dirac-hatom.cc File Reference

solve the hydrogen atom using the 4-component Dirac equation More...

#include <iostream>
#include <madchem.h>

Include dependency graph for dirac-hatom.cc:

Classes
struct	Ansatz0
struct	AnsatzBase
class	DiracParameters
struct	ExactSpinor
struct	LProjector
class	MatrixOperator
	class defining an operator in matrix form, fixed to size (4,4) More...
class	Metric
class	MyDerivativeOperator< T, NDIM >
struct	ncf
struct	ncf_cusp
struct	ncf_singularity
struct	Omega
struct	sgl_guess
struct	Sigma_ncf_cusp
struct	SphericalHarmonics
	returns the complex value of a given spherical harmonic More...
class	Spinor
	defines a 4-spinor More...
struct	spinorallocator
struct	stepfunction
struct	Xi
	following Dyall: p 104f More...

Enumerations
enum	Uplo { upper , lower }

Functions
template<typename ansatzT >
Spinor	apply_bsh (ansatzT &ansatz, const MatrixOperator &Hd, const MatrixOperator &Hv, const MatrixOperator &metric, const Spinor &spinor, const double energy)
void	apply_mask (std::vector< Spinor > &v)
double	compute_electronic_energy (const double energy)
double	compute_gamma (const double nuclear_charge)
Spinor	copy (const Spinor &other)
std::vector< Spinor >	copy (const std::vector< Spinor > &other)
template<typename ansatzT >
void	eigenvector_test (World &world, const ansatzT ansatz, ExactSpinor es)
double	generalized_laguerre (const double alpha, const long n, const double r)
Tensor< double_complex >	get_fock_transformation (World &world, const std::vector< Spinor > &spinors, const Tensor< double_complex > &overlap, const Tensor< double_complex > &fock)
double_complex	inner (const std::vector< Spinor > &bra, const std::vector< Spinor > ket)
template<typename AnsatzT >
std::vector< Spinor >	iterate (const std::vector< Spinor > &input, const std::vector< double > energy, const AnsatzT &ansatz, const int maxiter)
int	main (int argc, char *argv[])
MatrixOperator	make_alpha_p (World &world)
MatrixOperator	make_Hd (World &world, const std::pair< double_complex, std::string > &ll, const std::pair< double_complex, std::string > &ss)
	this is c sigma p + beta m c^2 More...
MatrixOperator	make_Hdiag (World &world, const LocalPotentialOperator< double_complex, 3 > &V1)
MatrixOperator	make_Hv (World &world, const double nuclear_charge)
	this is the nuclear potential on the diagonal More...
MatrixOperator	make_sp (World &world)
	returns a (2,2) matrix More...
double	mask1d (double x)
double	mask3d (const Vector< double, 3 > &ruser)
Tensor< double_complex >	matrix_inner (const std::vector< Spinor > &bra, const std::vector< Spinor > ket)
MatrixOperator	moments (World &world, int axis, int order)
template<typename T >
Spinor	operator* (const Spinor &arg, const T fac)
template<typename T >
std::vector< Spinor >	operator* (const std::vector< Spinor > &arg, const T fac)
template<typename T >
Spinor	operator* (const T fac, const Spinor &arg)
std::vector< Spinor >	operator+= (std::vector< Spinor > &left, const std::vector< Spinor > &right)
std::vector< Spinor >	operator- (const std::vector< Spinor > &left, const std::vector< Spinor > &right)
std::vector< Spinor >	operator-= (std::vector< Spinor > &left, const std::vector< Spinor > &right)
template<typename AnsatzT >
void	orthonormalize (std::vector< Spinor > &arg, const AnsatzT ansatz)
std::vector< Spinor >	orthonormalize_fock (const std::vector< Spinor > &arg, const std::vector< Spinor > &bra, Tensor< double_complex > &fock)
double	potn (double r)
template<typename ansatzT >
void	run (World &world, ansatzT ansatz, const int nuclear_charge, const commandlineparser &parser, const int nstates)
template<typename ansatzT >
std::vector< Spinor >	schrodinger2dirac (const std::vector< complex_function_3d > wf, const ansatzT &ansatz, const double nuclear_charge)
void	show_norms (const Spinor &bra, const Spinor &ket, const std::string &name)
std::vector< Spinor >	transform (World &world, const std::vector< Spinor > &v, const Tensor< double_complex > &c)
	Transforms a vector of functions according to new[i] = sum[j] old[j]*c[j,i]. More...
std::vector< Spinor >	truncate (std::vector< Spinor > arg)

