Herman-Skillman radial mesh

The primary wave function output data from the Herman-Skillman program are the products rR r), which are known as the numerical radial functions. The radial wave function itself can be recovered on division by the radial distance, r, and approximately near the origin by extrapolating to avoid the infinity. There is one other detail. For the purposes of the numerical integration procedure in the Herman-Skillman procedure the radial data are defined on a non-uniform grid, x, known as the Thomas-Fermi mesh (4). These are converted, in the output from hs.exe, to radial arrays specific to each atom, with... 

Run hs.exe and copy the output data for the lithium 2s radial function onto columns A and B of a new spreadsheet. This means that the Thomas-Fermi mesh will be the radial mesh for the remainder of the exercise. For simplicity delete column A the dimensionless x-mesh. Label the remaining columns of translated data from the Herman-Skillman output file, r[TF], r/ (rXi-2s) and enter the headers RDF-Li 2s and RDF-Slater in cells C 5 and D 5. 

Open fig3.4.xls and copy the Thomas-Fermi mesh data for the Herman-Skillman lithium numerical 2s radial function. 

Now, on worksheet Is , follow Figure 3.11 and enter the Herman-Skillman output with two empty columns of cells after the Thomas-Fermi mesh to allow for the recovery of the actual lithium Is and 2s radial function over the radial array, as in Chapter 1, with, as before, the irregular behaviour at the origin avoided using the INTERCEPT function of the EXCEL program, for example for the Is function... 

The least-squares procedure used to evaluate the coefficients involves sampling r (r ) on a grid of points, typically a radial distribution based on that of Herman and Skillman (every tenth point) coupled with an angular mesh consisting of the 12 vertices of a regular icosahedron or 14 points defined by the corners and face centers of a cube. Both of these grids are accurate through fifth-order spherical harmonics. 

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