radial_transform

class radial_transform.RadialTransform

A definition of (radial) grid points by means of a transformation.

The definition starts from a uniform 1D grid with spacing 1 and starting point 0: 0, 1, 2, 3, … npoint-1. These values are defined on the so-called t-axis. The transformation is a function r=f(t) that defines the actual grid points on the r-axis: f(0), f(1), f(2), … f(npoint-1). Different implementation for the function f are available.

Abstract class for radial transformation. Not use it directly

class radial_transform.IndentityRadialTransform(size)

For testing only

class radial_transform.PowerRadialTransform(rmin, rmax, size)

A power grid.

The grid points are distributed as follows:

\(r_i = r_0 i^{\alpha}\)

with

\(\alpha = \dfrac{\ln r_{N-1} - \ln r_0}{\ln N-1}\)

class radial_transform.ChebyshevRadialTransform(radii, size)

Radial grid for multi-center molecular integration.

This grid is based on Becke’s paper, the transformation requires the covalent radius radii of a given atom, such that;

\(r = radii \dfrac{1+x}{1-x}\)

References

Becke, A. D. A multi-center numerical integration scheme for polyatomic molecules. J. Chem. Phys. 88, 2547 (1988).

Parameters

• radii (float) – Atomic radii for the grid.

• size (int) – Number of grid points