Variables
static double	alpha1 =constants::fine_structure_constant
static double	clight =1.0/alpha1
static bool	debug =false
static double	epsilon =1.e-12
static double	lo =1.e-7
real_function_3d	mask
static double	nucexpt =3.0/nucrad
static double	nucrad =1e-8
static double	shift =0.0
static bool	use_ble =false
static bool	use_bsp =false

Detailed Description

solve the hydrogen atom using the 4-component Dirac equation

example usage: dirac-hatom –thresh=1.e-5 –k=7 –dirac="charge=100"

Enumeration Type Documentation

Uplo

enum Uplo

Enumerator
upper
lower

Function Documentation

apply_bsh()

template<typename ansatzT >

Spinor apply_bsh	(	ansatzT &	ansatz,
		const MatrixOperator &	Hd,
		const MatrixOperator &	Hv,
		const MatrixOperator &	metric,
		const Spinor &	spinor,
		const double	energy
	)

Truncate before undoing scaling

References alpha1, madness::apply(), clight, debug, energy, madness::g, lo, mu, madness::print(), show_norms(), madness::timer::tag(), Spinor::truncate(), madness::truncate(), and Spinor::world().

Referenced by iterate().

apply_mask()

void apply_mask

(

std::vector< Spinor > &

v

)

References madness::f, mask, and v.

Referenced by iterate(), and run().

compute_electronic_energy()

double compute_electronic_energy

(

const double

energy

)

References alpha1, c, energy, and shift.

Referenced by iterate().

compute_gamma()

double compute_gamma

(

const double

nuclear_charge

)

References alpha1.

Referenced by Ansatz0::energy(), ExactSpinor::Fvalue(), main(), Ansatz0::make_guess(), and ExactSpinor::psivalue().

copy() [1/2]

Spinor copy

(

const Spinor &

other

)

References Spinor::components, madness::copy(), and Spinor::world().

copy() [2/2]

std::vector<Spinor> copy

(

const std::vector< Spinor > &

other

)

References madness::copy().

eigenvector_test()

template<typename ansatzT >

void eigenvector_test	(	World &	world,
		const ansatzT	ansatz,
		ExactSpinor	es
	)

References alpha1, LProjector::analyze(), c, Spinor::components, madness::copy(), diff(), ExactSpinor::filename(), ExactSpinor::get_energy(), ExactSpinor::get_spinor(), madness::inner(), madness::norm2s(), ExactSpinor::print(), madness::print(), Spinor::print_norms(), madness::real(), and ExactSpinor::set_ansatz().

generalized_laguerre()

double generalized_laguerre	(	const double	alpha,
		const long	n,
		const double	r
	)

References alpha, and MADNESS_EXCEPTION.

Referenced by ExactSpinor::Fvalue(), sgl_guess::operator()(), and ExactSpinor::psivalue().

get_fock_transformation()

Tensor<double_complex> get_fock_transformation	(	World &	world,
		const std::vector< Spinor > &	spinors,
		const Tensor< double_complex > &	overlap,
		const Tensor< double_complex > &	fock
	)

References madness::WorldGopInterface::broadcast(), madness::World::gop, madness::Tensor< T >::ptr(), madness::BaseTensor::size(), madness::sygvp(), madness::Localizer::undo_degenerate_rotations(), and madness::Localizer::undo_reordering().

Referenced by orthonormalize_fock().

inner()

double_complex inner	(	const std::vector< Spinor > &	bra,
		const std::vector< Spinor >	ket
	)

References madness::inner().

iterate()

template<typename AnsatzT >

std::vector<Spinor> iterate	(	const std::vector< Spinor > &	input,
		const std::vector< double >	energy,
		const AnsatzT &	ansatz,
		const int	maxiter
	)

References apply_bsh(), apply_mask(), madness::XNonlinearSolver< T, C, Alloc >::clear_subspace(), compute_electronic_energy(), madness::conj_transpose(), madness::copy(), diff(), madness::XNonlinearSolver< T, C, Alloc >::do_print, energy, madness::FunctionDefaults< NDIM >::get_cell(), madness::inner(), lo, madness::matrix_inner(), maxiter, madness::norm2(), madness::orthonormalize(), orthonormalize_fock(), madness::plot_line(), madness::print_header2(), madness::print_header3(), madness::real(), residual(), madness::XNonlinearSolver< T, C, Alloc >::set_maxsub(), madness::World::size(), madness::truncate(), madness::XNonlinearSolver< T, C, Alloc >::update(), and madness::wall_time().

