Modeling the \alpha-\gamma isostructural phase transition of Cerium (Ce) within the framework of density functional theory (DFT) is challenging because the 4f electron in Ce is difficult to characterize. The use of a fraction of exact exchange in the hybrid functional [Phys. Rev. Lett. 109, 146402 (2012)] predicts the existence of the \alpha and \gamma phases but their relative energy is inconsistent with the experiments. In fact, the role of exact exchange in affecting properties of the \alpha and \gamma phases has not been well investigated. In this regard, we choose a variable amount of exact exchange (0.05 to 0.4) and systematically explore the properties of the \alpha and \gamma phases of Ce including cohesive energies, lattice constants, bulk moduli, magnetic moments, and 4f electron numbers. Notably, a small portion of exact exchange close to 0.1 yields an accurate description of these properties, in particular the predicted relative energy between the \alpha and \gamma phases agrees with the experiment. We further analyze the density of states, partial density of states, band structures and electron densities of the two phases. We observe that the exact exchange substantially affects the \gamma phase by localizing the 4f electrons, while it tends to delocalize the electrons in the \alpha phase. Our work provides deep insights into the structural and electronic structures of the \alpha and \gamma phases of Ce by elucidating the role of exact exchange in hybrid functional calculations.
(Photo)electrochemical surface reactions in realistic experimental systems occur under a constant-potential condition, while the ab-initio simulations of electrochemical reactions are mostly performed under a constant-charge condition. A charge-extrapolation scheme proposed...
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