#include <nemo.h>

Inheritance diagram for madness::Nemo:

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Collaboration diagram for madness::Nemo:

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Classes
struct	NemoCalculationParameters
	class holding parameters for a nemo calculation beyond the standard dft parameters from moldft More...

Public Member Functions
	Nemo (World &world, const commandlineparser &parser)
	ctor

std::vector< vecfuncT >	compute_all_cphf ()
	solve the CPHF equation for all displacements

vecfuncT	compute_cphf_parallel_term (const size_t iatom, const int iaxis) const

tensorT	compute_fock_matrix (const vecfuncT &nemo, const tensorT &occ) const
	compute the Fock matrix from scratch

Tensor< double >	compute_IR_intensities (const Tensor< double > &normalmodes, const vecfuncT &dens_pt) const
	compute the IR intensities in the double harmonic approximation

bool	do_ac () const

bool	do_pcm () const

bool	do_symmetry () const

AC< 3 >	get_ac () const

std::shared_ptr< SCF >	get_calc () const

const NemoCalculationParameters &	get_param () const

PCM	get_pcm () const

projector_irrep	get_symmetry_projector () const
	return the symmetry_projector

Tensor< double >	gradient (const Tensor< double > &x)
	compute the nuclear gradients

Tensor< double >	hessian (const Tensor< double > &x)
	returns the molecular hessian matrix at structure x

bool	is_dft () const

real_function_3d	kinetic_energy_potential (const vecfuncT &nemo) const

real_function_3d	make_ddensity (const real_function_3d &rhonemo, const int axis) const
	make the derivative of the density

real_function_3d	make_density (const Tensor< double > &occ, const vecfuncT &nemo) const
	make the density (alpha or beta)

real_function_3d	make_density (const tensorT &occ, const vecfuncT &bra, const vecfuncT &ket, const bool refine=false) const
	make the density using different bra and ket vectors

virtual std::shared_ptr< Fock< double, 3 > >	make_fock_operator () const
	construct the fock operator based on the calculation parameters (K or XC?)

real_function_3d	make_laplacian_density (const real_function_3d &rhonemo) const
	the Laplacian of the density

real_function_3d	make_sigma (const real_function_3d &rho1, const real_function_3d &rho2) const
	compute the reduced densities sigma (gamma) for GGA functionals

Molecule &	molecule ()
	return a reference to the molecule

Molecule &	molecule () const
	return a reference to the molecule

std::string	name () const

bool	provides_gradient () const
	Override this to return true if the derivative is implemented.

Tensor< double >	purify_hessian (const Tensor< double > &hessian) const
	purify and symmetrize the hessian

bool	selftest ()

vecfuncT	solve_cphf (const size_t iatom, const int iaxis, const Tensor< double > fock, const vecfuncT &guess, const vecfuncT &rhsconst, const Tensor< double > incomplete_hessian, const vecfuncT &parallel, const SCFProtocol &p, const std::string &xc_data) const
	solve the CPHF equations for the nuclear displacements

virtual double	value ()

virtual double	value (const Tensor< double > &x)
	Should return the value of the objective function.

Public Member Functions inherited from madness::NemoBase
	NemoBase (World &w)

virtual	~NemoBase ()

bool	check_convergence (const std::vector< double > energies, const std::vector< double > oldenergies, const double bsh_norm, const double delta_density, const CalculationParameters &param, const double econv, const double dconv) const

template<typename T , std::size_t NDIM>
Function< typename Tensor< T >::scalar_type, NDIM >	compute_density (const std::vector< Function< T, NDIM > > nemo) const

Tensor< double >	compute_gradient (const real_function_3d &rhonemo, const Molecule &molecule) const
	compute the nuclear gradients

template<typename T , std::size_t NDIM>
double	compute_kinetic_energy (const std::vector< Function< T, NDIM > > &nemo) const
	compute kinetic energy as square of the "analytical" expectation value

template<typename T , std::size_t NDIM>
double	compute_kinetic_energy1 (const std::vector< Function< T, NDIM > > &nemo) const
	compute kinetic energy as square of the "analytical" derivative of the orbitals

template<typename T , std::size_t NDIM>
double	compute_kinetic_energy1a (const std::vector< Function< T, NDIM > > &nemo) const
	compute kinetic energy as square of the "analytical" derivative of the orbitals

template<typename T , std::size_t NDIM>
double	compute_kinetic_energy2 (const std::vector< Function< T, NDIM > > &nemo) const
	compute kinetic energy as direct derivative of the orbitals (probably imprecise)

void	construct_nuclear_correlation_factor (const Molecule &molecule, const std::shared_ptr< PotentialManager > pm, const std::pair< std::string, double > ncf_parameter)

std::shared_ptr< NuclearCorrelationFactor >	get_ncf_ptr () const
	create an instance of the derived object based on the input parameters

virtual void	invalidate_factors_and_potentials ()

virtual bool	need_recompute_factors_and_potentials (const double thresh) const

template<typename T , std::size_t NDIM>
void	orthonormalize (std::vector< Function< T, NDIM > > &nemo, const Function< double, NDIM > metric=Function< double, NDIM >(), const double trantol=FunctionDefaults< NDIM >::get_thresh() *0.01) const
	orthonormalize the vectors

Public Member Functions inherited from madness::OptimizationTargetInterface
virtual	~OptimizationTargetInterface ()

double	test_gradient (Tensor< double > &x, double value_precision, bool doprint=true)
	Numerical test of the derivative ... optionally prints to stdout, returns max abs error.

virtual void	value_and_gradient (const Tensor< double > &x, double &value, Tensor< double > &gradient)
	Reimplement if more efficient to evaluate both value and gradient in one call.

