First-Principles Study of Piezoelectricity in PbTiO 3

Tables II and IV were incorrect. In Table II the previously calculated internal displacement gradients in the second and the fourth rows were incorrect, and in Table IVall previously calculated piezoelectric stress tensor elements were incorrect except for the homogeneous part of e33. The present results have been checked both with the finite strain and the strain linear response methods using the ABINIT package [1,2]. Most of the previous errors are arithmetic or transcription errors, while e15 was due to incomplete atomic relaxation.