Referenced by run().

main()

int main	(	int	argc,
		char *	argv[]
	)

References alpha, c, DiracParameters::charge(), compute_gamma(), energy_exact, madness::finalize(), madness::constants::fine_structure_constant, ExactSpinor::get_energy(), madness::initialize(), madness::commandlineparser::key_exists(), lo, DiracParameters::lo(), DiracParameters::nstates(), nucexpt, nucrad, DiracParameters::nucrad(), madness::QCCalculationParametersBase::print(), madness::print(), madness::print_centered(), madness::commandlineparser::print_map(), madness::info::print_revision_information(), madness::World::rank(), run(), madness::FunctionDefaults< NDIM >::set_cubic_cell(), madness::FunctionDefaults< NDIM >::set_k(), madness::FunctionDefaults< NDIM >::set_thresh(), madness::FunctionDefaults< NDIM >::set_truncate_mode(), madness::startup(), use_ble, DiracParameters::use_ble(), use_bsp, DiracParameters::use_bsp(), and madness::commandlineparser::value().

make_alpha_p()

MatrixOperator make_alpha_p

(

World &

world

)

References MatrixOperator::add_submatrix(), and make_sp().

Referenced by make_Hd(), and schrodinger2dirac().

make_Hd()

MatrixOperator make_Hd	(	World &	world,
		const std::pair< double_complex, std::string > &	ll,
		const std::pair< double_complex, std::string > &	ss
	)

this is c sigma p + beta m c^2

Parameters

[in]	ll	scalar on the LL (1,1) block
[in]	ss	scalar on the SS (2,2) block

References MatrixOperator::add_operator(), make_alpha_p(), V(), V1, and V2.

Referenced by Ansatz0::make_Hd().

make_Hdiag()

MatrixOperator make_Hdiag	(	World &	world,
		const LocalPotentialOperator< double_complex, 3 > &	V1
	)

References MatrixOperator::add_operator(), and V1.

Referenced by make_Hv(), Ansatz0::R(), and Ansatz0::Rinv().

make_Hv()

MatrixOperator make_Hv	(	World &	world,
		const double	nuclear_charge
	)

this is the nuclear potential on the diagonal

References make_Hdiag(), madness::Vector< T, N >::normf(), potn(), V(), and V1.

Referenced by Ansatz0::make_Hv().

make_sp()

MatrixOperator make_sp

(

World &

world

)

returns a (2,2) matrix

References MatrixOperator::add_operator(), alpha, c, madness::constants::fine_structure_constant, MADNESS_CHECK, use_ble, and use_bsp.

Referenced by make_alpha_p().

mask1d()

double mask1d

(

double

x

)

Referenced by mask3d().

mask3d()

double mask3d

(

const Vector< double, 3 > &

ruser

)

References lo, mask1d(), and madness::user_to_sim().

Referenced by run().

matrix_inner()

Tensor<double_complex> matrix_inner	(	const std::vector< Spinor > &	bra,
		const std::vector< Spinor >	ket
	)

References madness::inner().

moments()

MatrixOperator moments	(	World &	world,
		int	axis,
		int	order
	)

References MatrixOperator::add_operator(), axis, m, and pow().

operator*() [1/3]

template<typename T >

Spinor operator*	(	const Spinor &	arg,
		const T	fac
	)

References madness::arg().

operator*() [2/3]

template<typename T >

std::vector<Spinor> operator*	(	const std::vector< Spinor > &	arg,
		const T	fac
	)

References madness::arg(), and madness::copy().

operator*() [3/3]

template<typename T >

Spinor operator*	(	const T	fac,
		const Spinor &	arg
	)

References madness::arg().

