First-principles study for low-spin LaCoO$_{3}$ with structurally consistent Hubbard $U$

We use the local density approximation + Hubbard $U$ (LDA+$U$) method to calculate the structural and electronic properties of low-spin LaCoO$_{3}$. The Hubbard $U$ is obtained by first principles and consistent with each fully-optimized atomic structure at different pressures. With structurally consistent $U$, the fully-optimized atomic structure agrees with experimental data better than the calculations with fixed or vanishing $U$. A discussion on how the Hubbard $U$ affects the electronic and atomic structure of LaCoO$_{3}$ is also given.