of basis set: "Gaussian", "Slater", "Numerical" or "PW" for plane waves |
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| ~prim_num~ | ~dim~ | | | Total number of primitives |
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| ~shell_num~ | ~dim~ | | | Total number of shells |
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| ~nao_grid_num~ | ~dim~ | | | Total number of grid points for numerical orbitals |
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| ~interp_coeff_cnt~ | ~dim~ | | | Number of coefficients for the numerical orbital interpolator |
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| ~nucleus_index~ | ~index~ | ~[basis.shell_num]~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices |
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| ~shell_ang_mom~ | ~int~ | ~[basis.shell_num]~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta |
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| ~shell_factor~ | ~float~ | ~[basis.shell_num]~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$) |
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| ~r_power~ | ~int~ | ~[basis.shell_num]~ | ~(basis.shell_num)~ | Power to which $r$ is raised ($n_s$) |
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| ~nao_grid_start~ | ~index~ | ~[basis.shell_num]~ | ~(basis.shell_num)~ | Index of the first data point for a given numerical orbital |
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| ~nao_grid_size~ | ~dim~ | ~[basis.shell_num]~ | ~(basis.shell_num)~ | Number of data points per numerical orbital |
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| ~shell_index~ | ~index~ | ~[basis.prim_num]~ | ~(basis.prim_num)~ | One-to-one correspondence between primitives and shell index |
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| ~exponent~ | ~float~ | ~[basis.prim_num]~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) |
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| ~coefficient~ | ~float~ | ~[basis.prim_num]~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) |
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| ~prim_factor~ | ~float~ | ~[basis.prim_num]~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) |
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| ~e_cut~ | ~float~ | | | Energy cut-off for plane-wave calculations |
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| ~nao_grid_radius~ | ~float~ | ~[basis.nao_grid_num]~ | ~(basis.nao_grid_num)~ | Radii of grid points for numerical orbitals |
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| ~nao_grid_phi~ | ~float~ | ~[basis.nao_grid_num]~ | ~(basis.nao_grid_num)~ | Wave function values for numerical orbitals |
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| ~nao_grid_grad~ | ~float~ | ~[basis.nao_grid_num]~ | ~(basis.nao_grid_num)~ | Radial gradient of numerical orbitals |
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| ~nao_grid_lap~ | ~float~ | ~[basis.nao_grid_num]~ | ~(basis.nao_grid_num)~ | Laplacian of numerical orbitals |
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| ~interpolator_kind~ | ~str~ | | | Kind of spline, e.g. "Polynomial" |
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| ~interpolator_phi~ | ~float~ | ~[basis.nao_grid_num, basis.interp_coeff_cnt]~ | ~(basis.interp_coeff_cnt, basis.nao_grid_num)~ | Coefficients for numerical orbital interpolation function |
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| ~interpolator_grad~ | ~float~ | ~[basis.nao_grid_num, basis.interp_coeff_cnt]~ | ~(basis.interp_coeff_cnt, basis.nao_grid_num)~ | Coefficients for numerical orbital gradient interpolation function |
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| ~interpolator_lap~ | ~float~ | ~[basis.nao_grid_num, basis.interp_coeff_cnt]~ | ~(basis.interp_coeff_cnt, basis.nao_grid_num)~ | Coefficients for numerical orbital laplacian interpolation function |
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@ -360,32 +367,32 @@
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#+RESULTS:
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:results:
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#+begin_src python :tangle trex.json
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"basis": {
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"type" : [ "str" , [] ]
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, "prim_num" : [ "dim" , [] ]
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, "shell_num" : [ "dim" , [] ]
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, "nao_grid_num" : [ "dim" , [] ]
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, "interp_coeff_cnt" : [ "dim" , [] ]
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, "nucleus_index" : [ "index", [ "basis.shell_num" ] ]
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, "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ]
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, "shell_factor" : [ "float", [ "basis.shell_num" ] ]
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, "r_power" : [ "int" , [ "basis.shell_num" ] ]
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, "nao_grid_start" : [ "index", [ "basis.shell_num" ] ]
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, "nao_grid_size" : [ "dim" , [ "basis.shell_num" ] ]
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, "shell_index" : [ "index", [ "basis.prim_num" ] ]
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, "exponent" : [ "float", [ "basis.prim_num" ] ]
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, "coefficient" : [ "float", [ "basis.prim_num" ] ]
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, "prim_factor" : [ "float", [ "basis.prim_num" ] ]
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, "e_cut" : [ "float", [] ]
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, "nao_grid_radius" : [ "float", [ "basis.nao_grid_num" ] ]
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, "nao_grid_phi" : [ "float", [ "basis.nao_grid_num" ] ]
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, "nao_grid_grad" : [ "float", [ "basis.nao_grid_num" ] ]
