ExternalField::TDHF

Uses time-dependent Hartree-Fock method to include core-polarisation (RPA) corrections to matrix elements of some external field operator. More...

#include <TDHF.hpp>

Inherits ExternalField::CorePolarisation.

Inherited by ExternalField::TDHFbasis.

Public Member Functions
	TDHF (const DiracOperator::TensorOperator *const h, const HF::HartreeFock *const hf)
	Contruct TDHF operator: takes pointer to operator and to HF object.
virtual void	solve_core (const double omega, int max_its=100, const bool print=true) override
	Solves TDHF equations self-consistantly for core electrons at frequency omega. More...
virtual Method	method () const override
	Returns RPA method.
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. More...
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

Protected Attributes
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}

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

Detailed Description

Uses time-dependent Hartree-Fock method to include core-polarisation (RPA) corrections to matrix elements of some external field operator.

Solves set of TDHF equations

\[ (H -\epsilon \pm \omega)\delta\psi_b = -(\delta V + \delta\epsilon_c)\psi_b \]

self consistantly for each electron in the core to determine dV. (See 'ampsci.pdf' for detailed physics description). There is an option to limit the maximum number of iterations; set to 1 to get the first-order correction (nb: no damping is used for first iteration).

Construction

Requires a pointer to an operator (h), a const HF object (const pointer).

Usage

solve_core(omega) solves TDHF eqs for given frequency. Frequency should be positive, but is allowed to be negative (use as a test only, with care). Can be run again with a different frequency, typically does not need to be re-started from scratch. Then, dV(Fa,Fb) returns the correction to the matrix element:

\[ \langle \phi_a || \delta V || \phi_b \rangle \]

Member Function Documentation

solve_core()

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

overridevirtual

Solves TDHF equations 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 damping is used for first itteration]. If print=true, will write progress to screen.

Implements ExternalField::CorePolarisation.

Reimplemented in ExternalField::TDHFbasis.

solve_dPsi()

DiracSpinor ExternalField::TDHF::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.

Solves

\[ (H + \Sigma - \epsilon - \omega)X = -(h + \delta V - \delta\epsilon)\psi \]

or

\[ (H + \Sigma - \epsilon + \omega)Y = -(h^\dagger + \delta V^\dagger - \delta\epsilon)Psi\]

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

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

• ExternalField/TDHF.hpp
• ExternalField/TDHF.cpp