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Change NAO 'kinetic energy' fields to 'Laplacian'

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joguenzl 2023-05-16 14:13:45 +02:00
parent fb97b44a5f
commit b7d9f32bfb
1 changed files with 62 additions and 53 deletions
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@ -266,16 +266,19 @@
Where $u_i(\mathbf{r})$ is numerically tabulated on a dense logarithmic Where $u_i(\mathbf{r})$ is numerically tabulated on a dense logarithmic
grid. It is constructed to vanish for any $\mathbf{r}$ grid. It is constructed to vanish for any $\mathbf{r}$
outside of the grid. The reference points are stored in ~numgrid_r~ outside of the grid. The reference points are stored in ~numgrid_r~
and ~numgrid_phi~. Additionaly, a separate spline for the kinetic energy and ~numgrid_phi~. Additionaly, a separate spline for the gradient and Laplacian
can be stored in ~numgrid_kin~. The index of the first data point for can be stored in ~numgrid_grad~ and ~numgrid_lap~. The index of the first data point for
each shell is stored in ~numgrid_start~. each shell is stored in ~numgrid_start~, the number of data points per spline
is stored in ~numgrid_size~ for convenience.
FHI-aims uses cubic interpolation between the reference points. What kind of spline is used can be provided in the ~interpolator_kind~ field.
The interpolation coefficients are given in the ~interpolator~ array. For example, FHI-aims uses a cubic spline, so the ~interpolator_kind~ is
The number of coefficients per interpolation point is stored as \"polynomial\" and the ~interp_coeff_cnt~ is $4$. In this case, the first
~interp_coeff_cnt~ so that other interpolation functions can be interpolation coefficient per data point is the absolute term, the second is for
implemented if needed. The ~interpolator_kin~ array provides a spline for the linear term etc.
the kinetic energy. The interpolation coefficients for the wave function are given in the
~interpolator_phi~ array. The ~interpolator_grad~ and ~interpolator_lap~
arrays provide a spline for the gradient and Laplacian, respectively.
The argument passed to the interpolants is on the logarithmic scale of The argument passed to the interpolants is on the logarithmic scale of
the reference points: If the argument is an integer $i$, the interpolant the reference points: If the argument is an integer $i$, the interpolant
will return the value of $u(\mathbf{r})$ at the $i$th reference point. will return the value of $u(\mathbf{r})$ at the $i$th reference point.
@ -308,29 +311,32 @@
*** Data definitions *** Data definitions
#+NAME: basis #+NAME: basis
| Variable | Type | Dimensions | Description | | | Variable | Type | Dimensions | Description | |
|--------------------+---------+----------------------------------------------+------------------------------------------------------------------------------+---| |---------------------+---------+----------------------------------------------+------------------------------------------------------------------------------+---|
| ~type~ | ~str~ | | Type of basis set: "Gaussian", "Slater", "Numerical" or "PW" for plane waves | | | ~type~ | ~str~ | | Type of basis set: "Gaussian", "Slater", "Numerical" or "PW" for plane waves | |
| ~prim_num~ | ~dim~ | | Total number of primitives | | | ~prim_num~ | ~dim~ | | Total number of primitives | |
| ~shell_num~ | ~dim~ | | Total number of shells | | | ~shell_num~ | ~dim~ | | Total number of shells | |
| ~numgrid_num~ | ~dim~ | | Total number of grid points for numerical orbitals | | | ~numgrid_num~ | ~dim~ | | Total number of grid points for numerical orbitals | |
| ~interp_coeff_cnt~ | ~dim~ | | Number of coefficients for the numerical orbital interpolator | | | ~interp_coeff_cnt~ | ~dim~ | | Number of coefficients for the numerical orbital interpolator | |
| ~nucleus_index~ | ~index~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices | | | ~nucleus_index~ | ~index~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and atomic indices | |
| ~shell_ang_mom~ | ~int~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta | | | ~shell_ang_mom~ | ~int~ | ~(basis.shell_num)~ | One-to-one correspondence between shells and angular momenta | |
| ~shell_factor~ | ~float~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$) | | | ~shell_factor~ | ~float~ | ~(basis.shell_num)~ | Normalization factor of each shell ($\mathcal{N}_s$) | |
| ~r_power~ | ~int~ | ~(basis.shell_num)~ | Power to which $r$ is raised ($n_s$) | | | ~r_power~ | ~int~ | ~(basis.shell_num)~ | Power to which $r$ is raised ($n_s$) | |
| ~numgrid_start~ | ~index~ | ~(basis.shell_num)~ | Index of the first data point for a given numerical orbital | | | ~numgrid_start~ | ~index~ | ~(basis.shell_num)~ | Index of the first data point for a given numerical orbital | |
