operator class for the handling of DFT exchange-correlation functionals More...

#include <SCFOperators.h>

Inheritance diagram for madness::XCOperator< T, NDIM >:

Collaboration diagram for madness::XCOperator< T, NDIM >:

[legend]

Classes
struct	expme
	simple structure to take the pointwise exponential of a function, shifted by +14 More...

struct	logme
	simple structure to take the pointwise logarithm of a function, shifted by +14 More...

Public Member Functions
	XCOperator (World &world)
	default ctor without information about the XC functional More...

	XCOperator (World &world, const Nemo *nemo, int ispin=0)
	ctor with a Nemo calculation, will initialize the necessary intermediates More...

	XCOperator (World &world, const Nemo *scf, const real_function_3d &arho, const real_function_3d &brho, int ispin=0)
	ctor with an Nemo calculation, will initialize the necessary intermediates More...

	XCOperator (World &world, const SCF *scf, const real_function_3d &arho, const real_function_3d &brho, int ispin=0, std::string deriv="abgv")
	ctor with an SCF calculation, will initialize the necessary intermediates More...

	XCOperator (World &world, const SCF *scf, int ispin=0, std::string deriv="abgv")
	ctor with an SCF calculation, will initialize the necessary intermediates More...

	XCOperator (World &world, std::string xc_data, const bool spin_polarized, const real_function_3d &arho, const real_function_3d &brho, std::string deriv="abgv")
	custom ctor with information about the XC functional More...

real_function_3d	apply_xc_kernel (const real_function_3d &density, const vecfuncT grad_dens_pt=vecfuncT()) const
	construct the xc kernel and apply it directly on the (response) density More...

double	compute_xc_energy () const
	compute the xc energy using the precomputed intermediates vf and delrho More...

std::string	info () const
	print some information about this operator More...

real_function_3d	make_xc_potential () const
	return the local xc potential More...

T	operator() (const Function< T, NDIM > &bra, const Function< T, NDIM > &ket) const
	compute the matrix element <bra \| op \| ket> More...

Function< T, NDIM >	operator() (const Function< T, NDIM > &ket) const
	apply the xc potential on an orbitals More...

std::vector< Function< T, NDIM > >	operator() (const std::vector< Function< T, NDIM > > &vket) const
	apply the xc potential on a set of orbitals More...

Tensor< T >	operator() (const std::vector< Function< T, NDIM >> &vbra, const std::vector< Function< T, NDIM >> &vket) const

XCOperator &	set_extra_truncation (const double &fac)

void	set_ispin (const int i) const
	set the spin state this operator is acting on More...

Public Member Functions inherited from madness::SCFOperatorBase< T, NDIM >
	SCFOperatorBase ()=default

	SCFOperatorBase (std::shared_ptr< MacroTaskQ > taskq)

virtual	~SCFOperatorBase ()

virtual tensorT	operator() (const vecfuncT &vbra, const vecfuncT &vket) const =0
	compute the matrix <vbra \| op \| vket> More...

virtual vecfuncT	operator() (const vecfuncT &vket) const =0
	apply this operator on the argument vector of functions More...

Public Attributes
std::shared_ptr< XCfunctional >	xc
	interface to the actual XC functionals More...

Public Attributes inherited from madness::SCFOperatorBase< T, NDIM >
std::shared_ptr< MacroTaskQ >	taskq =0

Private Member Functions
bool	is_initialized () const
	check if the intermediates are initialized More...

vecfuncT	prep_xc_args (const real_function_3d &arho, const real_function_3d &brho) const
	compute the intermediates for the XC functionals More...

void	prep_xc_args_response (const real_function_3d &dens_pt, vecfuncT &xc_args, vecfuncT &ddens_pt) const
	compute the intermediates for the XC functionals More...

Private Attributes
std::string	dft_deriv
	which derivative operator to use More...

double	extra_truncation
	additional truncation for the densities in the XC kernel More...

int	ispin
	the XC functionals depend on the spin of the orbitals they act on More...

int	nbeta
	number of beta orbitals More...

std::shared_ptr< NuclearCorrelationFactor >	ncf
	the nuclear correlation factor, if it exists, for computing derivatives for GGA More...

World &	world
	the world More...

vecfuncT	xc_args
	functions that are need for the computation of the XC operator More...

