#include <hydrogen_radials.h>

Inheritance diagram for HydrogenRadials:

Collaboration diagram for HydrogenRadials:

Public Member Functions
	HydrogenRadials ()
	default constructor

HydrogenRadials &	operator= (const HydrogenRadials &rhs)
	overloaded assignment operator

HydrogenRadials *	clone () const
	copy constructor

	~HydrogenRadials ()
	destructor

void	build (const int itype=0, const double charge=1.0, const bool with_slater_screening=false, const int nmax=0, const double rcut=10.0, const double dr=0.01, const double conv_thr=1e-6, const int rank=0, const std::string symbol="", const std::string strategy="minimal-valence", std::ofstream *ptr_log=nullptr)
	build the hydrogen-like radial functions and push into NumericalRadials

std::vector< std::pair< int, int > >	unzip_strategy (const int nmax=0, const std::string strategy="minimal-valence")
	parse the strategy string to get the n, l pairs

void	smooth (std::vector< double > &rgrid, std::vector< double > &rvalue, const double sigma=0.1)
	smooth the radial function to avoid high frequency noise in FFT-spherical bessel transform

double	generate_hydrogen_radial_toconv (const double charge, const bool with_slater_screening, const int n, const int l, const double conv_thr, const int rank, std::vector< double > &rgrid, std::vector< double > &rvalue, std::ofstream *ptr_log=nullptr)
	generate hydrogen-like radial functions for a given n, l, from 0.0 to a radius where the norm of radial function is converged

double	radial_norm (const std::vector< double > rgrid, const std::vector< double > rvalue)
	returns the norm of the radial function

std::map< std::pair< int, int >, std::pair< std::vector< double >, std::vector< double > > >	generate_orb (const double charge=1.0, const bool with_slater_screening=false, const int nmax=0, const double dr=0.01, const double conv_thr=1e-6, const int rank=0, const std::string strategy="minimal-valence", std::ofstream *ptr_log=nullptr)
	generate set of hydrogen-like radial functions for a given charge, nmax, dr, rank, strategy

std::map< std::pair< int, int >, std::pair< int, int > >	mapping_nl_lzeta (const int nmax=0, const std::string strategy="minimal-valence")
	mapping the n, l pairs to the l, zeta pairs

void	hydrogen (const double charge=1.0, const bool with_slater_screening=false, const int nmax=0, const double dr=0.01, const double conv_thr=1e-6, const int rank=0, const std::string strategy="minimal-valence", std::ofstream *ptr_log=nullptr)
	kernel function of hydrogen-like radial functions

double	slater_screening (const std::string symbol, const int n, const int l)
	return the Slater screening constant for calculating effective nuclear charge

Public Member Functions inherited from RadialSet
	RadialSet ()=default

	RadialSet (const RadialSet &)
	deep copy

RadialSet &	operator= (const RadialSet &)
	deep copy

virtual	~RadialSet ()

virtual void	to_numerical_orbital (Numerical_Orbital &, const int nk_legacy=4005, const double lcao_dk=0.01) const
	Overwrites the content of a Numerical_Orbital object with the current object.

virtual void	build (const std::string &, const int=0, std::ofstream *const =nullptr, const int=0)
	Builds the object from a file.

virtual void	build (const Numerical_Nonlocal &, const int=0, std::ofstream *const =nullptr)
	Builds from a Numerical_Nonlocal object.

virtual void	build (const std::string &, const int, const double, const double, std::ofstream *const =nullptr, const int=0)
	Builds from pseudopotential file.

virtual void	build (const int, const int, const double, const double=0.1, const double=0.01, const int=0, std::ofstream *=nullptr, const int=0)
	Builds with the truncated spherical Bessel functions.

void	write_abacus_orb (const std::string &, const int=0) const
	write any RadialSet object to a file in ABACUS numerical atomic orbital format.

const std::string &	symbol () const

int	itype () const

int	lmax () const

double	rcut_max () const

int	nzeta (const int l) const

int	nzeta_max () const

int	nchi () const

const NumericalRadial &	chi (const int l, const int izeta)

const NumericalRadial *	cbegin () const

const NumericalRadial *	cend () const

void	set_transformer (ModuleBase::SphericalBesselTransformer sbt, const int update=0)

void	set_grid (const bool for_r_space, const int ngrid, const double *grid, const char mode='i')
	Sets a common grid for all NumericalRadial objects.

void	set_uniform_grid (const bool for_r_space, const int ngrid, const double cutoff, const char mode='i', const bool enable_fft=false)
	Sets a common uniform grid for all NumericalRadial objects.

