Exceptionally long-ranged lattice relaxation in oxygen-deficient Ta2O5

• A charge-neutral oxygen vacancy in Ta2O5 can induce very long-ranged lattice relaxation.
• The long-ranged lattice relaxation is caused by long-ranged Hellmann–Feynman forces.
• We derive a universal formula describing the HF forces and the variation in charge density upon the creation of a vacancy.
• The crystal structure of Ta2O5 can be highly degenerate.

The lattice relaxation in oxygen-deficient Ta2O5 is investigated using first-principles calculations. The presence of a charge-neutral oxygen vacancy can result in a long-ranged lattice relaxation which extends beyond 18 Å from the vacancy site. The lattice relaxation has significant effects on the vacancy formation energy as well as the electronic structures. The long-ranged behavior of the lattice relaxation is explained in terms of the Hellmann–Feynman forces and the potential energy surface related to the variation of Ta–O bond lengths.