Additional Inherited Members
Public Types inherited from madness::SCFOperatorBase< T, NDIM >
typedef Function< T, NDIM >	functionT

typedef Tensor< T >	tensorT

typedef std::vector< functionT >	vecfuncT

Detailed Description

template<typename T, std::size_t NDIM>
class madness::XCOperator< T, NDIM >

operator class for the handling of DFT exchange-correlation functionals

Constructor & Destructor Documentation

◆ XCOperator() [1/6]

template<typename T , std::size_t NDIM>

madness::XCOperator< T, NDIM >::XCOperator ( World & world )

inline

default ctor without information about the XC functional

◆ XCOperator() [2/6]

template<typename T , std::size_t NDIM>

madness::XCOperator< T, NDIM >::XCOperator	(	World &	world,
		std::string	xc_data,
		const bool	spin_polarized,
		const real_function_3d &	arho,
		const real_function_3d &	brho,
		std::string	deriv = `"abgv"`
	)

custom ctor with information about the XC functional

References madness::XCOperator< T, NDIM >::nbeta, madness::Function< T, NDIM >::norm2(), madness::XCOperator< T, NDIM >::prep_xc_args(), madness::XCOperator< T, NDIM >::world, madness::XCOperator< T, NDIM >::xc, and madness::XCOperator< T, NDIM >::xc_args.

◆ XCOperator() [3/6]

template<typename T , std::size_t NDIM>

madness::XCOperator< T, NDIM >::XCOperator	(	World &	world,
		const SCF *	scf,
		int	ispin = `0`,
		std::string	deriv = `"abgv"`
	)

ctor with an SCF calculation, will initialize the necessary intermediates

References madness::CalculationParameters::nbeta(), madness::XCOperator< T, NDIM >::nbeta, madness::SCF::param, madness::CalculationParameters::spin_restricted(), madness::XCOperator< T, NDIM >::world, madness::CalculationParameters::xc(), and madness::XCOperator< T, NDIM >::xc.

◆ XCOperator() [4/6]

template<typename T , std::size_t NDIM>

madness::XCOperator< T, NDIM >::XCOperator	(	World &	world,
		const Nemo *	nemo,
		int	ispin = `0`
	)

ctor with a Nemo calculation, will initialize the necessary intermediates

◆ XCOperator() [5/6]

template<typename T , std::size_t NDIM>

madness::XCOperator< T, NDIM >::XCOperator	(	World &	world,
		const SCF *	scf,
		const real_function_3d &	arho,
		const real_function_3d &	brho,
		int	ispin = `0`,
		std::string	deriv = `"abgv"`
	)

ctor with an SCF calculation, will initialize the necessary intermediates

References madness::SCF::param, madness::XCOperator< T, NDIM >::prep_xc_args(), madness::CalculationParameters::spin_restricted(), madness::XCOperator< T, NDIM >::world, madness::CalculationParameters::xc(), madness::XCOperator< T, NDIM >::xc, and madness::XCOperator< T, NDIM >::xc_args.

◆ XCOperator() [6/6]

template<typename T , std::size_t NDIM>

madness::XCOperator< T, NDIM >::XCOperator	(	World &	world,
		const Nemo *	scf,
		const real_function_3d &	arho,
		const real_function_3d &	brho,
		int	ispin = `0`
	)

ctor with an Nemo calculation, will initialize the necessary intermediates

Member Function Documentation

◆ apply_xc_kernel()

template<typename T , std::size_t NDIM>

real_function_3d madness::XCOperator< T, NDIM >::apply_xc_kernel	(	const real_function_3d &	dens_pt,
		const vecfuncT	grad_dens_pt = `vecfuncT()`
	)		const

construct the xc kernel and apply it directly on the (response) density

apply the xc kernel on a perturbed density

the xc kernel is the second derivative of the xc functions wrt the density

Parameters

[in] density the (response) density on which the kernel is applied

Returns: kernel * density

cf Eq. (13) of T. Yanai, R. J. Harrison, and N. Handy, “Multiresolution quantum chemistry in multiwavelet bases: time-dependent density functional theory with asymptotically corrected potentials in local density and generalized gradient approximations,” Mol. Phys., vol. 103, no. 2, pp. 413–424, 2005.

the application of the xc kernel is (RHF only)

$\frac{\partial^2E_{xc}}{\partial \rho_\alpha^2}\circ\tilde\rho = second_{local} + second_{semilocal} + first_{semilocal}$

where the second partial derivatives are

$second_{local} = \frac{\partial^2 f_{xc}}{\partial \rho_\alpha^2}\tilde \rho + 2\frac{\partial^2 f_{xc}}{\partial \rho_\alpha\sigma_{\alpha\alpha}} \left(\vec\nabla \rho_a\cdot \vec \nabla\tilde\rho\right)$

the second partial derivatives that need to be multiplied with the density gradients

$second_{semilocal} = -\vec\nabla\cdot\left((\vec\nabla\rho) \left[2\frac{\partial^2 f_{xc}}{\partial\rho_\alpha\partial\sigma_{\alpha\alpha}}\tilde\rho + 4\frac{\partial^2 f_{xc}}{\partial\sigma_{\alpha\alpha}^2} \left(\vec\nabla\rho_\alpha\cdot\vec\nabla\tilde\rho\right)\right]\right)$

and the first derivatives that need to be multiplied with the density gradients

$first_{semilocal} = -\vec\nabla\cdot\left(2\frac{\partial f_{xc}}{\partial\sigma_{\alpha\alpha}}\vec\nabla\tilde\rho\right)$

References div(), madness::XCfunctional::is_gga(), madness::XCfunctional::is_spin_polarized(), MADNESS_ASSERT, MADNESS_EXCEPTION, madness::multi_to_multi_op_values(), op(), madness::refine_to_common_level(), madness::Function< T, NDIM >::truncate(), truncate(), and xc.

