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Periodic directions, vacuum, and dimensionality

Quantum ESPRESSO solves a periodically repeated three-dimensional simulation cell. Slabs and low-dimensional systems are configured via vacuum and k-point sampling in calculations.

Complete guide

Supercells, slabs, and vacuum

Cell repetition in the viewer allows inspecting extended lattices without modifying the underlying unit cell. Slabs and low-dimensional structures are constructed by explicitly introducing vacuum along the desired non-periodic direction (typically c).

Quantum ESPRESSO always assumes periodic boundary conditions in 3D: for a slab or 2D material, maintain sufficient vacuum separation between periodic replicas, set a single k-point along the vacuum direction (e.g. N × M × 1), and configure appropriate dipole/electrostatic corrections.

Common systems

SystemDisplay repetitionComputational checks
Bulk crystal2 × 2 × 2Converge a three-dimensional k mesh; use the intended primitive or conventional cell.
Slab / 2D sheet in a-b plane2 × 2 × 1Converge perpendicular vacuum and in-plane k mesh; usually one k-point along c. Review dipole or 2D isolation treatment when appropriate.
Wire along c1 × 1 × 2Converge vacuum in both transverse directions and sampling along the wire. The built-in c-vacuum action alone does not prepare this geometry.
Molecule / cluster1 × 1 × 1Use a sufficiently large 3D box; typically Gamma-only sampling. Check charged-system and dipole treatment as needed.

A reproducible slab check

  1. Orient the slab so its surface lies in the a-b plane.
  2. Add vacuum along c and inspect the actual cell and positions.
  3. Set cell repetition to 2 × 2 × 1 to inspect the in-plane extended surface without repeating along the vacuum direction.
  4. Set the k mesh to N by M by 1; choose N and M through convergence.
  5. Inspect generated or expert input for the appropriate electrostatic setup.
  6. Repeat with larger vacuum and denser in-plane sampling until the target quantity is stable.

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