Static Public Member Functions
static void	help ()

static void	print_parameters ()

static void	smoothen (real_function_3d &f)
	smooth a function by projecting it onto k-1 and then average with k

Static Public Member Functions inherited from madness::NemoBase
template<typename T , std::size_t NDIM>
static void	normalize (std::vector< Function< T, NDIM > > &nemo, const Function< double, NDIM > metric=Function< double, NDIM >())
	normalize the nemos

template<typename T >
static Tensor< T >	Q2 (const Tensor< T > &s)

Public Attributes
NemoCalculationParameters	param

Public Attributes inherited from madness::NemoBase
std::shared_ptr< NuclearCorrelationFactor >	ncf
	the nuclear correlation factor

real_function_3d	R
	the nuclear correlation factor

real_function_3d	R_square
	the square of the nuclear correlation factor

World &	world

Protected Member Functions
std::vector< double >	compute_energy_regularized (const vecfuncT &nemo, const vecfuncT &Jnemo, const vecfuncT &Knemo, const vecfuncT &Unemo) const
	given nemos, compute the HF energy using the regularized expressions for T and V

void	compute_nemo_potentials (const vecfuncT &nemo, vecfuncT &Jnemo, vecfuncT &Knemo, vecfuncT &xcnemo, vecfuncT &pcmnemo, vecfuncT &Unemo) const
	compute the reconstructed orbitals, and all potentials applied on nemo

real_function_3d	get_coulomb_potential (const vecfuncT &psi) const
	return the Coulomb potential

template<typename T , size_t NDIM>
void	load_function (std::vector< Function< T, NDIM > > &f, const std::string name) const
	load a function

vecfuncT	localize (const vecfuncT &nemo, const double dconv, const bool randomize) const
	localize the nemo orbitals

vecfuncT	make_cphf_constant_term (const size_t iatom, const int iaxis, const vecfuncT &R2nemo, const real_function_3d &rhonemo) const
	compute the constant term for the CPHF equations

Tensor< double >	make_incomplete_hessian () const
	compute the incomplete hessian

Tensor< double >	make_incomplete_hessian_response_part (const std::vector< vecfuncT > &xi) const
	compute the complementary incomplete hessian

void	make_plots (const real_function_3d &f, const std::string &name="function") const

template<typename solverT >
void	rotate_subspace (World &world, const tensorT &U, solverT &solver, int lo, int nfunc) const
	rotate the KAIN subspace (cf. SCF.cc)

template<typename T , size_t NDIM>
void	save_function (const std::vector< Function< T, NDIM > > &f, const std::string name) const
	save a function

void	set_protocol (const double thresh)
	adapt the thresholds consistently to a common value

double	solve (const SCFProtocol &proto)
	solve the HF equations

double	trantol () const
	return the threshold for vanishing elements in orbital rotations

Protected Attributes
AC< 3 >	ac
	asymptotic correction for DFT

std::shared_ptr< SCF >	calc

std::shared_ptr< real_convolution_3d >	poisson
	a poisson solver

projector_irrep	symmetry_projector

Private Types
typedef std::shared_ptr< real_convolution_3d >	poperatorT

Private Attributes
double	coords_sum
	sum of square of coords at last solved geometry

PCM	pcm
	polarizable continuum model

Friends
class	PNO

class	TDHF

Detailed Description

The Nemo class.

Member Typedef Documentation

◆ poperatorT

typedef std::shared_ptr<real_convolution_3d> madness::Nemo::poperatorT

private

Constructor & Destructor Documentation

◆ Nemo()

madness::Nemo::Nemo	(	World &	world,
		const commandlineparser &	parser
	)

ctor

Parameters

[in]	world1	the world
[in]	calc	the SCF

References calc, do_pcm(), madness::projector_irrep::get_verbosity(), molecule(), param, pcm, madness::CalculationParameters::pcm_data(), madness::CalculationParameters::pointgroup(), madness::projector_irrep::print_character_table(), madness::CalculationParameters::read_input_and_commandline_options(), madness::projector_irrep::set_ordering(), madness::projector_irrep::set_orthonormalize_irreps(), madness::projector_irrep::set_verbosity(), symmetry_projector, and madness::NemoBase::world.

