Files
file	ExCorr.h

file	ExCorr_internal.h

file	ExCorr_internal_GGA.h

file	ExCorr_internal_LDA.h

file	ExCorr_internal_mGGA.h

Classes
class	ExactExchange
	Exact-exchange calculator. More...

struct	IncludeTXC
	Which components to include in the results of ExCorr::operator() More...

class	ExCorr
	Exchange-Correlation energy calculator. More...

class	Functional
	Abstract base class for functionals. More...

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 >

class	FunctionalLDA
	Common interface to the compute kernels shared by all LDA functionals. More...

struct	LDA_calc< variant, nCount >

struct	LDA_calc< LDA_KE_TF, nCount >
	Specialization of LDA_calc for Thomas-Fermi kinetic energy (compute directly in n[s]) More...

struct	LDA_calc< LDA_X_Slater, nCount >
	Specialization of LDA_calc for Slater exchange (compute directly in n[s]; zeta not required) More...

struct	LDA_eval_C_PZ< para >

struct	LDA_eval_C_PW< spinID, prec >

struct	LDA_eval_C_VWN< spinID >

class	FunctionalMGGA
	Common interface to the compute kernels for mGGA-like functionals. More...

struct	mGGA_calc< variant, spinScaling, nCount >

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

struct	mGGA_calc< variant, false, nCount >

struct	ExCorr_OrbitalDep_GLLBsc
	Orbital-dependent GLLBsc functional. More...

Macros
#define	SwitchTemplate_spin(SwitchTemplate_functional, variant, nCount, fTemplate, argList)

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

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

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

Enumerations
enum	ExCorrType { ExCorrLDA_PZ, ExCorrLDA_PW, ExCorrLDA_PW_prec, ExCorrLDA_VWN, ExCorrLDA_Teter, ExCorrGGA_PBE, ExCorrGGA_PBEsol, ExCorrGGA_PW91, ExCorrMGGA_TPSS, ExCorrMGGA_revTPSS, ExCorrORB_GLLBsc, ExCorrPOT_LB94, ExCorrHYB_PBE0, ExCorrHYB_HSE06, ExCorrHYB_HSE12, ExCorrHYB_HSE12s, ExCorrHF }
	Types of exchange correlation functionals. More...

enum	KineticType { KineticNone, KineticTF, KineticVW, KineticPW91 }
	Types of kinetic energy functionals. More...

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...

enum	LDA_Variant { LDA_X_Slater, LDA_C_PZ, LDA_C_PW, LDA_C_PW_prec, LDA_C_VWN, LDA_XC_Teter, LDA_KE_TF }
	Available LDA functionals. More...

enum	mGGA_Variant { mGGA_X_TPSS, mGGA_C_TPSS, mGGA_X_revTPSS, mGGA_C_revTPSS }
	Available mGGA functionals. More...

Functions
__hostanddev__ void	loadSpinVector (array< const double *, 4 > x, int i, double &x0, vector3<> &xVec)
	Utility function for converting to/from spin-density matrices to scalar+vector combinations (via Pauli matrices)

__hostanddev__ void	accumSpinVectorGrad (const double &E_x0, const vector3<> &E_xVec, array< double *, 4 > E_x, int i)

__hostanddev__ void	spinDiagonalize_calc (int i, array< const double , 4 > n, array< const double , 4 > x, array< double *, 2 > xDiag)
	Transform spin-density-matrix-like quantity x into the basis where spin-density-matrix n is diagonal, and store the diagonal components in xDiag (for noncollinear magnetism)

__hostanddev__ void	spinDiagonalizeGrad_calc (int i, array< const double , 4 > n, array< const double , 4 > x, array< const double , 2 > E_xDiag, array< double , 4 > E_n, array< double *, 4 > E_x)
	Propagate gradients corresponding to spinDiagonalize_calc(), from E_xDiag and accumulate to E_n and E_x.

