Pulay stress

This corresponds to all points on the reciprocal lattice that lie within a sphere whose radius is related to the energy cutoff.

The points on the reciprocal lattice which represent the basis set will no longer correspond to a sphere, but an ellipsoid.

The Pulay stress is often nearly isotropic, and tends to result in an underestimate of the equilibrium volume.

[2] Similarly, the error occurs in any calculation where the basis set explicitly depends on the position of atomic nuclei (which are to change during the geometry optimization).

[3] The way to eliminate the erroneous forces is to use nuclear-position-independent basis functions,[4] to explicitly calculate and then subtract them from the conventionally obtained forces, or to self-consistently optimize the center of localization of the orbitals.

A plane wave basis set is created for the hexagonal lattice (left), using the reciprocal lattice vectors inside the red circle. Then the lattice relaxes into a cubic symmetry (right). Keeping the red circle basis constant results in lattice vectors taken from an ellipsoid instead of a spherical area (compare to the blue circle).