CHAPTER 09 · BASICS · CALCULATION TYPES

Structure optimization

Forces and stress, relax and vc-relax, BFGS, &IONS and &CELL, convergence criteria, and the post-vc-relax rerun.

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Structure optimization drives the forces (energy gradients with respect to atomic positions) and the stress (gradients with respect to the cell) to zero. relax moves atoms only; vc-relax (variable-cell) moves the cell too.

Input skeleton

&CONTROL
  calculation   = 'vc-relax'
  etot_conv_thr = 1.0d-5      ! Ry, energy change between ionic steps
  forc_conv_thr = 1.0d-4      ! Ry/bohr, force criterion
  nstep         = 100         ! max ionic steps
/
&ELECTRONS
  conv_thr = 1.0d-10          ! tighter SCF for vc-relax
/
&IONS
  ion_dynamics  = 'bfgs'
/
&CELL
  cell_dynamics  = 'bfgs'
  press_conv_thr = 0.1        ! kbar
  cell_dofree    = 'ibrav'    ! keep the Bravais symmetry
/
  • This run consumes forces and stress, so tighten the SCF conv_thr beyond your usual value. Forces from a sloppy density are noise, and BFGS wanders on noise.
  • cell_dofree constrains the cell degrees of freedom: 'all', 'ibrav' (keep the Bravais lattice), '2Dxy' (slabs: freeze z), 'volume', 'shape', and others.
  • Per-atom constraints go through the if_pos flags on ATOMIC_POSITIONS (Chapter 03).

The mandatory follow-up: Pulay stress

When vc-relax finishes, the final structure appears between Begin final coordinates and End final coordinates. Run a fresh scf on that structure.

The plane-wave basis is tied to the cell. When the cell changes, the basis set changes with it (Pulay stress), so the energy and stress of the last vc-relax step were computed in the old basis and cannot be trusted. QE prints a warning saying exactly this. Example E6 checks it on silicon.

Symmetry and the optimization path

QE detects the symmetry of the initial structure and preserves it throughout the optimization. This cuts both ways.

  • An atom on a symmetric site feels exactly zero force along directions the symmetry forbids, so it never moves off them. To find lower-energy broken-symmetry structures, distort the starting geometry slightly or set nosym=.true..
  • Conversely, keeping symmetry saves a great deal of compute. Choose deliberately.

When BFGS struggles

Symptom Response
Energy oscillates without converging Tighten the SCF conv_thr; check upscale
Fails while the cell changes a lot Increase cell_factor (default 2.0)
Diverges from the first step Inspect the starting structure: overlapping atoms, absurd distances
Forces are small but stress will not drop Check press_conv_thr; suspect an insufficient cutoff (stress is more cutoff-sensitive than energy)
Common mistakes

Keeping the lattice constant from vc-relax and also quoting the last step's energy. The lattice constant is fine; the energy carries Pulay contamination. Always use the energy from the fresh scf on the final structure. Also, stress demands higher cutoffs than energies and forces, so pass a stress-based convergence test before any vc-relax.

  • E6 · Si vc-relax: start from a deliberately wrong lattice constant, find equilibrium, and measure the usual PBE overestimate.
  • E13 · Slabs and AIMD: a slab relaxation with the bottom layers pinned via if_pos.