3. Aluminium: a k-point convergence study

Before trusting any production number, a DFT practitioner checks that it is converged with respect to the sampling parameters. This tutorial runs the most common such check — total energy against the k-point mesh — as a single prompt, and shows how LatticeMind turns the study’s three numbers into a conclusion.

Metals like aluminium are the demanding case: their partially filled bands make the total energy converge slowly with Brillouin-zone sampling, which is exactly why this check matters.

What you need

The same setup as Silicon: SCF, band structure & DOS. The three SCF runs complete in about three minutes altogether.

3.1. The prompt

Another of the shipped /examples prompts:

Set up a k-point convergence study for fcc aluminum comparing 6x6x6, 8x8x8,
and 10x10x10 meshes at fixed geometry.

3.2. What LatticeMind does

1. Sets up three SCF calculations of the same fcc aluminium cell, copied from one another and identical in every respect except kpoint.gridn. A mesh that is already in the study is not added twice.

2. Asks once for permission to run all three, then runs them and reads each total energy.

3. Compares them: the answer plots the energy against the mesh and leads with that figure and the change between neighbouring meshes.

3.3. The results

Mesh	Total energy (Ha)	ΔE to finest (meV)
6×6×6	−2.076958	−35.11
8×8×8	−2.075994	−8.89
10×10×10	−2.075667	0 (reference)

Fig. 3.3.1 Total-energy convergence of fcc Al. Each point is annotated with its distance to the finest mesh in meV; the dashed line is the 10×10×10 reference.

Reading the curve: refining from 6³ to 8³ moves the energy by ~26 meV, but the last refinement to 10³ changes it by under 9 meV. If your target accuracy is ~10 meV, the 8×8×8 mesh is the economical choice; for tighter work you would extend the series — “add a 12x12x12 mesh to the study” — and LatticeMind adds the fourth point to the same curve.

The same numbers appear in the evidence report that /report writes under results/, each tied to the run it came from.

3.4. What you learned

• A convergence study is one prompt, and its conclusion is a figure, not three disconnected numbers.

• The sweep is built as a sweep: the three inputs differ only in the mesh, so the comparison measures what it claims to.

• The study extends naturally — ask for another mesh and the curve grows.

The same pattern applies to other sampling knobs: a real-space resolution (domain.lowres) sweep is recognised and plotted the same way.