__hostanddev__ double	spinInterpolation (double zeta, double &f_zeta)
	LDA spin interpolation function f(zeta) and its derivative.

template<typename Para , typename Ferro >
__hostanddev__ double	spinInterpolate (double rs, double zeta, double &e_rs, double &e_zeta, const Para &para, const Ferro &ferro)
	Spin-interpolate an LDA functional given its paramagnetic and ferromagnetic functors.

template<typename Para , typename Ferro , typename Stiff >
__hostanddev__ double	spinInterpolate (double rs, double zeta, double &e_rs, double &e_zeta, const Para &para, const Ferro &ferro, const Stiff &stiff, const double fDblPrime0=4./(9 *(pow(2., 1./3)-1)))

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)].

template<LDA_Variant variant>
__hostanddev__ double	LDA_eval (double rs, double zeta, double &e_rs, double &e_zeta)

template<>
__hostanddev__ double	LDA_eval< LDA_C_PZ > (double rs, double zeta, double &e_rs, double &e_zeta)
	Perdew-Zunger correlation.

template<>
__hostanddev__ double	LDA_eval< LDA_C_PW > (double rs, double zeta, double &e_rs, double &e_zeta)
	Perdew-Wang correlation (original version, for numerical compatibility with LibXC's PW91)

template<>
__hostanddev__ double	LDA_eval< LDA_C_PW_prec > (double rs, double zeta, double &e_rs, double &e_zeta)
	Perdew-Wang correlation (extended precision version, for numerical compatibility with LibXC's PBE)

template<>
__hostanddev__ double	LDA_eval< LDA_C_VWN > (double rs, double zeta, double &e_rs, double &e_zeta)
	Vosko-Wilk-Nusair correlation.

template<>
__hostanddev__ double	LDA_eval< LDA_XC_Teter > (double rs, double zeta, double &e_rs, double &e_zeta)
	Teter LSD exchange & correlation [Phys. Rev. B 54, 1703 (1996)].

template<mGGA_Variant variant>
__hostanddev__ double	mGGA_eval (double rs, double s2, double q, double z, double &e_rs, double &e_s2, double &e_q, double &e_z)

template<mGGA_Variant variant>
__hostanddev__ double	mGGA_eval (double rs, double zeta, double g, double t2, double t2up, double t2dn, double zi2, double z, double &e_rs, double &e_zeta, double &e_g, double &e_t2, double &e_t2up, double &e_t2dn, double &e_zi2, double &e_z)

template<bool revised>
__hostanddev__ double	mGGA_TPSS_Exchange (double rs, double s2, double q, double z, double &e_rs, double &e_s2, double &e_q, double &e_z)

template<>
__hostanddev__ double	mGGA_eval< mGGA_X_TPSS > (double rs, double s2, double q, double z, double &e_rs, double &e_s2, double &e_q, double &e_z)
	TPSS Exchange: J.P. Perdew et al, Phys. Rev. Lett. 91, 146401 (2003)

template<>
__hostanddev__ double	mGGA_eval< mGGA_X_revTPSS > (double rs, double s2, double q, double z, double &e_rs, double &e_s2, double &e_q, double &e_z)
	revTPSS Exchange: J.P. Perdew et al, Phys. Rev. Lett. 103, 026403 (2009)

template<bool revised>
__hostanddev__ double	betaTPSS (double rs, double &beta_rs)
	Compute beta(rs) for the TPSS/revTPSS correlation functionals.

template<bool revised>
__hostanddev__ double	mGGA_TPSS_Correlation (double rs, double zeta, double g, double t2, double t2up, double t2dn, double zi2, double z, double &e_rs, double &e_zeta, double &e_g, double &e_t2, double &e_t2up, double &e_t2dn, double &e_zi2, double &e_z)

template<>
__hostanddev__ double	mGGA_eval< mGGA_C_TPSS > (double rs, double zeta, double g, double t2, double t2up, double t2dn, double zi2, double z, double &e_rs, double &e_zeta, double &e_g, double &e_t2, double &e_t2up, double &e_t2dn, double &e_zi2, double &e_z)
	TPSS Correlation: J.P. Perdew et al, Phys. Rev. Lett. 91, 146401 (2003)

template<>
__hostanddev__ double	mGGA_eval< mGGA_C_revTPSS > (double rs, double zeta, double g, double t2, double t2up, double t2dn, double zi2, double z, double &e_rs, double &e_zeta, double &e_g, double &e_t2, double &e_t2up, double &e_t2dn, double &e_zi2, double &e_z)
	revTPSS Correlation: J.P. Perdew et al, Phys. Rev. Lett. 103, 026403 (2009)

