  Cavansite is a visually stunning blue vanadosilicate mineral with limited
occurrences worldwide, whereas Pentagonite is a closely related dimorph with
similar physical and chemical properties, yet is extremely rare compared to
Cavansite. The reasons behind Pentagonite's exceptional rarity remain largely
unknown.
  In this study, (a) density functional theory (DFT) is utilized to investigate
the electronic structures of Cavansite and Pentagonite at ground state and
finite pressures; (b) a two-state Boltzmann probability model is then employed
to construct a comprehensive phase diagram that reveals the abundance of each
species across a wide range of pressure and temperature conditions; and (c)
dehydration characteristics of these two minerals are explored.
  The present analysis reveals the key factors that contribute to the relative
scarcity of Pentagonite, including differences in structural arrangement and
electronic configurations between the two minerals. Specifically, it shows that
(a) because of the peculiar arrangements of SiO4 polyhedra, Cavansite forms a
compact structure (about 2.7% less in volume) resulting in lower energy; (b) at
a temperature of about 650K only about 1% Pentagonite can form; (c) vanadium
induces a highly localized state in both of these otherwise large-band-gap
insulators resulting in an extremely weak magnetic phase that is unlikely to be
observed at any reasonable finite temperature; and (d) water molecules are
loosely bound inside the microporous crystals of Cavansite and Pentagonite,
suggesting potential applications of these minerals in various technological
fields.