| ~numgrid_size~ | ~dim~ | ~(basis.shell_num)~ | Number of data points per numerical orbital | | | ~numgrid_size~ | ~dim~ | ~(basis.shell_num)~ | Number of data points per numerical orbital | |
| ~shell_index~ | ~index~ | ~(basis.prim_num)~ | One-to-one correspondence between primitives and shell index | | | ~shell_index~ | ~index~ | ~(basis.prim_num)~ | One-to-one correspondence between primitives and shell index | |
| ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) | | | ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) | |
| ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) | | | ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) | |
| ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) | | | ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) | |
| ~e_cut~ | ~float~ | | Energy cut-off for plane-wave calculations | | | ~e_cut~ | ~float~ | | Energy cut-off for plane-wave calculations | |
| ~numgrid_radius~ | ~float~ | ~(basis.numgrid_num)~ | Radii of grid points for numerical orbitals | | | ~numgrid_radius~ | ~float~ | ~(basis.numgrid_num)~ | Radii of grid points for numerical orbitals | |
| ~numgrid_phi~ | ~float~ | ~(basis.numgrid_num)~ | Wave function values for numerical orbitals | | | ~numgrid_phi~ | ~float~ | ~(basis.numgrid_num)~ | Wave function values for numerical orbitals | |
| ~numgrid_kin~ | ~float~ | ~(basis.numgrid_num)~ | Kinetic energy of numerical orbitals | | | ~numgrid_grad~ | ~float~ | ~(basis.numgrid_num)~ | Radial gradient of numerical orbitals | |
| ~interpolator~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital interpolation function | | | ~numgrid_lap~ | ~float~ | ~(basis.numgrid_num)~ | Laplacian of numerical orbitals | |
| ~interpolator_kin~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital kinetic energy interpolation function | | | ~interpolator_kind~ | ~str~ | | Kind of spline, e.g. "polynomial" | |
| ~interpolator_phi~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital interpolation function | |
| ~interpolator_grad~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital gradient interpolation function | |
| ~interpolator_lap~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital laplacian interpolation function | |
@ -340,27 +346,30 @@
:results: :results:
#+begin_src python :tangle trex.json #+begin_src python :tangle trex.json
"basis": { "basis": {
"type" : [ "str" , [] ] "type" : [ "str" , [] ]
, "prim_num" : [ "dim" , [] ] , "prim_num" : [ "dim" , [] ]
, "shell_num" : [ "dim" , [] ] , "shell_num" : [ "dim" , [] ]
, "numgrid_num" : [ "dim" , [] ] , "numgrid_num" : [ "dim" , [] ]
, "interp_coeff_cnt" : [ "dim" , [] ] , "interp_coeff_cnt" : [ "dim" , [] ]
, "nucleus_index" : [ "index", [ "basis.shell_num" ] ] , "nucleus_index" : [ "index", [ "basis.shell_num" ] ]
, "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ] , "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ]
, "shell_factor" : [ "float", [ "basis.shell_num" ] ] , "shell_factor" : [ "float", [ "basis.shell_num" ] ]
, "r_power" : [ "int" , [ "basis.shell_num" ] ] , "r_power" : [ "int" , [ "basis.shell_num" ] ]
, "numgrid_start" : [ "index", [ "basis.shell_num" ] ] , "numgrid_start" : [ "index", [ "basis.shell_num" ] ]
, "numgrid_size" : [ "dim" , [ "basis.shell_num" ] ] , "numgrid_size" : [ "dim" , [ "basis.shell_num" ] ]
, "shell_index" : [ "index", [ "basis.prim_num" ] ] , "shell_index" : [ "index", [ "basis.prim_num" ] ]
, "exponent" : [ "float", [ "basis.prim_num" ] ] , "exponent" : [ "float", [ "basis.prim_num" ] ]
, "coefficient" : [ "float", [ "basis.prim_num" ] ] , "coefficient" : [ "float", [ "basis.prim_num" ] ]
, "prim_factor" : [ "float", [ "basis.prim_num" ] ] , "prim_factor" : [ "float", [ "basis.prim_num" ] ]
, "e_cut" : [ "float", [] ] , "e_cut" : [ "float", [] ]
, "numgrid_radius" : [ "float", [ "basis.numgrid_num" ] ] , "numgrid_radius" : [ "float", [ "basis.numgrid_num" ] ]
, "numgrid_phi" : [ "float", [ "basis.numgrid_num" ] ] , "numgrid_phi" : [ "float", [ "basis.numgrid_num" ] ]
, "numgrid_kin" : [ "float", [ "basis.numgrid_num" ] ] , "numgrid_grad" : [ "float", [ "basis.numgrid_num" ] ]
, "interpolator" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ] , "numgrid_lap" : [ "float", [ "basis.numgrid_num" ] ]
, "interpolator_kin" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ] , "interpolator_kind" : [ "str" , [] ]
, "interpolator_phi" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ]
, "interpolator_grad" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ]
, "interpolator_lap" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ]
} , } ,
#+end_src #+end_src
:end: :end: