ABC for the nuclear correlation factors. More...

#include <correlationfactor.h>

Inheritance diagram for madness::NuclearCorrelationFactor:

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Collaboration diagram for madness::NuclearCorrelationFactor:

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Classes
class	R_functor
class	RX_functor
	compute the derivative of R wrt the displacement of atom A, coord axis More...
class	square_times_V_derivative_functor
class	square_times_V_functor
class	U1_atomic_functor
	U1 functor for a specific atom. More...
class	U1_dot_U1_functor
	functor for a local U1 dot U1 potential More...
class	U1_functor
	functor for the local part of the U1 potential – NOTE THE SIGN More...
class	U1X_functor
	compute the derivative of U1 wrt the displacement of atom A, coord axis More...
class	U2_atomic_functor
	U2 functor for a specific atom. More...
class	U2_functor
class	U2X_functor
	compute the derivative of U2 wrt the displacement of atom A More...
class	U3_atomic_functor
	U3 functor for a specific atom. More...
class	U3_functor
class	U3X_functor
	compute the derivative of U3 wrt the displacement of atom A, coord axis More...

Public Types
enum	corrfactype { None , GradientalGaussSlater , GaussSlater , LinearSlater , Polynomial , Slater , poly4erfc , Two , Adhoc }
typedef std::shared_ptr< FunctionFunctorInterface< double, 3 > >	functorT

Public Member Functions
	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 double	Sr_div_S (const double &r, const double &Z) const =0
virtual double	Srr_div_S (const double &r, const double &Z) const =0
virtual double	Srrr_div_S (const double &r, const double &Z) const =0
virtual corrfactype	type () const =0
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
virtual 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 Public Attributes
static constexpr int	ncf_special_level =15
	projection depth of the factor's functions at the nuclei

Protected Attributes
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

Private Member Functions
virtual double	S (const double &r, const double &Z) const =0
	the correlation factor S wrt a given atom
virtual coord_3d	Sp (const coord_3d &vr1A, const double &Z) const =0
	the partial derivative of correlation factor S' wrt the cartesian coordinates
virtual double	Spp_div_S (const double &r, const double &Z) const =0
	the regularized potential wrt a given atom wrt the cartesian coordinate

Private Attributes
std::vector< size_t >	all_atoms_
double	eprec
	smoothing of the potential/step function
const Molecule &	molecule
	the molecule
double	vtol
	the threshold for initial projection
World &	world
	the world

Detailed Description

ABC for the nuclear correlation factors.

Member Typedef Documentation

◆ functorT

typedef std::shared_ptr< FunctionFunctorInterface<double,3> > madness::NuclearCorrelationFactor::functorT

Member Enumeration Documentation

◆ corrfactype

enum madness::NuclearCorrelationFactor::corrfactype

Enumerator
None
GradientalGaussSlater
GaussSlater
LinearSlater
Polynomial
Slater
poly4erfc
Two
Adhoc

Constructor & Destructor Documentation

◆ NuclearCorrelationFactor()

madness::NuclearCorrelationFactor::NuclearCorrelationFactor	(	World &	world,
		const Molecule &	mol )

inline

ctor

Parameters

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

References all_atoms_, eprec, molecule, vtol, and world.

◆ ~NuclearCorrelationFactor()

virtual madness::NuclearCorrelationFactor::~NuclearCorrelationFactor ( )

inlinevirtual

virtual destructor

Member Function Documentation

◆ all_atoms()

const std::vector< size_t > & madness::NuclearCorrelationFactor::all_atoms ( ) const

inline

indices of all atoms

References all_atoms_.

◆ apply_U()

virtual real_function_3d madness::NuclearCorrelationFactor::apply_U ( const real_function_3d & rhs ) const

inlinevirtual

apply the regularized potential U_nuc on a given function rhs

Reimplemented in madness::PseudoNuclearCorrelationFactor.

References axis, madness::Function< T, NDIM >::compress(), D, madness::free_space_derivative(), madness::Function< T, NDIM >::truncate(), madness::truncate(), U1(), U2(), and world.