Member Function Documentation

◆ compute_all_cphf()

std::vector< vecfuncT > madness::Nemo::compute_all_cphf ( )

solve the CPHF equation for all displacements

this function computes the nemo response F^X

$F^X = F^\perp + F^\parallel$

To reconstruct the unregularized orbital response (not recommended):

$i^X = R^X F + R F^X$

The orbital response i^X constructed in this way is automatically orthogonal to the occupied space because of the parallel term F^\parallel

Returns: a vector of the nemo response F^X for all displacements

References madness::apply(), calc, compute_cphf_parallel_term(), compute_fock_matrix(), madness::SCFProtocol::current_prec, madness::dot(), madness::CalculationParameters::econv(), madness::SCFProtocol::end_prec, madness::SCFProtocol::finished(), madness::QCCalculationParametersBase::get(), get_calc(), madness::SCFProtocol::initialize(), load_function(), make_cphf_constant_term(), make_density(), make_incomplete_hessian(), make_incomplete_hessian_response_part(), molecule(), madness::mul(), madness::Molecule::natom(), p(), param, madness::print(), madness::CalculationParameters::print_level(), madness::NemoBase::R_square, madness::World::rank(), madness::CalculationParameters::restart_cphf(), madness::save(), save_function(), set_protocol(), solve_cphf(), madness::stringify(), madness::timer::tag(), madness::truncate(), madness::wall_time(), madness::NemoBase::world, madness::CalculationParameters::xc(), and xi.

Referenced by hessian().

◆ compute_cphf_parallel_term()

vecfuncT madness::Nemo::compute_cphf_parallel_term	(	const size_t	iatom,
		const int	iaxis
	)		const

this function computes that part of the orbital response that is parallel to the occupied space.

$F^X = F^\perp + F^\parallel$

If no NCF's are used F^\parallel vanishes. If NCF's are used this term does not vanish because the derivatives of the NCF does not vanish, and it is given by

$F_i^\parallel = -\frac{1}{2}\sum_k|F_k ><F_k | (R^2)^X | F_i>$

References calc, madness::matrix_inner(), madness::mul(), madness::transform(), madness::truncate(), and madness::NemoBase::world.

Referenced by compute_all_cphf().

◆ compute_energy_regularized()

std::vector< double > madness::Nemo::compute_energy_regularized	(	const vecfuncT &	nemo,
		const vecfuncT &	Jnemo,
		const vecfuncT &	Knemo,
		const vecfuncT &	Unemo
	)		const

protected

given nemos, compute the HF energy using the regularized expressions for T and V

References madness::apply(), axis, calc, madness::NemoBase::compute_kinetic_energy(), madness::PCM::compute_pcm_energy(), madness::XCOperator< T, NDIM >::compute_xc_energy(), do_pcm(), madness::timer::end(), energy, madness::inner(), is_dft(), K(), param, pcm, madness::CalculationParameters::print_level(), madness::NemoBase::R_square, madness::World::rank(), madness::Tensor< T >::sum(), sum, madness::truncate(), and madness::NemoBase::world.

Referenced by solve().

◆ compute_fock_matrix()

tensorT madness::Nemo::compute_fock_matrix	(	const vecfuncT &	nemo,
		const tensorT &	occ
	)		const

compute the Fock matrix from scratch

References calc, compute_nemo_potentials(), do_pcm(), madness::matrix_inner(), madness::mul(), madness::NemoBase::R_square, T(), madness::truncate(), and madness::NemoBase::world.

Referenced by compute_all_cphf(), test_ethylene(), test_ne_boys(), and test_nemo().

◆ compute_IR_intensities()

Tensor< double > madness::Nemo::compute_IR_intensities	(	const Tensor< double > &	normalmodes,
		const vecfuncT &	dens_pt
	)		const

compute the IR intensities in the double harmonic approximation

use the projected normal modes; units are km/mol

Parameters

[in]	normalmodes	the normal modes
[in]	dens_pt	the perturbed densities for each nuclear displacement

Referenced by hessian().

◆ compute_nemo_potentials()

void madness::Nemo::compute_nemo_potentials	(	const vecfuncT &	nemo,
		vecfuncT &	Jnemo,
		vecfuncT &	Knemo,
		vecfuncT &	xcnemo,
		vecfuncT &	pcmnemo,
		vecfuncT &	Unemo
	)		const

protected

compute the reconstructed orbitals, and all potentials applied on nemo

to use these potentials in the fock matrix computation they must be multiplied by the nuclear correlation factor

Parameters

[in]	nemo	the nemo orbitals
[out]	Jnemo	Coulomb operator applied on the nemos
[out]	Knemo	exchange operator applied on the nemos
[out]	pcmnemo	PCM (solvent) potential applied on the nemos
[out]	Unemo	regularized nuclear potential applied on the nemos

to use these potentials in the fock matrix computation they must be multiplied by the nuclear correlation factor

Parameters

[in]	nemo	the nemo orbitals
[out]	psi	the reconstructed, full orbitals
[out]	Jnemo	Coulomb operator applied on the nemos
[out]	Knemo	exchange operator applied on the nemos
[out]	Vnemo	nuclear potential applied on the nemos
[out]	Unemo	regularized nuclear potential applied on the nemos

References ac, madness::AC< NDIM >::apply(), calc, madness::CalculationParameters::charge(), madness::PCM::compute_pcm_potential(), do_ac(), do_pcm(), madness::WorldGopInterface::fence(), madness::get_size(), madness::World::gop, K(), madness::XCOperator< T, NDIM >::make_xc_potential(), molecule(), param, pcm, madness::Coulomb< T, NDIM >::potential(), madness::CalculationParameters::print_level(), madness::scale(), madness::Exchange< T, NDIM >::set_symmetric(), madness::Exchange< T, NDIM >::set_taskq(), madness::Coulomb< T, NDIM >::set_taskq(), madness::World::size(), madness::stringify(), madness::timer::tag(), madness::truncate(), and madness::NemoBase::world.