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, "nao_grid_lap" : [ "float", [ "basis.nao_grid_num" ] ]
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, "interpolator_kind" : [ "str" , [] ]
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, "interpolator_phi" : [ "float", [ "basis.nao_grid_num", "basis.interp_coeff_cnt" ] ]
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, "interpolator_grad" : [ "float", [ "basis.nao_grid_num", "basis.interp_coeff_cnt" ] ]
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, "interpolator_lap" : [ "float", [ "basis.nao_grid_num", "basis.interp_coeff_cnt" ] ]
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} ,
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"basis": {
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"type" : [ "str" , [] ]
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, "prim_num" : [ "dim" , [] ]
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, "shell_num" : [ "dim" , [] ]
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, "nao_grid_num" : [ "dim" , [] ]
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, "interp_coeff_cnt" : [ "dim" , [] ]
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, "nucleus_index" : [ "index", [ "basis.shell_num" ] ]
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, "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ]
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, "shell_factor" : [ "float", [ "basis.shell_num" ] ]
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, "r_power" : [ "int" , [ "basis.shell_num" ] ]
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, "nao_grid_start" : [ "index", [ "basis.shell_num" ] ]
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, "nao_grid_size" : [ "dim" , [ "basis.shell_num" ] ]
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, "shell_index" : [ "index", [ "basis.prim_num" ] ]
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, "exponent" : [ "float", [ "basis.prim_num" ] ]
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, "coefficient" : [ "float", [ "basis.prim_num" ] ]
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, "prim_factor" : [ "float", [ "basis.prim_num" ] ]
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, "e_cut" : [ "float", [] ]
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, "nao_grid_radius" : [ "float", [ "basis.nao_grid_num" ] ]
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, "nao_grid_phi" : [ "float", [ "basis.nao_grid_num" ] ]
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, "nao_grid_grad" : [ "float", [ "basis.nao_grid_num" ] ]
|
||||
, "nao_grid_lap" : [ "float", [ "basis.nao_grid_num" ] ]
|
||||
, "interpolator_kind" : [ "str" , [] ]
|
||||
, "interpolator_phi" : [ "float", [ "basis.nao_grid_num", "basis.interp_coeff_cnt" ] ]
|
||||
, "interpolator_grad" : [ "float", [ "basis.nao_grid_num", "basis.interp_coeff_cnt" ] ]
|
||||
, "interpolator_lap" : [ "float", [ "basis.nao_grid_num", "basis.interp_coeff_cnt" ] ]
|
||||
} ,
|
||||
#+end_src
|
||||
:end:
|
||||
|
||||
|
|
@ -487,16 +494,16 @@ prim_factor =
|
|||
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 |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|----------------------+---------+----------------------+-------------------------+----------------------------------------------------------------------------------------|
|
||||
| ~max_ang_mom_plus_1~ | ~int~ | ~[nucleus.num]~ | ~(nucleus.num)~ | $\ell_{\max}+1$, one higher than the max angular momentum in the removed core orbitals |
|
||||
| ~z_core~ | ~int~ | ~[nucleus.num]~ | ~(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]~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the angular momentum $\ell$ |
|
||||
| ~nucleus_index~ | ~index~ | ~[ecp.num]~ | ~(ecp.num)~ | One-to-one correspondence between ECP items and the atom index |
|
||||
| ~exponent~ | ~float~ | ~[ecp.num]~ | ~(ecp.num)~ | $\alpha_{A q \ell}$ all ECP exponents |
|
||||
| ~coefficient~ | ~float~ | ~[ecp.num]~ | ~(ecp.num)~ | $\beta_{A q \ell}$ all ECP coefficients |
|
||||
| ~power~ | ~int~ | ~[ecp.num]~ | ~(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
|
||||
|
|
@ -604,21 +611,21 @@ power = [
|
|||
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) |
|
||||
| Variable | Type | Row-major Dimensions | Column-major 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]~ | ~(grid.num)~ | Discretized coordinate space |
|
||||
| ~weight~ | ~float~ | ~[grid.num]~ | ~(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]~ | ~(grid.ang_num)~ | Discretized angular space (if used) |
|
||||
| ~ang_weight~ | ~float~ | ~[grid.ang_num]~ | ~(grid.ang_num)~ | Angular grid weights (if used) |
|
||||
| ~rad_num~ | ~dim~ | | | Number of radial integration points (if used) |
|
||||
| ~rad_coord~ | ~float~ | ~[grid.rad_num]~ | ~(grid.rad_num)~ | Discretized radial space (if used) |
|
||||
| ~rad_weight~ | ~float~ | ~[grid.rad_num]~ | ~(grid.rad_num)~ | Radial grid weights (if used) |
|
||||
|
||||
#+CALL: json(data=grid, title="grid")
|
||||
|
||||
|
|
@ -684,12 +691,12 @@ power = [
|
|||
|
||||
|
||||
#+NAME: ao
|
||||
| Variable | Type | Dimensions | Description |
|
||||
|-----------------+---------+------------+--------------------------------------|
|
||||
| ~cartesian~ | ~int~ | | ~1~: true, ~0~: false |
|
||||
| ~num~ | ~dim~ | | Total number of atomic orbitals |
|
||||
| ~shell~ | ~index~ | ~(ao.num)~ | Basis set shell for each AO |
|
||||
| ~normalization~ | ~float~ | ~(ao.num)~ | Normalization factor $\mathcal{N}_i$ |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|-----------------+---------+----------------------+-------------------------+--------------------------------------|
|
||||
| ~cartesian~ | ~int~ | | | ~1~: true, ~0~: false |
|
||||
| ~num~ | ~dim~ | | | Total number of atomic orbitals |
|
||||
| ~shell~ | ~index~ | ~[ao.num]~ | ~(ao.num)~ | Basis set shell for each AO |
|
||||
| ~normalization~ | ~float~ | ~[ao.num]~ | ~(ao.num)~ | Normalization factor $\mathcal{N}_i$ |
|
||||
|
||||
#+CALL: json(data=ao, title="ao")
|
||||
|
||||
|
|
@ -722,18 +729,18 @@ power = [
|
|||
over atomic orbitals.
