3.3.12. horton/gbasis/ints.h – Evaluation of integrals of Gaussian basis functions

class GB2Integral

Public Functions

GB2Integral(long max_shell_type)
void reset(long shell_type0, long shell_type1, const double *r0, const double *r1)
virtual void add(double coeff, double alpha0, double alpha1, const double *scales0, const double *scales1) = 0
void cart_to_pure()
const long get_shell_type0() const
const long get_shell_type1() const

Protected Attributes

long shell_type0
long shell_type1
const double *r0
const double *r1
IterPow2 i2p
class GB2OverlapIntegral
#include <ints.h>

Compute the overlap integrals in a Gaussian orbital basis.

Public Functions

GB2OverlapIntegral(long max_shell_type)
virtual void add(double coeff, double alpha0, double alpha1, const double *scales0, const double *scales1)
class GB2KineticIntegral
#include <ints.h>

Compute the kinetic integrals in a Gaussian orbital basis.

Public Functions

GB2KineticIntegral(long max_shell_type)
virtual void add(double coeff, double alpha0, double alpha1, const double *scales0, const double *scales1)
class GB2NuclearAttractionIntegral
#include <ints.h>

Compute the nuclear attraction integrals in a Gaussian orbital basis.

Public Functions

GB2NuclearAttractionIntegral(long max_shell_type, double *charges, double *centers, long ncharge)
~GB2NuclearAttractionIntegral()
virtual void add(double coeff, double alpha0, double alpha1, const double *scales0, const double *scales1)

Private Members

double *charges
double *centers
long ncharge
double *work_g0
double *work_g1
double *work_g2
double *work_boys
class GB2MomentIntegral
#include <ints.h>

Compute the (multipole) moment integrals in a Gaussian orbital basis. < gto_a | (x - C_x)^l (y - C_y)^m (z - C_z)^n | gto_b >.

Public Functions

GB2MomentIntegral(long max_shell_type, long *xyz, double *center)

Initialize Moment integral calculator.

Parameters
  • max_shell_type -

    The highest angular momentum index suported

  • xyz -

    The powers of x,y,z in the integrals (l, m, n).

  • center -

    The center [C_x, C_y, C_z] around which the moment integrals arecomputed

virtual void add(double coeff, double alpha0, double alpha1, const double *scales0, const double *scales1)

Add integrals for a pair of primite shells to the current contraction.

Parameters
  • coeff -

    The contraction coefficient for the current primitive.

  • alpha0 -

    The exponent of the primitive shell 0.

  • alpha1 -

    The exponent of the primitive shell 1.

  • scales0 -

    The normalization constants for the basis functions in primitive shell 0.

  • scales1 -

    The normalization constants for the basis functions in primitive shell 1.

Private Members

long *xyz

Powers for x, y and z of the multipole moment.

double *center

The origin w.r.t. to which the multipole moment is computed.

class GB4Integral
#include <ints.h>

Base class for four-center integrals.

Public Functions

GB4Integral(long max_shell_type)

Initialize a GB4Integral object.

Parameters
  • max_shell_type -

    Highest angular momentum index to be expected in the reset method.

virtual void reset(long shell_type0, long shell_type1, long shell_type2, long shell_type3, const double *r0, const double *r1, const double *r2, const double *r3)

Set internal parameters for a new group of four contractions.

Parameters
  • shell_type0 -

    Angular momentum index for contraction 0.

  • shell_type1 -

    Angular momentum index for contraction 1.

  • shell_type2 -

    Angular momentum index for contraction 2.

  • shell_type3 -

    Angular momentum index for contraction 3.

  • r0 -

    Cartesian coordinates of center 0.

  • r1 -

    Cartesian coordinates of center 1.

  • r2 -

    Cartesian coordinates of center 2.

  • r3 -

    Cartesian coordinates of center 3.

virtual void add(double coeff, double alpha0, double alpha1, double alpha2, double alpha3, const double *scales0, const double *scales1, const double *scales2, const double *scales3) = 0

Add results for a combination of Cartesian primitive shells to the work array.

Parameters
  • coeff -

    Product of the contraction coefficients of the four primitives.

  • alpha0 -

    The exponent of primitive shell 0.

  • alpha1 -

    The exponent of primitive shell 1.

  • alpha2 -

    The exponent of primitive shell 2.

  • alpha3 -

    The exponent of primitive shell 3.

  • scales0 -

    The normalization prefactors for basis functions in primitive shell 0

  • scales1 -

    The normalization prefactors for basis functions in primitive shell 1

  • scales2 -

    The normalization prefactors for basis functions in primitive shell 2

  • scales3 -

    The normalization prefactors for basis functions in primitive shell 3

void cart_to_pure()

Transform the results in the work array from Cartesian to pure functions where needed.

const long get_shell_type0() const

Shell type of contraction 0.

const long get_shell_type1() const

Shell type of contraction 1.

const long get_shell_type2() const

Shell type of contraction 2.

const long get_shell_type3() const

Shell type of contraction 3.

Protected Attributes

long shell_type0

Shell type of contraction 0.

long shell_type1

Shell type of contraction 1.

long shell_type2

Shell type of contraction 2.

long shell_type3

Shell type of contraction 3.

const double *r0

Center of contraction 0.

const double *r1

Center of contraction 1.

const double *r2

Center of contraction 2.

const double *r3

Center of contraction 3.

struct libint_arg_t
#include <ints.h>

Arguments associated with one primitive shell in LibInt conventions.

Public Members

unsigned int am

Shell type in LibInt conventions.

const double *r

Center of a primitive shell.

double alpha

Exponent of a primitive shell.

class GB4IntegralLibInt
#include <ints.h>

Base class for four-center integrals that use LibInt.

