Performance of hybrid density functional theory for $\alpha $ \textit{versus} $\delta $-Pu

Hybrid density functional theory, which replaces a fraction of density functional theory exchange with exact Hartree-Fock exchange, has been used to study the electronic, geometric, and magnetic properties of $\alpha $--Pu and compared with our previous results for $\delta $--Pu. A non-magnetic (NM) ground state was realized for $\alpha $=0.55 ($\alpha $ indicating the fraction of the HF exchange) for $\delta $--Pu but the equilibrium atomic volume deviated from experiment by 19{\%}, the 5$f$ electron population was close to 4 and a 5$f$ DOS that shows anomalous localization and failed to match experimentally obtained PES data.\footnote{R. Atta-Fynn and A. K. Ray, Europhys. Lett. 85, 27008 (2009)} For $\alpha $-Pu, a NM ground state was obtained at 40{\%} HF exchange. Comparing the two phases at the NM ground state, the 5$f$ population is about the same, but energy differences between the different magnetic configurations for the two phases are observed. For $\delta $-Pu NM-FM and NM-AFM \textit{$\Delta $E} are 86.33 and 82.28 mRy/atom, respectively, and for $\alpha $-Pu the NM-FM and NM-AFM \textit{$\Delta $E} are 144.98 and 60.72 mRy/atom, respectively. The 5$f$ DOS for $\delta $-Pu show no DOS at the Fermi level but the presence of localized states, while for $\alpha $-Pu DOS show delocalization. Though hybrid density functional theory might not perform better compared to DFT for $\delta $-Pu, it shows promise for $\alpha $-Pu.