|
||||
|
||||
#+NAME: ao_1e_int
|
||||
| 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~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp}} \vert q \rangle$ |
|
||||
| ~core_hamiltonian~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ |
|
||||
| ~overlap_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ (imaginary part) |
|
||||
| ~kinetic_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ (imaginary part) |
|
||||
| ~potential_n_e_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ (imaginary part) |
|
||||
| ~ecp_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ECP}} \vert q \rangle$ (imaginary part) |
|
||||
| ~core_hamiltonian_im~ | ~float~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ (imaginary part) |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|-----------------------+---------+----------------------+-------------------------+--------------------------------------------------------------------------|
|
||||
| ~overlap~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ |
|
||||
| ~kinetic~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ |
|
||||
| ~potential_n_e~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ |
|
||||
| ~ecp~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ecp}} \vert q \rangle$ |
|
||||
| ~core_hamiltonian~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ |
|
||||
| ~overlap_im~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert q \rangle$ (imaginary part) |
|
||||
| ~kinetic_im~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{T}_e \vert q \rangle$ (imaginary part) |
|
||||
| ~potential_n_e_im~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ne}} \vert q \rangle$ (imaginary part) |
|
||||
| ~ecp_im~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{V}_{\text{ECP}} \vert q \rangle$ (imaginary part) |
|
||||
| ~core_hamiltonian_im~ | ~float~ | ~[ao.num, ao.num]~ | ~(ao.num, ao.num)~ | $\langle p \vert \hat{h} \vert q \rangle$ (imaginary part) |
|
||||
|
||||
#+CALL: json(data=ao_1e_int, title="ao_1e_int")
|
||||
|
||||
|
|
@ -780,14 +787,14 @@ power = [
|
|||
\]
|
||||
|
||||
#+NAME: ao_2e_int
|
||||
| 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 |
|
||||
| ~eri_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for ERI |
|
||||
| ~eri_cholesky~ | ~float sparse~ | ~(ao.num, ao.num, ao_2e_int.eri_cholesky_num)~ | Cholesky decomposition of the ERI |
|
||||
| ~eri_lr_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for long range ERI |
|
||||
| ~eri_lr_cholesky~ | ~float sparse~ | ~(ao.num, ao.num, ao_2e_int.eri_lr_cholesky_num)~ | Cholesky decomposition of the long range ERI |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|-----------------------+----------------+---------------------------------------------------+---------------------------------------------------+-----------------------------------------------|
|
||||
| ~eri~ | ~float sparse~ | ~[ao.num, ao.num, ao.num, ao.num]~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Electron repulsion integrals |
|
||||
| ~eri_lr~ | ~float sparse~ | ~[ao.num, ao.num, ao.num, ao.num]~ | ~(ao.num, ao.num, ao.num, ao.num)~ | Long-range electron repulsion integrals |
|
||||
| ~eri_cholesky_num~ | ~dim~ | | | Number of Cholesky vectors for ERI |
|
||||
| ~eri_cholesky~ | ~float sparse~ | ~[ao_2e_int.eri_cholesky_num, ao.num, ao.num]~ | ~(ao.num, ao.num, ao_2e_int.eri_cholesky_num)~ | Cholesky decomposition of the ERI |
|
||||
| ~eri_lr_cholesky_num~ | ~dim~ | | | Number of Cholesky vectors for long range ERI |
|
||||
| ~eri_lr_cholesky~ | ~float sparse~ | ~[ao_2e_int.eri_lr_cholesky_num, ao.num, ao.num]~ | ~(ao.num, ao.num, ao_2e_int.eri_lr_cholesky_num)~ | Cholesky decomposition of the long range ERI |
|
||||
|
||||
#+CALL: json(data=ao_2e_int, title="ao_2e_int")
|
||||
|
||||
|
|
@ -798,7 +805,7 @@ power = [
|
|||
"eri" : [ "float sparse", [ "ao.num", "ao.num", "ao.num", "ao.num" ] ]
|
||||
, "eri_lr" : [ "float sparse", [ "ao.num", "ao.num", "ao.num", "ao.num" ] ]
|
||||
, "eri_cholesky_num" : [ "dim" , [] ]
|
||||
, "eri_cholesky" : [ "float sparse", [ "ao_2e_int.eri_cholesky_num", "ao.num", "ao.num" ] ]
|
||||
, "eri_cholesky" : [ "float sparse", [ "ao_2e_int.eri_cholesky_num", "ao.num", "ao.num" ] ]
|
||||
, "eri_lr_cholesky_num" : [ "dim" , [] ]
|
||||
, "eri_lr_cholesky" : [ "float sparse", [ "ao_2e_int.eri_lr_cholesky_num", "ao.num", "ao.num" ] ]
