  The potential energy landscape (PEL) formalism is a statistical mechanical
approach to describe supercooled liquids and glasses. Here we use the PEL
formalism to study the pressure-induced transformations between low-density
amorphous ice (LDA) and high-density amorphous ice (HDA) using computer
simulations of the TIP4P/2005 molecular model of water. We find that the
properties of the PEL sampled by the system during the LDA-HDA transformation
exhibit anomalous behavior. In particular, at conditions where the change in
density during the LDA-HDA transformation is approximately discontinuous,
reminiscent of a first-order phase transition, we find that (i) the inherent
structure (IS) energy, $e_\text{IS}(V)$, is a concave function of the volume,
and (ii) the IS pressure, $P_\text{IS}(V)$, exhibits a van der Waals-like loop.
In addition, the curvature of the PEL at the IS is anomalous, a non-monotonic
function of $V$. In agreement with previous studies, our work suggests that
conditions (i) and (ii) are necessary (but not sufficient) signatures of the
PEL for the LDA-HDA transformation to be reminiscent of a first-order phase
transition. We also find that one can identify two different regions of the
PEL, one associated to LDA and another to HDA. Our computer simulations are
performed using a wide range of compression/decompression and cooling rates. In
particular, our slowest cooling rate (0.01 K/ns) is within the experimental
rates employed in hyperquenching experiments to produce LDA. Interestingly, the
LDA-HDA transformation pressure that we obtain at $T=80$ K and at different
rates extrapolates remarkably well to the corresponding experimental pressure.
