Diffusion

1. Confirm the user's target observable and pick the right keyword. Do not assume diffusion implies ionic conductivity or vice versa.
2. Equilibrate in NPT (or NVT if cell is fixed), then switch to NVE for production. Active thermostats should not be left on during a Green-Kubo viscosity or equilibrium MSD segment.
3. For ionic conductivity, require the user to specify which species are the mobile carriers and set up group labels in model.xyz accordingly.
4. For Arrhenius analysis, require at least three temperatures.
5. For low-dimensional or confined systems, explicitly state the geometry convention before reporting conductivity.

Workflow: self-diffusion via MSD + VAC

Annotated example (see assets/examples/diffusion/run.in):

potential   nep.txt
velocity    2500
time_step   2

# equilibrate at 2500 K (above melting) then cool to target
ensemble    npt_scr 2500 2500 100 0 50 1000
dump_thermo 100
run         10000

ensemble    npt_scr 1800 1800 100 0 50 1000
dump_thermo 100
run         10000

# production in NVE, both MSD and VAC running simultaneously
ensemble    nve
dump_thermo 100
compute_msd 1 2000
compute_sdc 1 2000
run         20000

• compute_msd sample_interval Nc — writes msd.out with the mean-square displacement up to Nc time-lags, sampled every sample_interval steps.
• compute_sdc sample_interval Nc — writes sdc.out with velocity autocorrelation and its running integral, from which the diffusion coefficient is read off as the long-time plateau.

Fit the diffusion coefficient from the linear region of msd.out:

python scripts/fit_msd_diffusion.py msd.out --start-frac 0.3 --end-frac 0.9

Rules for a trustworthy diffusion number

• use an NVE production segment unless the physics demands a thermostat
• the MSD must reach a linear-in-time region long enough to fit with statistical confidence
• the VAC running integral should plateau — if it does not, the run is too short
• multiple seeds or initializations are encouraged for fluids

Workflow: shear viscosity

Annotated example (see assets/examples/viscosity/run.in):

potential   nep.txt
velocity    2500
time_step   2

ensemble    npt_scr 2500 2500 100 0 50 1000
dump_thermo 100
run         10000

ensemble    npt_scr 1600 1600 100 0 50 1000
dump_thermo 100
run         10000

ensemble          nve
dump_thermo       100
compute_viscosity 1 1000
run               50000

• compute_viscosity sample_interval Nc — writes viscosity.out with the off-diagonal stress autocorrelation and its running integral.

The Green-Kubo viscosity is the long-time plateau of the integral; inspect it like a heat-flux autocorrelation. Multiple seeds are strongly recommended because stress fluctuations are noisy.

Workflow: ionic conductivity

Species-selective MSD plus the Nernst-Einstein relation (see the 24_Ionic_Conductivity tutorial for a complete LLZO example).

1. Build model.xyz with a group:I:M column flagging the mobile species.
2. Run multi-temperature NPT → NVE with species-resolved MSD:

   compute_msd 1 2000 group 0 0
   

   The group 0 0 syntax means "compute MSD for group method 0, group index 0", i.e. the first grouping scheme, first label. Adjust to the mobile species' label.
3. Extract the diffusion coefficient D_ion from the linear region.
4. Apply Nernst-Einstein:

   σ = (N_ion * q^2) / (V * k_B * T) * D_ion
   

5. Repeat at 3+ temperatures and fit an Arrhenius line to estimate the activation energy.

Convergence checklist

• structure is equilibrated in the target state
• production is in NVE (or the target ensemble explicitly justified)
• MSD is linear over the fit window
• VAC integral has plateaued
• for ionic conductivity: group labels match the intended carrier
• for Arrhenius: at least three temperatures
• low-dimensional geometry convention stated if applicable

Read first

• references/diffusion-viscosity-ionic.md

Read when needed:

• references/core-files-and-ensembles.md
• references/gpumd-keyword-cheatsheet.md
• references/tutorial-map.md

Bundled templates and helpers

• assets/examples/diffusion/run.in
• assets/examples/diffusion/model.xyz
• assets/examples/viscosity/run.in
• scripts/fit_msd_diffusion.py
• scripts/parse_thermo.py

Expected output

1. an equilibration + production input file for the selected observable
2. an extraction recipe for msd.out, sdc.out, or viscosity.out
3. the convergence and uncertainty discussion
4. (ionic) group definition and Nernst-Einstein post-processing

Cross-skill pointers

• For generating initial configurations of liquid or molten systems (mixtures, melts, solutions), use packmol-generate-mixture to pack molecules into a simulation box before converting to model.xyz.
• For structure manipulation (supercells, substitutions) → pymatgen-structure.

References

• compute_msd: https://gpumd.org/gpumd/input_parameters/compute_msd.html
• compute_sdc: https://gpumd.org/gpumd/input_parameters/compute_sdc.html
• compute_viscosity: https://gpumd.org/gpumd/input_parameters/compute_viscosity.html
• GPUMD-Tutorials: 09_Silicon_diffusion, 10_Silicon_viscosity, 24_Ionic_Conductivity, 28_thermal_transport_superionic_EMD