operator+=()

std::vector<Spinor> operator+=	(	std::vector< Spinor > &	left,
		const std::vector< Spinor > &	right
	)

operator-()

std::vector<Spinor> operator-	(	const std::vector< Spinor > &	left,
		const std::vector< Spinor > &	right
	)

References madness::copy().

operator-=()

std::vector<Spinor> operator-=	(	std::vector< Spinor > &	left,
		const std::vector< Spinor > &	right
	)

orthonormalize()

template<typename AnsatzT >

void orthonormalize	(	std::vector< Spinor > &	arg,
		const AnsatzT	ansatz
	)

References std::abs(), madness::arg(), madness::matrix_inner(), max, Q(), madness::NemoBase::Q2(), madness::transform(), and madness::truncate().

orthonormalize_fock()

std::vector<Spinor> orthonormalize_fock	(	const std::vector< Spinor > &	arg,
		const std::vector< Spinor > &	bra,
		Tensor< double_complex > &	fock
	)

References madness::arg(), madness::conj(), get_fock_transformation(), madness::inner(), and madness::transform().

Referenced by iterate().

potn()

double potn

(

double

r

)

References e(), nucexpt, and madness::constants::pi.

Referenced by converge(), converge2s(), doit(), energy(), expV(), initial_loadbal(), loadbal(), main(), make_Hv(), preloadbal(), print_info(), print_stats(), and propagate().

run()

template<typename ansatzT >

void run	(	World &	world,
		ansatzT	ansatz,
		const int	nuclear_charge,
		const commandlineparser &	parser,
		const int	nstates
	)

References apply_mask(), ExactSpinor::compute_F, ExactSpinor::cusp_a, ExactSpinor::get_energy(), guess(), iterate(), mask, mask3d(), madness::matrix_inner(), madness::orthonormalize(), madness::print(), madness::print_header2(), madness::Function< T, NDIM >::reconstruct(), schrodinger2dirac(), and madness::Function< T, NDIM >::truncate().

Referenced by main(), and madness::archive::ArchiveStoreImpl< ParallelOutputArchive< VectorOutputArchive >, WorldContainer< keyT, valueT > >::store().

schrodinger2dirac()

template<typename ansatzT >

std::vector<Spinor> schrodinger2dirac	(	const std::vector< complex_function_3d >	wf,
		const ansatzT &	ansatz,
		const double	nuclear_charge
	)

References alpha1, Spinor::components, make_alpha_p(), madness::truncate(), and w().

Referenced by run().

show_norms()

void show_norms	(	const Spinor &	bra,
		const Spinor &	ket,
		const std::string &	name
	)

References Spinor::components, madness::inner(), m, madness::name(), madness::print(), and Spinor::world().

Referenced by apply_bsh().

transform()

std::vector<Spinor> transform	(	World &	world,
		const std::vector< Spinor > &	v,
		const Tensor< double_complex > &	c
	)

Transforms a vector of functions according to new[i] = sum[j] old[j]*c[j,i].

Uses sparsity in the transformation matrix — set small elements to zero to take advantage of this.

References c, madness::WorldGopInterface::fence(), madness::gaxpy(), madness::World::gop, m, MADNESS_ASSERT, PROFILE_BLOCK, and v.

truncate()

std::vector<Spinor> truncate

(

std::vector< Spinor >

arg

)

References a, and madness::arg().

Referenced by DipoleVector::DipoleVector(), NuclearVector::NuclearVector(), madness::XCOperator< T, NDIM >::apply_xc_kernel(), madness::XCOperator< T, NDIM >::compute_xc_energy(), DF::exchange(), DF::iterate(), molresponseExchange(), madness::XCOperator< T, NDIM >::prep_xc_args(), madness::XCOperator< T, NDIM >::prep_xc_args_response(), and vector_to_PQ().

