First-principles calculation of stress tensor in the LSDA+U formalism

We derive the stress-tensor formula within the LSDA+U scheme by differentiating analytically the LSDA+U total-energy function with respect to the strain tensor. The rotationally invariant form of the LSDA+U functional is employed and the double-counting correction is considered in the fully localized limit and around mean field. The electronic wave functions are expanded with either pseudoatomic orbitals (PAOs) or plane waves. In the PAO-basis case, the orthogonality stress term is included. Our LSDA+U stress-tensor formula is numerically tested with antiferromagnetic NiO and reproduces successfully the stress values obtained from numerical derivatives of the total-energy values. As an application, we study elastic constants, bulk moduli, and sound velocities of NiO and MnO, obtaining results in good agreement with experimental data.