Detailed Description

Set of two-parameter parametric electron potentials.

Enumerations
enum class	Type { Green , Tietz }
	Parametric potential type. More...

Functions
double	green (int Z, double r, double H, double d)
	Green parametric potential at r; electron part only (no nuclear).

double	tietz (int Z, double r, double g, double t)
	Tietz parametric potential at r; electron part only (no nuclear).

int	defaultGreenCore (int z, double &H, double &d)
	Default Green parameters H and d for given Z, tuned to match HF core.

int	defaultGreen (int z, double &H, double &d)
	Default Green parameters H and d for given Z, tuned to experiment.

int	defaultTietz (int z, double &g, double &t)
	Default Tietz parameters g and t for given Z, tuned to experiment.

std::vector< double >	GreenPotential (int z, const std::vector< double > &r_array, double H=0, double d=0)
	Green parametric potential (electron part) on given radial points.

std::vector< double >	TietzPotential (int z, const std::vector< double > &r_array, double g=0, double t=0)
	Tietz parametric potential (electron part) on given radial points.

Enumeration Type Documentation

◆ Type

enum class Parametric::Type

strong

Parametric potential type.

Green : Green potential, parameters H, d (see green)
Tietz : Tietz potential, parameters g, t (see tietz)

Function Documentation

◆ green()

double Parametric::green	(	int	Z,
		double	r,
		double	H,
		double	d
	)

Green parametric potential at r; electron part only (no nuclear).

\[ V(r) = \frac{Z}{r} - \frac{1}{r} \left[ 1 + \frac{Z-1}{H\,(e^{r/d} - 1) + 1} \right]. \]

The total potential is V(r) - Z/r. Returns 0 at r = 0, and for Z = 1 (no screening electrons).

◆ tietz()

double Parametric::tietz	(	int	Z,
		double	r,
		double	g,
		double	t
	)

Tietz parametric potential at r; electron part only (no nuclear).

\[ V(r) = \frac{Z}{r} - \frac{1}{r} \left[ 1 + \frac{(Z-1)\,e^{-g r}}{(1 + t r)^2} \right]. \]

The total potential is V(r) - Z/r. Returns 0 at r = 0.

◆ defaultGreenCore()

int Parametric::defaultGreenCore	(	int	z,
		double &	H,
		double &	d
	)

Default Green parameters H and d for given Z, tuned to match HF core.

Tabulated for selected Z, linearly interpolated in between. For Z > 113, H = 5.0, d = 0.75.

Returns: Always 0; H and d are set by reference.

Note: For Z = 1, H = d = 0: unused, since there is no screening.

◆ defaultGreen()

int Parametric::defaultGreen	(	int	z,
		double &	H,
		double &	d
	)

Default Green parameters H and d for given Z, tuned to experiment.

Fitted to the lowest valence J=1/2 states for selected Z; crude quadratic fit in Z otherwise.

Returns: Always 0; H and d are set by reference.

◆ defaultTietz()

int Parametric::defaultTietz	(	int	z,
		double &	g,
		double &	t
	)

Default Tietz parameters g and t for given Z, tuned to experiment.

Fitted to the lowest valence J=1/2 states for selected Z; crude quadratic fit in Z otherwise.

Returns: Always 0; g and t are set by reference.

◆ GreenPotential()

std::vector< double > Parametric::GreenPotential	(	int	z,
		const std::vector< double > &	r_array,
		double	H = `0`,
		double	d = `0`
	)

Green parametric potential (electron part) on given radial points.

See green(). If H*d is (near) zero, the core-tuned defaults are used (defaultGreenCore).

Parameters

z	Nuclear charge
r_array	Radial points
H	Green parameter H (0: default)
d	Green parameter d (0: default)

Returns: V(r) at each point of r_array; excludes nuclear potential.

◆ TietzPotential()

std::vector< double > Parametric::TietzPotential	(	int	z,
		const std::vector< double > &	r_array,
		double	g = `0`,
		double	t = `0`
	)

Tietz parametric potential (electron part) on given radial points.

See tietz(). If g*t is (near) zero, the experiment-tuned defaults are used (defaultTietz).