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Breit potentials for one- (Hartree-Fock Breit) and two-body Breit integrals.

#include <Breit.hpp>

Classes
struct	Params
	Parameters for constructing Breit interaction operator (s,m,n,o,p,f) More...

Public Member Functions
	Breit ()
	Constructs Breit with default parameters.

	Breit (const Params &params)
	Constructs Breit interaction operator from parameters.

void	update_scale (double t_scale=1.0, double t_M=1.0, double t_N=1.0, double t_O=1.0, double t_P=1.0)
	Update all scaling factors.

void	update_lambda_f (double lambda_f)
	Update frequency scaling factor.

void	fill_gb (const std::vector< DiracSpinor > &basis, int t_max_k=99)
	Precompute Breit integral lookup tables for rapid evaluation.

double	scale_factor () const
	Returns the overall scaling factor.

DiracSpinor	VbrFa (const DiracSpinor &Fa, const std::vector< DiracSpinor > &core) const
	Calculates Breit contribution with automatic frequency dependence.

DiracSpinor	dV_Br (int kappa, int K, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Xbeta, const DiracSpinor &Ybeta) const
	Breit-TDHF: Breit correction to the TDHF correction to Hartree-Fock.

DiracSpinor	Bkv_bcd (int k, int kappa_v, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Direct Breit two-body integral "right-hand-side".

DiracSpinor	BPkv_bcd (int k, int kappa_v, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Exchange Breit two-body integral "right-hand-side".

DiracSpinor	BWkv_bcd (int k, int kappa_v, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Anti-symmetrised Breit two-body integral "right-hand-side".

double	Bk_abcd (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Reduced static Breit two-body matrix element.

double	BPk_abcd (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Reduced static exchange Breit two-body matrix element.

double	BWk_abcd (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Reduced static anti-symmetrised Breit two-body matrix element.

double	Bk_abcd_2 (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Reduced static Breit matrix element (tabulated, fast lookup)

double	BPk_abcd_2 (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Reduced exchange Breit matrix element (tabulated, fast lookup)

double	BWk_abcd_2 (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Reduced anti-symmetrised Breit matrix element (tabulated, fast lookup)

double	de2_HF (const DiracSpinor &Fv, const std::vector< DiracSpinor > &holes, const std::vector< DiracSpinor > &excited) const
	The one-body Breit (Breit-Hartree-Fock) correction to second-order energy.

double	de2 (const DiracSpinor &Fv, const std::vector< DiracSpinor > &holes, const std::vector< DiracSpinor > &excited) const
	The two-body Breit correction to second-order energy.

double	Bk_abcd_freqw (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Frequency-dependent reduced Breit two-body matrix element.

double	BPk_abcd_freqw (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Frequency-dependent reduced exchange Breit two-body matrix element.

double	BWk_abcd_freqw (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd) const
	Frequency-dependent reduced anti-symmetrised Breit two-body matrix element.

double	Bk_abcd_freqw (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd, const double w) const
	Frequency-dependent reduced Breit two-body matrix element (explicit frequency)

double	BPk_abcd_freqw (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd, const double w) const
	Frequency-dependent reduced exchange Breit two-body matrix element (explicit frequency)

double	BWk_abcd_freqw (int k, const DiracSpinor &Fa, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd, const double w) const
	Frequency-dependent reduced anti-symmetrised Breit two-body matrix element (explicit frequency)

DiracSpinor	Bkv_bcd_freqw (int k, int kappa_v, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd, const double w) const
	Frequency-dependent Breit two-body integral "right-hand-side".

DiracSpinor	BPkv_bcd_freqw (int k, int kappa_v, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd, const double w) const
	Frequency-dependent exchange Breit two-body integral "right-hand-side".

DiracSpinor	BWkv_bcd_freqw (int k, int kappa_v, const DiracSpinor &Fb, const DiracSpinor &Fc, const DiracSpinor &Fd, const double w) const
	Frequency-dependent anti-symmetrised Breit two-body integral "right-hand-side".

Static Public Member Functions
static bool	Bk_SR (int k, const DiracSpinor &v, const DiracSpinor &w, const DiracSpinor &x, const DiracSpinor &y)
	Selection rule check for Breit integrals.

static std::pair< int, int >	k_minmax (const DiracSpinor &a, const DiracSpinor &b, const DiracSpinor &c, const DiracSpinor &d)
	Determine valid multipolarity range for Breit integrals.

static std::pair< int, int >	k_minmax_tj (int tja, int tjb, int tjc, int tjd)
	Determine valid multipolarity range for Breit integrals from quantum numbers.