|
||||
} ,
|
||||
|
|
@ -808,17 +815,17 @@ power = [
|
|||
** Molecular orbitals (mo group)
|
||||
|
||||
#+NAME: mo
|
||||
| Variable | Type | Dimensions | Description |
|
||||
|------------------+---------+--------------------+--------------------------------------------------------------------------|
|
||||
| ~type~ | ~str~ | | Free text to identify the set of MOs (HF, Natural, Local, CASSCF, /etc/) |
|
||||
| ~num~ | ~dim~ | | Number of MOs |
|
||||
| ~coefficient~ | ~float~ | ~(ao.num, mo.num)~ | MO coefficients |
|
||||
| ~coefficient_im~ | ~float~ | ~(ao.num, mo.num)~ | MO coefficients (imaginary part) |
|
||||
| ~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 |
|
||||
| ~energy~ | ~float~ | ~(mo.num)~ | For canonical MOs, corresponding eigenvalue |
|
||||
| ~spin~ | ~int~ | ~(mo.num)~ | For UHF wave functions, 0 is $\alpha$ and 1 is $\beta$ |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|------------------+---------+----------------------+-------------------------+--------------------------------------------------------------------------|
|
||||
| ~type~ | ~str~ | | | Free text to identify the set of MOs (HF, Natural, Local, CASSCF, /etc/) |
|
||||
| ~num~ | ~dim~ | | | Number of MOs |
|
||||
| ~coefficient~ | ~float~ | ~[mo.num, ao.num]~ | ~(ao.num, mo.num)~ | MO coefficients |
|
||||
| ~coefficient_im~ | ~float~ | ~[mo.num, ao.num]~ | ~(ao.num, mo.num)~ | MO coefficients (imaginary part) |
|
||||
| ~class~ | ~str~ | ~[mo.num]~ | ~(mo.num)~ | Choose among: Core, Inactive, Active, Virtual, Deleted |
|
||||
| ~symmetry~ | ~str~ | ~[mo.num]~ | ~(mo.num)~ | Symmetry in the point group |
|
||||
| ~occupation~ | ~float~ | ~[mo.num]~ | ~(mo.num)~ | Occupation number |
|
||||
| ~energy~ | ~float~ | ~[mo.num]~ | ~(mo.num)~ | For canonical MOs, corresponding eigenvalue |
|
||||
| ~spin~ | ~int~ | ~[mo.num]~ | ~(mo.num)~ | For UHF wave functions, 0 is $\alpha$ and 1 is $\beta$ |
|
||||
|
||||
#+CALL: json(data=mo, title="mo")
|
||||
|
||||
|
|
@ -846,18 +853,18 @@ power = [
|
|||
the basis of molecular orbitals.
|
||||
|
||||
#+NAME: mo_1e_int
|
||||
| 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~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ECP}} \vert j \rangle$ |
|
||||
| ~core_hamiltonian~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{h} \vert j \rangle$ |
|
||||
| ~overlap_im~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert j \rangle$ (imaginary part) |
|
||||
| ~kinetic_im~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{T}_e \vert j \rangle$ (imaginary part) |
|
||||
| ~potential_n_e_im~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ne}} \vert j \rangle$ (imaginary part) |
|
||||
| ~ecp_im~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ECP}} \vert j \rangle$ (imaginary part) |
|
||||
| ~core_hamiltonian_im~ | ~float~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{h} \vert j \rangle$ (imaginary part) |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|-----------------------+---------+----------------------+-------------------------+--------------------------------------------------------------------------|
|
||||
| ~overlap~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert j \rangle$ |
|
||||
| ~kinetic~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{T}_e \vert j \rangle$ |
|
||||
| ~potential_n_e~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ne}} \vert j \rangle$ |
|
||||
| ~ecp~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ECP}} \vert j \rangle$ |
|
||||
| ~core_hamiltonian~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{h} \vert j \rangle$ |
|
||||
| ~overlap_im~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert j \rangle$ (imaginary part) |
|
||||
| ~kinetic_im~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{T}_e \vert j \rangle$ (imaginary part) |
|
||||
| ~potential_n_e_im~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ne}} \vert j \rangle$ (imaginary part) |
|
||||
| ~ecp_im~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{V}_{\text{ECP}} \vert j \rangle$ (imaginary part) |
|
||||
| ~core_hamiltonian_im~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | $\langle i \vert \hat{h} \vert j \rangle$ (imaginary part) |
|
||||
|
||||
#+CALL: json(data=mo_1e_int, title="mo_1e_int")
|
||||
|
||||
|
|
@ -886,14 +893,14 @@ power = [
|
|||
the basis of molecular orbitals.
