  We study the thermodynamic properties of the clinoatacamite compound,
Cu_2(OH)_3Cl, by considering several approximate models. They include the
Heisenberg model on (i) the uniform pyrochlore lattice, (ii) a very anisotropic
pyrochlore lattice, and (iii) a kagome lattice weakly coupled to spins that sit
on a triangular lattice. We utilize the exact diagonalization of small clusters
with periodic boundary conditions and implement a numerical linked-cluster
expansion approach for quantum lattice models with reduced symmetries, which
allows us to solve model (iii) in the thermodynamic limit. We find a very good
agreement between the experimental uniform susceptibility and the numerical
results for models (ii) and (iii), which suggests a weak ferromagnetic coupling
between the kagome and triangular layers in clinoatacamite. We also study
thermodynamic properties in a geometrical transition between a planar
pyrochlore lattice and the kagome lattice.