Class Documentation

◆ HF::Breit::Params

struct HF::Breit::Params

Class Members
double	scale {1.0}	Overall scaling factor for Breit contributions (default 1.0)
double	m {1.0}	Scaling for M term (Gaunt part, default 1.0)
double	n {1.0}	Scaling for N term (Gaunt part, default 1.0)
double	o {1.0}	Scaling for O term (retarded part, default 1.0)
double	p {1.0}	Scaling for P term (retarded part, default 1.0)
double	lambda_f {0.0}	Scaling factor for frequency in frequency-dependent Breit (default 0.0 = static)

Constructor & Destructor Documentation

◆ Breit() [1/2]

HF::Breit::Breit ( )

inline

Constructs Breit with default parameters.

Equivalent to Breit(Params{}). See Breit::Params for default values.

◆ Breit() [2/2]

HF::Breit::Breit ( const Params & params )

inlineexplicit

Constructs Breit interaction operator from parameters.

Creates a Breit operator with scaling factors specified in Params. See Params for documentation of each scaling factor.

Parameters

params Params struct containing all scaling factors

Member Function Documentation

◆ update_scale()

void HF::Breit::update_scale	(	double	t_scale = `1.0`,
		double	t_M = `1.0`,
		double	t_N = `1.0`,
		double	t_O = `1.0`,
		double	t_P = `1.0`
	)

inline

Update all scaling factors.

Updates the overall scaling factor, individual term scaling factors (M, N, O, P), and the frequency scaling factor for frequency-dependent Breit calculations.

Parameters

t_scale	Overall scaling factor (default 1.0)
t_M	Scaling for M term (Gaunt part, default 1.0)
t_N	Scaling for N term (Gaunt part, default 1.0)
t_O	Scaling for O term (retarded part, default 1.0)
t_P	Scaling for P term (retarded part, default 1.0)

Note: Does not update lambda_f (f-dependent scaling). Use update_lambda_f() for that.

◆ update_lambda_f()

void HF::Breit::update_lambda_f ( double lambda_f )

inline

Update frequency scaling factor.

Sets the scaling factor for the frequency in frequency-dependent Breit calculations. The frequency used in the integrals is multiplied by this factor.

Parameters

lambda_f Frequency scaling factor (should be > 0; default 1.0)

Note: Setting lambda_f to very small values approaches the static Breit limit.

◆ Bk_SR()

static bool HF::Breit::Bk_SR	(	int	k,
		const DiracSpinor &	v,
		const DiracSpinor &	w,
		const DiracSpinor &	x,
		const DiracSpinor &	y
	)

inlinestatic

Selection rule check for Breit integrals.

Tests whether the four-body Breit integral B^k_{vwxy} is nonzero based on angular momentum selection rules.

Parameters

k	Multipolarity (angular momentum rank of the interaction)
v	(w,x,y): electron states

Returns: True if the integral is potentially nonzero (angular momentum selection rules are satisfied); false if the integral vanishes.

◆ k_minmax()

static std::pair< int, int > HF::Breit::k_minmax	(	const DiracSpinor &	a,
		const DiracSpinor &	b,
		const DiracSpinor &	c,
		const DiracSpinor &	d
	)

inlinestatic

Determine valid multipolarity range for Breit integrals.

Minimum and maximum allowed multipolarity k for a four-body Breit integral.

Parameters

a	(b,c,d) electron states

Returns: A pair {k_min, k_max} giving the valid multipolarity range. Returns with k_max < k_min (invalid range) if no valid k exists.

Note: This is the static method analogue of Coulomb::k_minmax_tj, adapted for the four-body Breit structure.

◆ k_minmax_tj()

static std::pair< int, int > HF::Breit::k_minmax_tj	(	int	tja,
		int	tjb,
		int	tjc,
		int	tjd
	)

inlinestatic

Determine valid multipolarity range for Breit integrals from quantum numbers.

As k_minmax but for 2*j (doesn't require DiracSpinors)

◆ fill_gb()

void HF::Breit::fill_gb	(	const std::vector< DiracSpinor > &	basis,
		int	t_max_k = `99`
	)

Precompute Breit integral lookup tables for rapid evaluation.

Pre-calculates and stores reduced Breit integrals for all unique pairs of basis orbitals and all multipolarity values k, enabling much faster integral lookups via the Bk_abcd_2() family of functions. This trades memory for speed, allowing rapid evaluation in HF iterations.

