  Correlation-driven phenomena in molecular periodic systems are challenging to
predict computationally not only because such systems are periodically infinite
but also because they are typically strongly correlated. Here we generalize the
variational two-electron reduced density matrix (2-RDM) theory to compute the
energies and properties of strongly correlated periodic systems. The 2-RDM of
the unit cell is directly computed subject to necessary $N$-representability
conditions such that the unit-cell 2-RDM represents at least one $N$-electron
density matrix. Two canonical but non-trivial systems, periodic metallic
hydrogen chains and periodic acenes, are treated to demonstrate the
methodology. We show that, while single-reference correlation theories do not
capture the strong (static) correlation effects in either of these molecular
systems, the periodic variational 2-RDM theory predicts the Mott
metal-to-insulator transition in the hydrogen chains and the length-dependent
polyradical formation in acenes. For both hydrogen chains and acenes the
periodic calculations are compared with previous non-periodic calculations with
the results showing a significant change in energies and increase in the
electron correlation from the periodic boundary conditions. The 2-RDM theory,
which allows for much larger active spaces than are traditionally possible, is
applicable to studying correlation-driven phenomena in general periodic
molecular solids and materials.
