The shipped kernel functions

Functions
XcKernelValue	excgrid::SlaterExchange (double rhoA, double rhoB)
XcKernelValue	excgrid::Vwn5Correlation (double rhoA, double rhoB)
XcKernelValue	excgrid::Vwn3Correlation (double rhoA, double rhoB)
XcKernelValue	excgrid::Pw92Correlation (double rhoA, double rhoB)
XcKernelValue	excgrid::Becke88Exchange (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::Pw91Exchange (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::PbeExchange (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::RevPbeExchange (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::RpbeExchange (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::MPw91Exchange (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::PbeSolExchange (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::LypCorrelation (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::PbeCorrelation (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::Pw91Correlation (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)
XcKernelValue	excgrid::P86Correlation (double rhoA, double rhoB, double sigmaAa, double sigmaAb, double sigmaBb)

Detailed Description

Every LDA/GGA functional below is generated by the Yacas codegen pipeline (xc_defs/*.ey -> generated/*.cpp, committed; see tools/regenerate.py and the maintainer guide). The generated definitions live in excgrid/generated/ and are ordinary library sources - this header is the hand-written declaration surface, kept in sync by the add-a-functional procedure (docs/maintainer-guide.md). Order-1 kernels only - the energy density and the first derivatives, because Vxc assembly consumes nothing above that tier; second/third derivative tiers are a documented generator extension for the analytic-gradient track.

Function Documentation

Becke88Exchange()

XcKernelValue excgrid::Becke88Exchange	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

Becke 1988 GGA exchange.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

LypCorrelation()

XcKernelValue excgrid::LypCorrelation	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

Lee-Yang-Parr 1988 GGA correlation.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

MPw91Exchange()

XcKernelValue excgrid::MPw91Exchange	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

mPW91 GGA exchange.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

P86Correlation()

XcKernelValue excgrid::P86Correlation	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

Perdew 1986 GGA correlation.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

PbeCorrelation()

XcKernelValue excgrid::PbeCorrelation	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

Perdew-Burke-Ernzerhof 1996 GGA correlation.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

PbeExchange()

XcKernelValue excgrid::PbeExchange	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

Perdew-Burke-Ernzerhof 1996 GGA exchange.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

PbeSolExchange()

XcKernelValue excgrid::PbeSolExchange	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

PBEsol GGA exchange.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

Pw91Correlation()

XcKernelValue excgrid::Pw91Correlation	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

Perdew-Wang 1991 GGA correlation.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

Pw91Exchange()

XcKernelValue excgrid::Pw91Exchange	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

Perdew-Wang 1991 GGA exchange.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

Pw92Correlation()

XcKernelValue excgrid::Pw92Correlation	(	double	rhoA,
		double	rhoB )

PW92 LDA correlation.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.

Returns

The energy density and its spin-density derivatives.

RevPbeExchange()

XcKernelValue excgrid::RevPbeExchange	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

revPBE GGA exchange.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

RpbeExchange()

XcKernelValue excgrid::RpbeExchange	(	double	rhoA,
		double	rhoB,
		double	sigmaAa,
		double	sigmaAb,
		double	sigmaBb )

RPBE (Hammer-Hansen-Norskov 1999) GGA exchange.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.
sigmaAa	grad(rhoA) . grad(rhoA).
sigmaAb	grad(rhoA) . grad(rhoB).
sigmaBb	grad(rhoB) . grad(rhoB).

Returns

The energy density and its first derivatives.

SlaterExchange()

XcKernelValue excgrid::SlaterExchange	(	double	rhoA,
		double	rhoB )

Slater (Dirac) LDA exchange.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.

Returns

The energy density and its spin-density derivatives.

Vwn3Correlation()

XcKernelValue excgrid::Vwn3Correlation	(	double	rhoA,
		double	rhoB )

VWN3 LDA correlation (the RPA-parameter parametrization) - distinct from VWN5, never conflated.

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.

Returns

The energy density and its spin-density derivatives.

Vwn5Correlation()

XcKernelValue excgrid::Vwn5Correlation	(	double	rhoA,
		double	rhoB )

VWN5 LDA correlation (the interpolation-V parametrization).

Parameters

rhoA	The alpha-spin density.
rhoB	The beta-spin density.

Returns

The energy density and its spin-density derivatives.