A Gaussian basis function used by chemistry electronic structure codes. More...

#include <gaussian.h>

Inheritance diagram for slymer::GaussianFunction:

Collaboration diagram for slymer::GaussianFunction:

Public Member Functions
	GaussianFunction ()
	Default constructor: Make the function 0.

	GaussianFunction (const GaussianType type, const std::array< double, 3 > &center, const double expcoeff)
	Create an uncontracted Gaussian orbital (shortcut to the more general constructor for Gaussian orbitals).

	GaussianFunction (const GaussianType type, const std::array< double, 3 > &center, const std::vector< double > &expcoeff, const std::vector< double > &coeff)
	Create a Gaussian orbital (uncontracted or contracted) from quantum chemistry codes.

double	operator() (const madness::coord_3d &r) const
	Evaluate the Gaussian function at the specified point.

virtual double	operator() (const std::array< double, 3 > &x) const override
	Evaluate the Gaussian function at the specified point.

GaussianFunction	operator* (const double rhs) const
	Multiply the GaussianFunction by a scalar.

GaussianFunction	operator* (const GaussianFunction &rhs) const
	Multiply two GaussianFunctions.

GaussianFunction &	operator*= (const double rhs)
	Multiply the GaussianFunction by a scalar.

GaussianFunction &	operator*= (const GaussianFunction &rhs)
	Multiply the GaussianFunction by another.

GaussianFunction	operator+ (const GaussianFunction &rhs) const
	Add two GaussianFunction objects, resulting in a new one.

GaussianFunction &	operator+= (const GaussianFunction &rhs)
	Add a GaussianFunction to this GaussianFunction.

GaussianFunction	operator- () const
	Additive inverse of the GaussianFunction (deep copy).

GaussianFunction	operator- (const GaussianFunction &rhs) const
	Subtract a GaussianFunction from this one, returning the difference.

GaussianFunction &	operator-= (const GaussianFunction &rhs)
	Subtract a GaussianFunction from this one.

GaussianFunction	operator/ (const double rhs) const
	Divide the GaussianFunction by a scalar.

GaussianFunction &	operator/= (const double rhs)
	Divide the GaussianFunction by a scalar.

Public Member Functions inherited from slymer::BasisFunction
virtual	~BasisFunction ()=default

Public Attributes
std::array< double, 3 >	center
	The center of the gaussian.

std::vector< double >	expcoeff
	The exponent coefficients.

Protected Types
using	TermT = std::pair< double, PrimitiveGaussian >
	Helper class for storing terms in the sum of Gaussian primitives.

Protected Member Functions
void	removeSmallTerms (const double eps=1.e-6)
	Removes terms with very small linear expansion coefficients.

Protected Attributes
std::forward_list< TermT >	terms
	The list of terms in the sum of Gaussian primitives.

Detailed Description

A Gaussian basis function used by chemistry electronic structure codes.

This basis function has the form

$\sum_j c_j x^{l_j} y^{m_j} z^{n_j} \exp[f_j(\vec{x})],$

where $f_j(\vec{x})$ is a quadratic function. Note that this functional form is a bit more general than that used by standard electronic structure codes; we do not require the prinicpal axes of the Gaussian function to be coincident with the x-, y-, and z-axes. This class can also hold/handle any linear combination of primitive Gaussian functions (the exponents and centers do not have to be the same).

Member Typedef Documentation

◆ TermT

using slymer::GaussianFunction::TermT = std::pair<double, PrimitiveGaussian>

protected

Helper class for storing terms in the sum of Gaussian primitives.

Constructor & Destructor Documentation

◆ GaussianFunction() [1/3]

slymer::GaussianFunction::GaussianFunction ( )

inline

Default constructor: Make the function 0.

◆ GaussianFunction() [2/3]

slymer::GaussianFunction::GaussianFunction	(	const GaussianType	type,
		const std::array< double, 3 > &	center,
		const std::vector< double > &	expcoeff,
		const std::vector< double > &	coeff
	)

Create a Gaussian orbital (uncontracted or contracted) from quantum chemistry codes.

Both Cartesian and spherical orbitals are supported. The expcoeff and coeff parameters must be arrays. If the orbital is uncontracted, the arrays will be length 1.

All uncontracted primitive Gaussian orbitals used underneath the GaussianFunction are normalized.

Exceptions

invalid_argument If a non-positive exponential coefficient is passed or if the lengths of expcoeff and coeff are not equal.

Parameters

[in]	type	The orbital type (from enum OrbitalType).
[in]	center	The center of the Gaussian orbital.
[in]	expcoeff	Array of coefficients in the exponents of the primitive Gaussians.
[in]	coeff	Array of linear expansion coefficients of the primitive Gaussians.

References center, expcoeff, removeSmallTerms(), and terms.

◆ GaussianFunction() [3/3]

slymer::GaussianFunction::GaussianFunction	(	const GaussianType	type,
		const std::array< double, 3 > &	center,
		const double	expcoeff
	)

inline

Create an uncontracted Gaussian orbital (shortcut to the more general constructor for Gaussian orbitals).

Parameters

[in]	type	The orbital type (from enum OrbitalType).
[in]	center	The center of the Gaussian orbital.
[in]	expcoeff	The coefficient in the exponent of the primitive Gaussian.

References expcoeff.