|
||||
|
||||
#+NAME: mo_2e_int
|
||||
| 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 |
|
||||
| ~eri_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for ERI |
|
||||
| ~eri_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, mo_2e_int.eri_cholesky_num)~ | Cholesky decomposition of the ERI |
|
||||
| ~eri_lr_cholesky_num~ | ~dim~ | | Number of Cholesky vectors for long range ERI |
|
||||
| ~eri_lr_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, mo_2e_int.eri_lr_cholesky_num)~ | Cholesky decomposition of the long range ERI |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|-----------------------+----------------+---------------------------------------------------+---------------------------------------------------+-----------------------------------------------|
|
||||
| ~eri~ | ~float sparse~ | ~[mo.num, mo.num, mo.num, mo.num]~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Electron repulsion integrals |
|
||||
| ~eri_lr~ | ~float sparse~ | ~[mo.num, mo.num, mo.num, mo.num]~ | ~(mo.num, mo.num, mo.num, mo.num)~ | Long-range electron repulsion integrals |
|
||||
| ~eri_cholesky_num~ | ~dim~ | | | Number of Cholesky vectors for ERI |
|
||||
| ~eri_cholesky~ | ~float sparse~ | ~[mo_2e_int.eri_cholesky_num, mo.num, mo.num]~ | ~(mo.num, mo.num, mo_2e_int.eri_cholesky_num)~ | Cholesky decomposition of the ERI |
|
||||
| ~eri_lr_cholesky_num~ | ~dim~ | | | Number of Cholesky vectors for long range ERI |
|
||||
| ~eri_lr_cholesky~ | ~float sparse~ | ~[mo_2e_int.eri_lr_cholesky_num, mo.num, mo.num]~ | ~(mo.num, mo.num, mo_2e_int.eri_lr_cholesky_num)~ | Cholesky decomposition of the long range ERI |
|
||||
|
||||
#+CALL: json(data=mo_2e_int, title="mo_2e_int")
|
||||
|
||||
|
|
@ -941,11 +948,11 @@ power = [
|
|||
An illustration on how to read determinants is presented in the [[./examples.html][examples]].
|
||||
|
||||
#+NAME: determinant
|
||||
| Variable | Type | Dimensions | Description |
|
||||
|---------------+------------------+---------------------+--------------------------------------------------------|
|
||||
| ~num~ | ~dim readonly~ | | Number of determinants |
|
||||
| ~list~ | ~int special~ | ~(determinant.num)~ | List of determinants as integer bit fields |
|
||||
| ~coefficient~ | ~float buffered~ | ~(determinant.num)~ | Coefficients of the determinants from the CI expansion |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|---------------+------------------+----------------------+-------------------------+--------------------------------------------------------|
|
||||
| ~num~ | ~dim readonly~ | | | Number of determinants |
|
||||
| ~list~ | ~int special~ | ~[determinant.num]~ | ~(determinant.num)~ | List of determinants as integer bit fields |
|
||||
| ~coefficient~ | ~float buffered~ | ~[determinant.num]~ | ~(determinant.num)~ | Coefficients of the determinants from the CI expansion |
|
||||
|
||||
#+CALL: json(data=determinant, title="determinant")
|
||||
|
||||
|
|
@ -977,11 +984,11 @@ power = [
|
|||
the basis of Slater determinants.
|
||||
|
||||
#+NAME: csf
|
||||
| Variable | Type | Dimensions | Description |
|
||||
|-------------------+------------------+-----------------------------+-----------------------------------------|
|
||||
| ~num~ | ~dim readonly~ | | Number of CSFs |
|
||||
| ~coefficient~ | ~float buffered~ | ~(csf.num)~ | Coefficients $C_I$ of the CSF expansion |
|
||||
| ~det_coefficient~ | ~float sparse~ | ~(determinant.num,csf.num)~ | Projection on the determinant basis |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|-------------------+------------------+------------------------------+------------------------------+-----------------------------------------|
|
||||
| ~num~ | ~dim readonly~ | | | Number of CSFs |
|
||||
| ~coefficient~ | ~float buffered~ | ~[csf.num]~ | ~(csf.num)~ | Coefficients $C_I$ of the CSF expansion |
|
||||
| ~det_coefficient~ | ~float sparse~ | ~[csf.num, determinant.num]~ | ~(determinant.num, csf.num)~ | Projection on the determinant basis |
|
||||
|
||||
#+CALL: json(data=csf, title="csf")
|
||||
|
||||
|
|
@ -1040,16 +1047,16 @@ power = [
|
|||
- $\dots$
|
||||
|
||||
#+NAME: amplitude
|
||||
| Variable | Type | Dimensions | Description |
|
||||
|-----------------+----------------+-------------------------------------------------------------+-------------------------------------------------|
|
||||