◆ atoms_near()

std::vector< size_t > madness::NuclearCorrelationFactor::atoms_near	(	const double *	x,
		const double *	y,
		const double *	z,
		const int	npts ) const

inline

atoms whose screening sphere meets the bounding sphere of a set of points

The projection hands a functor all quadrature points of one box at once; an atom screened out here is beyond its screening radius at every one of them.

References d, madness::Atom::get_coords(), lo, molecule, madness::Vector< T, N >::normf(), npts, p(), madness::Atom::q, and screening_radius().

◆ dsmoothed_unitvec()

coord_3d madness::NuclearCorrelationFactor::dsmoothed_unitvec	(	const coord_3d &	xyz,
		const int	axis,
		double	smoothing = 0.0 ) const

inline

derivative of smoothed unit vector wrt the electronic coordinate

note the sign change for exchanging nuclear and electronic coordinates

$\‍[ \frac{\partial \vec n}{\partial x} = -\frac{\partial \vec n}{\partial X} \‍]$

the derivative wrt x is given by

$\‍[\frac{\partial\vec n}{\partial x} = \left\{\frac{\left(r^2-x^2\right) \mathrm{erf}\left(\frac{r}{s}\right)}{r^3} +\frac{2 x^2 e^{-\frac{r^2}{s^2}}}{\sqrt{\pi } r^2 s}, x y \left(\frac{2 e^{-\frac{r^2}{s^2}}}{\sqrt{\pi } r^2 s} -\frac{\mathrm{erf}\left(\frac{r}{s}\right)}{r^3}\right), x z \left(\frac{2 e^{-\frac{r^2}{s^2}}}{\sqrt{\pi } r^2 s} -\frac{\mathrm{erf}\left(\frac{r}{s}\right)}{r^3}\right)\right\} \‍]$

References axis, eprec, madness::Vector< T, N >::normf(), p(), madness::constants::pi, and madness::r2().

◆ function()

virtual real_function_3d madness::NuclearCorrelationFactor::function ( ) const

inlinevirtual

return the nuclear correlation factor

References madness::FunctionFactory< T, NDIM >::functor(), ncf_special_level, madness::FunctionFactory< T, NDIM >::special_level(), madness::FunctionFactory< T, NDIM >::thresh(), madness::FunctionFactory< T, NDIM >::truncate_on_project(), vtol, and world.

◆ initialize()

void madness::NuclearCorrelationFactor::initialize ( const double vtol1 )

inline

initialize the regularized potentials U1 and U2

References axis, madness::FunctionDefaults< NDIM >::special_level, madness::FunctionDefaults< NDIM >::thresh, madness::FunctionDefaults< NDIM >::truncate_on_project, madness::FunctionFactory< T, NDIM >::functor(), madness::FunctionDefaults< NDIM >::get_thresh(), ncf_special_level, madness::Function< T, NDIM >::set_thresh(), madness::FunctionFactory< T, NDIM >::special_level(), madness::FunctionFactory< T, NDIM >::thresh(), madness::FunctionFactory< T, NDIM >::truncate_on_project(), U1_function, U2_function, vtol, and world.

◆ inverse()

virtual real_function_3d madness::NuclearCorrelationFactor::inverse ( ) const

inlinevirtual

return the inverse nuclear correlation factor

References madness::FunctionFactory< T, NDIM >::functor(), ncf_special_level, madness::FunctionFactory< T, NDIM >::special_level(), madness::FunctionFactory< T, NDIM >::thresh(), madness::FunctionFactory< T, NDIM >::truncate_on_project(), vtol, and world.

◆ S()

virtual double madness::NuclearCorrelationFactor::S	(	const double &	r,
		const double &	Z ) const

privatepure virtual

the correlation factor S wrt a given atom

Parameters

[in]	r	the distance of the req'd coord to the nucleus
[in]	Z	the nuclear charge

Returns: the nuclear correlation factor S_A(r_1A)

Implemented in madness::AdhocNuclearCorrelationFactor, madness::GaussSlater, madness::GradientalGaussSlater, madness::LinearSlater, madness::poly4erfc, madness::Polynomial< N >, madness::PseudoNuclearCorrelationFactor, and madness::Slater.

References Z.

