Early stage spin-state transition in LaCoO$_{3}$ investigated by first principles

The existence of intermediate-spin (IS) state cobalt and its role in the thermally-induced spin-state transition in LaCoO$_{3}$ has been controversial. Using the local density approximation + Hubbard $U$ (LDA+$U)$ method, we have successfully stabilized isolated single high-spin (HS) and IS excited cobalt ions~in an array of low-spin (LS) cobalt in LaCoO$_{3}$. The Hubbard $U$ is self-consistently determined from first principles. We show that at low temperatures, for isolated single ions, HS cobalt is the first excited state. Low concentrations of isolated IS cobalt produce a metallic state. This result supports the conclusions of quantum chemistry calculations on clusters, and contrasts with results from periodic calculations with 100{\%} IS and HS cobalt population.~It is also consistent with recent experiments at very low densities of excited states at low temperatures.