Detailed Description

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)

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

Value:

switch(variant) \
        {       case LDA_X_Slater:  fTemplate< LDA_X_Slater,  nCount> argList; break; \
                case LDA_C_PZ:      fTemplate< LDA_C_PZ,      nCount> argList; break; \
                case LDA_C_PW:      fTemplate< LDA_C_PW,      nCount> argList; break; \
                case LDA_C_PW_prec: fTemplate< LDA_C_PW_prec, nCount> argList; break; \
                case LDA_C_VWN:     fTemplate< LDA_C_VWN,     nCount> argList; break; \
                case LDA_XC_Teter:  fTemplate< LDA_XC_Teter,  nCount> argList; break; \
                case LDA_KE_TF:     fTemplate< LDA_KE_TF,     nCount> argList; break; \
                default: break; \
        }

Switch a function fTemplate templated over LDA variant and spin count, over all supported functionals with nCount being a compile-time constant (Used by the thread and gpu launchers of FunctionalLDA::evaluate) (This is needed to switch from a run-time variant to a compile-time template argument)

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

Value:

switch(variant) \
        {       case mGGA_X_TPSS:    fTemplate< mGGA_X_TPSS,     true, nCount> argList; break; \
                case mGGA_C_TPSS:    fTemplate< mGGA_C_TPSS,    false, nCount> argList; break; \
                case mGGA_X_revTPSS: fTemplate< mGGA_X_revTPSS,  true, nCount> argList; break; \
                case mGGA_C_revTPSS: fTemplate< mGGA_C_revTPSS, false, nCount> argList; break; \
                default: break; \
        }

Switch a function fTemplate templated over mGGA 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 FunctionalMGGA::evaluate) (This is needed to switch from a run-time variant to a compile-time template argument)

#define SwitchTemplate_spin	(	SwitchTemplate_functional,
		variant,
		nCount,
		fTemplate,
		argList
	)

Value:

switch(nCount) \
        {       case 1: { SwitchTemplate_functional(variant,1, fTemplate,argList) break; } \
                case 2: { SwitchTemplate_functional(variant,2, fTemplate,argList) break; } \
                default: break; \
        }

Switch a function fTemplate templated over a functional variant and spin count SwitchTemplate_functional is a macro such as SwitchTemplate_LDA (This is needed to switch from a run-time nCount to a compile-time template argument)

Enumeration Type Documentation

enum ExCorrType

Types of exchange correlation functionals.

Enumerator
ExCorrLDA_PZ	Perdew-Zunger LDA.
ExCorrLDA_PW	Perdew-Wang LDA (original version used in PW91)
ExCorrLDA_PW_prec	Perdew-Wang LDA with higher precision constants used in PBE.
ExCorrLDA_VWN	Vosko-Wilk-Nusair LDA.
ExCorrLDA_Teter	Teter93 LSDA functional.
ExCorrGGA_PBE	PBE GGA functional.
ExCorrGGA_PBEsol	PBE GGA functional reparametrized for solids.
ExCorrGGA_PW91	PW91 GGA functional.
ExCorrMGGA_TPSS	TPSS meta-GGA functional.
ExCorrMGGA_revTPSS	revised meta-GGA functional
ExCorrORB_GLLBsc	GLLB-sc orbital-dependent potential (no total energy)
ExCorrPOT_LB94	Leeuwen-Baerends potentialfunctional (no total energy)
ExCorrHYB_PBE0	PBE0 Hybrid GGA functional.
ExCorrHYB_HSE06	HSE06 Screened Hybrid GGA functional.
ExCorrHYB_HSE12s	Reparametrized screened exchange functional for accuracy.
ExCorrHF	Reparametrized screened exchange functional for minimum screening length. Hartree-Fock

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.

enum KineticType

Types of kinetic energy functionals.

Enumerator
KineticNone	No kinetic energy (default)
KineticTF	Thomas-Fermi LDA kinetic energy.
KineticVW	von Weisacker GGA kinetic energy
KineticPW91	PW91 GGA kinetic energy.

enum LDA_Variant

Available LDA functionals.