Private Member Functions
std::vector< double >	generate_hydrogen_radial_segment (const double charge=1.0, const bool with_slater_screening=false, const int n=0, const int l=0, const double rmin=0.0, const double rmax=10.0, const double dr=0.01, const int rank=0, std::ofstream *ptr_log=nullptr)
	generate hydrogen-like radial functions for a given n, l, in a given range [rmin, rmax]

Private Attributes
Assoc_Laguerre	assoc_laguerre_
	Associated Laguerre polynomials generator.

Additional Inherited Members
Protected Member Functions inherited from RadialSet
void	cleanup ()
	Deallocates memory and reset all class members to default values.

int	index (const int l, const int izeta) const
	Gets the index in chi_ array from (l,izeta).

void	indexing ()
	Builds index_map_ from nzeta_, nzeta_max_ and lmax_.

void	set_rcut_max ()
	Sets rcut_max_ to be the maximum rcut of all NumericalRadial objects.

Protected Attributes inherited from RadialSet
std::string	symbol_ = ""
	usually the chemical symbol

int	itype_ = 0
	usually the index for element in calculation

int	lmax_ = -1
	maximum angular momentum among all NumericalRadial objects

double	rcut_max_ = 0.0
	maximum rcut (NOT rmax!) among all NumericalRadial objects

int *	nzeta_ = nullptr
	number of NumericalRadial objects for each angular momentum

int	nzeta_max_ = 0
	maximum number of NumericalRadial objects among each angular momentum

int	nchi_ = 0
	total number of NumericalRadial objects

NumericalRadial *	chi_ = nullptr
	array of NumericalRadial objects

int *	index_map_ = nullptr
	A map from (l,izeta) to an index in chi_ array.

Constructor & Destructor Documentation

◆ HydrogenRadials()

HydrogenRadials::HydrogenRadials ( )

inline

default constructor

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◆ ~HydrogenRadials()

HydrogenRadials::~HydrogenRadials ( )

inline

destructor

Member Function Documentation

◆ build()

void HydrogenRadials::build	(	const int	itype = `0`,
		const double	charge = `1.0`,
		const bool	with_slater_screening = `false`,
		const int	nmax = `0`,
		const double	rcut = `10.0`,
		const double	dr = `0.01`,
		const double	conv_thr = `1e-6`,
		const int	rank = `0`,
		const std::string	symbol = `""`,
		const std::string	strategy = `"minimal-valence"`,
		std::ofstream *	ptr_log = `nullptr`
	)

virtual

build the hydrogen-like radial functions and push into NumericalRadials

Parameters

itype	index of the atom type
charge	charge of the nucleus
nmax	maxmium principal quantum number
rcut	cutoff radius of the radial function (not used anymore)
dr	step size of the radial grid
rank	MPI rank
symbol	element symbol, seems only useful when storing orbital information to file
strategy	strategy string
ptr_log	pointer to the log ofstream

Reimplemented from RadialSet.

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◆ clone()

HydrogenRadials * HydrogenRadials::clone ( ) const

inlinevirtual

copy constructor

Returns: a copy of the HydrogenRadials object

Implements RadialSet.

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◆ generate_hydrogen_radial_segment()

std::vector< double > HydrogenRadials::generate_hydrogen_radial_segment	(	const double	charge = `1.0`,
		const bool	with_slater_screening = `false`,
		const int	n = `0`,
		const int	l = `0`,
		const double	rmin = `0.0`,
		const double	rmax = `10.0`,
		const double	dr = `0.01`,
		const int	rank = `0`,
		std::ofstream *	ptr_log = `nullptr`
	)

private

generate hydrogen-like radial functions for a given n, l, in a given range [rmin, rmax]

Parameters

charge	charge of the nucleus
n	principal quantum number
l	angular momentum quantum number
rmin	the minimal radius
rmax	the maximal radius
dr	step size of the radial grid
rank	MPI rank
ptr_log	pointer to the log ofstream

Returns: the radial function stored in std::vector<double>

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◆ generate_hydrogen_radial_toconv()

double HydrogenRadials::generate_hydrogen_radial_toconv	(	const double	charge,
		const bool	with_slater_screening,
		const int	n,
		const int	l,
		const double	conv_thr,
		const int	rank,
		std::vector< double > &	rgrid,
		std::vector< double > &	rvalue,
		std::ofstream *	ptr_log = `nullptr`
	)

generate hydrogen-like radial functions for a given n, l, from 0.0 to a radius where the norm of radial function is converged

Parameters

charge	charge of the nucleus
n	principal quantum number
l	angular momentum quantum number
converge_threshold	the threshold of norm of radial function, if not reached, will continue to increase the radius
rank	MPI rank
rgrid	returned radial grid
rvalue	returned radial function
ptr_log	pointer to the log ofstream