Referenced by compute_fock_matrix(), and solve().

◆ do_ac()

bool madness::Nemo::do_ac ( ) const

inline

References madness::CalculationParameters::ac_data(), and param.

Referenced by compute_nemo_potentials(), and make_fock_operator().

◆ do_pcm()

bool madness::Nemo::do_pcm ( ) const

inline

References param, and madness::CalculationParameters::pcm_data().

Referenced by Nemo(), compute_energy_regularized(), compute_fock_matrix(), compute_nemo_potentials(), make_fock_operator(), and solve().

◆ do_symmetry()

bool madness::Nemo::do_symmetry ( ) const

inline

References madness::projector_irrep::get_pointgroup(), and symmetry_projector.

Referenced by madness::OEP::iterate(), and solve().

◆ get_ac()

AC< 3 > madness::Nemo::get_ac ( ) const

inline

References ac.

◆ get_calc()

std::shared_ptr< SCF > madness::Nemo::get_calc ( ) const

inline

References calc.

Referenced by madness::Coulomb< T, NDIM >::Coulomb(), madness::Exchange< T, NDIM >::ExchangeImpl< T, NDIM >::ExchangeImpl(), madness::F12Potentials::F12Potentials(), madness::PNO::PNO(), compute_all_cphf(), madness::Coulomb< double, 3 >::compute_density(), madness::OEP::compute_exchange_potential(), madness::Coulomb< T, NDIM >::compute_potential(), madness::PNO::grow_rank(), madness::PNO::guess_virtuals(), hessian(), madness::F12Potentials::initialize_active_mos(), madness::PNO::initialize_pairs(), madness::OEP::iterate(), madness::PNO::iterate_pairs_internal(), kinetic_energy_potential(), madness::OEP::load_restartdata(), localize(), main(), madness::PNO::make_bsh_operators(), make_cphf_constant_term(), make_incomplete_hessian(), make_laplacian_density(), madness::PNO::nact(), madness::PNO::nocc(), madness::PNO::oit(), madness::ParametrizedExchange::operator()(), madness::F12Potentials::read_cabs_from_file(), madness::OEP::save_restartdata(), set_protocol(), solve(), solve_cphf(), test_ethylene(), test_fock(), test_ne_boys(), test_nemo(), and trantol().

◆ get_coulomb_potential()

real_function_3d madness::Nemo::get_coulomb_potential ( const vecfuncT & psi ) const

protected

return the Coulomb potential

References calc, MADNESS_ASSERT, make_density(), param, psi(), madness::Function< T, NDIM >::scale(), and madness::CalculationParameters::spin_restricted().

◆ get_param()

const NemoCalculationParameters & madness::Nemo::get_param ( ) const

inline

References param.

◆ get_pcm()

PCM madness::Nemo::get_pcm ( ) const

inline

References pcm.

◆ get_symmetry_projector()

projector_irrep madness::Nemo::get_symmetry_projector ( ) const

inline

return the symmetry_projector

References symmetry_projector.

◆ gradient()

Tensor< double > madness::Nemo::gradient ( const Tensor< double > & x )

virtual

compute the nuclear gradients

Reimplemented from madness::OptimizationTargetInterface.

References madness::Atom::atomic_number, madness::atomic_number_to_symbol(), calc, madness::NemoBase::compute_gradient(), madness::grad(), make_density(), madness::print(), madness::World::rank(), madness::Function< T, NDIM >::refine(), madness::Function< T, NDIM >::scale(), madness::NemoBase::world, madness::Atom::x, madness::Atom::y, and madness::Atom::z.

◆ help()

static void madness::Nemo::help ( )

inlinestatic

References madness::print(), and madness::print_header2().

Referenced by main().

◆ hessian()

Tensor< double > madness::Nemo::hessian ( const Tensor< double > & x )

returns the molecular hessian matrix at structure x

compute the nuclear hessian

References madness::Tensor< T >::absmax(), madness::constants::au2invcm, calc, compute_all_cphf(), compute_frequencies(), compute_IR_intensities(), compute_reduced_mass(), madness::timer::end(), madness::QCCalculationParametersBase::get(), get_calc(), hessian(), madness::inner(), make_ddensity(), make_density(), molecule(), madness::mul(), madness::Molecule::natom(), madness::Molecule::nuclear_repulsion_hessian(), param, madness::print(), madness::CalculationParameters::print_level(), purify_hessian(), madness::NemoBase::R_square, madness::World::rank(), save_function(), madness::Tensor< T >::scale(), madness::BaseTensor::size(), sum, madness::transpose(), madness::truncate(), madness::wall_time(), madness::NemoBase::world, and xi.

Referenced by hessian(), and purify_hessian().

◆ is_dft()

bool madness::Nemo::is_dft ( ) const

inline

References calc.

Referenced by compute_energy_regularized(), make_cphf_constant_term(), and solve_cphf().

◆ kinetic_energy_potential()

real_function_3d madness::Nemo::kinetic_energy_potential ( const vecfuncT & nemo ) const

compute the kinetic energy potential using Eq. (16) of R. A. King and N. C. Handy, “Kinetic energy functionals from the Kohn–Sham potential,” Phys. Chem. Chem. Phys., vol. 2, no. 22, pp. 5049–5056, 2000.