| ~single~ | ~float sparse~ | ~(mo.num,mo.num)~ | Single excitation amplitudes |
|
||||
| ~single_exp~ | ~float sparse~ | ~(mo.num,mo.num)~ | Exponentialized single excitation amplitudes |
|
||||
| ~double~ | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num)~ | Double excitation amplitudes |
|
||||
| ~double_exp~ | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num)~ | Exponentialized double excitation amplitudes |
|
||||
| ~triple~ | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Triple excitation amplitudes |
|
||||
| ~triple_exp~ | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Exponentialized triple excitation amplitudes |
|
||||
| ~quadruple~ | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Quadruple excitation amplitudes |
|
||||
| ~quadruple_exp~ | ~float sparse~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Exponentialized quadruple excitation amplitudes |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|-----------------+----------------+-------------------------------------------------------------+-------------------------------------------------------------+-------------------------------------------------|
|
||||
| ~single~ | ~float sparse~ | ~[mo.num,mo.num]~ | ~(mo.num,mo.num)~ | Single excitation amplitudes |
|
||||
| ~single_exp~ | ~float sparse~ | ~[mo.num,mo.num]~ | ~(mo.num,mo.num)~ | Exponentialized single excitation amplitudes |
|
||||
| ~double~ | ~float sparse~ | ~[mo.num,mo.num,mo.num,mo.num]~ | ~(mo.num,mo.num,mo.num,mo.num)~ | Double excitation amplitudes |
|
||||
| ~double_exp~ | ~float sparse~ | ~[mo.num,mo.num,mo.num,mo.num]~ | ~(mo.num,mo.num,mo.num,mo.num)~ | Exponentialized double excitation amplitudes |
|
||||
| ~triple~ | ~float sparse~ | ~[mo.num,mo.num,mo.num,mo.num,mo.num,mo.num]~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Triple excitation amplitudes |
|
||||
| ~triple_exp~ | ~float sparse~ | ~[mo.num,mo.num,mo.num,mo.num,mo.num,mo.num]~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Exponentialized triple excitation amplitudes |
|
||||
| ~quadruple~ | ~float sparse~ | ~[mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num]~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Quadruple excitation amplitudes |
|
||||
| ~quadruple_exp~ | ~float sparse~ | ~[mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num]~ | ~(mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num,mo.num)~ | Exponentialized quadruple excitation amplitudes |
|
||||
|
||||
#+CALL: json(data=amplitude, title="amplitude")
|
||||
|
||||
|
|
@ -1092,7 +1099,7 @@ power = [
|
|||
\Gamma_{ijkl}^{\downarrow \downarrow} &=&
|
||||
\langle \Psi | \hat{a}^{\dagger}_{k\beta}\, \hat{a}^{\dagger}_{l\beta} \hat{a}_{j\beta}\, \hat{a}_{i\beta} | \Psi \rangle \\
|
||||
\Gamma_{ijkl}^{\uparrow \downarrow} &=&
|
||||
\langle \Psi | \hat{a}^{\dagger}_{k\alpha}\, \hat{a}^{\dagger}_{l\beta} \hat{a}_{j\beta}\, \hat{a}_{i\alpha} | \Psi \rangle
|
||||
\langle \Psi | \hat{a}^{\dagger}_{k\alpha}\, \hat{a}^{\dagger}_{l\beta} \hat{a}_{j\beta}\, \hat{a}_{i\alpha} | \Psi \rangle
|
||||
+ \langle \Psi | \hat{a}^{\dagger}_{l\alpha}\, \hat{a}^{\dagger}_{k\beta} \hat{a}_{i\beta}\, \hat{a}_{j\alpha} | \Psi \rangle \\
|
||||
\end{eqnarray*}
|
||||
and the spin-summed one-body density matrix is
|
||||
|
|
@ -1124,25 +1131,25 @@ power = [
|
|||
$g_{ik}(\mathbf{r}_1) = \phi_i(\mathbf{r}_1) \phi_k(\mathbf{r}_1)$.
|
||||
|
||||
#+NAME: rdm
|
||||
| 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 |
|
||||
| ~1e_transition~ | ~float~ | ~(mo.num, mo.num, state.num, state.num) | One-particle transition density matrices |
|
||||
| ~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 |
|
||||
| ~2e_transition~ | ~float sparse~ | ~(mo.num, mo.num, mo.num, mo.num, state.num, state.num) | Two-particle transition density matrices |
|
||||
| ~2e_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
|
||||
| ~2e_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_cholesky_num)~ | Cholesky decomposition of the two-body RDM (spin trace) |
|
||||
| ~2e_upup_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
|
||||
| ~2e_upup_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_upup_cholesky_num)~ | Cholesky decomposition of the two-body RDM (\uparrow\uparrow) |
|
||||
| ~2e_dndn_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
|
||||