Returns: the rmax of present radial function

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◆ generate_orb()

std::map< std::pair< int, int >, std::pair< std::vector< double >, std::vector< double > > > HydrogenRadials::generate_orb	(	const double	charge = `1.0`,
		const bool	with_slater_screening = `false`,
		const int	nmax = `0`,
		const double	dr = `0.01`,
		const double	conv_thr = `1e-6`,
		const int	rank = `0`,
		const std::string	strategy = `"minimal-valence"`,
		std::ofstream *	ptr_log = `nullptr`
	)

generate set of hydrogen-like radial functions for a given charge, nmax, dr, rank, strategy

Parameters

charge	charge of the nucleus
nmax	maxmium principal quantum number
dr	step size of the radial grid
rank	MPI rank
strategy	strategy string
ptr_log	pointer to the log ofstream

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◆ hydrogen()

void HydrogenRadials::hydrogen	(	const double	charge = `1.0`,
		const bool	with_slater_screening = `false`,
		const int	nmax = `0`,
		const double	dr = `0.01`,
		const double	conv_thr = `1e-6`,
		const int	rank = `0`,
		const std::string	strategy = `"minimal-valence"`,
		std::ofstream *	ptr_log = `nullptr`
	)

kernel function of hydrogen-like radial functions

Parameters

charge	charge of the nucleus
nmax	maxmium principal quantum number
dr	step size of the radial grid
conv_thr	convergence threshold of the norm of radial function
rank	MPI rank
strategy	strategy string
ptr_log	pointer to the log ofstream

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◆ mapping_nl_lzeta()

std::map< std::pair< int, int >, std::pair< int, int > > HydrogenRadials::mapping_nl_lzeta	(	const int	nmax = `0`,
		const std::string	strategy = `"minimal-valence"`
	)

mapping the n, l pairs to the l, zeta pairs

Parameters

nmax	maxmium principal quantum number
strategy	strategy string

Returns: a map of n, l pairs to l, zeta pairs

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◆ operator=()

HydrogenRadials & HydrogenRadials::operator= ( const HydrogenRadials & rhs )

overloaded assignment operator

Parameters

rhs	HydrogenRadials object to be assigned

Returns: a reference to the assigned HydrogenRadials object

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◆ radial_norm()

double HydrogenRadials::radial_norm	(	const std::vector< double >	rgrid,
		const std::vector< double >	rvalue
	)

returns the norm of the radial function

Parameters

rgrid	radial grid
rvalue	radial function

Returns: norm of the radial function

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◆ slater_screening()

double HydrogenRadials::slater_screening	(	const std::string	symbol,
		const int	n,
		const int	l
	)

return the Slater screening constant for calculating effective nuclear charge

Note: hoping to get a more accurate estimation of hydrogen-like atom radial function, by including many-electron effect in this way

algorithm: https://laney.edu/pinar-alscher/wp-content/uploads/sites/219/2016/04/Slater-rules-revised.pdf

Parameters

n	principal quantum number
l	angular momentum quantum number

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◆ smooth()

void HydrogenRadials::smooth	(	std::vector< double > &	rgrid,
		std::vector< double > &	rvalue,
		const double	sigma = `0.1`
	)

smooth the radial function to avoid high frequency noise in FFT-spherical bessel transform

Parameters

rgrid	radial grid
rvalue	radial function
sigma	sigma of the Gaussian kernel

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◆ unzip_strategy()

std::vector< std::pair< int, int > > HydrogenRadials::unzip_strategy	(	const int	nmax = `0`,
		const std::string	strategy = `"minimal-valence"`
	)

parse the strategy string to get the n, l pairs

Parameters

nmax	maxmium principal quantum number
strategy	strategy string

Returns: a vector of n, l pairs

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Member Data Documentation

◆ assoc_laguerre_

Assoc_Laguerre HydrogenRadials::assoc_laguerre_

private

Associated Laguerre polynomials generator.

The documentation for this class was generated from the following files:

/home/runner/work/abacus-develop/abacus-develop/source/source_basis/module_nao/hydrogen_radials.h
/home/runner/work/abacus-develop/abacus-develop/source/source_basis/module_nao/hydrogen_radials.cpp

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ HydrogenRadials()

◆ ~HydrogenRadials()

Member Function Documentation

◆ build()

◆ clone()

◆ generate_hydrogen_radial_segment()

◆ generate_hydrogen_radial_toconv()

◆ generate_orb()

◆ hydrogen()

◆ mapping_nl_lzeta()

◆ operator=()

◆ radial_norm()

◆ slater_screening()

◆ smooth()

◆ unzip_strategy()

Member Data Documentation

◆ assoc_laguerre_