◆ screening_radius()

virtual double madness::NuclearCorrelationFactor::screening_radius ( const double ) const

inlinevirtual

distance from nucleus A beyond which its contributions to the functors are negligible

A factor that returns a finite radius guarantees that beyond it S_A - 1 and S'_A/S_A are below ~1e-14 relative to their magnitude at the nucleus, and that S''_A/S_A equals the Coulomb tail -Z_A/r to the same accuracy. Infinite (the default) keeps every atom in every term.

Reimplemented in madness::Slater.

Referenced by atoms_near().

◆ smoothed_unitvec()

coord_3d madness::NuclearCorrelationFactor::smoothed_unitvec	(	const coord_3d &	xyz,
		double	smoothing = 0.0 ) const

inline

smoothed unit vector for the computation of the U1 potential

note the identity for exchanging nuclear and electronic coordinates (there is a sign change, unlike for the smoothed potential)

$\‍[ \vec n = \frac{\partial \rho}{\partial x} = -\frac{\partial \rho}{\partial X} \‍]$

$\‍[\vec n = \left\{\frac{x \mathrm{erf}\left(\frac{r}{s}\right)}{r}, \frac{y \mathrm{erf}\left(\frac{r}{s}\right)}{r}, \frac{z \mathrm{erf}\left(\frac{r}{s}\right)}{r}\right\} \‍]$

References eprec, molecule, madness::Vector< T, N >::normf(), madness::constants::pi, and xi.

Referenced by madness::GaussSlater::Sp(), madness::GradientalGaussSlater::Sp(), madness::LinearSlater::Sp(), madness::poly4erfc::Sp(), madness::Polynomial< N >::Sp(), and madness::Slater::Sp().

◆ Sp()

virtual coord_3d madness::NuclearCorrelationFactor::Sp	(	const coord_3d &	vr1A,
		const double &	Z ) const

privatepure virtual

the partial derivative of correlation factor S' wrt the cartesian coordinates

Parameters

[in]	vr1A	the vector of the req'd coord to the nucleus
[in]	Z	the nuclear charge

Returns: the gradient of the nuclear correlation factor S'_A(r_1A)

Implemented in madness::AdhocNuclearCorrelationFactor, madness::GaussSlater, madness::GradientalGaussSlater, madness::LinearSlater, madness::poly4erfc, madness::Polynomial< N >, madness::PseudoNuclearCorrelationFactor, and madness::Slater.

References Z.

◆ Spp_div_S()

virtual double madness::NuclearCorrelationFactor::Spp_div_S	(	const double &	r,
		const double &	Z ) const

privatepure virtual

the regularized potential wrt a given atom wrt the cartesian coordinate

S" is the Cartesian Laplacian applied on the NCF. Note the difference to Srr_div_S, which is the second derivative wrt the distance rho. this is: -S"/S - Z/r

Parameters

[in]	r	the distance of the req'd coord to the nucleus
[in]	Z	the nuclear charge

Returns: the Laplacian of the nuclear correlation factor divided by the correlation factor minus the nuclear potential

Implemented in madness::AdhocNuclearCorrelationFactor, madness::GaussSlater, madness::GradientalGaussSlater, madness::LinearSlater, madness::poly4erfc, madness::Polynomial< N >, madness::PseudoNuclearCorrelationFactor, and madness::Slater.

References Z.

◆ square()

virtual real_function_3d madness::NuclearCorrelationFactor::square ( ) const

inlinevirtual

return the square of the nuclear correlation factor

References madness::FunctionFactory< T, NDIM >::functor(), ncf_special_level, R2, madness::FunctionFactory< T, NDIM >::special_level(), madness::FunctionFactory< T, NDIM >::thresh(), madness::FunctionFactory< T, NDIM >::truncate_on_project(), vtol, and world.

◆ square_times_V_derivative()

virtual real_function_3d madness::NuclearCorrelationFactor::square_times_V_derivative	(	const int	iatom,
		const int	axis ) const

inlinevirtual

return the square of the nuclear correlation factor multiplied with the derivative of the nuclear potential for the specified atom

Returns: R^2 * \frac{\partial Z_A/r_{1A}}{\partial X_A}

References axis, madness::func(), madness::FunctionFactory< T, NDIM >::functor(), molecule, ncf_special_level, R2, madness::FunctionFactory< T, NDIM >::special_level(), madness::FunctionFactory< T, NDIM >::thresh(), madness::FunctionFactory< T, NDIM >::truncate_on_project(), vtol, and world.

