#include <electronic/ExCorr_internal_LDA.h>

Classes
class	FunctionalGGA
	Common interface to the compute kernels for GGA-like functionals. More...

struct	GGA_calc< variant, spinScaling, nCount >

struct	GGA_calc< variant, true, nCount >
	Specialization of GGA_calc for spin-scaling functionals (exchange and KE) More...

struct	GGA_calc< variant, false, nCount >
	Specialization of GGA_calc for functionals that do not spin-scale (correlation) More...

struct	GGA_calc< GGA_X_GLLBsc, true, nCount >

struct	GGA_calc< GGA_X_LB94, true, nCount >

Macros
#define	SwitchTemplate_GGA(variant, nCount, fTemplate, argList)

Enumerations
enum	GGA_Variant { GGA_X_PBE, GGA_C_PBE, GGA_X_PBEsol, GGA_C_PBEsol, GGA_X_PW91, GGA_C_PW91, GGA_X_wPBE_SR, GGA_X_GLLBsc, GGA_X_LB94, GGA_KE_VW, GGA_KE_PW91 }
	Available GGA functionals. More...

Functions
template<GGA_Variant variant>
__hostanddev__ double	GGA_eval (double rs, double s2, double &e_rs, double &e_s2)

template<GGA_Variant variant>
__hostanddev__ double	GGA_eval (double rs, double zeta, double g, double t2, double &e_rs, double &e_zeta, double &e_g, double &e_t2)

__hostanddev__ double	slaterExchange (double rs, double &e_rs)
	Slater exchange as a function of rs (PER PARTICLE):

__hostanddev__ double	GGA_PBE_exchange (const double kappa, const double mu, double rs, double s2, double &e_rs, double &e_s2)
	PBE GGA exchange [JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)].

template<>
__hostanddev__ double	GGA_eval< GGA_X_PBE > (double rs, double s2, double &e_rs, double &e_s2)
	PBE GGA exchange [JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)].

template<>
__hostanddev__ double	GGA_eval< GGA_X_PBEsol > (double rs, double s2, double &e_rs, double &e_s2)
	PBEsol GGA exchange [JP Perdew et al, Phys. Rev. Lett. 100, 136406 (2008)].

__hostanddev__ double	GGA_PW91_Enhancement (double s2, double &F_s2, const double P, const double Q, const double R, const double S, const double T, const double U)

template<>
__hostanddev__ double	GGA_eval< GGA_X_PW91 > (double rs, double s2, double &e_rs, double &e_s2)
	PW91 GGA exchange [JP Perdew et al, Phys. Rev. B 46, 6671 (1992)].

template<int n>
__hostanddev__ double	integralErfcGaussian (double A, double B, double &result_A, double &result_B)
	Evaluate $\int_0^\infty dy y^n e^{-Ay^2} \textrm{erfc}{By}$ and its derivatives.

template<>
__hostanddev__ double	integralErfcGaussian< 1 > (double A, double B, double &result_A, double &result_B)

template<>
__hostanddev__ double	integralErfcGaussian< 2 > (double A, double B, double &result_A, double &result_B)

template<>
__hostanddev__ double	integralErfcGaussian< 3 > (double A, double B, double &result_A, double &result_B)

template<>
__hostanddev__ double	integralErfcGaussian< 5 > (double A, double B, double &result_A, double &result_B)

template<>
__hostanddev__ double	GGA_eval< GGA_X_wPBE_SR > (double rs, double s2, double &e_rs, double &e_s2)

__hostanddev__ double	PW91_H0 (const double gamma, double beta, double g3, double t2, double ecUnif, double &H0_beta, double &H0_g3, double &H0_t2, double &H0_ecUnif)

__hostanddev__ double	GGA_PBE_correlation (const double beta, const double beta_rs, double rs, double zeta, double g, double t2, double &e_rs, double &e_zeta, double &e_g, double &e_t2)

template<>
__hostanddev__ double	GGA_eval< GGA_C_PBE > (double rs, double zeta, double g, double t2, double &e_rs, double &e_zeta, double &e_g, double &e_t2)
	PBE GGA correlation [JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)].

template<>
__hostanddev__ double	GGA_eval< GGA_C_PBEsol > (double rs, double zeta, double g, double t2, double &e_rs, double &e_zeta, double &e_g, double &e_t2)
	PBEsol GGA correlation [JP Perdew et al, Phys. Rev. Lett. 100, 136406 (2008)].

template<>
__hostanddev__ double	GGA_eval< GGA_C_PW91 > (double rs, double zeta, double g, double t2, double &e_rs, double &e_zeta, double &e_g, double &e_t2)
	PW91 GGA correlation [JP Perdew et al, Phys. Rev. B 46, 6671 (1992)].

__hostanddev__ double	TFKinetic (double rs, double &e_rs)
	Thomas Fermi kinetic energy as a function of rs (PER PARTICLE):

template<>
__hostanddev__ double	GGA_eval< GGA_KE_VW > (double rs, double s2, double &e_rs, double &e_s2)
	von Weisacker gradient correction to Thomas Fermi LDA kinetic energy (with correct gradient expansion parameter lambda)

template<>
__hostanddev__ double	GGA_eval< GGA_KE_PW91 > (double rs, double s2, double &e_rs, double &e_s2)
	PW91k GGA kinetic energy [PRB 46, 6671-6687 (1992)] parameterized by Lembarki and Chermette [PRA 50, 5328-5331 (1994)].

