Recommended atomic setup

This page gives one practical starting recipe for atom-centered radial calculations.

If you want the API details for the constructors used here, also see:

Short version

For an atom of nuclear charge Z, start with:

s = 0.2
c = s / (2Z)
rmax = 30.0 bohr for a first-row atom

In code:

using GaussletBases

Z = 2.0
s = 0.2

map = AsinhMapping(c = s / (2Z), s = s)

spec = RadialBasisSpec(:G10;
    rmax = 30.0,
    mapping = map,
)

rb = build_basis(spec)
grid = radial_quadrature(rb)

This is the recommended package starting point. It deliberately leaves the deeper construction controls at their standard defaults.

What the main knobs mean

s controls the overall radial spacing.
c = s / (2Z) sets the near-origin scale in a way that naturally tightens as Z grows.
rmax is the center of the last retained radial gausslet.

What about x-gaussians?

There are two practical regimes here.

For a first one-electron check such as hydrogen, it is reasonable to start with no extra near-origin supplement:

xgaussians = XGaussian[]

For more serious atomic / IDA work, the default paper-parity two-function supplement is:

xgaussians = [XGaussian(alpha = 0.0936), XGaussian(alpha = 0.0236)]

Those extra functions are meant to improve the near-origin radial behavior without changing the outer mapping family. If the diagnostics remain clean without them for the problem you care about, it is also fine to leave them out. These are the published optimized widths for the K = 6 radial-gausslet paper construction; they are not meant to imply a fresh per-run optimization.

So the front-door interpretation is:

the default front-door behavior is the paper-style two-function supplement
xgaussian_count = 0 turns that supplement off
xgaussian_count = 1 keeps only the first preset function
explicit xgaussians = [...] is the advanced override when you really want to pick the alphas yourself

Advanced construction controls

The first-read code example intentionally hides the following controls:

reference_spacing = 1.0
tails = 6
odd_even_kmax = 6
tail_spacing = 10.0
xgaussian_count = 2

Why:

reference_spacing = 1.0 is the standard default
tails is construction padding, not a scientific modeling knob
odd_even_kmax is a real accuracy knob, but not something a new user should choose before the basic workflow is working
tail_spacing = 10.0 is the standard AsinhMapping default
xgaussian_count = 2 is the current recommended radial default

So the practical rule is:

do not expose these in the beginner examples
revisit them only when tuning accuracy or debugging basis construction

The library also owns two separate internal extents:

a build/setup extent in mapped u space used while constructing the basis
an active quadrature extent in mapped u space used for operators and diagnostics

Those internal extents are not the same thing as user-facing rmax.

What to check

After building the basis, inspect:

diag = basis_diagnostics(rb)
diag.overlap_error
diag.D

Those are the quickest signs that the basis and quadrature are behaving sensibly. diag.overlap_error is the first orthonormality check. diag.D is the aggregate center/moment mismatch and is often the next thing to watch when you are deciding whether the near-origin setup needs tightening.

For the normal workflow, let the package choose the internal quadrature extent:

grid = radial_quadrature(rb)

The expert keyword quadrature_rmax still exists for compatibility, but it is not part of the recommended front-door story.

What this page is for

This page is the practical tuning page. If you want the workflow taught more gently before the advanced knobs appear, start with: