projgen.cpp File Reference

#include "projgen.h"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <cstdio>
#include <numeric>
#include "source_base/cubic_spline.h"
#include "source_base/math_integral.h"
#include "source_base/math_sphbes.h"

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Functions
void	projgen (const int l, const int nr, const double *r, const double *chi, const double rcut, const int nbes, std::vector< double > &alpha)
	Generates a projector's radial function for DFT+U.
void	smoothgen (const int nr, const double *r, const double *chi, const double rcut, std::vector< double > &alpha)

Function Documentation

projgen()

void projgen	(	const int	l,
		const int	nr,
		const double *	r,
		const double *	chi,
		const double	rcut,
		const int	nbes,
		std::vector< double > &	alpha
	)

Generates a projector's radial function for DFT+U.

Starting with a numerical radial function chi on grid r with angular momentum l, given a smaller cutoff radius rcut and the number of spherical Bessel components (j_l), this function generates a new radial function alpha of the same l on the truncated grid which satisfies the following conditions:

• alpha = \sum_p j_l(theta[p]*r/rcut) * c[p] where theta[p] is the p-th zero of j_l;
• \int_0^rcut alpha(r) r^2 dr = 1 (normalization);
• \int_0^rcut alpha(r) chi(r) r^2 dr is maximized;

Parameters

[in]	l	angular momentum
[in]	nr	number of grid points
[in]	r	radial grid
[in]	chi	radial function
[in]	rcut	cutoff radius of the projector
[in]	nbes	number of spherical Bessel components
[out]	alpha	new radial function of the projector

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smoothgen()

void smoothgen	(	const int	nr,
		const double *	r,
		const double *	chi,
		const double	rcut,
		std::vector< double > &	alpha
	)

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