◆ Sr_div_S()

virtual double madness::NuclearCorrelationFactor::Sr_div_S	(	const double &	r,
		const double &	Z ) const

pure virtual

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

$\‍[ \rho = |\vec r - \vec R_A | \‍]$

Implemented in madness::AdhocNuclearCorrelationFactor, madness::GaussSlater, madness::GradientalGaussSlater, madness::LinearSlater, madness::poly4erfc, madness::Polynomial< N >, madness::PseudoNuclearCorrelationFactor, and madness::Slater.

References Z.

Referenced by madness::GaussSlater::U2X_spherical(), madness::GradientalGaussSlater::U2X_spherical(), madness::Polynomial< N >::U2X_spherical(), and madness::Slater::U2X_spherical().

◆ Srr_div_S()

virtual double madness::NuclearCorrelationFactor::Srr_div_S	(	const double &	r,
		const double &	Z ) const

pure virtual

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

$\‍[ \rho = |\vec r - \vec R_A | \‍]$

Implemented in madness::AdhocNuclearCorrelationFactor, madness::GaussSlater, madness::GradientalGaussSlater, madness::LinearSlater, madness::poly4erfc, madness::Polynomial< N >, madness::PseudoNuclearCorrelationFactor, and madness::Slater.

References Z.

Referenced by madness::GaussSlater::U2X_spherical(), madness::GradientalGaussSlater::U2X_spherical(), madness::Polynomial< N >::U2X_spherical(), and madness::Slater::U2X_spherical().

◆ Srrr_div_S()

virtual double madness::NuclearCorrelationFactor::Srrr_div_S	(	const double &	r,
		const double &	Z ) const

pure virtual

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

$\‍[ \rho = |\vec r - \vec R_A | \‍]$

Implemented in madness::AdhocNuclearCorrelationFactor, madness::GaussSlater, madness::GradientalGaussSlater, madness::LinearSlater, madness::poly4erfc, madness::Polynomial< N >, madness::PseudoNuclearCorrelationFactor, and madness::Slater.

References Z.

Referenced by madness::GaussSlater::U2X_spherical(), madness::GradientalGaussSlater::U2X_spherical(), madness::Polynomial< N >::U2X_spherical(), and madness::Slater::U2X_spherical().

◆ type()

virtual corrfactype madness::NuclearCorrelationFactor::type ( ) const

pure virtual

Implemented in madness::AdhocNuclearCorrelationFactor, madness::GaussSlater, madness::GradientalGaussSlater, madness::LinearSlater, madness::poly4erfc, madness::Polynomial< N >, madness::PseudoNuclearCorrelationFactor, and madness::Slater.

◆ U1()

virtual const real_function_3d madness::NuclearCorrelationFactor::U1 ( const int axis ) const

inlinevirtual

return the U1 term of the correlation function

References axis, and U1_function.

Referenced by madness::AdhocNuclearCorrelationFactor::AdhocNuclearCorrelationFactor(), and apply_U().

◆ U1vec()

std::vector< real_function_3d > madness::NuclearCorrelationFactor::U1vec ( ) const

inline

return the U1 functions in a vector

References U1_function.

◆ U2()

virtual const real_function_3d madness::NuclearCorrelationFactor::U2 ( ) const

inlinevirtual

return the U2 term of the correlation function

Reimplemented in madness::PseudoNuclearCorrelationFactor.

References U2_function.

Referenced by madness::AdhocNuclearCorrelationFactor::AdhocNuclearCorrelationFactor(), and apply_U().

◆ U2X_spherical()

virtual double madness::NuclearCorrelationFactor::U2X_spherical	(	const double &	r,
		const double &	Z,
		const double &	rcut ) const

inlinevirtual

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

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

Reimplemented in madness::GaussSlater, madness::GradientalGaussSlater, madness::poly4erfc, madness::Polynomial< N >, madness::PseudoNuclearCorrelationFactor, and madness::Slater.

