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What do the cutoffs and k-point grid control?
ecutwfc is the kinetic-energy cutoff for the plane-wave wavefunctions, in Ry. ecutrho, also in Ry, sets the cutoff for the charge density and potential. In the QE 7.5 input reference, ecutwfc is required and ecutrho defaults to four times its value. Quantum ESPRESSO pw.x input reference.
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K_POINTS controls how the Brillouin zone is sampled. An automatically generated grid samples reciprocal-space directions on a uniform mesh. These are separate convergence choices: a stable energy at one cutoff does not show that a k-point grid is dense enough, and a dense grid does not establish that the plane-wave basis is converged.
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How do I choose ecutwfc in Quantum ESPRESSO?
Use the pseudopotential’s documentation or recommended settings to choose a starting value, then test higher cutoffs for your own calculation. A suggested cutoff is a starting point, not proof that the quantity you care about has converged.
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- Record the QE release, exchange-correlation setup, structure, and exact pseudopotential filenames and types. Use documentation matching the installed release.
- Choose a starting
ecutwfcbased on the pseudopotential guidance. - Run a sequence of calculations at increasing
ecutwfc, changing no other input that could affect the comparison. - Compare the same target result at each value—for example, total energy, forces, stress, or a specified electronic property.
- Choose and report a project-appropriate tolerance. The official references do not prescribe a universal cutoff sequence or acceptable error threshold.
For example, if forces are the quantity used to assess a structure, compare forces across the cutoff sequence rather than relying only on total-energy changes. The tolerance and evidence needed depend on the study; do not imply that a setting is converged without stating what was tested.
What should ecutrho be relative to ecutwfc?
QE’s default is ecutrho = 4 * ecutwfc. The appropriate ratio depends in part on the pseudopotential family and calculation conditions.
| Pseudopotential or condition | QE guidance |
|---|---|
| Norm-conserving | Keep the default ratio, according to the QE input reference. Reducing it can introduce noise, especially in forces and stress. |
| Ultrasoft | A larger value is often desirable; QE gives “8 to 12 times ecutwfc, typically.” This is guidance, not a universal constant. |
| PAW | Four times ecutwfc can often work, but augmentation-charge shape matters. QE says testing is mandatory. |
QE also notes that higher ecutrho may be needed with gradient-corrected functionals, especially for cells containing vacuum, or with pseudopotentials that lack nonlinear core correction. Where those conditions apply, test ecutrho as its own convergence axis rather than assuming that a converged ecutwfc settles it. QE pw.x input reference.
How dense should my k-point grid be?
Test the uniform grid against the same target quantity used to assess the calculation. Increase sampling in the periodic reciprocal-space directions as needed, keeping other settings fixed. The QE documentation defines how to enter a grid but does not prescribe a universal mesh density or points-per-length rule.
Mesh dimensions should reflect reciprocal-cell geometry. A cell change or a supercell changes the reciprocal lattice, so a previously suitable grid should not be copied blindly without considering the new cell and the quantity being calculated. Treat grid density as directional, not as a single number independent of structure.
Automatic grid syntax and offsets
In pw.x, an automatic grid is specified by six integers after K_POINTS automatic:
K_POINTS automatic
nk1 nk2 nk3 sk1 sk2 sk3nk1, nk2, and nk3 are the grid dimensions. Each offset, sk1 through sk3, is 0 or 1: 0 leaves that direction unshifted, while 1 shifts it by half a grid step. QE’s user guide describes automatic generation as following the Monkhorst-Pack convention; points are handled in the irreducible Brillouin zone subject to symmetry unless settings such as nosym change that behavior. PW user guide: input data.
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Should I use the same k-point grid for SCF, DOS, and bands?
Not necessarily. The sampling should match the calculation’s purpose. QE’s guide describes an SCF calculation followed by an NSCF calculation using the grid desired for the subsequent electronic-structure output. A density-of-states calculation and a band path have different sampling needs.
SCF and density of states
For DOS, the guide recommends an automatically generated uniform grid and tetrahedron occupations. Converge the grid for the DOS features or other property you plan to report; an SCF grid that was adequate for total energy alone is not automatically adequate for that output.
Band structures
A band calculation uses an NSCF calculation at a fixed SCF potential, with eigenvalues sampled along a selected path or grid as appropriate. A path through chosen lines in reciprocal space is not the same thing as a uniform grid for Brillouin-zone integration. State which sampling was used rather than describing a band path as a converged integration mesh. PW user guide: electronic-structure calculations.
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Change one convergence axis at a time so that the effect of each setting is interpretable. Once a choice is made for one axis, keep it fixed while testing the next.
- Fix the calculation definition. Record the release, functional, structure, pseudopotential files, occupation treatment, and target observable.
- Test
ecutwfc. Increase it through a documented sequence and compare the same observable against the tolerance selected for the work. - Test
ecutrhowhere appropriate. Follow the pseudopotential-family guidance, then increase it if needed and compare the target result independently. - Test the k-point mesh. With cutoffs fixed, increase sampling in relevant reciprocal directions and compare the same observable. Consider offsets, symmetry, metallicity and occupation treatment, and the downstream calculation.
- Keep evidence. Report the tested values and observed changes, not just the final setting. Include grid dimensions and offsets, pseudopotential identities, the convergence quantity, and the tolerance.
This workflow is practical guidance derived from QE’s input definitions and cautions; the official references do not supply a universal threshold that makes every energy, force, stress, or electronic property converged.
What changes in variable-cell optimization?
In variable-cell optimization, QE’s guide explains that plane waves and G-vectors use the starting cell during optimization and the final cell for the last step. If results differ substantially between the last steps, the plane-wave basis may be far from converged; increase ecutwfc and/or ecutrho and assess the calculation again. PW user guide PDF.
What should I report for reproducibility?
- Quantum ESPRESSO release and relevant computational details.
- Exchange-correlation setup and the exact pseudopotential files and types.
ecutwfcandecutrho, in Ry.- The k-point specification: uniform grid dimensions and offsets, or the band path used; include the symmetry treatment where relevant.
- The target observable, convergence tolerance, values tested, and the changes observed across the sequence.
QE notes that FFT grid dimensions depend on cutoff, cell, and FFT-library constraints. Different libraries or machines can therefore produce different FFT dimensions and small energy differences, another reason to document software and computational details. PW user guide PDF.
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