A nuclear correlation factor class. More...

#include <correlationfactor.h>

Inheritance diagram for madness::Polynomial< N >:

Collaboration diagram for madness::Polynomial< N >:

[legend]

Public Member Functions
	Polynomial (World &world, const Molecule &mol, const double a)
	ctor
corrfactype	type () const
Public Member Functions inherited from madness::NuclearCorrelationFactor
	NuclearCorrelationFactor (World &world, const Molecule &mol)
	ctor
virtual	~NuclearCorrelationFactor ()
	virtual destructor
const std::vector< size_t > &	all_atoms () const
	indices of all atoms
virtual real_function_3d	apply_U (const real_function_3d &rhs) const
	apply the regularized potential U_nuc on a given function rhs
std::vector< size_t >	atoms_near (const double x, const double y, const double *z, const int npts) const
	atoms whose screening sphere meets the bounding sphere of a set of points
coord_3d	dsmoothed_unitvec (const coord_3d &xyz, const int axis, double smoothing=0.0) const
	derivative of smoothed unit vector wrt the electronic coordinate
virtual real_function_3d	function () const
	return the nuclear correlation factor
void	initialize (const double vtol1)
	initialize the regularized potentials U1 and U2
virtual real_function_3d	inverse () const
	return the inverse nuclear correlation factor
virtual double	screening_radius (const double) const
	distance from nucleus A beyond which its contributions to the functors are negligible
coord_3d	smoothed_unitvec (const coord_3d &xyz, double smoothing=0.0) const
	smoothed unit vector for the computation of the U1 potential
virtual real_function_3d	square () const
	return the square of the nuclear correlation factor
virtual real_function_3d	square_times_V_derivative (const int iatom, const int axis) const
virtual const real_function_3d	U1 (const int axis) const
	return the U1 term of the correlation function
std::vector< real_function_3d >	U1vec () const
	return the U1 functions in a vector
virtual const real_function_3d	U2 () const
	return the U2 term of the correlation function

Private Member Functions
double	a_param () const
double	S (const double &r, const double &Z) const
	the nuclear correlation factor
coord_3d	Sp (const coord_3d &vr1A, const double &Z) const
	radial part first derivative of the nuclear correlation factor
double	Spp_div_S (const double &r, const double &Z) const
	second derivative of the nuclear correlation factor
double	Sr_div_S (const double &r, const double &Z) const
double	Srr_div_S (const double &r, const double &Z) const
double	Srrr_div_S (const double &r, const double &Z) const
double	U2X_spherical (const double &r, const double &Z, const double &rcut) const
	derivative of the U2 potential wrt nuclear coordinate X (spherical part)

Static Private Member Functions
static double	b_param (const double &a)
	the cutoff

Private Attributes
double	a_
	length scale parameter a, default chosen that linear terms in U2 vanish

Additional Inherited Members
Public Types inherited from madness::NuclearCorrelationFactor
enum	corrfactype { None , GradientalGaussSlater , GaussSlater , LinearSlater , Polynomial , Slater , poly4erfc , Two , Adhoc }
typedef std::shared_ptr< FunctionFunctorInterface< double, 3 > >	functorT
Static Public Attributes inherited from madness::NuclearCorrelationFactor
static constexpr int	ncf_special_level =15
	projection depth of the factor's functions at the nuclei
Protected Attributes inherited from madness::NuclearCorrelationFactor
std::vector< real_function_3d >	U1_function
	the three components of the U1 potential
real_function_3d	U2_function
	the purely local U2 potential, having absorbed the nuclear pot V_nuc

Detailed Description

template<std::size_t N>
class madness::Polynomial< N >

A nuclear correlation factor class.

should reduce to quartic for N=4

Template Parameters

N	the exponent of the polynomial

Constructor & Destructor Documentation

◆ Polynomial()

template<std::size_t N>

madness::Polynomial< N >::Polynomial	(	World &	world,
		const Molecule &	mol,
		const double	a )

inline

ctor

Parameters

[in]	world	the world
[in]	mol	molecule with the sites of the nuclei

length scale parameter a, default chosen that linear terms in U2 vanish

References madness::NuclearCorrelationFactor::NuclearCorrelationFactor(), a, a_, N, and madness::NuclearCorrelationFactor::world.

Member Function Documentation

◆ a_param()

template<std::size_t N>

double madness::Polynomial< N >::a_param ( ) const

inlineprivate

References a_.

Referenced by S(), Sp(), Spp_div_S(), Sr_div_S(), Srr_div_S(), Srrr_div_S(), and U2X_spherical().

◆ b_param()

template<std::size_t N>

double madness::Polynomial< N >::b_param ( const double & a )

inlinestaticprivate

the cutoff

References a, and N.

Referenced by S(), Sp(), Spp_div_S(), Sr_div_S(), Srr_div_S(), and Srrr_div_S().

◆ S()

template<std::size_t N>

double madness::Polynomial< N >::S	(	const double &	r,
		const double &	Z ) const

inlineprivatevirtual

the nuclear correlation factor

Implements madness::NuclearCorrelationFactor.

References a, a_param(), madness::arg(), b, b_param(), madness::power(), and Z.

◆ Sp()

template<std::size_t N>

coord_3d madness::Polynomial< N >::Sp	(	const coord_3d &	vr1A,
		const double &	Z ) const

inlineprivatevirtual

radial part first derivative of the nuclear correlation factor

Implements madness::NuclearCorrelationFactor.

References a, a_param(), b, b_param(), madness::Vector< T, N >::normf(), madness::power(), madness::NuclearCorrelationFactor::smoothed_unitvec(), and Z.

◆ Spp_div_S()

template<std::size_t N>

double madness::Polynomial< N >::Spp_div_S	(	const double &	r,
		const double &	Z ) const

inlineprivatevirtual

second derivative of the nuclear correlation factor

-1/2 S"/S - Z/r

Implements madness::NuclearCorrelationFactor.

References a, a_param(), b, b_param(), N, madness::power(), and Z.

◆ Sr_div_S()

template<std::size_t N>

double madness::Polynomial< N >::Sr_div_S	(	const double &	r,
		const double &	Z ) const

inlineprivatevirtual

first derivative of the NCF with respect to the relative distance rho

$\‍[ \frac{\partial S(\rho)}{\partial \rho} \frac{1}{S(\rho)} \‍]$

where the distance of the electron to the nucleus A is given by

$\‍[ \rho = |\vec r - \vec R_A | \‍]$

Implements madness::NuclearCorrelationFactor.

References a, a_param(), b, b_param(), N, madness::power(), and Z.

◆ Srr_div_S()

template<std::size_t N>

double madness::Polynomial< N >::Srr_div_S	(	const double &	r,
		const double &	Z ) const

inlineprivatevirtual

second derivative of the NCF with respect to the relative distance rho

$\‍[ \frac{\partial^2 S(\rho)}{\partial \rho^2} \frac{1}{S(\rho)} \‍]$

where the distance of the electron to the nucleus A is given by

$\‍[ \rho = |\vec r - \vec R_A | \‍]$

Implements madness::NuclearCorrelationFactor.

References a, a_param(), b, b_param(), N, madness::power(), and Z.

◆ Srrr_div_S()

template<std::size_t N>

double madness::Polynomial< N >::Srrr_div_S	(	const double &	r,
		const double &	Z ) const

inlineprivatevirtual

third derivative of the NCF with respect to the relative distance rho

$\‍[ \frac{\partial^3 S(\rho)}{\partial \rho^3} \frac{1}{S(\rho)} \‍]$

where the distance of the electron to the nucleus A is given by

$\‍[ \rho = |\vec r - \vec R_A | \‍]$

Implements madness::NuclearCorrelationFactor.

References a, a_param(), b, b_param(), N, madness::power(), madness::power< 2 >(), and Z.

◆ type()

template<std::size_t N>

corrfactype madness::Polynomial< N >::type ( ) const

inlinevirtual

Implements madness::NuclearCorrelationFactor.

References madness::NuclearCorrelationFactor::Polynomial.

◆ U2X_spherical()

template<std::size_t N>

double madness::Polynomial< N >::U2X_spherical	(	const double &	r,
		const double &	Z,
		const double &	rcut ) const

inlineprivatevirtual

derivative of the U2 potential wrt nuclear coordinate X (spherical part)

need to reimplement this for all derived classes due to the range for r -> 0, where the singular terms cancel. With

$\‍[ \rho = \left| \vec r- \vec R_A \right| \‍]$

returns the term in the parenthesis without the the derivative of rho

$\‍[\frac{\partial U_2}{\partial X_A} = \frac{\partial \rho}{\partial X} \left(-\frac{1}{2}\frac{S''' S - S'' S'}{S^2} + \frac{1}{\rho^2}\frac{S'}{S} - \frac{1}{\rho} \frac{S''S - S'^2}{S^2} + \frac{Z_A}{\rho^2}\right) \‍]$