diff --git a/trex.org b/trex.org index 857fdb0..c7014f3 100644 --- a/trex.org +++ b/trex.org @@ -266,16 +266,19 @@ Where $u_i(\mathbf{r})$ is numerically tabulated on a dense logarithmic grid. It is constructed to vanish for any $\mathbf{r}$ outside of the grid. The reference points are stored in ~numgrid_r~ - and ~numgrid_phi~. Additionaly, a separate spline for the kinetic energy - can be stored in ~numgrid_kin~. The index of the first data point for - each shell is stored in ~numgrid_start~. + and ~numgrid_phi~. Additionaly, a separate spline for the gradient and Laplacian + can be stored in ~numgrid_grad~ and ~numgrid_lap~. The index of the first data point for + 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. - The interpolation coefficients are given in the ~interpolator~ array. - The number of coefficients per interpolation point is stored as - ~interp_coeff_cnt~ so that other interpolation functions can be - implemented if needed. The ~interpolator_kin~ array provides a spline for - the kinetic energy. + What kind of spline is used can be provided in the ~interpolator_kind~ field. + For example, FHI-aims uses a cubic spline, so the ~interpolator_kind~ is + \"polynomial\" and the ~interp_coeff_cnt~ is $4$. In this case, the first + interpolation coefficient per data point is the absolute term, the second is for + the linear term etc. + 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 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. @@ -308,29 +311,32 @@ *** Data definitions #+NAME: basis - | Variable | Type | Dimensions | Description | | - |--------------------+---------+----------------------------------------------+------------------------------------------------------------------------------+---| - | ~type~ | ~str~ | | Type of basis set: "Gaussian", "Slater", "Numerical" or "PW" for plane waves | | - | ~prim_num~ | ~dim~ | | Total number of primitives | | - | ~shell_num~ | ~dim~ | | Total number of shells | | - | ~numgrid_num~ | ~dim~ | | Total number of grid points for numerical orbitals | | - | ~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 | | - | ~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 ($\mathcal{N}_s$) | | - | ~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_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 | | - | ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) | | - | ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) | | - | ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) | | - | ~e_cut~ | ~float~ | | Energy cut-off for plane-wave calculations | | - | ~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_kin~ | ~float~ | ~(basis.numgrid_num)~ | Kinetic energy of numerical orbitals | | - | ~interpolator~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital interpolation function | | - | ~interpolator_kin~ | ~float~ | ~(basis.interp_coeff_cnt,basis.numgrid_num)~ | Coefficients for numerical orbital kinetic energy interpolation function | | + | Variable | Type | Dimensions | Description | | + |---------------------+---------+----------------------------------------------+------------------------------------------------------------------------------+---| + | ~type~ | ~str~ | | Type of basis set: "Gaussian", "Slater", "Numerical" or "PW" for plane waves | | + | ~prim_num~ | ~dim~ | | Total number of primitives | | + | ~shell_num~ | ~dim~ | | Total number of shells | | + | ~numgrid_num~ | ~dim~ | | Total number of grid points for numerical orbitals | | + | ~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 | | + | ~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 ($\mathcal{N}_s$) | | + | ~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_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 | | + | ~exponent~ | ~float~ | ~(basis.prim_num)~ | Exponents of the primitives ($\gamma_{ks}$) | | + | ~coefficient~ | ~float~ | ~(basis.prim_num)~ | Coefficients of the primitives ($a_{ks}$) | | + | ~prim_factor~ | ~float~ | ~(basis.prim_num)~ | Normalization coefficients for the primitives ($f_{ks}$) | | + | ~e_cut~ | ~float~ | | Energy cut-off for plane-wave calculations | | + | ~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_grad~ | ~float~ | ~(basis.numgrid_num)~ | Radial gradient of numerical orbitals | | + | ~numgrid_lap~ | ~float~ | ~(basis.numgrid_num)~ | Laplacian of numerical orbitals | | + | ~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: #+begin_src python :tangle trex.json "basis": { - "type" : [ "str" , [] ] - , "prim_num" : [ "dim" , [] ] - , "shell_num" : [ "dim" , [] ] - , "numgrid_num" : [ "dim" , [] ] - , "interp_coeff_cnt" : [ "dim" , [] ] - , "nucleus_index" : [ "index", [ "basis.shell_num" ] ] - , "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ] - , "shell_factor" : [ "float", [ "basis.shell_num" ] ] - , "r_power" : [ "int" , [ "basis.shell_num" ] ] - , "numgrid_start" : [ "index", [ "basis.shell_num" ] ] - , "numgrid_size" : [ "dim" , [ "basis.shell_num" ] ] - , "shell_index" : [ "index", [ "basis.prim_num" ] ] - , "exponent" : [ "float", [ "basis.prim_num" ] ] - , "coefficient" : [ "float", [ "basis.prim_num" ] ] - , "prim_factor" : [ "float", [ "basis.prim_num" ] ] - , "e_cut" : [ "float", [] ] - , "numgrid_radius" : [ "float", [ "basis.numgrid_num" ] ] - , "numgrid_phi" : [ "float", [ "basis.numgrid_num" ] ] - , "numgrid_kin" : [ "float", [ "basis.numgrid_num" ] ] - , "interpolator" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ] - , "interpolator_kin" : [ "float", [ "basis.numgrid_num", "basis.interp_coeff_cnt" ] ] + "type" : [ "str" , [] ] + , "prim_num" : [ "dim" , [] ] + , "shell_num" : [ "dim" , [] ] + , "numgrid_num" : [ "dim" , [] ] + , "interp_coeff_cnt" : [ "dim" , [] ] + , "nucleus_index" : [ "index", [ "basis.shell_num" ] ] + , "shell_ang_mom" : [ "int" , [ "basis.shell_num" ] ] + , "shell_factor" : [ "float", [ "basis.shell_num" ] ] + , "r_power" : [ "int" , [ "basis.shell_num" ] ] + , "numgrid_start" : [ "index", [ "basis.shell_num" ] ] + , "numgrid_size" : [ "dim" , [ "basis.shell_num" ] ] + , "shell_index" : [ "index", [ "basis.prim_num" ] ] + , "exponent" : [ "float", [ "basis.prim_num" ] ] + , "coefficient" : [ "float", [ "basis.prim_num" ] ] + , "prim_factor" : [ "float", [ "basis.prim_num" ] ] + , "e_cut" : [ "float", [] ] + , "numgrid_radius" : [ "float", [ "basis.numgrid_num" ] ] + , "numgrid_phi" : [ "float", [ "basis.numgrid_num" ] ] + , "numgrid_grad" : [ "float", [ "basis.numgrid_num" ] ] + , "numgrid_lap" : [ "float", [ "basis.numgrid_num" ] ] + , "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: