Similar to the time-dependent Hartree-Fock method, but expands dPsi corrections using a basis to include core-polarisation (RPA) corrections to matrix elements of some external field operator. More...

#include <TDHFbasis.hpp>

Inherits ExternalField::TDHF.

Public Member Functions
	TDHFbasis (const DiracOperator::TensorOperator const h, const HF::HartreeFock const hf, const std::vector< DiracSpinor > &basis)

virtual void	solve_core (const double omega, int max_its=100, const bool print=true) override final
	Solves TDHF equations self-consistantly for core electrons at frequency omega, using basis expansion.

virtual Method	method () const override final
	Returns RPA method.

delta epsilon psi f delta epsilon Psi f DiracSpinor	form_dPsi (const DiracSpinor &Fv, const double omega, dPsiType XorY, const int kappa_beta, const std::vector< DiracSpinor > &spectrum, StateType st=StateType::ket, bool incl_dV=true) const
	Forms \delta Psi_v for valence state Fv (including core pol.) - 1 kappa.

std::vector< DiracSpinor >	form_dPsis (const DiracSpinor &Fv, const double omega, dPsiType XorY, const std::vector< DiracSpinor > &spectrum, StateType st=StateType::ket, bool incl_dV=true) const
	Forms \delta Psi_v for valence state Fv for all kappas (see form_dPsi)

TDHFbasis &	operator= (const TDHFbasis &)=delete

	TDHFbasis (const TDHFbasis &)=default

Public Member Functions inherited from ExternalField::TDHF
	TDHF (const DiracOperator::TensorOperator const h, const HF::HartreeFock const hf)
	Contruct TDHF operator: takes pointer to operator and to HF object.

virtual void	clear () override final
	Clears the dPsi orbitals (sets to zero)

double	dV (const DiracSpinor &Fa, const DiracSpinor &Fb, bool conj) const
	Calculate reduced matrix element <a\|\|dV\|\|b> or <a\|\|dV*\|\|b>. Will exclude orbital 'Fexcl' from sum over core (for tests only)

virtual double	dV (const DiracSpinor &Fa, const DiracSpinor &Fb) const override final
	As above, but automatically determines if 'conjugate' version required (Based on sign of [en_a-en_b])

DiracSpinor	dV_rhs (const int kappa_n, const DiracSpinor &Fm, bool conj=false) const
	Returns "reduced partial matrix element RHS": dV\|\|Fb}. Note: Fa * dV_rhs(..) equiv to dV(..)

const std::vector< DiracSpinor > &	get_dPsis (const DiracSpinor &Fc, dPsiType XorY) const
	Returns const ref to dPsi orbitals for given core orbital Fc.

const DiracSpinor &	get_dPsi_x (const DiracSpinor &Fc, dPsiType XorY, const int kappa_x) const
	Returns const reference to dPsi orbital of given kappa.

DiracSpinor	solve_dPsi (const DiracSpinor &Fv, const double omega, dPsiType XorY, const int kappa_beta, const MBPT::CorrelationPotential *const Sigma=nullptr, StateType st=StateType::ket, bool incl_dV=true) const
	Forms \delta Psi_v for valence state Fv (including core pol.) - 1 kappa.

std::vector< DiracSpinor >	solve_dPsis (const DiracSpinor &Fv, const double omega, dPsiType XorY, const MBPT::CorrelationPotential *const Sigma=nullptr, StateType st=StateType::ket, bool incl_dV=true) const
	Forms \delta Psi_v for valence state Fv for all kappas (see solve_dPsi)

TDHF &	operator= (const TDHF &)=delete

	TDHF (const TDHF &)=default

Public Member Functions inherited from ExternalField::CorePolarisation
double	last_eps () const
	Returns eps (convergance) of last solve_core run.

double	last_its () const
	Returns its (# of iterations) of last solve_core run.

double	last_omega () const
	Returns omega (frequency) of last solve_core run.

int	rank () const

int	parity () const

bool	imagQ () const

double &	eps_target ()
	Convergance target.

double	eps_target () const
	Convergance target.

double	eta () const
	Damping factor; 0 means no damping. Must have 0 <= eta < 1.

void	set_eta (double eta)
	Set/update damping factor; 0 means no damping. Must have 0 <= eta < 1.

CorePolarisation &	operator= (const CorePolarisation &)=delete

	CorePolarisation (const CorePolarisation &)=default

Additional Inherited Members
Protected Member Functions inherited from ExternalField::CorePolarisation
	CorePolarisation (const DiracOperator::TensorOperator *const h)

Protected Attributes inherited from ExternalField::TDHF
std::vector< std::vector< DiracSpinor > >	m_X {}

std::vector< std::vector< DiracSpinor > >	m_Y {}

std::vector< std::vector< DiracSpinor > >	m_hFcore {}

const HF::HartreeFock *const	p_hf

const std::vector< DiracSpinor >	m_core

const double	m_alpha

const HF::Breit *const	p_VBr

Protected Attributes inherited from ExternalField::CorePolarisation
const DiracOperator::TensorOperator *	m_h

double	m_core_eps {1.0}

int	m_core_its {0}

double	m_core_omega {0.0}

int	m_rank

int	m_pi

bool	m_imag

double	m_eta {0.4}

double	m_eps {1.0e-10}

Detailed Description

Similar to the time-dependent Hartree-Fock method, but expands dPsi corrections using a basis to include core-polarisation (RPA) corrections to matrix elements of some external field operator.

Like the TDHF method, but uses a basis: Note: Benefit is we can include Breit into dV while using a basis (unlike diagramRPA method). Downside, it's quite slow (though maybe could be made much more efficient)

Member Function Documentation

◆ form_dPsi()

DiracSpinor ExternalField::TDHFbasis::form_dPsi	(	const DiracSpinor &	Fv,
		const double	omega,
		dPsiType	XorY,
		const int	kappa_beta,
		const std::vector< DiracSpinor > &	spectrum,
		StateType	st = `StateType::ket`,
		bool	incl_dV = `true`
	)		const

Forms \delta Psi_v for valence state Fv (including core pol.) - 1 kappa.

Solves or Returns \( \chi_\beta \) for given kappa_beta, where

\[ X_{j,m} = (-1)^{j_\beta-m}tjs(j,k,j;-m,0,m)\chi_j \]

XorY takes values: dPsiType::X or dPsiType::Y. st takes values: StateType::ket or StateType::bra. Solves by expanding over basis. To include correlations, use basis with correlations.

◆ form_dPsis()

std::vector< DiracSpinor > ExternalField::TDHFbasis::form_dPsis	(	const DiracSpinor &	Fv,
		const double	omega,
		dPsiType	XorY,
		const std::vector< DiracSpinor > &	spectrum,
		StateType	st = `StateType::ket`,
		bool	incl_dV = `true`
	)		const

Forms \delta Psi_v for valence state Fv for all kappas (see form_dPsi)

Forms \delta Psi_v for valence state Fv for all kappas (see solve_dPsi)

◆ method()

virtual Method ExternalField::TDHFbasis::method ( ) const

inlinefinaloverridevirtual

Returns RPA method.

Reimplemented from ExternalField::TDHF.

◆ solve_core()

void ExternalField::TDHFbasis::solve_core	(	const double	omega,
		int	max_its = `100`,
		const bool	print = `true`
	)

finaloverridevirtual

Solves TDHF equations self-consistantly for core electrons at frequency omega, using basis expansion.

Solves TDHF equations (using a basis to expand the states) self-consistantly for core electrons at frequency omega. Will iterate up to a maximum of max_its. Set max_its=1 to get first-order correction [note: no dampling is used for first itteration]. If print=true, will write progress to screen