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How to Calculate Band Structures and Density of States with Quantum ESPRESSO

By Freedom251 Team · · 6 min read

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Quantum ESPRESSO uses two different follow-up calculations after a converged self-consistent (SCF) run: a bands calculation samples an ordered k-point path to show energy versus wave vector, while a non-self-consistent (NSCF) calculation samples a Brillouin-zone mesh for density of states (DOS). Process the first with bands.x, the second with dos.x, and use projwfc.x when you need atom- or orbital-resolved information.

What is the difference between bands and nscf?

Both calculations use the converged potential from SCF, but they sample reciprocal space differently and answer different questions. Quantum ESPRESSO’s electronic-structure guide distinguishes the selected k-points used for band calculations from the mesh used for further processing such as DOS.

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Follow-up calculation K-point sampling What it provides Post-processing
calculation='bands' An ordered path through chosen points in reciprocal space, often along high-symmetry directions Eigenvalues at each point on that path, for plotting band dispersion bands.x
calculation='nscf' A Brillouin-zone mesh for integration over reciprocal space Eigenvalues sampled across the zone, suitable for estimating states as a function of energy dos.x for total DOS; projwfc.x for projected quantities

A high-symmetry path is sparse by design and is not a substitute for the mesh used to calculate DOS. Conversely, a regular mesh alone does not usually produce the path-resolved band plot you want.

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How do I calculate a band structure in Quantum ESPRESSO?

1. Converge an SCF calculation

Run pw.x with calculation='scf' and verify that the total energy and other quantities relevant to your material are converged with respect to settings such as the plane-wave cutoffs and SCF k-point mesh. This establishes the self-consistent charge density and potential for follow-up calculations. Choose a prefix and outdir, and preserve both: later runs and post-processors must read the data produced by this calculation. The official guide describes the SCF-first sequence in its SCF, bands and NSCF workflow.

2. Run a fixed-potential calculation along an ordered path

Prepare a separate pw.x input with calculation='bands', using the same system identity and data location as the SCF run. Supply the path as ordered k-points: each point’s position in the input determines the path through reciprocal space. Use enough nbnd bands to cover the energy window you intend to inspect, including unoccupied states if they matter to your question. The appropriate number depends on the material and desired energy range; there is no universal value.

In Quantum ESPRESSO input, k-point coordinates and the selected K_POINTS format must agree. Consult the input descriptions for the format and labels supported by your installed release rather than copying coordinates or syntax without checking their convention.

3. Extract bands with bands.x

Run bands.x with matching prefix and outdir. It reads the band calculation data, extracts and reorders the eigenvalues, and writes a filband file that can be used by plotband.x. Its input reference also documents a gnuplot-oriented output option. See the version 7.5 bands.x input description for the supported parameters and output files.

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Keep the path definition and point labels available when plotting. The horizontal coordinate represents progress along the chosen path, not a universal distance independent of that path; labels and segment boundaries are needed to interpret it.

How do I calculate DOS in Quantum ESPRESSO?

1. Run a separate NSCF calculation on a mesh

Starting from the converged SCF result, prepare a distinct pw.x input with calculation='nscf'. Use a Brillouin-zone k-point mesh suited to integration, rather than reusing the band-path points. Ensure the calculation includes enough bands to cover the energies of interest. The mesh density, band count and other settings must be tested for the specific material and quantity; the Quantum ESPRESSO references do not prescribe one universally adequate mesh.

2. Calculate total DOS with dos.x

Run dos.x against the NSCF data, setting the same prefix and outdir. Configure the energy range, energy grid and broadening according to the system and the resolution you need. The program calculates the total DOS from the sampled eigenvalues; its available input controls and output details are in the version 7.5 dos.x input description.

DOS is sensitive to sampling and broadening: a coarse mesh can miss or distort features, and broadening smooths peaks while reducing visible detail. Check that the result is stable as you refine the mesh and vary broadening for the question at hand. Do not assume a smooth curve alone proves convergence.

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How do I get projected DOS or fat bands?

Projected DOS and local DOS with projwfc.x

Use projwfc.x when total DOS is not enough and you want contributions associated with atomic or orbital character. It projects the calculated wavefunctions onto orthogonalized atomic wavefunctions and can compute Löwdin charges, projected DOS, local DOS and k-resolved DOS. It needs the relevant wavefunctions, so point it to the matching calculation data with the same prefix and outdir. Consult the version 7.5 projwfc.x input description for the projection options.

Watch the units: the degauss input for projwfc.x is in Ry, while its energy grid and DOS output are in eV. A number intended as eV but entered as Ry changes the broadening substantially.

Projected bands and fat-band plots

A projected-band plot encodes orbital or atomic contribution at each k-point, commonly by changing the size or color of a band marker. The Quantum ESPRESSO users mailing list has discussed a workflow using k-resolved projwfc.x output and PyProcar as one visualization option; that post is an example, not a universal or official plotting prescription. Check the current February 2026 mailing-list discussion and the visualization tool’s current documentation for compatibility and input requirements before adopting a command sequence.

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Why does my band plot look wrong, or why can’t Quantum ESPRESSO find the Fermi energy?

Check the k-point path and band ordering

  • Confirm that path points are in the intended sequence. Unsorted points or repeated consecutive points can lead to unpredictable plots, as noted in the version 7.5 post-processing guide.
  • Inspect apparent jumps and crossings instead of assuming a fixed band index follows one unique physical state. Band reordering and crossing resolution do not work in every case; the displayed connectivity can depend on the sorting convention and plotter.
  • Check the requested nbnd and energy window. A plot that ends abruptly may simply lack calculated bands over the range you want to show.

Check consistency between calculations and post-processors

  • Use matching prefix and outdir values in pw.x and the corresponding bands.x, dos.x or projwfc.x input. A mismatch can make a post-processor look for data that is not there or read an unintended calculation.
  • Make sure you are post-processing the right run: bands.x needs the bands calculation data, while total DOS should be generated from the NSCF mesh calculation.
  • Check the units and energy reference used in the output and plotting settings before comparing curves or band energies.

Diagnose Fermi-energy trouble in DOS processing

A specific documented failure case occurs when a Methfessel–Paxton smearing of order 1 is used with very few k-points: the integrated DOS can become non-monotonic, making Fermi-energy location problematic. The Quantum ESPRESSO user guide identifies Gaussian or cold smearing as alternatives for this situation. This is a targeted troubleshooting option, not a universal recommendation; first confirm the k-point sampling and smearing settings. See the guide’s DOS and Fermi-energy discussion.

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What should be converged before interpreting the plots?

Convergence is specific to the material, calculation settings and scientific question. There is no single mesh or broadening value that guarantees a reliable band plot or DOS across systems. In practice, check the following independently rather than treating a successful run as proof that every output is converged:

  • SCF settings: verify the charge density and potential are stable with respect to the computational settings that control the ground state.
  • Band-path sampling: choose a physically meaningful path and enough points to resolve the dispersion and features being discussed.
  • Number of bands: include all states needed for the chosen energy window.
  • DOS mesh: refine the Brillouin-zone mesh and compare the features relevant to your conclusion.
  • DOS broadening and grid: test whether peak positions and integrated behavior remain meaningful as the energy-grid resolution and broadening change.
  • Data identity: retain the same calculation files and matching prefix/outdir across each post-processing step.

Quantum ESPRESSO’s input documentation index links to the executable-specific references; the cited command behavior and parameter units above correspond to the version 7.5 input pages where specified.

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band structuredensity of statesDFTmaterials scienceQuantum ESPRESSO

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