Enumerator
LDA_X_Slater	LDA exchange (Slater functional)
LDA_C_PZ	Perdew-Zunger LDA correlation.
LDA_C_PW	Perdew-Wang LDA correlation.
LDA_C_PW_prec	Perdew-Wang LDA correlation (with higher precision constants used in PBE)
LDA_C_VWN	Vosko-Wilk-Nusair LDA correlation.
LDA_XC_Teter	Teter LDA exchange and correlation.
LDA_KE_TF	Thomas-Fermi kinetic energy functional.

enum mGGA_Variant

Available mGGA functionals.

Enumerator
mGGA_X_TPSS	TPSS mGGA exchange.
mGGA_C_TPSS	TPSS mGGA correlation.
mGGA_X_revTPSS	revTPSS mGGA exchange
mGGA_C_revTPSS	revTPSS mGGA correlation

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

template<LDA_Variant variant>

__hostanddev__ double LDA_eval	(	double	rs,
		double	zeta,
		double &	e_rs,
		double &	e_zeta
	)

LDA interface inner layer (specialize for each functional): Return energy density given rs and zeta and set gradients w.r.t rs and zeta

template<mGGA_Variant variant>

__hostanddev__ double mGGA_eval	(	double	rs,
		double	s2,
		double	q,
		double	z,
		double &	e_rs,
		double &	e_s2,
		double &	e_q,
		double &	e_z
	)

GGA interface inner layer for spin-scaling functionals (specialized for each such functional): Return energy density given dimensionless quantities rs, s2, q and z, and set gradients w.r.t them See the PBE / TPSS refs for definitions of these quantities

template<mGGA_Variant variant>

__hostanddev__ double mGGA_eval	(	double	rs,
		double	zeta,
		double	g,
		double	t2,
		double	t2up,
		double	t2dn,
		double	zi2,
		double	z,
		double &	e_rs,
		double &	e_zeta,
		double &	e_g,
		double &	e_t2,
		double &	e_t2up,
		double &	e_t2dn,
		double &	e_zi2,
		double &	e_z
	)

GGA interface inner layer for functionals that do not spin-scale (specialized for each such functional): Return energy density given rs, zeta, g, t2 (see PW91 ref for definitions of these), t2up, t2dn (the individual spin versions of t2) zi2 (the dimensionless grad zeta squared term) and z = tauW/tau (totals, not spin resolved) and set gradients w.r.t them

template<bool revised>

__hostanddev__ double mGGA_TPSS_Correlation	(	double	rs,
		double	zeta,
		double	g,
		double	t2,
		double	t2up,
		double	t2dn,
		double	zi2,
		double	z,
		double &	e_rs,
		double &	e_zeta,
		double &	e_g,
		double &	e_t2,
		double &	e_t2up,
		double &	e_t2dn,
		double &	e_zi2,
		double &	e_z
	)

TPSS or revTPSS Correlation depending on revised = false/true J.P. Perdew et al, Phys. Rev. Lett. 91, 146401 (2003) [TPSS] J.P. Perdew et al, Phys. Rev. Lett. 103, 026403 (2009) [revTPSS]

template<bool revised>

__hostanddev__ double mGGA_TPSS_Exchange	(	double	rs,
		double	s2,
		double	q,
		double	z,
		double &	e_rs,
		double &	e_s2,
		double &	e_q,
		double &	e_z
	)

TPSS or revTPSS Exchange depending on revised = false/true J.P. Perdew et al, Phys. Rev. Lett. 91, 146401 (2003) [TPSS] J.P. Perdew et al, Phys. Rev. Lett. 103, 026403 (2009) [revTPSS]

__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).

template<typename Para , typename Ferro , typename Stiff >

__hostanddev__ double spinInterpolate	(	double	rs,
		double	zeta,
		double &	e_rs,
		double &	e_zeta,
		const Para &	para,
		const Ferro &	ferro,
		const Stiff &	stiff,
		const double	fDblPrime0 = `4./(9*(pow(2., 1./3)-1))`
	)

Spin-interpolate an LDA functional given its paramagnetic, ferromagnetic and spin-stiffness functors (This is the spin-inteprolation technique used in the VWN and PW correlation functionals) (For numerical compatibility with the original PW routine, the f"(0) scale factor may be over-ridden)

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