cube_radial_distribution

By Pierre Beaujean (pierre.beaujean@unamur.be).

Version 0.1 (Development).

Synopsis

cube_radial_distribution - Radial distribution

usage: cube_radial_distribution [-h] [-v] [-S] [-c CENTER] [--dr DR]
                                [--n-polar N_POLAR]
                                [--n-azimuthal N_AZIMUTHAL] [-d DATA]
                                infile

Positional arguments:

infile

Density cube

Optional arguments:

-h, --help

show this help message and exit

-v, --version

show program’s version number and exit

-S, --square

square cube before

-c, --center

Center

--dr

Increment of radius

--n-polar

Number of subdivision for the integration over theta

--n-azimuthal

Number of subdivision for the integration over phi

-d, --data

data of the cube

More information

Report the radial distribution of a cube around a given center [by default \((0,0,0)\)].

Note

Please cite [P. Beaujean and B. Champagne, Inorg. Chem. 2022, 61, 1928], if you use this program. This publication also showcase the kind of results you can expect and the analysis that may be extracted.

The charge in a given region of the space, located by \(\mathbf{r}\) and in an element of volume \(d\mathbf{r}\), is given by

\[q(\mathbf{r}) = \rho(\mathbf{r})\,d\mathbf{r}.\]

Integration over whole space gives the number of particles, \(Q\). In spherical coordinates, \(d\mathbf{r} = r^2\sin{\theta}\,dr\,d\theta\,d\phi\), this integral becomes

\[Q = \int_0^{2\pi}\int_0^{\pi}\int_0^{\infty} \rho(r,\theta,\phi)\,r^2\,\sin{\theta}\,dr\,d\theta\,d\phi.\]

Thus, the radial distribution is given by

(1)\[\frac{dQ(r)}{dr} = r^2\,\int_0^{2\pi}\int_0^{\pi} \rho(r,\theta,\phi)\sin{\theta}\,d\theta\,d\phi,\]

Equation (1) is obtained numerically by interpolation over the cube.