Parameters

basis	The set of basis orbitals to use
t_max_k	Maximum multipolarity k to compute (default 99). Actual maximum used is the minimum of this value and the physical constraint k_minmax() for the given basis.

Warning: This function uses substantial memory – use with caution for large calculations. Have mostly found the speedup is not worth the memory cost, so this is generally not used anymore. Used in CI.

Note: Must be called once before using the faster variants Bk_abcd_2(), BPk_abcd_2(), or BWk_abcd_2(). Calling it multiple times will recompute and overwrite previous results.

Warning: ONLY for static Breit

◆ scale_factor()

double HF::Breit::scale_factor ( ) const

inline

Returns the overall scaling factor.

◆ VbrFa()

DiracSpinor HF::Breit::VbrFa	(	const DiracSpinor &	Fa,
		const std::vector< DiracSpinor > &	core
	)		const

Calculates Breit contribution with automatic frequency dependence.

Computes the Hartree-Fock Breit interaction V_br*Fa for a valence electron interacting with the core. This is the direct Breit contribution from all core electrons.

Will be static version is lambda = 0, otherwise, frequency-dependent.

Parameters

Fa	Valence electron state
core	Core electron states

Returns: The Breit-Hartree-Fock potential applied to Fa, computed at the appropriate frequency regime based on m_lambda_f.

Note: For frequency-dependent calculations, this may be substantially slower due to spherical Bessel function evaluation in the radial integrals.

◆ dV_Br()

DiracSpinor HF::Breit::dV_Br	(	int	kappa,
		int	K,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Xbeta,
		const DiracSpinor &	Ybeta
	)		const

Breit-TDHF: Breit correction to the TDHF correction to Hartree-Fock.

Calculates the Breit correction to the TDHF potential, dV. This represents the response of the Breit field to the core electron perturbations.

Parameters

kappa	Dirac quantum number of the resulting state/projection
K	Multipolarity (rank) of the RPA operator
Fa	Electron state (acting on this)
Fb	Core state undergoing perturbation
Xbeta	X perturbation to core state: from ExternalField::TDHF
Ybeta	Y perturbation to core state: from ExternalField::TDHF

Returns: The reduced RPA correction dV_Br*Fa

Note: Only frequency-independent for now

◆ Bkv_bcd()

DiracSpinor HF::Breit::Bkv_bcd	(	int	k,
		int	kappa_v,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Direct Breit two-body integral "right-hand-side".

Computes the radial function of the direct part of the reduced Breit operator acting on an orbital with quantum number kappa_v. This is defined such that the two-body matrix element factorises as:

\[ B^k_{abcd} = \langle a | B^k_v(b,c,d) \rangle \]

Note: Frequency independent version

See Bk_abcd()

◆ BPkv_bcd()

DiracSpinor HF::Breit::BPkv_bcd	(	int	k,
		int	kappa_v,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Exchange Breit two-body integral "right-hand-side".

See Bkv_bcd() and BPk_abcd()

Note: Frequency independent version

◆ BWkv_bcd()

DiracSpinor HF::Breit::BWkv_bcd	(	int	k,
		int	kappa_v,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Anti-symmetrised Breit two-body integral "right-hand-side".

See Bkv_bcd() and BWk_abcd()

Note: Frequency independent version

◆ Bk_abcd()

double HF::Breit::Bk_abcd	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Reduced static Breit two-body matrix element.

Calculates the static (frequency-independent) reduced two-body Breit matrix element B^k_{abcd}, the Breit analogue of the Coulomb Q^k integral.

Note: Frequency independent version

Parameters

k	Multipolarity (angular momentum rank of the interaction)
Fa	(Fb,Fc,Fd) electron states

Returns: The static reduced Breit matrix element B^k_{abcd}.

Note: Selection rules depend on angular momentum quantum numbers via Bk_SR(). Use k_minmax() to determine the valid multipolarity range before calling.; This function re-computes all radial integrals each call. For repeated calls with the same basis, call fill_gb() once, then use the faster variant Bk_abcd_2() instead.

◆ BPk_abcd()

double HF::Breit::BPk_abcd	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Reduced static exchange Breit two-body matrix element.

Calculates the static reduced exchange Breit matrix element P(B)^k_{abcd}, the Breit analogue of the Coulomb P^k integral.

Note: Frequency independent version

◆ BWk_abcd()

double HF::Breit::BWk_abcd	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Reduced static anti-symmetrised Breit two-body matrix element.

Calculates the static reduced anti-symmetrised Breit matrix element W(B)^k_{abcd} = B^k_{abcd} + P(B)^k_{abcd}.

