ExternalField::TDHFbasis

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Like TDHF, but solves the TDHF equations via basis expansion.

Same physics as TDHF; see that class for full description. The perturbed core orbitals are found via the basis expansion

\[ \varphi^a_\pm = \sum_n \frac{\ket{n}\matel{n}{t_\pm + \delta V_\pm}{a}}{\en_a - \en_n \pm \omega}, \]

rather than by solving the inhomogeneous ODE directly.

Warning

Does not currently work correctly for frequency-dependent operators unless they depend only on the magnitude \( |\omega| \). The method assumes \( t_- = t_+^\dag \), whereas the correct relation is \( t_-(\omega) = t_+^\dag(-\omega) \). This will be fixed in a future update.

#include <TDHFbasis.hpp>

Inheritance diagram for ExternalField::TDHFbasis:

Public Member Functions
	TDHFbasis (const DiracOperator::TensorOperator *const h, const HF::HartreeFock *const hf, const std::vector< DiracSpinor > &basis)
	Constructs TDHFbasis for operator h using the provided basis.
virtual void	solve_core (const double omega, int max_its=100, const bool print=true) override final
	See TDHF::solve_core(); same notes and warnings apply.
virtual Method	method () const override final
	Returns RPA method.
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 varphi^v_pm for valence state Fv: single kappa channel.
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 varphi^v_pm for valence state Fv: all kappa channels.
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)
	Constructs TDHF for operator h.
virtual void	clear () override final
	Clears the internal state back to pre solve_core()
double	dV (const DiracSpinor &Fa, const DiracSpinor &Fb, bool conj) const
	Returns reduced matrix element \(\redmatel{a}{\delta V}{b}\), or the conjugate \(\redmatel{a}{\delta V^\dagger}{b}\) if conj=true.
virtual double	dV (const DiracSpinor &Fa, const DiracSpinor &Fb) const override final
	Returns reduced matrix element <n||dV_pm||m> (see namespace doc for dV_pm)
DiracSpinor	dV_rhs (int kappa_n, const DiracSpinor &Fm, bool conj=false) const override
	Returns [dV_pm * phi_m]_kappa: RHS of TDHF eq., projected onto kappa (see namespace doc)
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 ref 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 \(\varphi^v_\pm\) for valence state Fv (including core pol.): single kappa channel.
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 \(\varphi^v_\pm\) for all kappa channels; 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
	Rank of the operator.
int	parity () const
	Parity of the operator.
bool	imagQ () const
	Returns true if the operator is imaginary.
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}

Constructor & Destructor Documentation

TDHFbasis()

ExternalField::TDHFbasis::TDHFbasis	(	const DiracOperator::TensorOperator *const	h,
		const HF::HartreeFock *const	hf,
		const std::vector< DiracSpinor > &	basis
	)

Constructs TDHFbasis for operator h using the provided basis.

Parameters

h	External field operator.
hf	HF::HartreeFock object defining the core.
basis	Single-particle basis used to expand \( \varphi^a_\pm \). The entire basis is used; caller must ensure all required states are present.

Member Function Documentation

solve_core()

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

finaloverridevirtual

See TDHF::solve_core(); same notes and warnings apply.

Reimplemented from ExternalField::TDHF.

method()

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

inlinefinaloverridevirtual

Returns RPA method.

Reimplemented from ExternalField::TDHF.

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 varphi^v_pm for valence state Fv: single kappa channel.

Solves the TDHF equation via basis expansion for a single kappa channel; see TDHF::solve_dPsi() for the equation. Returns \( \chi_\beta \) for given kappa_beta, where

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

Parameters

Fv	Valence state \( \phi_v \).
omega	Perturbation frequency \( \omega \).
XorY	Selects X or Y solution; see dPsiType.
kappa_beta	Kappa quantum number of the target channel.
spectrum	Single-particle spectrum used to expand the solution.
st	Bra or ket convention; see StateType.
incl_dV	Include the induced potential \( \delta V \) if true.

Note

To include correlations, use a basis with correlations.

To exclude excitations to occupied states, remove them from the basis.

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 varphi^v_pm for valence state Fv: all kappa channels.

Calls form_dPsi() for all allowed \( \kappa \) channels.

Parameters

Fv	Valence state \( \phi_v \).
omega	Perturbation frequency \( \omega \).
XorY	Selects the X or Y solution; see dPsiType.
spectrum	Single-particle spectrum used to construct the solution.
st	Bra or ket convention; see StateType.
incl_dV	Include the induced potential \( \delta V \) if true.

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

• ExternalField/TDHFbasis.hpp
• ExternalField/TDHFbasis.cpp