Parametric_potentials.hpp

#pragma once
#include <vector>
 
//! Set of two-parameter parametric electron potentials
namespace Parametric {
 
/*!
  @brief Parametric potential type.
 
  @details
  - Green : Green potential, parameters H, d (see green)
  - Tietz : Tietz potential, parameters g, t (see tietz)
*/
enum class Type { Green, Tietz };
 
/*!
  @brief Green parametric potential at r; electron part only (no nuclear).
 
  @details
  \f[
    V(r) = \frac{Z}{r} - \frac{1}{r}
      \left[ 1 + \frac{Z-1}{H\,(e^{r/d} - 1) + 1} \right].
  \f]
 
  The total potential is V(r) - Z/r. 
  Returns 0 at r = 0, and for Z = 1 (no screening electrons).
*/
double green(int Z, double r, double H, double d);
 
/*!
  @brief Tietz parametric potential at r; electron part only (no nuclear).
 
  @details
  \f[
    V(r) = \frac{Z}{r} - \frac{1}{r}
      \left[ 1 + \frac{(Z-1)\,e^{-g r}}{(1 + t r)^2} \right].
  \f]
  The total potential is V(r) - Z/r. Returns 0 at r = 0.
*/
double tietz(int Z, double r, double g, double t);
 
/*!
  @brief Default Green parameters H and d for given Z, tuned to match HF core.
 
  @details
  Tabulated for selected Z, linearly interpolated in between. For Z > 113,
  H = 5.0, d = 0.75.
 
  @return Always 0; H and d are set by reference.
 
  @note For Z = 1, H = d = 0: unused, since there is no screening.
*/
int defaultGreenCore(int z, double &H, double &d);
 
/*!
  @brief Default Green parameters H and d for given Z, tuned to experiment.
 
  @details
  Fitted to the lowest valence J=1/2 states for selected Z; crude quadratic
  fit in Z otherwise.
 
  @return Always 0; H and d are set by reference.
*/
int defaultGreen(int z, double &H, double &d);
 
/*!
  @brief Default Tietz parameters g and t for given Z, tuned to experiment.
 
  @details
  Fitted to the lowest valence J=1/2 states for selected Z; crude quadratic
  fit in Z otherwise.
 
  @return Always 0; g and t are set by reference.
*/
int defaultTietz(int z, double &g, double &t);
 
/*!
  @brief Green parametric potential (electron part) on given radial points.
 
  @details
  See green(). If H*d is (near) zero, the core-tuned defaults are used
  (defaultGreenCore).
 
  @param z        Nuclear charge
  @param r_array  Radial points
  @param H        Green parameter H (0: default)
  @param d        Green parameter d (0: default)
 
  @return V(r) at each point of @p r_array; excludes nuclear potential.
*/
std::vector<double> GreenPotential(int z, const std::vector<double> &r_array,
                                   double H = 0, double d = 0);
 
/*!
  @brief Tietz parametric potential (electron part) on given radial points.
 
  @details
  See tietz(). If g*t is (near) zero, the experiment-tuned defaults are used
  (defaultTietz).
 
  @param z        Nuclear charge
  @param r_array  Radial points
  @param g        Tietz parameter g (0: default)
  @param t        Tietz parameter t (0: default)
 
  @return V(r) at each point of @p r_array; excludes nuclear potential.
*/
std::vector<double> TietzPotential(int z, const std::vector<double> &r_array,
                                   double g = 0, double t = 0);
} // namespace Parametric