References madness::apply(), madness::binary_op(), calc, diff(), madness::dot(), madness::gaxpy(), get_calc(), madness::mul(), madness::norm2(), madness::constants::pi, poisson, madness::print(), madness::NemoBase::R, madness::NemoBase::R_square, madness::save(), madness::scale(), madness::SmoothingOperator3D(), madness::sub(), sum, and madness::NemoBase::world.

◆ load_function()

template<typename T , size_t NDIM>

void madness::Nemo::load_function	(	std::vector< Function< T, NDIM > > &	f,
		const std::string	name
	)		const

protected

load a function

References madness::f, name(), madness::print(), madness::World::rank(), and madness::NemoBase::world.

Referenced by compute_all_cphf().

◆ localize()

vecfuncT madness::Nemo::localize	(	const vecfuncT &	nemo,
		const double	dconv,
		const bool	randomize
	)		const

protected

localize the nemo orbitals

localize the nemo orbitals according to Pipek-Mezey or Foster-Boys

References aobasis, calc, madness::Localizer::compute_localization_matrix(), get_calc(), molecule(), madness::NemoBase::normalize(), madness::NemoBase::R, madness::Localizer::set_method(), madness::Localizer::set_metric(), madness::transform(), madness::transpose(), madness::truncate(), and madness::NemoBase::world.

Referenced by madness::OEP::iterate(), and solve().

◆ make_cphf_constant_term()

vecfuncT madness::Nemo::make_cphf_constant_term	(	const size_t	iatom,
		const int	iaxis,
		const vecfuncT &	R2nemo,
		const real_function_3d &	rhonemo
	)		const

protected

compute the constant term for the CPHF equations

mainly all terms with the nuclear correlation factor's derivatives

References calc, madness::Coulomb< T, NDIM >::compute_potential(), get_calc(), is_dft(), madness::CalculationParameters::lo(), param, madness::Coulomb< T, NDIM >::potential(), Q(), madness::Exchange< T, NDIM >::set_bra_and_ket(), madness::BaseTensor::size(), madness::truncate(), and madness::NemoBase::world.

Referenced by compute_all_cphf().

◆ make_ddensity()

real_function_3d madness::Nemo::make_ddensity	(	const real_function_3d &	rhonemo,
		const int	axis
	)		const

make the derivative of the density

$\nabla\rho = 2R^X R \rho_R + R^2\nabla \rho_R$

Parameters

[in]	rhonemo	the regularized density
[in]	axis	the component of the nabla operator

Returns: the gradient of the reconstructed density

References axis, madness::copy(), madness::NemoBase::R_square, madness::Function< T, NDIM >::refine(), and madness::NemoBase::world.

Referenced by hessian().

◆ make_density() [1/2]

real_function_3d madness::Nemo::make_density	(	const Tensor< double > &	occ,
		const vecfuncT &	nemo
	)		const

make the density (alpha or beta)

References calc, and madness::NemoBase::world.

Referenced by compute_all_cphf(), madness::Coulomb< T, NDIM >::compute_potential(), get_coulomb_potential(), gradient(), hessian(), make_incomplete_hessian(), madness::ParametrizedExchange::operator()(), solve_cphf(), and value().

◆ make_density() [2/2]

real_function_3d madness::Nemo::make_density	(	const tensorT &	occ,
		const vecfuncT &	bra,
		const vecfuncT &	ket,
		const bool	refine = `false`
	)		const

make the density using different bra and ket vectors

e.g. for computing the perturbed density \sum_i \phi_i \phi_i^X or when using nemos: \sum_i R2nemo_i nemo_i

References calc, madness::compress(), madness::WorldGopInterface::fence(), madness::Function< T, NDIM >::gaxpy(), madness::World::gop, madness::mul(), madness::refine(), and madness::NemoBase::world.

◆ make_fock_operator()

std::shared_ptr< Fock< double, 3 > > madness::Nemo::make_fock_operator ( ) const

virtual

construct the fock operator based on the calculation parameters (K or XC?)

Reimplemented from madness::NemoBase.

Reimplemented in madness::OEP.

References ac, madness::AC< NDIM >::apply(), calc, madness::CalculationParameters::charge(), madness::PCM::compute_pcm_potential(), do_ac(), do_pcm(), K(), MADNESS_CHECK, madness::XCOperator< T, NDIM >::make_xc_potential(), molecule(), param, pcm, madness::Coulomb< T, NDIM >::potential(), madness::LocalPotentialOperator< T, NDIM >::set_info(), madness::LocalPotentialOperator< T, NDIM >::set_potential(), madness::Exchange< T, NDIM >::set_symmetric(), madness::CalculationParameters::spin_restricted(), and madness::NemoBase::world.

Referenced by madness::Fock< T, NDIM >::Fock(), and test_nemo().