Member Function Documentation

◆ operator()() [1/2]

double slymer::GaussianFunction::operator() ( const madness::coord_3d & r ) const

inline

Evaluate the Gaussian function at the specified point.

Parameters

[in] x The point.

Returns: The Gaussian function evaluated at the point x.

References operator()().

◆ operator()() [2/2]

double slymer::GaussianFunction::operator() ( const std::array< double, 3 > & x ) const

overridevirtual

Evaluate the Gaussian function at the specified point.

Parameters

[in] x The point.

Returns: The Gaussian function evaluated at the point x.

Implements slymer::BasisFunction.

References terms.

Referenced by operator()().

◆ operator*() [1/2]

GaussianFunction slymer::GaussianFunction::operator* ( const double rhs ) const

inline

Multiply the GaussianFunction by a scalar.

Parameters

[in] rhs The scalar multiplicative factor.

Returns: The scaled GaussianFunction.

◆ operator*() [2/2]

GaussianFunction slymer::GaussianFunction::operator* ( const GaussianFunction & rhs ) const

Multiply two GaussianFunctions.

Parameters

[in] rhs The right-hand GaussianFunction object.

Returns: The product.

References removeSmallTerms(), and terms.

◆ operator*=() [1/2]

GaussianFunction & slymer::GaussianFunction::operator*= ( const double rhs )

Multiply the GaussianFunction by a scalar.

Parameters

[in] rhs The scalar multiplicative factor.

Returns: This GaussianFunction, which has been scaled.

References removeSmallTerms(), and terms.

Referenced by operator/=().

◆ operator*=() [2/2]

GaussianFunction & slymer::GaussianFunction::operator*= ( const GaussianFunction & rhs )

inline

Multiply the GaussianFunction by another.

Parameters

[in] rhs The right-hand GaussianFunction object.

Returns: This GaussianFunction, which is now the product.

References terms.

◆ operator+()

GaussianFunction slymer::GaussianFunction::operator+ ( const GaussianFunction & rhs ) const

Add two GaussianFunction objects, resulting in a new one.

Parameters

[in] rhs The right-hand GaussianFunction.

Returns: The sum of this GaussianFunction and rhs.

References terms.

◆ operator+=()

GaussianFunction & slymer::GaussianFunction::operator+= ( const GaussianFunction & rhs )

Add a GaussianFunction to this GaussianFunction.

Parameters

[in] rhs The right-hand GaussianFunction.

Returns: The sum of this GaussianFunction and rhs, stored in *this.

References terms.

Referenced by operator-=().

◆ operator-() [1/2]

GaussianFunction slymer::GaussianFunction::operator- ( ) const

Additive inverse of the GaussianFunction (deep copy).

Returns: The negated function.

References terms.

◆ operator-() [2/2]

GaussianFunction slymer::GaussianFunction::operator- ( const GaussianFunction & rhs ) const

inline

Subtract a GaussianFunction from this one, returning the difference.

Parameters

[in] rhs The GaussianFunction to be subtracted.

Returns: The difference of the two GaussianFunction objects.

◆ operator-=()

GaussianFunction & slymer::GaussianFunction::operator-= ( const GaussianFunction & rhs )

inline

Subtract a GaussianFunction from this one.

Parameters

[in] rhs The GaussianFunction to be subtracted.

Returns: This GaussianFunction (the difference).

References operator+=().

◆ operator/()

GaussianFunction slymer::GaussianFunction::operator/ ( const double rhs ) const

inline

Divide the GaussianFunction by a scalar.

Parameters

[in] rhs The scalar factor.

Returns: The scaled GaussianFunction.

◆ operator/=()

GaussianFunction & slymer::GaussianFunction::operator/= ( const double rhs )

inline

Divide the GaussianFunction by a scalar.

Does not check that the scalar is nonzero.

Parameters

[in] rhs The scalar factor.

Returns: This GaussianFunction, which has been scaled.

References operator*=().

◆ removeSmallTerms()

void slymer::GaussianFunction::removeSmallTerms ( const double eps = 1.e-6 )

inlineprotected

Removes terms with very small linear expansion coefficients.

Parameters

[in] eps The threshold for "small". Defaults to 1.e-6.

References std::abs(), and terms.

Referenced by GaussianFunction(), operator*(), and operator*=().

Member Data Documentation

◆ center

std::array<double, 3> slymer::GaussianFunction::center

The center of the gaussian.

Referenced by GaussianFunction().

◆ expcoeff

std::vector<double> slymer::GaussianFunction::expcoeff

The exponent coefficients.

Referenced by GaussianFunction(), GaussianFunction(), and slymer::Gaussian_Functor::special_level().

◆ terms

std::forward_list<TermT> slymer::GaussianFunction::terms

protected

The list of terms in the sum of Gaussian primitives.

Referenced by GaussianFunction(), operator()(), operator*(), operator*=(), operator*=(), operator+(), operator+=(), operator-(), and removeSmallTerms().

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

Public Member Functions

Public Attributes

Protected Types

Protected Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ TermT

Constructor & Destructor Documentation

◆ GaussianFunction() [1/3]

◆ GaussianFunction() [2/3]

◆ GaussianFunction() [3/3]

Member Function Documentation

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ removeSmallTerms()

Member Data Documentation

◆ center

◆ expcoeff

◆ terms