| ~2e_dndn_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_dndn_cholesky_num)~ | Cholesky decomposition of the two-body RDM (\downarrow\downarrow) |
|
||||
| ~2e_updn_cholesky_num~ | ~dim~ | | Number of Cholesky vectors |
|
||||
| ~2e_updn_cholesky~ | ~float sparse~ | ~(mo.num, mo.num, rdm.2e_updn_cholesky_num)~ | Cholesky decomposition of the two-body RDM (\uparrow\downarrow) |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|------------------------+----------------+----------------------------------------------------------+----------------------------------------------------------+-----------------------------------------------------------------------|
|
||||
| ~1e~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | One body density matrix |
|
||||
| ~1e_up~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | \uparrow-spin component of the one body density matrix |
|
||||
| ~1e_dn~ | ~float~ | ~[mo.num, mo.num]~ | ~(mo.num, mo.num)~ | \downarrow-spin component of the one body density matrix |
|
||||
| ~1e_transition~ | ~float~ | ~[state.num, state.num, mo.num, mo.num]~ | ~(mo.num, mo.num, state.num, state.num)~ | One-particle transition density matrices |
|
||||
| ~2e~ | ~float sparse~ | ~[mo.num, mo.num, mo.num, mo.num]~ | ~(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]~ | ~(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]~ | ~(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]~ | ~(mo.num, mo.num, mo.num, mo.num)~ | \uparrow\downarrow component of the two-body reduced density matrix |
|
||||
| ~2e_transition~ | ~float sparse~ | ~[state.num, state.num, mo.num, mo.num, mo.num, mo.num]~ | ~(mo.num, mo.num, mo.num, mo.num, state.num, state.num)~ | Two-particle transition density matrices |
|
||||
| ~2e_cholesky_num~ | ~dim~ | | | Number of Cholesky vectors |
|
||||
| ~2e_cholesky~ | ~float sparse~ | ~[rdm.2e_cholesky_num, mo.num, mo.num]~ | ~(mo.num, mo.num, rdm.2e_cholesky_num)~ | Cholesky decomposition of the two-body RDM (spin trace) |
|
||||
| ~2e_upup_cholesky_num~ | ~dim~ | | | Number of Cholesky vectors |
|
||||
| ~2e_upup_cholesky~ | ~float sparse~ | ~[rdm.2e_upup_cholesky_num, mo.num, mo.num]~ | ~(mo.num, mo.num, rdm.2e_upup_cholesky_num)~ | Cholesky decomposition of the two-body RDM (\uparrow\uparrow) |
|
||||
| ~2e_dndn_cholesky_num~ | ~dim~ | | | Number of Cholesky vectors |
|
||||
| ~2e_dndn_cholesky~ | ~float sparse~ | ~[rdm.2e_dndn_cholesky_num, mo.num, mo.num]~ | ~(mo.num, mo.num, rdm.2e_dndn_cholesky_num)~ | Cholesky decomposition of the two-body RDM (\downarrow\downarrow) |
|
||||
| ~2e_updn_cholesky_num~ | ~dim~ | | | Number of Cholesky vectors |
|
||||
| ~2e_updn_cholesky~ | ~float sparse~ | ~[rdm.2e_updn_cholesky_num, mo.num, mo.num]~ | ~(mo.num, mo.num, rdm.2e_updn_cholesky_num)~ | Cholesky decomposition of the two-body RDM (\uparrow\downarrow) |
|
||||
|
||||
#+CALL: json(data=rdm, title="rdm")
|
||||
|
||||
|
|
@ -1217,7 +1224,7 @@ power = [
|
|||
\sum_{p=2}^{N_\text{ord}^b} b_{p+1}\, [f_{\text{ee}}(r_{ij})]^p - J_{\text{ee},ij}^\infty
|
||||
\right]
|
||||
\]
|
||||
|
||||
|
||||
$\delta^{\uparrow\downarrow}_{ij}$ is zero when the electrons $i$ and
|
||||
$j$ have the same spin, and one otherwise.
|
||||
|
||||
|
|
@ -1242,9 +1249,9 @@ power = [
|
|||
$J_{\text{eN}}$ and $J_{\text{ee}}$ have an asymptotic value of zero:
|
||||
|
||||
\[
|
||||
J_{\text{eN}}^{\infty} =
|
||||
J_{\text{eN}}^{\infty} =
|
||||
\frac{a_{1,\alpha}\, \kappa_\alpha^{-1}}{1+a_{2,\alpha}\,
|
||||
\kappa_\alpha^{-1}} + \sum_{p=2}^{N_\text{ord}^a} a_{p+1,\alpha}\, \kappa_\alpha^{-p}
|
||||
\kappa_\alpha^{-1}} + \sum_{p=2}^{N_\text{ord}^a} a_{p+1,\alpha}\, \kappa_\alpha^{-p}
|
||||
\]
|
||||
\[
|
||||
J_{\text{ee},ij}^{\infty} =
|
||||
|
|
@ -1329,19 +1336,19 @@ power = [
|
|||
*** Table of values
|
||||
|
||||
#+name: jastrow
|
||||
| Variable | Type | Dimensions | Description |
|
||||
|---------------+---------+---------------------+-----------------------------------------------------------------|
|
||||
| ~type~ | ~str~ | | Type of Jastrow factor: ~CHAMP~ or ~Mu~ |
|
||||
| ~en_num~ | ~dim~ | | Number of Electron-nucleus parameters |
|
||||
| ~ee_num~ | ~dim~ | | Number of Electron-electron parameters |
|
||||
| ~een_num~ | ~dim~ | | Number of Electron-electron-nucleus parameters |
|
||||
| ~en~ | ~float~ | ~(jastrow.en_num)~ | Electron-nucleus parameters |
|
||||