◆ make_incomplete_hessian()

Tensor< double > madness::Nemo::make_incomplete_hessian ( ) const

protected

compute the incomplete hessian

incomplete hessian is the nuclear-nuclear contribution, and the contribution from the second derivative of the nuclear potential, and also the derivative of the nuclear correlation factor. i.e. all contributions that do not contain the regularized perturbed density, but it will contain parts of the perturbed density

References get_calc(), madness::inner(), make_density(), molecule(), madness::Molecule::natom(), madness::Molecule::nuclear_repulsion_hessian(), madness::NemoBase::R_square, madness::refine(), and madness::NemoBase::world.

Referenced by compute_all_cphf().

◆ make_incomplete_hessian_response_part()

Tensor< double > madness::Nemo::make_incomplete_hessian_response_part ( const std::vector< vecfuncT > & xi ) const

protected

compute the complementary incomplete hessian

Parameters

[in] xi the response functions including the parallel part

References madness::_(), calc, madness::dot(), h(), madness::inner(), molecule(), madness::Molecule::natom(), madness::NemoBase::R_square, madness::NemoBase::world, and xi.

Referenced by compute_all_cphf().

◆ make_laplacian_density()

real_function_3d madness::Nemo::make_laplacian_density ( const real_function_3d & rhonemo ) const

the Laplacian of the density

The Laplacian should currently only be used for subsequent convolution with a Green's function (which is reasonably stable), but not on its own!

The Laplacian of the cuspy density is numerically fairly unstable:

a singular term may be rewritten using the nuclear potential (see below)
the Laplacian of the regularized density is still very noisy

It may be computed as

$\Delta \rho = \Delta (R^2 \rho_R) = \Delta (R^2) \rho_R + 2\nabla R \nabla \rho_R + R^2 \Delta \rho_R = 2 R^2 U1^2 \rho_R -4 R^2 ( U-V ) \rho_R + R^2 \Delta\rho_R$

where we can use the identity

$U=V + R^{-1}[T,R] -2 R (U-V) = \Delta R + 2\nabla R\dot \nabla$

first term comes from the definition of the U potential as the commutator over the kinetic energy (aka the Laplacian)

Parameters

[in] rhonemo the regularized density \rho_R

Returns: the laplacian of the reconstructed density \Delta (R^2\rho_R)

References axis, madness::copy(), get_calc(), madness::constants::pi, poisson, madness::NemoBase::R_square, madness::Function< T, NDIM >::refine(), madness::save(), smoothen(), madness::truncate(), and madness::NemoBase::world.

◆ make_plots()

void madness::Nemo::make_plots	(	const real_function_3d &	f,
		const std::string &	name = `"function"`
	)		const

inlineprotected

References madness::f, madness::FunctionDefaults< NDIM >::get_cell_min_width(), name(), madness::plot_line(), madness::plot_plane(), and madness::NemoBase::world.

◆ make_sigma()

real_function_3d madness::Nemo::make_sigma	(	const real_function_3d &	rho1,
		const real_function_3d &	rho2
	)		const

compute the reduced densities sigma (gamma) for GGA functionals

the reduced density is given by

$\sigma = \nabla\rho_1 \nabla\rho_2 = (\nabla R^2 \rho_{R,1} + R^2 \nabla \rho_{R,1}) \cdot (\nabla R^2 \rho_{R,2} + R^2 \nabla \rho_{R,2}) = 4R^4 U_1^2 \rho_{R,1}\rho_{R,2} + 2R^4 \vec U_1 \left(\rho_{R,1}\nabla \rho_{R,2} + \nabla\rho_{R,1} \rho_{R,2}\right) + R^4 \nabla \rho_{R,1}\cdot \nabla\rho_{R,2}$

References madness::dot(), madness::FunctionDefaults< NDIM >::get_thresh(), madness::grad(), madness::NemoBase::R_square, madness::FunctionDefaults< NDIM >::set_thresh(), thresh, and madness::NemoBase::world.

◆ molecule() [1/2]

Molecule & madness::Nemo::molecule ( )

inlinevirtual

return a reference to the molecule

Reimplemented from madness::MolecularOptimizationTargetInterface.

References calc.

Referenced by Nemo(), compute_all_cphf(), compute_IR_intensities(), compute_nemo_potentials(), hessian(), localize(), make_fock_operator(), make_incomplete_hessian(), make_incomplete_hessian_response_part(), solve_cphf(), test_ethylene(), and test_ne_boys().

◆ molecule() [2/2]

Molecule & madness::Nemo::molecule ( ) const

inline

return a reference to the molecule

References calc.

◆ name()

std::string madness::Nemo::name ( ) const

inlinevirtual

Implements madness::QCPropertyInterface.

Reimplemented in madness::OEP.

Referenced by load_function(), make_plots(), and save_function().

◆ print_parameters()

static void madness::Nemo::print_parameters ( )

inlinestatic

References param, madness::QCCalculationParametersBase::print(), madness::print(), and madness::Molecule::print_parameters().

Referenced by main().

◆ provides_gradient()

bool madness::Nemo::provides_gradient ( ) const

inlinevirtual

Override this to return true if the derivative is implemented.

Reimplemented from madness::OptimizationTargetInterface.

◆ purify_hessian()

Tensor< double > madness::Nemo::purify_hessian ( const Tensor< double > & hessian ) const

purify and symmetrize the hessian

The hessian should be symmetric, but it is not, because

$\langle i^{Y_B}|H^{X_A}|i\rangle \neq \langle i|H^{X_A}|i^{Y_B}\rangle$

does holds analytically, but not numerically. If the two numbers differ, pick the more trustworthy, which is the one with a heavy atom causing the perturbed density and the light atom being the nuclear singularity.

