Akmx

rmin   0.001
rmax  20.0
akmx  400.0
nr    512

These are parameters to setup a logarithmic grid for radial orbitals. An unique grid is used for all orbitals, therefore it is important to setup it's parameters carefully in order not to loose a precious precision of the numerical representation of radial orbitals. However, currently, the default settings are rather conservative in terms of precision. Normally, the default settings are best to guarantee a highest achievable precision. Default settings can be invoked by removing the parameters from input file, or setting these parameters to a negative value.

The logarithmic grid is used in the code to discretize the values of radial orbitals.

(1)

\begin{align} r_i = r_{\mathrm{min}} \mathrm{e}^{dr (i-1)} \end{align}

(2)

\begin{align} dr = (\log(r_{max})-\log(r_{min}))/(N-1). \end{align}

In momentum space, the radial grid has to be complementary with the radial grid in coordinate space

(3)

\begin{align} p_i = p_{\mathrm{min}} \mathrm{e}^{dp (i-1)} \end{align}

(4)

\begin{align} p_{\mathrm{min}} = \exp (\log(p_{\mathrm{max}})-\log(r_{max})+\log(r_{min})) \end{align}