  Plutonium is the most exotic and mysterious element in the periodic table. It
has 6 metallic phases and peculiar physical properties not yet understood. One
of the most intriguing properties of Pu is that relatively small changes of
temperature can induce transitions between different structures, that are
accompanied by very large changes of equilibrium volumes. This fact has
stimulated extensive theoretical and experimental studies. In spite of this, a
convincing explanation of the metallurgic properties of Pu based on fundamental
principles is still lacking, and none of the previous theories has been able to
describe simultaneously the energetics and the $f$ electronic structure of all
of the phases of Pu on the same footing. Here we provide a bird's eye view of
Pu by studying the zero-temperature pressure-volume phase diagram and the $f$
electronic structure of all of its crystalline phases from first principles. In
particular, we clarify the way in which the $f$-electron correlations determine
its unusual energetics. Our theoretical energetics and ground-state $f$
electronic structure are both in good quantitative agreement with the
experiments.
