Convergence Testing

Purpose

Before production calculations, verify that results are converged with respect to key numerical parameters. The two most important are:

1. ENCUT (planewave cutoff energy) -- controls basis set completeness
2. KPOINTS (k-point mesh density) -- controls Brillouin zone sampling

Convergence is reached when the target property (energy, forces, band gap) changes by less than a threshold (typically 1 meV/atom for energy).

Fan-Out Pattern

Convergence tests use a fan-out DAG: one input structure feeds into multiple independent single_point calculations with different parameter values.

                   +--> single_point(ENCUT=300)
                   |
structure_input ---+--> single_point(ENCUT=400)
                   |
                   +--> single_point(ENCUT=500)
                   |
                   +--> single_point(ENCUT=600)
                   |
                   +--> single_point(ENCUT=700)

Use single_point (not geo_opt) to isolate the parameter effect without geometry changes confounding the comparison.

MCP Workflow: ENCUT Convergence

Step 1: Create workflow

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "create", "name": "ENCUT convergence - TiO2"
}}

Step 2: Add single_point tasks at each ENCUT

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_conv",
  "task_type": "single_point",
  "params": {"software": "vasp", "ENCUT": 300, "system_name": "ENCUT=300"}
}}

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_conv",
  "task_type": "single_point",
  "params": {"software": "vasp", "ENCUT": 400, "system_name": "ENCUT=400"}
}}

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_conv",
  "task_type": "single_point",
  "params": {"software": "vasp", "ENCUT": 500, "system_name": "ENCUT=500"}
}}

Repeat for ENCUT = 600, 700, 800.

Step 3: Submit

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "submit", "workflow_id": "wf_conv"
}}

Step 4: Check results

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "get_result", "workflow_id": "wf_conv", "task_id": "task_encut300"
}}

{"tool": "catgo_analyze", "arguments": {
  "action": "convergence", "workflow_id": "wf_conv"
}}

MCP Workflow: KPOINTS Convergence

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_conv",
  "task_type": "single_point",
  "params": {"software": "vasp", "ENCUT": 520, "KPOINTS": [2,2,1],
             "system_name": "2x2x1"}
}}

{"tool": "catgo_workflow_engine", "arguments": {
  "action": "add_task", "workflow_id": "wf_conv",
  "task_type": "single_point",
  "params": {"software": "vasp", "ENCUT": 520, "KPOINTS": [4,4,1],
             "system_name": "4x4x1"}
}}

Repeat for 6x6x1, 8x8x1. Use the converged ENCUT from the previous test.

Python API

ENCUT Convergence

from catgo.workflow import Workflow

wf = Workflow("ENCUT convergence - TiO2")
inp = wf.add_task("structure_input", structure=tio2_json)

encut_values = [300, 400, 500, 600, 700, 800]
tasks = {}
for encut in encut_values:
    tasks[encut] = wf.add_task("single_point",
        structure=inp.output.structure,
        software="vasp", ENCUT=encut,
        system_name=f"ENCUT={encut}")

wf.submit()

KPOINTS Convergence

wf = Workflow("KPOINTS convergence - TiO2 slab")
inp = wf.add_task("structure_input", structure=tio2_slab_json)

kpoints_list = [[2,2,1], [4,4,1], [6,6,1], [8,8,1], [10,10,1]]
for kp in kpoints_list:
    label = f"{kp[0]}x{kp[1]}x{kp[2]}"
    wf.add_task("single_point",
        structure=inp.output.structure,
        software="vasp", ENCUT=520, KPOINTS=kp,
        system_name=label)

wf.submit()

Convergence Criteria

Property	Threshold	Typical Converged ENCUT
Total energy	1 meV/atom	1.3x max(ENMAX) in POTCAR
Forces	5 meV/A	Same as energy
Band gap	10 meV	May need higher ENCUT
Stress tensor	0.1 kbar	Often needs 1.5x ENMAX

Recommended ENCUT Values by Element Type

System	Starting ENCUT Range	Notes
Simple metals (Cu, Pt)	300-500	Usually converges quickly
Oxides (TiO2, RuO2)	400-600	O has high ENMAX
Nitrides, carbides	400-600	N, C have moderate ENMAX
F-containing	500-800	F has very high ENMAX

Two-Stage Strategy

1. ENCUT first: Fix KPOINTS at a moderate value (e.g., 4x4x4), sweep ENCUT. Pick the converged ENCUT.
2. KPOINTS second: Fix ENCUT at converged value, sweep KPOINTS. Pick the converged mesh.

This avoids the combinatorial explosion of testing all ENCUT x KPOINTS pairs.

Common Pitfalls

1. Always use single_point, not geo_opt. Geometry changes at different ENCUT introduce noise that masks the convergence behavior.
2. For slab models, only converge the in-plane k-points (e.g., NxNx1). The vacuum direction needs only 1 k-point.
3. ENCUT should be at least 1.3x the maximum ENMAX in the POTCAR. Check POTCAR ENMAX values before choosing the test range.
4. Report energy per atom (E_total / N_atoms), not total energy, for meaningful comparison across different systems.
5. Always plot E vs parameter -- convergence should be monotonic. Non-monotonic behavior suggests other issues (e.g., SCF convergence).