Variable Documentation

alpha1

double alpha1 =constants::fine_structure_constant

static

Referenced by ExactSpinor::ExactSpinor(), apply_bsh(), ExactSpinor::compute_C(), compute_electronic_energy(), ExactSpinor::compute_en(), ExactSpinor::compute_energy(), compute_gamma(), eigenvector_test(), Ansatz0::energy(), ExactSpinor::Fvalue(), main(), Ansatz0::make_Hd(), AnsatzBase::mu(), ExactSpinor::print(), ExactSpinor::psivalue(), and schrodinger2dirac().

clight

double clight =1.0/alpha1

static

Referenced by apply_bsh(), and Spinor::truncate().

debug

bool debug =false

static

Referenced by madness::GFit< T, NDIM >::GFit(), apply_bsh(), madness::Cloud::do_load(), madness::WorldGopInterface::fence(), madness::WorldGopInterface::fence_impl(), madness::get_charge_from_file(), madness::CCTimer::info(), madness::CCConvolutionOperator< T, NDIM >::init_op(), madness::Cloud::load_from_cache(), madness::GTHPseudopotential< Q >::load_pseudo_from_file(), madness::Cloud::load_tuple(), madness::AtomicBasisSet::modify_dmat_psp(), madness::FunctionDefaults< NDIM >::print(), AtomicBasisSet::read_file(), madness::AtomicBasisSet::read_file(), madness::Cloud::set_debug(), madness::FunctionDefaults< NDIM >::set_defaults(), and madness::Cloud::store_other().

epsilon

double epsilon =1.e-12

static

Referenced by stepfunction::operator()(), and ncf_singularity::operator()().

lo

double lo =1.e-7

static

Referenced by madness::cartesian_grid< NDIM >::cartesian_grid(), madness::F12Potentials::F12Potentials(), madness::GFit< T, NDIM >::GFit(), MolecularNuclearPotentialFunctor2::MolecularNuclearPotentialFunctor2(), madness::SystolicMatrixAlgorithm< T >::SystolicMatrixAlgorithm(), madness::NuclearCorrelationFactor::U1X_functor::U1X_functor(), madness::NuclearCorrelationFactor::U2X_functor::U2X_functor(), madness::adq(), madness::adq1(), APPLY(), madness::APPLY(), madness::SCF::APPLY(), apply_bsh(), madness::TDHF::apply_G(), madness::FunctionImpl< T, NDIM >::autorefine_square_test(), madness::GFit< T, NDIM >::bsh_fit(), madness::GFit< T, NDIM >::bsh_fit_ndim(), madness::GFit< T, NDIM >::BSHFit(), madness::BSHOperator(), madness::BSHOperator3D(), madness::BSHOperatorPtr(), madness::BSHOperatorPtr3D(), madness::Exchange< T, NDIM >::ExchangeImpl< T, NDIM >::MacroTaskExchangeSimple::compute_batch_in_asymmetric_matrix(), madness::Exchange< T, NDIM >::ExchangeImpl< T, NDIM >::MacroTaskExchangeSimple::compute_diagonal_batch_in_symmetric_matrix(), madness::Exchange< T, NDIM >::ExchangeImpl< T, NDIM >::MacroTaskExchangeSimple::compute_offdiagonal_batch_in_symmetric_matrix(), madness::GFit< T, NDIM >::CoulombFit(), madness::CoulombOperator(), madness::CoulombOperatorPtr(), cplxfunc0(), cplxfunc1(), cplxfunc2(), cplxvec0(), cplxvec1(), cplxvec2(), madness::do_adq(), Plotter::dolineplot(), draw_line(), madness::GFit< T, NDIM >::f12_fit(), madness::GFit< T, NDIM >::F12Fit(), madness::GFit< T, NDIM >::f12sq_fit(), madness::GFit< T, NDIM >::F12sqFit(), madness::GFit< T, NDIM >::F2GFit(), madness::F2GOperator(), madness::F2GOperatorPtr(), madness::GFit< T, NDIM >::FGFit(), madness::FGOperator(), madness::FGOperatorPtr(), madness::GFit< T, NDIM >::GaussFit(), madness::GaussOperator(), madness::GaussOperatorPtr(), madness::TDHF::TDHFParameters::get_ccc_parameters(), madness::GradBSHOperator(), GradBSHOperator_Joel(), madness::GradCoulombOperator(), madness::GradSlaterOperator(), madness::SCF::group_orbital_sets(), madness::DQueue< T >::grow(), madness::TDHF::initialize(), madness::cartesian_grid< NDIM >::initialize(), iterate(), madness::Exchange< T, NDIM >::ExchangeImpl< T, NDIM >::K_large_memory(), madness::Exchange< T, NDIM >::ExchangeImpl< T, NDIM >::K_small_memory(), madness::trajectory< NDIM >::line_internal(), madness::trajectory< NDIM >::line_xyz(), madness::Localizer::localize_new(), logplot(), main(), make_bsh_operators(), madness::SeparatedConvolution< Q, NDIM >::make_coeff_for_operator(), make_k(), make_pts(), SurfaceMoleculeInteraction::make_surfcharge(), madness::SeparatedConvolution< Q, NDIM >::make_tt_representation(), mask3(), madness::mask3(), mask3d(), molresponseExchange(), newK(), refop::operator()(), madness::orthonormalize_canonical(), madness::PeriodicBSHOp(), madness::PeriodicBSHOperator3D(), madness::PeriodicBSHOperatorPtr3D(), madness::PeriodicBSHOpPtr(), madness::PeriodicCoulombOp(), madness::PeriodicCoulombOpPtr(), madness::PeriodicHFExchangeOperator(), SurfaceMoleculeInteraction::perturbed_molecular_pot(), madness::XCfunctional::plot(), plot(), madness::plot_line(), Calculation::plot_p(), madness::plot_plane(), Calculation::plot_z(), madness::PM_q(), madness::GFit< T, NDIM >::print_accuracy(), madness::GFit< T, NDIM >::prune_small_coefficients(), random_gaussian(), RandomGaussian(), realfunc0(), realfunc1(), realfunc2(), realvec0(), realvec1(), realvec2(), madness::Coulomb< T, NDIM >::reset_poisson_operator_ptr(), madness::Nemo::rotate_subspace(), madness::SCF::rotate_subspace(), run(), madness::FunctionDefaults< NDIM >::set_cubic_cell(), madness::FunctionDefaults< NDIM >::set_length_scale(), madness::FunctionFunctorInterface< T, NDIM >::set_length_scale(), set_poisson(), madness::Exchange< T, NDIM >::ExchangeImpl< T, NDIM >::set_poisson(), madness::Random::setstate(), madness::GFit< T, NDIM >::slater_fit(), madness::SlaterF12Operator(), madness::SlaterF12OperatorPtr(), madness::SlaterF12sqOperator(), madness::SlaterF12sqOperatorPtr(), madness::GFit< T, NDIM >::SlaterFit(), madness::SlaterOperator(), madness::SlaterOperatorPtr(), madness::SlaterOperatorPtr_ND(), solve(), test(), test_apply_push_1d(), test_combined_operators(), test_exchange(), test_gconv(), test_gence2(), test_modified(), test_op(), test_per(), test_recursive_application(), and madness::FunctionImpl< T, NDIM >::tnorm().

mask

real_function_3d mask

Referenced by EmbeddedDirichlet::EmbeddedDirichlet(), madness::ThreadBinder::ThreadBinder(), apply_mask(), madness::ThreadBinder::bind(), iterate(), main(), madness::smooth< T, NDIM >::make_inv_mask(), madness::smooth< T, NDIM >::make_mask(), madness::smooth< T, NDIM >::merge_functions(), mtxmq(), madness::divide_add_interpolate::operator()(), run(), and Calculation::set_protocol().

nucexpt

double nucexpt =3.0/nucrad

static

Referenced by main(), and potn().

nucrad

double nucrad =1e-8

static

Referenced by main().

shift

double shift =0.0

static

Referenced by madness::SeparatedConvolution< Q, NDIM >::apply(), KPeriodicBSHOperator::apply(), madness::SeparatedConvolution< Q, NDIM >::apply2(), madness::SeparatedConvolution< Q, NDIM >::apply2_lowdim(), madness::TDHF::apply_G(), compute_electronic_energy(), madness::Zcis::compute_residuals(), madness::ThreadPool::default_nthread(), madness::SeparatedConvolution< Q, NDIM >::estimate_costs(), main(), MiniDFT::make_bsh_operators(), make_bsh_operators(), madness::SeparatedConvolution< Q, NDIM >::make_tt_representation(), TestPmap::owner(), test_converged_function(), test_convergence(), update(), and MiniDFT::update().

use_ble

bool use_ble =false

static

Referenced by main(), and make_sp().

use_bsp

bool use_bsp =false

static

Referenced by main(), and make_sp().