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

Abstract

We derive the stress-tensor formula within the $\text{LSDA}+U$ scheme by differentiating analytically the $\text{LSDA}+U$ total-energy function with respect to the strain tensor. The rotationally invariant form of the $\text{LSDA}+U$ 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 $\text{LSDA}+U$ 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.