Grid::Radial Namespace Reference

Functions
void	baker (int nbase, double R, double *r, double *w, int mult=1)
	Radial quadratures.
void	baker (int nbase, double R, std::vector< double > &r, std::vector< double > &w, int mult)
void	murray (int n, double R, double *r, double *w)
void	treutler_m4 (int n, double R, double *r, double *w, double alpha)
void	mura (int n, double R, double *r, double *w)

Function Documentation

baker() [1/2]

void Grid::Radial::baker	(	int	nbase,
		double	R,
		double *	r,
		double *	w,
		int	mult = 1
	)

Radial quadratures.

This namespace contains functions that generate grids and weights for numerical integration

 / inf     2
 |     dr r  g(r) ~ \sum_i w[i] g(r[i])
 /  0

Baker, J., Andzelm, J., Scheiner, A., & Delley, B. (1994). The effect of grid quality and weight derivatives in density functional calculations. The Journal of chemical physics, 101(10), 8894-8902.

Zhang, I. Y., Ren, X., Rinke, P., Blum, V., & Scheffler, M. (2013). Numeric atom-centered-orbital basis sets with valence-correlation consistency from H to Ar. New Journal of Physics, 15(12), 123033.

Note

nbase is the number of points of the "base" grid, i.e., before applying the "radial multiplier" introduced by Zhang et al. The true number of grid points is (nbase+1) * mult - 1.

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baker() [2/2]

void Grid::Radial::baker	(	int	nbase,
		double	R,
		std::vector< double > &	r,
		std::vector< double > &	w,
		int	mult
	)

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mura()

void Grid::Radial::mura	(	int	n,
		double	R,
		double *	r,
		double *	w
	)

Mura, M. E., & Knowles, P. J. (1996). Improved radial grids for quadrature in molecular density‐functional calculations. The Journal of chemical physics, 104(24), 9848-9858.

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murray()

void Grid::Radial::murray	(	int	n,
		double	R,
		double *	r,
		double *	w
	)

Murray, C. W., Handy, N. C., & Laming, G. J. (1993). Quadrature schemes for integrals of density functional theory. Molecular Physics, 78(4), 997-1014.

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treutler_m4()

void Grid::Radial::treutler_m4	(	int	n,
		double	R,
		double *	r,
		double *	w,
		double	alpha = 0.6
	)

Treutler, O., & Ahlrichs, R. (1995). Efficient molecular numerical integration schemes. The Journal of Chemical Physics, 102(1), 346-354.

Note

M4 reduces to M3 at alpha = 0.

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