Suitable choice of a radial grid is key to obtaining accurate numerical solutions of the integro-differential equations of density-functional theory. The codes in our test suite make different choices for the radial grid. Two codes make perhaps the simplest choice, an exponentially increasing grid

with three parameters: the minimum radius, ,
the maximum radius, , and the number of intervals, *N*.
The application of the exponential
grid to the atomic Schrödinger equation has been discussed
by Desclaux[8].
For one code we used *N* = 15788,
, and .
(All distances are in atomic units.)
Another code used , ,
and ; in this case, the energies were
extrapolated to using an or
dependence, depending on the quantity in question.

Another code chooses a grid which is nearly linear near the origin,
and exponentially increasing at large *r*,

which again is determined by three parameters, *a*, *b*, and *N*.
This grid includes the origin explicitly as .
In this case, we took , , and ,
leading to *N* = 7058 for H, increasing to *N* = 9021 for U,
and to for H, decreasing to for U.

A fourth code uses a change of variable technique:

A uniform grid is taken in the transformed variable from
to where the parameters are taken to be
, for atomic number *Z*, and .
The number of points increased from *N* = 2113 for H to
*N* = 2837 for U.
The density of points chosen in the latter two codes - linear near the
origin and exponentially increasing at large *r* -
is similar to that suggested from theoretical considerations[9].