Class GB2AttractionIntegral

Inheritance Relationships

Base Type

Derived Types

Class Documentation

class GB2AttractionIntegral : public GB2Integral

Compute the nuclear attraction integrals in a Gaussian orbital basis.

Subclassed by GB2ErfAttractionIntegral, GB2GaussAttractionIntegral, GB2NuclearAttractionIntegral

Public Functions

GB2AttractionIntegral(long max_shell_type, double *charges, double *centers, long ncharge)

Initialize a GB2AttractionIntegral object.

Parameters
  • max_shell_type: Highest angular momentum index to be expected in the reset method.

~GB2AttractionIntegral()
virtual void add(double coeff, double alpha0, double alpha1, const double *scales0, const double *scales1)

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

Parameters
  • coeff: Product of the contraction coefficients of the two primitives.
  • alpha0: The exponent of primitive shell 0.
  • alpha1: The exponent of primitive shell 1.
  • scales0: The normalization prefactors for basis functions in primitive shell 0
  • scales1: The normalization prefactors for basis functions in primitive shell 1

virtual void laplace_of_potential(double gamma, double arg, long mmax, double *output) = 0

Evaluate the Laplace transform of the the potential applied to nuclear attraction terms.

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
  • gamma: Sum of the exponents of the two gaussian functions involved in the integral. Similar to the first term in Eq. (3) in Ahlrichs’ paper.
  • arg: Rescaled distance between the two centers obtained from the application of the Gaussian product theorem. Equivalent to 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.