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Change NAO 'kinetic energy' fields to 'Laplacian'
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joguenzl
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fb97b44a5f
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115
trex.org
115
trex.org
@ -266,16 +266,19 @@
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Where $u_i(\mathbf{r})$ is numerically tabulated on a dense logarithmic
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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 ~numgrid_r~
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and ~numgrid_phi~. Additionaly, a separate spline for the kinetic energy
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can be stored in ~numgrid_kin~. The index of the first data point for
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each shell is stored in ~numgrid_start~.
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and ~numgrid_phi~. Additionaly, a separate spline for the gradient and Laplacian
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can be stored in ~numgrid_grad~ and ~numgrid_lap~. The index of the first data point for
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each shell is stored in ~numgrid_start~, the number of data points per spline
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is stored in ~numgrid_size~ for convenience.
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FHI-aims uses cubic interpolation between the reference points.
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The interpolation coefficients are given in the ~interpolator~ array.
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The number of coefficients per interpolation point is stored as
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~interp_coeff_cnt~ so that other interpolation functions can be
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implemented if needed. The ~interpolator_kin~ array provides a spline for
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the kinetic energy.
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What kind of spline is used can be provided in the ~interpolator_kind~ field.
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For example, FHI-aims uses a cubic spline, so the ~interpolator_kind~ is
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\"polynomial\" and the ~interp_coeff_cnt~ is $4$. In this case, the first
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interpolation coefficient per data point is the absolute term, the second is for
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the linear term etc.
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The interpolation coefficients for the wave function are given in the
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~interpolator_phi~ array. The ~interpolator_grad~ and ~interpolator_lap~
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arrays provide a spline for the gradient and Laplacian, respectively.
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The argument passed to the interpolants is on the logarithmic scale of
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the reference points: If the argument is an integer $i$, the interpolant
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will return the value of $u(\mathbf{r})$ at the $i$th reference point.
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@ -308,29 +311,32 @@
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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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| ~numgrid_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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| ~numgrid_start~ | ~index~ | ~(basis.shell_num)~ | Index of the first data point for a given numerical orbital | |
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| ~numgrid_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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| ~numgrid_radius~ | ~float~ | ~(basis.numgrid_num)~ | Radii of grid points for numerical orbitals | |
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| ~numgrid_phi~ | ~float~ | ~(basis.numgrid_num)~ | Wave function values for numerical orbitals | |
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| ~numgrid_kin~ | ~float~ | ~(basis.numgrid_num)~ | Kinetic energy of numerical orbitals | |
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| ~interpolator~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital interpolation function | |
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| ~interpolator_kin~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital kinetic energy interpolation function | |
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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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| ~numgrid_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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| ~numgrid_start~ | ~index~ | ~(basis.shell_num)~ | Index of the first data point for a given numerical orbital | |
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| ~numgrid_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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| ~numgrid_radius~ | ~float~ | ~(basis.numgrid_num)~ | Radii of grid points for numerical orbitals | |
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| ~numgrid_phi~ | ~float~ | ~(basis.numgrid_num)~ | Wave function values for numerical orbitals | |
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| ~numgrid_grad~ | ~float~ | ~(basis.numgrid_num)~ | Radial gradient of numerical orbitals | |
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| ~numgrid_lap~ | ~float~ | ~(basis.numgrid_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.numgrid_num)~ | Coefficients for numerical orbital interpolation function | |
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| ~interpolator_grad~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital gradient interpolation function | |
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| ~interpolator_lap~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital laplacian interpolation function | |
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@ -340,27 +346,30 @@
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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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, "numgrid_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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, "numgrid_start" : [ "index", [ "basis.shell_num" ] ]
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, "numgrid_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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, "numgrid_radius" : [ "float", [ "basis.numgrid_num" ] ]
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, "numgrid_phi" : [ "float", [ "basis.numgrid_num" ] ]
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, "numgrid_kin" : [ "float", [ "basis.numgrid_num" ] ]
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, "interpolator" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ]
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, "interpolator_kin" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ]
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"type" : [ "str" , [] ]
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, "prim_num" : [ "dim" , [] ]
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, "shell_num" : [ "dim" , [] ]
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, "numgrid_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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, "numgrid_start" : [ "index", [ "basis.shell_num" ] ]
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, "numgrid_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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, "numgrid_radius" : [ "float", [ "basis.numgrid_num" ] ]
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, "numgrid_phi" : [ "float", [ "basis.numgrid_num" ] ]
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, "numgrid_grad" : [ "float", [ "basis.numgrid_num" ] ]
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, "numgrid_lap" : [ "float", [ "basis.numgrid_num" ] ]
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, "interpolator_kind" : [ "str" , [] ]
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, "interpolator_phi" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ]
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, "interpolator_grad" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ]
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, "interpolator_lap" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ]
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} ,
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#+end_src
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:end:
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