Public Functions

GB4IntegralLibInt(long max_shell_type)

Initialize a GB4IntegralLibInt object.

Parameters
  • max_shell_type -

    Highest angular momentum index to be expected in the reset method.

~GB4IntegralLibInt()
virtual void reset(long shell_type0, long shell_type1, long shell_type2, long shell_type3, const double *r0, const double *r1, const double *r2, const double *r3)

Set internal parameters for a new group of four contractions.

See base class for details.

virtual void add(double coeff, double alpha0, double alpha1, double alpha2, double alpha3, const double *scales0, const double *scales1, const double *scales2, const double *scales3)

Add results for a combination of Cartesian primitive shells to the work array.

See base class for details.

virtual void laplace_of_potential(double prefac, double rho, double t, long mmax, double *output) = 0

Evaluate the Laplace transform of the the potential.

For theoretical details and the precise definition of the Laplace transform, we refer to the following paper:

Ahlrichs, R. A simple algebraic derivation of the Obara-Saika scheme for general two-electron interaction potentials. Phys. Chem. Chem. Phys. 8, 3072–3077 (2006). 10.1039/B605188J

For the general definition of this transform, see Eq. (8) in the reference above. Section 5 contains solutions of the Laplace transform for several popular cases.

Parameters
  • prefac -

    Prefactor with which all results in the output array are multiplied.

  • rho -

    See Eq. (3) in Ahlrichs’ paper.

  • t -

    Rescaled distance between the two centers obtained from the application of the Gaussian product theorem. See Eq. (5) in Ahlrichs’ paper.

  • mmax -

    Maximum derivative of the Laplace transform to be considered.

  • output -

    Output array. The size must be at least mmax + 1.

Private Members

Libint_eri_t erieval

LibInt runtime object.

libint_arg_t libint_args[4]

Arguments (shell info) for libint.

long order[4]

Re-ordering of shells for compatibility with LibInt.

double ab[3]

Relative vector from shell 2 to 0 (LibInt order).

double cd[3]

Relative vector from shell 3 to 1 (LibInt order).

double ab2

Norm squared of ab.

double cd2

Norm squared of cd.

class GB4ElectronRepulsionIntegralLibInt
#include <ints.h>

Electron repulsion four-center integrals.

The potential is 1/r.

Public Functions

GB4ElectronRepulsionIntegralLibInt(long max_shell_type)

Initialize a GB4ElectronRepulsionIntegralLibInt object.

Parameters
  • max_shell_type -

    Highest angular momentum index to be expected in the reset method.

virtual void laplace_of_potential(double prefac, double rho, double t, long mmax, double *output)

Evaluate the Laplace transform of the ordinary Coulomb potential.

See Eq. (39) in Ahlrichs’ paper. This is basically a rescaled Boys function.

See base class for more details.

class GB4ErfIntegralLibInt
#include <ints.h>

Short-range electron repulsion four-center integrals.

The potential is erf(mu*r)/r.

Public Functions

GB4ErfIntegralLibInt(long max_shell_type, double mu)

Initialize a GB4ErfIntegralLibInt object.

Parameters
  • max_shell_type -

    Highest angular momentum index to be expected in the reset method.

  • mu -

    The range-separation parameter

virtual void laplace_of_potential(double prefac, double rho, double t, long mmax, double *output)

Evaluate the Laplace transform of the long-range Coulomb potential. (The short-range part is damped away using an error function.) See (52) in Ahlrichs’ paper.

See base class for more details.

const double get_mu() const

The range-separation parameter.

Private Members

double mu

The range-separation parameter.

class GB4GaussIntegralLibInt
#include <ints.h>

Gaussian electron repulsion four-center integrals.

The potential is c exp(-alpha r^2).

Public Functions

GB4GaussIntegralLibInt(long max_shell_type, double c, double alpha)

Initialize a GB4GaussIntegralLibInt object.

Parameters
  • max_shell_type -

    Highest angular momentum index to be expected in the reset method.

  • c -

    Coefficient of the gaussian.

  • alpha -

    Exponential parameter of the gaussian.

virtual void laplace_of_potential(double prefac, double rho, double t, long mmax, double *output)

Evaluate the Laplace transform of the Gaussian potential.

See Ahlrichs’ paper for details. This type of potential is used in the papers of P.M.W Gill et al. and J. Toulouse et al.:

Gill, P. M. W., & Adamson, R. D. (1996). A family of attenuated Coulomb operators. Chem. Phys. Lett., 261(1-2), 105–110. http://doi.org/10.1016/0009-2614(96)00931-1

Toulouse, J., Colonna, F., & Savin, A. (2004). Long-range-short-range separation of the electron-electron interaction in density-functional theory. Phys. Rev. A, 70, 62505. http://doi.org/10.1103/PhysRevA.70.062505

See base class for more details.

const double get_c() const

Coefficient of the gaussian.

const double get_alpha() const

Exponential parameter of the gaussian.

Private Members

double c

Coefficient of the gaussian.

double alpha

Exponential parameter of the gaussian.

class GB4RAlphaIntegralLibInt
#include <ints.h>

Gaussian electron repulsion four-center integrals.

The potential is r^alpha.

Public Functions

GB4RAlphaIntegralLibInt(long max_shell_type, double alpha)

Initialize a GB4RAlphaIntegralLibInt object.

Parameters
  • max_shell_type -

    Highest angular momentum index to be expected in the reset method.

  • alpha -

    The power of r in the potential.

virtual void laplace_of_potential(double prefac, double rho, double t, long mmax, double *output)

Evaluate the Laplace transform of the r^alpha potential. See Eq. (49) in Ahlrichs’ paper.

See base class for more details.

const double get_alpha() const

The power of r.

Private Members

double alpha

The power of r.