  We have investigated the structure of Co$_2$CO$_3$(OH)$_2$ using Density
Functional Theory (DFT) simulations as well as Powder X-Ray Diffraction (PXRD)
measurements on samples synthesized via deposition from aqueous solution. We
consider two possible monoclinic phases, with closely related but symmetrically
different crystal structures, based on those of the minerals malachite and
rosasite, as well as an orthorhombic phase that can be seen as a common parent
structure for the two monoclinic phases, and a triclinic phase with the
structure of the mineral kolwezite. Our DFT simulations predict that the
rosasite-like and the malachite-like phases are two different local minima of
the potential energy landscape for Co$_2$CO$_3$(OH)$_2$, and are practically
degenerate in energy, while the orthorhombic and triclinic structures are
unstable and experience barrierless transformations to the malachite phase upon
relaxation. The best fit to the PXRD data is obtained using a rosasite model
(monoclinic with space group P1121/n and cell parameters a = 3.1408(4) {\AA}, b
= 12.2914(17) {\AA}, c = 9.3311(16) {\AA}, $\gamma$ = 82.299(16)$^{\circ}$).
However, some features of the PXRD pattern are still not well accounted for by
this refinement and the residual parameters are relatively poor. We discuss the
relationship between the rosasite and malachite phases of Co$_2$CO$_3$(OH)$_2$
and show that they can be seen as polytypes. Based on the similar calculated
stability of these two polytypes, we speculate that some level of stacking
disorder could account for the poor fit of our PXRD data. The possibility that
Co$_2$CO$_3$(OH)$_2$ could crystallize, under different growth conditions, as
either rosasite or malachite, or even as a stacking-disordered phase
intermediate between the two, requires further investigation.
