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Public Member Functions | Private Member Functions | Private Attributes | List of all members
TwoCenterIntegrator Class Reference

A class to compute two-center integrals. More...

#include <two_center_integrator.h>

Collaboration diagram for TwoCenterIntegrator:

Public Member Functions

 TwoCenterIntegrator ()
 
 TwoCenterIntegrator (const TwoCenterIntegrator &)=delete
 
TwoCenterIntegrator & operator= (const TwoCenterIntegrator &)=delete
 
 ~TwoCenterIntegrator ()
 
void tabulate (const RadialCollection &bra, const RadialCollection &ket, const char op, const int nr, const double cutoff)
 Tabulates the radial part of a two-center integral.
 
void calculate (const int itype1, const int l1, const int izeta1, const int m1, const int itype2, const int l2, const int izeta2, const int m2, const ModuleBase::Vector3< double > &vR, double *out=nullptr, double *grad_out=nullptr) const
 Compute the two-center integrals.
 
void snap (const int itype1, const int l1, const int izeta1, const int m1, const int itype2, const ModuleBase::Vector3< double > &vR, const bool deriv, std::vector< std::vector< double > > &out) const
 Compute a batch of two-center integrals.
 
size_t table_memory () const
 Returns the amount of heap memory used by table_ (in bytes).
 

Private Member Functions

int ylm_index (const int l, const int m) const
 Returns the index of (l,m) in the array of spherical harmonics.
 

Private Attributes

bool is_tabulated_
 
char op_
 
TwoCenterTable table_
 

Detailed Description

A class to compute two-center integrals.

This class computes two-center integrals 

                /    
         I(R) = | dr phi1(r) (op) phi2(r - R)
                /

as well as their gradients, where op is 1 (overlap) or minus Laplacian (kinetic), and phi1, phi2 are "atomic-orbital-like" functions of the form 

         phi(r) = chi(|r|) * Ylm(r/|r|)

where chi is some numerical radial function and Ylm is some real spherical harmonics.

This class is designed to efficiently compute the two-center integrals between two "collections" of the above functions with various R, e.g., the overlap integrals between all numerical atomic orbitals and all Kleinman-Bylander nonlocal projectors, the overlap & kinetic integrals between all numerical atomic orbitals, etc. This is done by tabulating the radial part of the integrals on an r-space grid and the real Gaunt coefficients in advance.

See the developer's document for more details.

Constructor & Destructor Documentation

◆ TwoCenterIntegrator() [1/2]

TwoCenterIntegrator::TwoCenterIntegrator ( )

◆ TwoCenterIntegrator() [2/2]

TwoCenterIntegrator::TwoCenterIntegrator ( const TwoCenterIntegrator &  )
delete

◆ ~TwoCenterIntegrator()

TwoCenterIntegrator::~TwoCenterIntegrator ( )
inline

Member Function Documentation

◆ calculate()

void TwoCenterIntegrator::calculate ( const int  itype1,
const int  l1,
const int  izeta1,
const int  m1,
const int  itype2,
const int  l2,
const int  izeta2,
const int  m2,
const ModuleBase::Vector3< double > &  vR,
double *  out = nullptr,
double *  grad_out = nullptr 
) const

Compute the two-center integrals.

This function calculates the two-center integral 

                /    
         I(R) = | dr phi1(r) (op_) phi2(r - R)
                /

or its gradient by using the tabulated radial part and real Gaunt coefficients.

Parameters
[in]itype1Element index of orbital 1.
[in]l1Angular momentum of orbital 1.
[in]izeta1Zeta number of orbital 1.
[in]m1Magnetic quantum number of orbital 1.
[in]itype2Element index of orbital 2.
[in]l2Angular momentum of orbital 2.
[in]izeta2Zeta number of orbital 2.
[in]m2Magnetic quantum number of orbital 2.
[in]vRR2 - R1.
[out]outTwo-center integral. The integral will not be computed if out is nullptr.
[out]grad_outGradient of the integral. grad_out[0], grad_out[1] and grad_out[2] are the x, y, z components of the gradient. The gradient will not be computed if grad_out is nullptr.
Note
out and grad_out cannot be both nullptr.
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◆ operator=()

TwoCenterIntegrator & TwoCenterIntegrator::operator= ( const TwoCenterIntegrator &  )
delete

◆ snap()

void TwoCenterIntegrator::snap ( const int  itype1,
const int  l1,
const int  izeta1,
const int  m1,
const int  itype2,
const ModuleBase::Vector3< double > &  vR,
const bool  deriv,
std::vector< std::vector< double > > &  out 
) const

Compute a batch of two-center integrals.

This function calculates the two-center integrals (and optionally their gradients) between one orbital and all orbitals of a certain type from the other collection.

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◆ table_memory()

size_t TwoCenterIntegrator::table_memory ( ) const
inline

Returns the amount of heap memory used by table_ (in bytes).

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◆ tabulate()

void TwoCenterIntegrator::tabulate ( const RadialCollection &  bra,
const RadialCollection &  ket,
const char  op,
const int  nr,
const double  cutoff 
)

Tabulates the radial part of a two-center integral.

Parameters
[in]braThe radial functions of the first collection.
[in]ketThe radial functions of the second collection.
[in]opOperator, could be 'S' or 'T'.
[in]nrNumber of r-space grid points.
[in]cutoffr-space cutoff radius.
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◆ ylm_index()

int TwoCenterIntegrator::ylm_index ( const int  l,
const int  m 
) const
private

Returns the index of (l,m) in the array of spherical harmonics.

Spherical harmonics in ABACUS are stored in the following order:

index 0 1 2 3 4 5 6 7 8 9 10 11 12 ... l 0 1 1 1 2 2 2 2 2 3 3 3 3 ... m 0 0 1 -1 0 1 -1 2 -2 0 1 -1 2 ...

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Member Data Documentation

◆ is_tabulated_

bool TwoCenterIntegrator::is_tabulated_
private

◆ op_

char TwoCenterIntegrator::op_
private

◆ table_

TwoCenterTable TwoCenterIntegrator::table_
private
The documentation for this class was generated from the following files:
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