  Electronic correlations and spin-orbit interactions in plutonium create
variations in the bonding behavior of each of its allotropes. In $\delta$-Pu,
the 5f electrons lie at the tipping point between itinerant and localized
behavior which makes the creation of predictive models very difficult. We
perform density functional theory calculations to study the effect of
correlated descriptions on the mechanical properties of $\delta$-Pu. We find
that 7.5% $E_{xx}$ in the HSE functional yields the experimental lattice
parameters, moreover, this functional recovers the experimental elastic
constants while other approximations fail. The electronic structure of the
hybrid functional yields several signatures of strong correlations including
orbital-selective bonding of a single 5f electron and a pseudogap-like feature
which work in tandem to improve the description of mechanical properties. We
show how the emergence of orbital-selective bonding in the hybrid functional
can be understood through an Anderson impurity picture which predicts the
augmentation of $\pi$-bonding, the decrease of $\sigma$-bonding, and expands
the volume of the cell, enabling the accurate description of the mechanical
properties of $\delta$-Pu.