Detailed Description

Shared CPU-GPU implementation of GGA functionals

Macro Definition Documentation

#define SwitchTemplate_GGA	(	variant,
		nCount,
		fTemplate,
		argList
	)

Value:

switch(variant) \
        {       case GGA_X_PBE:     fTemplate< GGA_X_PBE,     true, nCount> argList; break; \
                case GGA_C_PBE:     fTemplate< GGA_C_PBE,    false, nCount> argList; break; \
                case GGA_X_PBEsol:  fTemplate< GGA_X_PBEsol,  true, nCount> argList; break; \
                case GGA_C_PBEsol:  fTemplate< GGA_C_PBEsol, false, nCount> argList; break; \
                case GGA_X_PW91:    fTemplate< GGA_X_PW91,    true, nCount> argList; break; \
                case GGA_C_PW91:    fTemplate< GGA_C_PW91,   false, nCount> argList; break; \
                case GGA_X_wPBE_SR: fTemplate< GGA_X_wPBE_SR, true, nCount> argList; break; \
                case GGA_X_GLLBsc:  fTemplate< GGA_X_GLLBsc,  true, nCount> argList; break; \
                case GGA_X_LB94:    fTemplate< GGA_X_LB94,    true, nCount> argList; break; \
                case GGA_KE_VW:     fTemplate< GGA_KE_VW,     true, nCount> argList; break; \
                case GGA_KE_PW91:   fTemplate< GGA_KE_PW91,   true, nCount> argList; break; \
                default: break; \
        }

Switch a function fTemplate templated over GGA variant, spin scaling behavior and spin count, over all supported functionals with nCount being a compile-time constant NOTE: The second argument to fTemplate must correspond to the spin-scaling behavior of each functional (Used by the thread and gpu launchers of FunctionalGGA::evaluate) (This is needed to switch from a run-time variant to a compile-time template argument)

Enumeration Type Documentation

enum GGA_Variant

Available GGA functionals.

Enumerator
GGA_X_PBE	Perdew-Burke-Ernzerhof GGA exchange.
GGA_C_PBE	Perdew-Burke-Ernzerhof GGA correlation.
GGA_X_PBEsol	Perdew-Burke-Ernzerhof GGA exchange reparametrized for solids.
GGA_C_PBEsol	Perdew-Burke-Ernzerhof GGA correlation reparametrized for solids.
GGA_X_PW91	Perdew-Wang 1991 GGA exchange.
GGA_C_PW91	Perdew-Wang 1991 GGA correlation.
GGA_X_wPBE_SR	Short-ranged part of omega-PBE exchange (used in HSE06 hybrid)
GGA_X_GLLBsc	Semi-local part of GLLB-sc exchange (potential-only, equal to 2x PBEsol per-particle energy)
GGA_X_LB94	van Leeuwen-Baerends asymptotically-correct exchange potential correction (potential-only)
GGA_KE_VW	von Weisacker gradient correction to Thomas Fermi LDA kinetic energy
GGA_KE_PW91	Teter GGA kinetic energy.

Function Documentation

template<GGA_Variant variant>

__hostanddev__ double GGA_eval	(	double	rs,
		double	s2,
		double &	e_rs,
		double &	e_s2
	)

GGA interface inner layer for spin-scaling functionals (specialized for each such functional): Return energy density given rs and dimensionless gradient squared s2, and set gradients w.r.t rs and s2

template<GGA_Variant variant>

__hostanddev__ double GGA_eval	(	double	rs,
		double	zeta,
		double	g,
		double	t2,
		double &	e_rs,
		double &	e_zeta,
		double &	e_g,
		double &	e_t2
	)

GGA interface inner layer for functionals that do not spin-scale (specialized for each such functional): Return energy density given rs, zeta, g(zeta) and dimensionless gradient squared t2, and set gradients w.r.t rs, zeta, g(zeta) and t2 (see PW91 ref for definitions)

template<>

__hostanddev__ double GGA_eval< GGA_X_wPBE_SR >	(	double	rs,
		double	s2,
		double &	e_rs,
		double &	e_s2
	)

Short-ranged omega-PBE GGA exchange - used in the HSE06 hybrid functional [J Heyd, G E Scuseria, and M Ernzerhof, J. Chem. Phys. 118, 3865 (2003)]

__hostanddev__ double GGA_PBE_correlation	(	const double	beta,
		const double	beta_rs,
		double	rs,
		double	zeta,
		double	g,
		double	t2,
		double &	e_rs,
		double &	e_zeta,
		double &	e_g,
		double &	e_t2
	)

PBE GGA correlation [JP Perdew, K Burke, and M Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)] If beta depends on rs (as in revTPSS), beta_rs (=dbeta/drs) is propagated to e_rs

__hostanddev__ double GGA_PW91_Enhancement	(	double	s2,
		double &	F_s2,
		const double	P,
		const double	Q,
		const double	R,
		const double	S,
		const double	T,
		const double	U
	)

Functional form of the PW91 Exchange Enhancement factor (also used in some KE functionals) Implements equation (8) in [JP Perdew et al, Phys. Rev. B 46, 6671 (1992)] and its gradients P,Q,R,S,T,U are the parameters in order of appearance in that equation

__hostanddev__ double PW91_H0	(	const double	gamma,
		double	beta,
		double	g3,
		double	t2,
		double	ecUnif,
		double &	H0_beta,
		double &	H0_g3,
		double &	H0_t2,
		double &	H0_ecUnif
	)

The H0 function (equations 13,14) of PW91 and its derivatives. Also the H fuunction (equations 7,8) of PBE. The notation is a mixture, picking the shortest of both references: using g from PW91 (phi in PBE) and gamma from PBE (beta^2/(2*alpha) in PW91).

Classes

Macros

Enumerations

Functions

Detailed Description

Macro Definition Documentation

Enumeration Type Documentation

Function Documentation