Parameters

[in] hessian the raw hessian

Returns: a symmetrized hessian

References calc, madness::copy(), diff(), hessian(), and madness::print().

Referenced by hessian().

◆ rotate_subspace()

template<typename solverT >

void madness::Nemo::rotate_subspace	(	World &	world,
		const tensorT &	U,
		solverT &	solver,
		int	lo,
		int	nfunc
	)		const

protected

rotate the KAIN subspace (cf. SCF.cc)

References madness::WorldGopInterface::fence(), madness::World::gop, lo, madness::transform(), trantol(), v, and madness::NemoBase::world.

Referenced by madness::OEP::iterate(), and solve().

◆ save_function()

template<typename T , size_t NDIM>

void madness::Nemo::save_function	(	const std::vector< Function< T, NDIM > > &	f,
		const std::string	name
	)		const

protected

save a function

References madness::f, name(), madness::print(), madness::World::rank(), and madness::NemoBase::world.

Referenced by compute_all_cphf(), and hessian().

◆ selftest()

bool madness::Nemo::selftest ( )

inlinevirtual

Implements madness::QCPropertyInterface.

Reimplemented in madness::OEP.

◆ set_protocol()

void madness::Nemo::set_protocol ( const double thresh )

inlineprotected

adapt the thresholds consistently to a common value

References calc, madness::NemoBase::construct_nuclear_correlation_factor(), madness::CoulombOperatorPtr(), madness::timer::end(), get_calc(), madness::CalculationParameters::lo(), madness::Nemo::NemoCalculationParameters::ncf(), madness::NemoBase::need_recompute_factors_and_potentials(), param, poisson, madness::CalculationParameters::print_level(), madness::set_thresh(), thresh, and madness::NemoBase::world.

Referenced by madness::OEP::analyze(), compute_all_cphf(), madness::OEP::selftest(), value(), and madness::OEP::value().

◆ smoothen()

static void madness::Nemo::smoothen ( real_function_3d & f )

inlinestatic

smooth a function by projecting it onto k-1 and then average with k

kept it here for further testing

References madness::f, k, and madness::project().

Referenced by make_laplacian_density().

◆ solve()

double madness::Nemo::solve ( const SCFProtocol & proto )

protected

solve the HF equations

References madness::Tensor< T >::absmax(), calc, madness::NemoBase::check_convergence(), madness::NemoBase::compute_density(), compute_energy_regularized(), compute_nemo_potentials(), madness::copy(), madness::SCFProtocol::dconv, madness::QCPropertyInterface::density(), madness::BaseTensor::dim(), madness::CalculationParameters::do_localize(), do_pcm(), do_symmetry(), madness::CalculationParameters::econv(), madness::SCFProtocol::econv, madness::timer::end(), energy, get_calc(), madness::BSHApply< T, NDIM >::levelshift, madness::BSHApply< T, NDIM >::lo, localize(), madness::matrix_inner(), madness::CalculationParameters::maxiter(), madness::BSHApply< T, NDIM >::metric, madness::mul(), madness::norm2(), madness::NemoBase::normalize(), madness::CalculationParameters::orbitalshift(), madness::NemoBase::orthonormalize(), param, madness::print(), madness::CalculationParameters::print_level(), madness::NemoBase::R, madness::NemoBase::R_square, madness::World::rank(), residual(), rotate_subspace(), madness::CalculationParameters::save(), madness::BaseTensor::size(), madness::World::size(), symmetry_projector, T(), madness::timer::tag(), madness::transform(), trantol(), madness::truncate(), madness::wall_time(), and madness::NemoBase::world.

Referenced by value().

◆ solve_cphf()

vecfuncT madness::Nemo::solve_cphf	(	const size_t	iatom,
		const int	iaxis,
		const Tensor< double >	fock,
		const vecfuncT &	guess,
		const vecfuncT &	rhsconst,
		const Tensor< double >	incomplete_hessian,
		const vecfuncT &	parallel,
		const SCFProtocol &	proto,
		const std::string &	xc_data
	)		const

solve the CPHF equations for the nuclear displacements

solve the CPHF equation for the nuclear displacements

this function computes that part of the orbital response that is orthogonal to the occupied space. If no NCF's are used this corresponds to the normal response. If NCF's are used the part parallel to the occupied space must be added!

$F^X = F^\perp + F^\parallel$

cf parallel_CPHF()

Parameters

[in]	iatom	the atom A to be moved
[in]	iaxis	the coordinate X of iatom to be moved

Returns: \ket{i^X} or \ket{F^\perp}

Parameters

[in]	iatom	the atom A to be moved
[in]	iaxis	the coordinate X of iatom to be moved

Returns: \frac{\partial}{\partial X_A} \varphi

References madness::_(), madness::Tensor< T >::absmax(), madness::apply(), b, calc, madness::Coulomb< T, NDIM >::compute_potential(), madness::copy(), madness::SCFProtocol::dconv, madness::CalculationParameters::do_localize(), madness::dot(), madness::gaxpy(), get_calc(), guess(), h(), madness::inner(), is_dft(), K(), madness::CalculationParameters::lo(), make_density(), molecule(), madness::mul(), madness::Molecule::natom(), norm(), madness::norm2(), madness::norm2s(), param, madness::Coulomb< T, NDIM >::potential(), madness::print(), Q(), madness::NemoBase::R_square, madness::World::rank(), residual(), madness::scale(), madness::Exchange< T, NDIM >::set_bra_and_ket(), madness::Exchange< T, NDIM >::set_symmetric(), madness::World::size(), madness::CalculationParameters::spin_restricted(), madness::stringify(), madness::transform(), trantol(), madness::truncate(), V(), madness::NemoBase::world, xc, and xi.

