ewalena::GaussianTypeOrbital< dim, ValueType > Class Template Reference

Origin-centered Gaussian functions for use in orbital calculations. More...

#include <include/ewalena/numerics/basis_gto.h>

Inheritance diagram for ewalena::GaussianTypeOrbital< dim, ValueType >:

Collaboration diagram for ewalena::GaussianTypeOrbital< dim, ValueType >:

List of all members.

Public Member Functions
ValueType	alpha () const
	GaussianTypeOrbital ()
ValueType	grad (const ewalena::Point< dim, ValueType > &point) const
ValueType	integral (const GaussianTypeOrbital< dim, ValueType > &gaussian_i, const GaussianTypeOrbital< dim, ValueType > &gaussian_j)
ValueType	integral (const GaussianTypeOrbital< dim, ValueType > &gaussian_i, const GaussianTypeOrbital< dim, ValueType > &gaussian_j, const GaussianTypeOrbital< dim, ValueType > &gaussian_k, const GaussianTypeOrbital< dim, ValueType > &gaussian_l)
ValueType	laplacian (const ewalena::Point< dim, ValueType > &point) const
ValueType	laplacian (const GaussianTypeOrbital< dim, ValueType > &gaussian_i, const GaussianTypeOrbital< dim, ValueType > &gaussian_j)
std::string	name () const
void	reinit_alpha (const ValueType &alpha)
ValueType	value (const ewalena::Point< dim, ValueType > &point) const
	~GaussianTypeOrbital ()
Private Attributes
ValueType	__alpha

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Detailed Description

template<int dim, typename ValueType = double>
class ewalena::GaussianTypeOrbital< dim, ValueType >

Origin-centered Gaussian functions for use in orbital calculations.

Simplest possible Gaussian-type orbitals. (This should be reflected similar to way finite elements work in deal.II BasisStaeSystem(GaussianTypeOrbitals<dim>, N).

The shapes are described as tables of factors and coefficients. The factors and coefficient define Gaussian primitives, which needs to be contracted (summed over) to determine a radial orbital. The basis functions possess a usual radial-angular decomposition:

\[ g({ x})=R_l({ r}) Y_{lm}(,)\,,\]

where $Y_{lm}(,)$ is an angular dependent spherical harmonic $(l,m)$ are projection quantum numbers. The function $R_l({ x})=A{ x}^l[-{ x}^2]$ is a radial (orbital) function. The origin-centered Gaussian functions ($g({ x}):=R({ x})$) then have the form:

\[ g({{ x}})=({2}{})^{3}{4} [-{ x}^2] \]

These are normally (ie. almost always) fitted to SlaterTypeOrbitals.

Author:

Toby D. Young 2012.

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Constructor & Destructor Documentation

template<int dim, typename ValueType = double>

ewalena::GaussianTypeOrbital< dim, ValueType >::GaussianTypeOrbital

(

)

[inline]

Constructor. The number of contractions this basis set has must be provided.

template<int dim, typename ValueType = double>

ewalena::GaussianTypeOrbital< dim, ValueType >::~GaussianTypeOrbital

(

)

Destructor.

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Member Function Documentation

template<int dim, typename ValueType = double>

ValueType ewalena::GaussianTypeOrbital< dim, ValueType >::alpha

(

)

const

Return $$.

template<int dim, typename ValueType = double>

ValueType ewalena::GaussianTypeOrbital< dim, ValueType >::grad

(

const ewalena::Point< dim, ValueType > &

point

)

const

Return the gradient of this Gaussian at this point.

template<int dim, typename ValueType = double>

ValueType ewalena::GaussianTypeOrbital< dim, ValueType >::integral	(	const GaussianTypeOrbital< dim, ValueType > &	gaussian_i,
		const GaussianTypeOrbital< dim, ValueType > &	gaussian_j
	)

Return the integral of two Gaussians.

template<int dim, typename ValueType = double>

ValueType ewalena::GaussianTypeOrbital< dim, ValueType >::integral	(	const GaussianTypeOrbital< dim, ValueType > &	gaussian_i,
		const GaussianTypeOrbital< dim, ValueType > &	gaussian_j,
		const GaussianTypeOrbital< dim, ValueType > &	gaussian_k,
		const GaussianTypeOrbital< dim, ValueType > &	gaussian_l
	)

Return the integral of four Gaussians.

template<int dim, typename ValueType = double>

ValueType ewalena::GaussianTypeOrbital< dim, ValueType >::laplacian

(

const ewalena::Point< dim, ValueType > &

point

)

const

Return the Laplacian of this Gaussian at this point.

template<int dim, typename ValueType = double>

ValueType ewalena::GaussianTypeOrbital< dim, ValueType >::laplacian	(	const GaussianTypeOrbital< dim, ValueType > &	gaussian_i,
		const GaussianTypeOrbital< dim, ValueType > &	gaussian_j
	)

Return the integral of two Gaussians.

template<int dim, typename ValueType = double>

std::string ewalena::GaussianTypeOrbital< dim, ValueType >::name

(

)

const [virtual]

Name of this basis state.

Reimplemented from ewalena::BasisBase< dim, ValueType >.

template<int dim, typename ValueType = double>

void ewalena::GaussianTypeOrbital< dim, ValueType >::reinit_alpha

(

const ValueType &

alpha

)

Initialise a (new) constant to this Gaussian-type orbital.

template<int dim, typename ValueType = double>

ValueType ewalena::GaussianTypeOrbital< dim, ValueType >::value

(

const ewalena::Point< dim, ValueType > &

point

)

const [virtual]

Return the value of this Gaussian-type orbital at this point.

Reimplemented from ewalena::BasisBase< dim, ValueType >.

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Member Data Documentation

template<int dim, typename ValueType = double>

ValueType ewalena::GaussianTypeOrbital< dim, ValueType >::__alpha [private]

Variable holding the constant of this orbital.

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

• include/ewalena/numerics/basis_gto.h