◆ compute_xc_energy()

template<typename T , std::size_t NDIM>

double madness::XCOperator< T, NDIM >::compute_xc_energy

compute the xc energy using the precomputed intermediates vf and delrho

References MADNESS_EXCEPTION, madness::refine_to_common_level(), madness::Function< T, NDIM >::trace(), truncate(), and xc.

Referenced by madness::SCF::apply_potential(), madness::Nemo::compute_energy_regularized(), and test_XCOperator().

◆ info()

template<typename T , std::size_t NDIM>

std::string madness::XCOperator< T, NDIM >::info ( ) const

inlinevirtual

print some information about this operator

Implements madness::SCFOperatorBase< T, NDIM >.

◆ is_initialized()

template<typename T , std::size_t NDIM>

bool madness::XCOperator< T, NDIM >::is_initialized ( ) const

inlineprivate

check if the intermediates are initialized

References madness::XCOperator< T, NDIM >::xc_args.

◆ make_xc_potential()

template<typename T , std::size_t NDIM>

real_function_3d madness::XCOperator< T, NDIM >::make_xc_potential

return the local xc potential

Referenced by madness::SCF::apply_potential(), madness::Nemo::compute_nemo_potentials(), and madness::Nemo::make_fock_operator().

◆ operator()() [1/4]

template<typename T , std::size_t NDIM>

T madness::XCOperator< T, NDIM >::operator()	(	const Function< T, NDIM > &	bra,
		const Function< T, NDIM > &	ket
	)		const

inlinevirtual

compute the matrix element <bra | op | ket>

Parameters

bra	bra state
ket	ket state

Returns: the matrix element <bra | op | ket>

Implements madness::SCFOperatorBase< T, NDIM >.

References MADNESS_EXCEPTION.

◆ operator()() [2/4]

template<typename T , std::size_t NDIM>

Function<T,NDIM> madness::XCOperator< T, NDIM >::operator() ( const Function< T, NDIM > & ket ) const

inlinevirtual

apply the xc potential on an orbitals

Implements madness::SCFOperatorBase< T, NDIM >.

References madness::XCOperator< T, NDIM >::operator()().

◆ operator()() [3/4]

template<typename T , std::size_t NDIM>

std::vector< Function< T, NDIM > > madness::XCOperator< T, NDIM >::operator() ( const std::vector< Function< T, NDIM > > & vket ) const

apply the xc potential on a set of orbitals

Referenced by madness::XCOperator< T, NDIM >::operator()().

◆ operator()() [4/4]

template<typename T , std::size_t NDIM>

Tensor<T> madness::XCOperator< T, NDIM >::operator()	(	const std::vector< Function< T, NDIM >> &	vbra,
		const std::vector< Function< T, NDIM >> &	vket
	)		const

inline

References MADNESS_EXCEPTION.

◆ prep_xc_args()

template<typename T , std::size_t NDIM>

vecfuncT madness::XCOperator< T, NDIM >::prep_xc_args	(	const real_function_3d &	arho,
		const real_function_3d &	brho
	)		const

private

compute the intermediates for the XC functionals

prepare xc args

Parameters

[in]	arho	density of the alpha orbitals
[in]	brho	density of the beta orbitals (necessary only if spin-polarized)

Returns: xc_args vector of intermediates as described above

References copy(), madness::dot(), madness::WorldGopInterface::fence(), madness::World::gop, madness::grad(), madness::grad_ble_one(), madness::grad_bspline_one(), madness::XCfunctional::is_gga(), madness::XCfunctional::is_spin_polarized(), madness::Function< T, NDIM >::reconstruct(), truncate(), madness::unary_op(), madness::Function< T, NDIM >::world(), and xc.

Referenced by madness::XCOperator< T, NDIM >::XCOperator().