Referenced by compute_all_cphf().

◆ trantol()

double madness::Nemo::trantol ( ) const

inlineprotected

return the threshold for vanishing elements in orbital rotations

References calc, and get_calc().

Referenced by rotate_subspace(), solve(), and solve_cphf().

◆ value() [1/2]

virtual double madness::Nemo::value ( )

inlinevirtual

Reimplemented in madness::OEP.

References calc, and value().

Referenced by main(), test_fock(), test_nemo(), and value().

◆ value() [2/2]

double madness::Nemo::value ( const Tensor< double > & x )

virtual

Friends And Related Symbol Documentation

◆ PNO

friend class PNO

friend

◆ TDHF

friend class TDHF

friend

Member Data Documentation

◆ ac

AC<3> madness::Nemo::ac

protected

asymptotic correction for DFT

Referenced by compute_nemo_potentials(), get_ac(), and make_fock_operator().

◆ calc

std::shared_ptr<SCF> madness::Nemo::calc

protected

Referenced by Nemo(), madness::OEP::OEP(), madness::OEP::analyze(), compute_all_cphf(), madness::OEP::compute_and_print_final_energies(), compute_cphf_parallel_term(), madness::OEP::compute_E_first(), madness::OEP::compute_energy(), compute_energy_regularized(), compute_fock_matrix(), compute_nemo_potentials(), get_calc(), get_coulomb_potential(), gradient(), hessian(), is_dft(), madness::OEP::iterate(), kinetic_energy_potential(), madness::OEP::load_restartdata(), localize(), make_cphf_constant_term(), make_density(), make_density(), make_fock_operator(), make_incomplete_hessian_response_part(), molecule(), molecule(), madness::OEP::output_calc_info_schema(), purify_hessian(), madness::OEP::save_restartdata(), madness::OEP::selftest(), set_protocol(), solve(), madness::OEP::solve(), solve_cphf(), trantol(), value(), madness::OEP::value(), value(), and madness::OEP::value().

◆ coords_sum

double madness::Nemo::coords_sum

mutableprivate

sum of square of coords at last solved geometry

Referenced by value().

◆ param

NemoCalculationParameters madness::Nemo::param

◆ pcm

PCM madness::Nemo::pcm

private

polarizable continuum model

Referenced by Nemo(), compute_energy_regularized(), compute_nemo_potentials(), get_pcm(), and make_fock_operator().

◆ poisson

std::shared_ptr<real_convolution_3d> madness::Nemo::poisson

protected

a poisson solver

Referenced by kinetic_energy_potential(), make_laplacian_density(), and set_protocol().

◆ symmetry_projector

projector_irrep madness::Nemo::symmetry_projector

protected

Referenced by Nemo(), do_symmetry(), get_symmetry_projector(), madness::OEP::iterate(), and solve().

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

Classes

Public Member Functions

Static Public Member Functions

Public Attributes

Protected Member Functions

Protected Attributes

Private Types

Private Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ poperatorT

Constructor & Destructor Documentation

◆ Nemo()

Member Function Documentation

◆ compute_all_cphf()

◆ compute_cphf_parallel_term()

◆ compute_energy_regularized()

◆ compute_fock_matrix()

◆ compute_IR_intensities()

◆ compute_nemo_potentials()

◆ do_ac()

◆ do_pcm()

◆ do_symmetry()

◆ get_ac()

◆ get_calc()

◆ get_coulomb_potential()

◆ get_param()

◆ get_pcm()

◆ get_symmetry_projector()

◆ gradient()

◆ help()

◆ hessian()

◆ is_dft()

◆ kinetic_energy_potential()

◆ load_function()

◆ localize()

◆ make_cphf_constant_term()

◆ make_ddensity()

◆ make_density() [1/2]

◆ make_density() [2/2]

◆ make_fock_operator()

◆ make_incomplete_hessian()

◆ make_incomplete_hessian_response_part()

◆ make_laplacian_density()

◆ make_plots()

◆ make_sigma()

◆ molecule() [1/2]

◆ molecule() [2/2]

◆ name()

◆ print_parameters()

◆ provides_gradient()

◆ purify_hessian()

◆ rotate_subspace()

◆ save_function()

◆ selftest()

◆ set_protocol()

◆ smoothen()

◆ solve()

◆ solve_cphf()

◆ trantol()

◆ value() [1/2]

◆ value() [2/2]

Friends And Related Symbol Documentation

◆ PNO

◆ TDHF

Member Data Documentation

◆ ac

◆ calc

◆ coords_sum

◆ param

◆ pcm

◆ poisson

◆ symmetry_projector