| ~ee~ | ~float~ | ~(jastrow.ee_num)~ | Electron-electron 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 |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|---------------+---------+----------------------+-------------------------+-----------------------------------------------------------------|
|
||||
| ~type~ | ~str~ | | | Type of Jastrow factor: ~CHAMP~ or ~Mu~ |
|
||||
| ~en_num~ | ~dim~ | | | Number of Electron-nucleus parameters |
|
||||
| ~ee_num~ | ~dim~ | | | Number of Electron-electron parameters |
|
||||
| ~een_num~ | ~dim~ | | | Number of Electron-electron-nucleus parameters |
|
||||
| ~en~ | ~float~ | ~[jastrow.en_num]~ | ~(jastrow.en_num)~ | Electron-nucleus parameters |
|
||||
| ~ee~ | ~float~ | ~[jastrow.ee_num]~ | ~(jastrow.ee_num)~ | Electron-electron parameters |
|
||||
| ~een~ | ~float~ | ~[jastrow.een_num]~ | ~(jastrow.een_num)~ | Electron-electron-nucleus parameters |
|
||||
| ~en_nucleus~ | ~index~ | ~[jastrow.en_num]~ | ~(jastrow.en_num)~ | Nucleus relative to the eN parameter |
|
||||
| ~een_nucleus~ | ~index~ | ~[jastrow.een_num]~ | ~(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]~ | ~(nucleus.num)~ | $\kappa$ value in CHAMP Jastrow for electron-nucleus distances |
|
||||
|
||||
#+CALL: json(data=jastrow, title="jastrow")
|
||||
|
||||
|
|
@ -1349,17 +1356,17 @@ power = [
|
|||
:results:
|
||||
#+begin_src python :tangle trex.json
|
||||
"jastrow": {
|
||||
"type" : [ "str" , [] ]
|
||||
, "en_num" : [ "dim" , [] ]
|
||||
, "ee_num" : [ "dim" , [] ]
|
||||
, "een_num" : [ "dim" , [] ]
|
||||
, "en" : [ "float" , [ "jastrow.en_num" ] ]
|
||||
, "ee" : [ "float" , [ "jastrow.ee_num" ] ]
|
||||
, "een" : [ "float" , [ "jastrow.een_num" ] ]
|
||||
, "en_nucleus" : [ "index" , [ "jastrow.en_num" ] ]
|
||||
, "een_nucleus" : [ "index" , [ "jastrow.een_num" ] ]
|
||||
, "ee_scaling" : [ "float" , [] ]
|
||||
, "en_scaling" : [ "float" , [ "nucleus.num" ] ]
|
||||
"type" : [ "str" , [] ]
|
||||
, "en_num" : [ "dim" , [] ]
|
||||
, "ee_num" : [ "dim" , [] ]
|
||||
, "een_num" : [ "dim" , [] ]
|
||||
, "en" : [ "float", [ "jastrow.en_num" ] ]
|
||||
, "ee" : [ "float", [ "jastrow.ee_num" ] ]
|
||||
, "een" : [ "float", [ "jastrow.een_num" ] ]
|
||||
, "en_nucleus" : [ "index", [ "jastrow.en_num" ] ]
|
||||
, "een_nucleus" : [ "index", [ "jastrow.een_num" ] ]
|
||||
, "ee_scaling" : [ "float", [] ]
|
||||
, "en_scaling" : [ "float", [ "nucleus.num" ] ]
|
||||
} ,
|
||||
#+end_src
|
||||
:end:
|
||||
|
|
@ -1375,12 +1382,12 @@ power = [
|
|||
of $\uparrow$-spin and then all the $\downarrow$-spin.
|
||||
|
||||
#+name: qmc
|
||||
| Variable | Type | Dimensions | Description |
|
||||
|----------+---------+------------------------------+---------------------------------------|
|
||||
| ~num~ | ~dim~ | | Number of 3N-dimensional points |
|
||||
| ~point~ | ~float~ | ~(3, electron.num, qmc.num)~ | 3N-dimensional points |
|
||||
| ~psi~ | ~float~ | ~(qmc.num)~ | Wave function evaluated at the points |
|
||||
| ~e_loc~ | ~float~ | ~(qmc.num)~ | Local energy evaluated at the points |
|
||||
| Variable | Type | Row-major Dimensions | Column-major Dimensions | Description |
|
||||
|----------+---------+------------------------------+------------------------------+---------------------------------------|
|
||||
| ~num~ | ~dim~ | | | Number of 3N-dimensional points |
|
||||
| ~point~ | ~float~ | ~[qmc.num, electron.num, 3]~ | ~(3, electron.num, qmc.num)~ | 3N-dimensional points |
|
||||
| ~psi~ | ~float~ | ~[qmc.num]~ | ~(qmc.num)~ | Wave function evaluated at the points |
|
||||
| ~e_loc~ | ~float~ | ~[qmc.num]~ | ~(qmc.num)~ | Local energy evaluated at the points |
|
||||
|
||||
#+CALL: json(data=qmc, title="qmc", last=1)
|
||||
|
||||
|
|
@ -1410,7 +1417,7 @@ for line in data:
|
|||
name = '"'+line[0]+'"'
|
||||
typ = '"'+line[1]+'"'
|
||||
dims = line[2]
|
||||
if '(' in dims:
|
||||
if '[' in dims:
|
||||
dims = dims.strip()[1:-1]
|
||||
dims = [ '"'+x.strip()+'"' for x in dims.split(',') ]
|
||||
dims = "[ " + ", ".join(dims) + " ]"
|
||||
|
|
@ -1426,10 +1433,9 @@ for line in data:
|
|||
name = '"'+line[0]+'"'
|
||||
typ = '"'+line[1]+'"'
|
||||
dims = line[2]
|
||||
if '(' in dims:
|
||||
if '[' in dims:
|
||||
dims = dims.strip()[1:-1]
|
||||
dims = [ '"'+x.strip()+'"' for x in dims.split(',') ]
|
||||
dims.reverse()
|
||||
dims = "[ " + ", ".join(dims) + " ]"
|
||||
else:
|
||||
if dims.strip() != "":
|
||||
|
|
|
|||
Loading…
Reference in New Issue