◆ prep_xc_args_response()

template<typename T , std::size_t NDIM>

void madness::XCOperator< T, NDIM >::prep_xc_args_response	(	const real_function_3d &	dens_pt,
		vecfuncT &	xc_args,
		vecfuncT &	ddens_pt
	)		const

private

compute the intermediates for the XC functionals

add intermediates for the response kernels to xc_args

Parameters

[in]	dens_pt	perturbed densities from CPHF or TDDFT equations
[in,out]	xc_args	vector of intermediates as described above
[out]	ddens_pt	xyz-derivatives of dens_pt

References madness::dot(), madness::WorldGopInterface::fence(), madness::World::gop, madness::grad(), madness::XCfunctional::is_gga(), madness::XCfunctional::is_spin_polarized(), print(), truncate(), madness::Function< T, NDIM >::world(), xc, and zeta.

◆ set_extra_truncation()

template<typename T , std::size_t NDIM>

XCOperator& madness::XCOperator< T, NDIM >::set_extra_truncation ( const double & fac )

inline

References madness::XCOperator< T, NDIM >::extra_truncation, madness::print(), madness::World::rank(), and madness::XCOperator< T, NDIM >::world.

◆ set_ispin()

template<typename T , std::size_t NDIM>

void madness::XCOperator< T, NDIM >::set_ispin ( const int i ) const

inline

set the spin state this operator is acting on

References madness::XCOperator< T, NDIM >::ispin.

Referenced by test_XCOperator().

Member Data Documentation

◆ dft_deriv

template<typename T , std::size_t NDIM>

std::string madness::XCOperator< T, NDIM >::dft_deriv

private

which derivative operator to use

◆ extra_truncation

template<typename T , std::size_t NDIM>

double madness::XCOperator< T, NDIM >::extra_truncation

private

additional truncation for the densities in the XC kernel

the densities in the DFT kernal are processed as their inverses, so noise in the small density regions might amplify and lead to inaccurate results. Extra truncation will tighten the truncation threshold by a specified factor, default is 0.01.

Referenced by madness::XCOperator< T, NDIM >::set_extra_truncation().

◆ ispin

template<typename T , std::size_t NDIM>

int madness::XCOperator< T, NDIM >::ispin

mutableprivate

the XC functionals depend on the spin of the orbitals they act on

Referenced by madness::XCOperator< T, NDIM >::set_ispin().

◆ nbeta

template<typename T , std::size_t NDIM>

int madness::XCOperator< T, NDIM >::nbeta

private

number of beta orbitals

Referenced by madness::XCOperator< T, NDIM >::XCOperator().

◆ ncf

template<typename T , std::size_t NDIM>

std::shared_ptr<NuclearCorrelationFactor> madness::XCOperator< T, NDIM >::ncf

private

the nuclear correlation factor, if it exists, for computing derivatives for GGA

◆ world

template<typename T , std::size_t NDIM>

World& madness::XCOperator< T, NDIM >::world

private

the world

Referenced by madness::Coulomb< double, 3 >::Coulomb(), madness::XCOperator< T, NDIM >::XCOperator(), and madness::XCOperator< T, NDIM >::set_extra_truncation().

◆ xc

template<typename T , std::size_t NDIM>

std::shared_ptr<XCfunctional> madness::XCOperator< T, NDIM >::xc

interface to the actual XC functionals

Referenced by madness::XCOperator< T, NDIM >::XCOperator().

◆ xc_args

template<typename T , std::size_t NDIM>

vecfuncT madness::XCOperator< T, NDIM >::xc_args

mutableprivate

functions that are need for the computation of the XC operator

the ordering of the intermediates is fixed, but the code can handle non-initialized functions, so if e.g. no GGA is requested, all the corresponding vector components may be left empty. For the ordering of the intermediates see xcfunctional::xc_arg

Referenced by madness::XCOperator< T, NDIM >::XCOperator(), and madness::XCOperator< T, NDIM >::is_initialized().

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

Classes

Public Member Functions

Public Attributes

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

template<typename T, std::size_t NDIM> class madness::XCOperator< T, NDIM >

Constructor & Destructor Documentation

◆ XCOperator() [1/6]

◆ XCOperator() [2/6]

◆ XCOperator() [3/6]

◆ XCOperator() [4/6]

◆ XCOperator() [5/6]

◆ XCOperator() [6/6]

Member Function Documentation

◆ apply_xc_kernel()

◆ compute_xc_energy()

◆ info()

◆ is_initialized()

◆ make_xc_potential()

◆ operator()() [1/4]

◆ operator()() [2/4]

◆ operator()() [3/4]

◆ operator()() [4/4]

◆ prep_xc_args()

◆ prep_xc_args_response()

◆ set_extra_truncation()

◆ set_ispin()

Member Data Documentation

◆ dft_deriv

◆ extra_truncation

◆ ispin

◆ nbeta

◆ ncf

◆ world

◆ xc

◆ xc_args

template<typename T, std::size_t NDIM>
class madness::XCOperator< T, NDIM >