MADNESS 0.10.1
Public Member Functions | Private Member Functions | Private Attributes | List of all members
madness::LinearSlater Class Reference

A nuclear correlation factor class. More...

#include <correlationfactor.h>

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Public Member Functions

 LinearSlater (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
 
virtual real_function_3d apply_U (const real_function_3d &rhs) const
 apply the regularized potential U_nuc on a given function rhs
 
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
 
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
 
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)
 

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
 

Private Attributes

double a_
 the length scale parameter a
 

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
 
- 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

A nuclear correlation factor class.

The nuclear correlation factor is given by [f R = \prod S_A ; S_A= -Z_A r_{1A} exp(-Z_A r_{1A}) + 1 ]f

Constructor & Destructor Documentation

◆ LinearSlater()

madness::LinearSlater::LinearSlater ( World &  world,
const Molecule &  mol,
const double  a 
)
inline

ctor

Parameters
[in]worldthe world
[in]molmolecule with the sites of the nuclei

References a, madness::Molecule::get_eprec(), madness::print(), madness::World::rank(), and madness::NuclearCorrelationFactor::world.

Member Function Documentation

◆ a_param()

double madness::LinearSlater::a_param ( ) const
inlineprivate

◆ S()

double madness::LinearSlater::S ( const double &  r,
const double &  Z 
) const
inlineprivatevirtual

the nuclear correlation factor

Implements madness::NuclearCorrelationFactor.

References b, and Z.

◆ Sp()

coord_3d madness::LinearSlater::Sp ( const coord_3d &  vr1A,
const double &  Z 
) const
inlineprivatevirtual

radial part first derivative of the nuclear correlation factor

Implements madness::NuclearCorrelationFactor.

References b, madness::NuclearCorrelationFactor::smoothed_unitvec(), and Z.

◆ Spp_div_S()

double madness::LinearSlater::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 b, and Z.

◆ Sr_div_S()

double madness::LinearSlater::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, and Z.

◆ Srr_div_S()

double madness::LinearSlater::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, and Z.

◆ Srrr_div_S()

double madness::LinearSlater::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, and Z.

◆ type()

corrfactype madness::LinearSlater::type ( ) const
inlinevirtual

Implements madness::NuclearCorrelationFactor.

References madness::NuclearCorrelationFactor::LinearSlater.

Member Data Documentation

◆ a_

double madness::LinearSlater::a_
private

the length scale parameter a

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