References MADNESS_EXCEPTION, madness::print(), rcut, world, and Z.

Member Data Documentation

◆ all_atoms_

std::vector<size_t> madness::NuclearCorrelationFactor::all_atoms_

private

Referenced by NuclearCorrelationFactor(), and all_atoms().

◆ eprec

double madness::NuclearCorrelationFactor::eprec

private

smoothing of the potential/step function

Referenced by NuclearCorrelationFactor(), dsmoothed_unitvec(), and smoothed_unitvec().

◆ molecule

const Molecule& madness::NuclearCorrelationFactor::molecule

private

the molecule

Referenced by NuclearCorrelationFactor(), madness::NuclearCorrelationFactor::RX_functor::RX_functor(), madness::NuclearCorrelationFactor::U1X_functor::U1X_functor(), atoms_near(), smoothed_unitvec(), and square_times_V_derivative().

◆ ncf_special_level

int madness::NuclearCorrelationFactor::ncf_special_level =15

staticconstexpr

projection depth of the factor's functions at the nuclei

The functors' default (6) can miss the exp(-a Z r) features, of width 1/(aZ), at a loose threshold for Z above ~30: on NBr3 and PBr3 the k6 rung then starts hundreds of hartree off and never converges. 15 is what the nuclear-potential functors use (potentialmanager.h); it costs seconds per rung.

Referenced by madness::NemoBase::construct_nuclear_correlation_factor(), function(), initialize(), inverse(), square(), and square_times_V_derivative().

◆ U1_function

std::vector<real_function_3d> madness::NuclearCorrelationFactor::U1_function

protected

the three components of the U1 potential

Referenced by madness::AdhocNuclearCorrelationFactor::AdhocNuclearCorrelationFactor(), initialize(), U1(), and U1vec().

◆ U2_function

real_function_3d madness::NuclearCorrelationFactor::U2_function

protected

the purely local U2 potential, having absorbed the nuclear pot V_nuc

Referenced by madness::AdhocNuclearCorrelationFactor::AdhocNuclearCorrelationFactor(), initialize(), and U2().

◆ vtol

double madness::NuclearCorrelationFactor::vtol

private

the threshold for initial projection

Referenced by NuclearCorrelationFactor(), function(), initialize(), inverse(), square(), and square_times_V_derivative().

◆ world

World& madness::NuclearCorrelationFactor::world

private

the world

Referenced by madness::AdhocNuclearCorrelationFactor::AdhocNuclearCorrelationFactor(), madness::GaussSlater::GaussSlater(), madness::GradientalGaussSlater::GradientalGaussSlater(), madness::LinearSlater::LinearSlater(), NuclearCorrelationFactor(), madness::poly4erfc::poly4erfc(), madness::Polynomial< N >::Polynomial(), madness::PseudoNuclearCorrelationFactor::PseudoNuclearCorrelationFactor(), madness::Slater::Slater(), apply_U(), function(), initialize(), inverse(), square(), square_times_V_derivative(), and U2X_spherical().

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

correlationfactor.h

Classes

Public Types

Public Member Functions

Static Public Attributes

Protected Attributes

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ functorT

Member Enumeration Documentation

◆ corrfactype

Constructor & Destructor Documentation

◆ NuclearCorrelationFactor()

◆ ~NuclearCorrelationFactor()

Member Function Documentation

◆ all_atoms()

◆ apply_U()

◆ atoms_near()

◆ dsmoothed_unitvec()

◆ function()

◆ initialize()

◆ inverse()

◆ S()

◆ screening_radius()

◆ smoothed_unitvec()

◆ Sp()

◆ Spp_div_S()

◆ square()

◆ square_times_V_derivative()

◆ Sr_div_S()

◆ Srr_div_S()

◆ Srrr_div_S()

◆ type()

◆ U1()

◆ U1vec()

◆ U2()

◆ U2X_spherical()

Member Data Documentation

◆ all_atoms_

◆ eprec

◆ molecule

◆ ncf_special_level

◆ U1_function

◆ U2_function

◆ vtol

◆ world