Note: Frequency independent version

◆ Bk_abcd_2()

double HF::Breit::Bk_abcd_2	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Reduced static Breit matrix element (tabulated, fast lookup)

A faster implementation of Bk_abcd() that looks up pre-tabulated integrals computed by fill_gb(). Reduces computational cost, at significant memory cost.

The result is the same as Bk_abcd() for the same inputs, provided fill_gb() has been called at least once on a basis containing Fa, Fb, Fc, Fd.

Parameters

k	Multipolarity (angular momentum rank of the interaction)
Fa	(Fb,Fc,Fd) electron states

Returns: The reduced Breit matrix element B^k_{abcd}, retrieved from the cached m_gb tables.

Note: REQUIRES: fill_gb() must have been called before this function can be used. If fill_gb() has not been called, this function returns zero or garbage data. This function assumes the spinors Fa, Fb, Fc, Fd were members of the basis passed to fill_gb(); using spinors outside that basis is undefined.

Warning: Do not use this function unless fill_gb() has been successfully called.

Note: Only implemented for frequency independent case

◆ BPk_abcd_2()

double HF::Breit::BPk_abcd_2	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Reduced exchange Breit matrix element (tabulated, fast lookup)

A much faster implementation of BPk_abcd() that looks up pre-tabulated exchange integrals computed by fill_gb(). Reduces computational cost from O(radial grid size) per call to O(1) lookup.

The result is identical to BPk_abcd() for the same inputs, provided fill_gb() has been called at least once on a basis containing all four electron states.

Parameters

k	Multipolarity (angular momentum rank of the interaction)
Fa	(Fb,Fc,Fd) electron states

Returns: The reduced exchange Breit matrix element P(B)^k_{abcd}, retrieved from the cached m_gb tables.

Note: REQUIRES: fill_gb() must have been called before this function can be used. The spinors must be members of the basis provided to fill_gb().

Warning: Do not use this function unless fill_gb() has been successfully called.

Note: Only implemented for frequency independent case

◆ BWk_abcd_2()

double HF::Breit::BWk_abcd_2	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Reduced anti-symmetrised Breit matrix element (tabulated, fast lookup)

A much faster implementation of BWk_abcd() that looks up pre-tabulated integrals computed by fill_gb(). Combines the tabulated direct and exchange terms for O(1) evaluation.

The result is identical to BWk_abcd() for the same inputs, provided fill_gb() has been called at least once on a basis containing all four electron states.

Parameters

k	Multipolarity (angular momentum rank of the interaction)
Fa	(Fb,Fc,Fd) electron states

Returns: The reduced anti-symmetrised Breit matrix element W(B)^k_{abcd} = Bk_abcd_2(...) + BPk_abcd_2(...), retrieved from cached m_gb tables.

Note: REQUIRES: fill_gb() must have been called before this function can be used. The spinors must be members of the basis provided to fill_gb().

Warning: Do not use this function unless fill_gb() has been successfully called.

Note: Only implemented for frequency independent case

◆ de2_HF()

double HF::Breit::de2_HF	(	const DiracSpinor &	Fv,
		const std::vector< DiracSpinor > &	holes,
		const std::vector< DiracSpinor > &	excited
	)		const

The one-body Breit (Breit-Hartree-Fock) correction to second-order energy.

Calculates the one-body Breit (Breit-Hartree-Fock) correction to second-order energy for a single-valence atom. This is included automatically if Breit is included into Hartree-Fock. (The lowest-order Breit correction <v|V_Br|v> not included.)

Parameters

Fv	The valence electron state of interest
holes	Occupied core electron states
excited	Virtual excited electron states

Returns: The one-body Breit correction to second-order energy: delta E^(2, 1).

Note: This represents only the one-particle (Hartree-Fock) contribution. The two-particle (Sigma) contribution is computed by de2(). For Breit-Coulomb self-consistent HF, this is already accounted for and should not be added separately.

Warning: May significantly overcount or undercount energy shifts if Breit-Coulomb HF is not self-consistent. Use primarily as a correction term in perturbative Breit-on-Coulomb calculations.

Note: Will automatically include freuqnecy-dependence if lambda non-zero

◆ de2()

double HF::Breit::de2	(	const DiracSpinor &	Fv,
		const std::vector< DiracSpinor > &	holes,
		const std::vector< DiracSpinor > &	excited
	)		const

The two-body Breit correction to second-order energy.

Calculates the two-body Breit correction to second-order energy for a single-valence atom. This is not included automatically if Breit is included into Hartree-Fock, since it requires modification of two-body Coulomb integals.

