ContinuumOrbitals

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Stores set of continuum orbitals, and solves using Hartree-Fock method.

Solves in the Hartree-Fock potential (solveContinuumHF), or in a H-like potential with effective charge (solveContinuumZeff, or analytically with solveContinuumZeffAnalytic). Orbitals are energy-normalised (see DiracODE::solveContinuum). Each solve appends to orbitals (see clear).

#include <ContinuumOrbitals.hpp>

Public Member Functions
	ContinuumOrbitals (const Wavefunction &wf)
	Takes existing Wavefunction object to construct.
	ContinuumOrbitals (const HF::HartreeFock *hf)
	Construct with Hartree-Fock pointer.
ContinuumOrbitals &	operator= (const ContinuumOrbitals &)=default
	ContinuumOrbitals (const ContinuumOrbitals &)=default
int	solveContinuumHF (double ec, int min_l, int max_l, const DiracSpinor *psi=nullptr, bool force_rescale=false, bool subtract_self=true, bool force_orthog=true, bool average_tail=false)
	Solves continuum states with energy ec between min/max l.
int	solveContinuumZeff (double ec, int min_l, int max_l, double Z_eff, const DiracSpinor *Fi, bool force_orthog, bool average_tail=false)
	Solves cntm states using simple H-like potential with Z_eff.
int	solveContinuumZeffAnalytic (double ec, int min_l, int max_l, double Z_eff, const DiracSpinor *Fi, bool force_orthog)
	As solveContinuumZeff, but uses exact analytic Dirac-Coulomb states.
double	check_orthog (bool print=true) const
	Checks orthogonality between cntm and core orbitals.
void	clear ()
	Resets (deletes) all orbitals.

Public Attributes
std::vector< DiracSpinor >	orbitals {}
	The continuum orbitals (each solve appends to this list)

Constructor & Destructor Documentation

ContinuumOrbitals() [1/2]

ContinuumOrbitals::ContinuumOrbitals

(

const Wavefunction &

wf

)

Takes existing Wavefunction object to construct.

Stores the grid, alpha, and a pointer to its HF object (may be nullptr if HF not set; only the Zeff methods may then be used).

Warning

The HF pointer is stored: wf must outlive this object.

ContinuumOrbitals() [2/2]

ContinuumOrbitals::ContinuumOrbitals

(

const HF::HartreeFock *

hf

)

Construct with Hartree-Fock pointer.

Pointer is stored: must outlive this object. Must not be nullptr.

Member Function Documentation

solveContinuumHF()

int ContinuumOrbitals::solveContinuumHF	(	double	ec,
		int	min_l,
		int	max_l,
		const DiracSpinor *	psi = nullptr,
		bool	force_rescale = false,
		bool	subtract_self = true,
		bool	force_orthog = true,
		bool	average_tail = false
	)

Solves continuum states with energy ec between min/max l.

Solves for each kappa with min_l <= l <= max_l, in the HF local potential (vnuc + vdir + vrad). For non-local methods (HartreeFock, ApproxHF), exchange with the full core is then included iteratively (damped; at most 50 iterations, until |dF|^2/|F|^2 < 1e-6; no warning if not converged).

Parameters

ec	Continuum energy (au, > 0)
min_l	Minimum l
max_l	Maximum l
psi	Ionised (bound) state; optional (nullptr: none)
force_rescale	Rescale large-r part of the local potential, so it falls off no slower than -Zion/r: V(r) -> min(V(r), -Zion/r), with Zion = max(1, -r V(r)) at the last grid point
subtract_self	Subtract the self-interaction of psi from the direct potential, \( y^0_{\psi\psi}(r) \) (V^{N-1} potential of the ion)
force_orthog	Orthogonalise to the core states of the same kappa, and to psi (to psi also at each exchange iteration)
average_tail	Fill the (zeroed) unresolved high-r tail with a local average (see DiracODE::averageTail); done after exchange, before orthogonalisation

Returns

0 on success; 1 if there is no Hartree-Fock object (constructed from a Wavefunction with no HF): prints a warning, and no orbitals are solved.

Note

force_rescale and subtract_self only apply for the HartreeFock, Hartree, and ApproxHF methods.

solveContinuumZeff()

int ContinuumOrbitals::solveContinuumZeff	(	double	ec,
		int	min_l,
		int	max_l,
		double	Z_eff,
		const DiracSpinor *	Fi,
		bool	force_orthog,
		bool	average_tail = false
	)

Solves cntm states using simple H-like potential with Z_eff.

Potential is \( -Z_{\rm eff}/r \) (point-like). Usually, \( Z_{\rm eff} = n\sqrt{2 I_{njl}} \), with \( I_{njl} \) the ionisation energy (au) and n the principal quantum number of the initial state.

Parameters

ec	Continuum energy (au, > 0)
min_l	Minimum l
max_l	Maximum l
Z_eff	Effective charge
Fi	Ionised (bound) state; may be nullptr
force_orthog	Orthogonalise to Fi (only; not the core)
average_tail	Fill the (zeroed) unresolved high-r tail with a local average (see DiracODE::averageTail)

Returns

0 (always).

solveContinuumZeffAnalytic()

int ContinuumOrbitals::solveContinuumZeffAnalytic	(	double	ec,
		int	min_l,
		int	max_l,
		double	Z_eff,
		const DiracSpinor *	Fi,
		bool	force_orthog
	)

As solveContinuumZeff, but uses exact analytic Dirac-Coulomb states.

Uses exact analytic Dirac-Coulomb functions rather than solving the ODE numerically (see DiracSpinor::exactHlike_cntm). Evaluated pointwise over the entire grid, so there is no tail cut-off (cf. solveContinuumZeff).

Returns

0 (always).

Warning

Relativistic case requires FLINT (see DiracContinuum::available): otherwise prints a warning, and the orbitals are NaN (or an assert fails, in debug builds).

check_orthog()

double ContinuumOrbitals::check_orthog

(

bool

print = true

)

const

Checks orthogonality between cntm and core orbitals.

Overlaps with core states of the same kappa; prints each if print.

Returns

Worst eps: the largest-magnitude overlap (signed); 0 if no HF.

clear()

void ContinuumOrbitals::clear

(

)

Resets (deletes) all orbitals.

Member Data Documentation

orbitals

std::vector<DiracSpinor> ContinuumOrbitals::orbitals {}

The continuum orbitals (each solve appends to this list)

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

• Wavefunction/ContinuumOrbitals.hpp
• Wavefunction/ContinuumOrbitals.cpp