Note: This is just the energy shift - Breit can be included fully into MBPT calculations self-consistantly another way (see MBPT)

Note
Only frequency independent

◆ Bk_abcd_freqw() [1/2]

double HF::Breit::Bk_abcd_freqw	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Frequency-dependent reduced Breit two-body matrix element.

Automatically determines frequency, based on DiracSpinors
Frequency-dependent analogue of Bk_abcd(). See Bkv_bcd_freqw().

◆ BPk_abcd_freqw() [1/2]

double HF::Breit::BPk_abcd_freqw	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Frequency-dependent reduced exchange Breit two-body matrix element.

Automatically determines frequency, based on DiracSpinors
Frequency-dependent analogue of BPk_abcd(). See Bkv_bcd_freqw().

◆ BWk_abcd_freqw() [1/2]

double HF::Breit::BWk_abcd_freqw	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd
	)		const

Frequency-dependent reduced anti-symmetrised Breit two-body matrix element.

Automatically determines frequency, based on DiracSpinors
Frequency-dependent analogue of BWk_abcd(). See Bkv_bcd_freqw().

◆ Bk_abcd_freqw() [2/2]

double HF::Breit::Bk_abcd_freqw	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd,
		const double	w
	)		const

Frequency-dependent reduced Breit two-body matrix element (explicit frequency)

Frequency-dependent analogue of Bk_abcd(). See Bkv_bcd_freqw().

◆ BPk_abcd_freqw() [2/2]

double HF::Breit::BPk_abcd_freqw	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd,
		const double	w
	)		const

Frequency-dependent reduced exchange Breit two-body matrix element (explicit frequency)

Frequency-dependent analogue of BPk_abcd(). See Bkv_bcd_freqw().

◆ BWk_abcd_freqw() [2/2]

double HF::Breit::BWk_abcd_freqw	(	int	k,
		const DiracSpinor &	Fa,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd,
		const double	w
	)		const

Frequency-dependent reduced anti-symmetrised Breit two-body matrix element (explicit frequency)

Frequency-dependent analogue of BWk_abcd(). See Bkv_bcd_freqw().

◆ Bkv_bcd_freqw()

DiracSpinor HF::Breit::Bkv_bcd_freqw	(	int	k,
		int	kappa_v,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd,
		const double	w
	)		const

Frequency-dependent Breit two-body integral "right-hand-side".

Frequency-dependent breit analogue of Bkv_bcd()

◆ BPkv_bcd_freqw()

DiracSpinor HF::Breit::BPkv_bcd_freqw	(	int	k,
		int	kappa_v,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd,
		const double	w
	)		const

Frequency-dependent exchange Breit two-body integral "right-hand-side".

Frequency-dependent version of BPkv_bcd(). See Bkv_bcd_freqw().

◆ BWkv_bcd_freqw()

DiracSpinor HF::Breit::BWkv_bcd_freqw	(	int	k,
		int	kappa_v,
		const DiracSpinor &	Fb,
		const DiracSpinor &	Fc,
		const DiracSpinor &	Fd,
		const double	w
	)		const

Frequency-dependent anti-symmetrised Breit two-body integral "right-hand-side".

Frequency-dependent version of BWkv_bcd(). See Bkv_bcd_freqw().

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

HF/Breit.hpp
HF/Breit.cpp

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Classes

Public Member Functions

Static Public Member Functions

Class Documentation

◆ HF::Breit::Params

Constructor & Destructor Documentation

◆ Breit() [1/2]

◆ Breit() [2/2]

Member Function Documentation

◆ update_scale()

◆ update_lambda_f()

◆ Bk_SR()

◆ k_minmax()

◆ k_minmax_tj()

◆ fill_gb()

◆ scale_factor()

◆ VbrFa()

◆ dV_Br()

◆ Bkv_bcd()

◆ BPkv_bcd()

◆ BWkv_bcd()

◆ Bk_abcd()

◆ BPk_abcd()

◆ BWk_abcd()

◆ Bk_abcd_2()

◆ BPk_abcd_2()

◆ BWk_abcd_2()

◆ de2_HF()

◆ de2()

◆ Bk_abcd_freqw() [1/2]

◆ BPk_abcd_freqw() [1/2]

◆ BWk_abcd_freqw() [1/2]

◆ Bk_abcd_freqw() [2/2]

◆ BPk_abcd_freqw() [2/2]

◆ BWk_abcd_freqw() [2/2]

◆ Bkv_bcd_freqw()

◆ BPkv_bcd_freqw()

◆ BWkv_bcd_freqw()