  We investigate the electronic and magnetic properties of the frustrated
triangular-lattice antiferromagnets Cs$_2$CuCl$_4$ and Cs$_2$CuBr$_4$ in the
framework of density functional theory. Analysis of the exchange couplings J
and J' using the available X-ray structural data corroborates the values
obtained from experimental results for Cs$_2$CuBr$_4$ but not for
Cs$_2$CuCl$_4$. In order to understand this discrepancy, we perform a detailed
study of the effect of structural optimization on the exchange couplings of
Cs$_2$CuCl$_4$ employing different exchange-correlation functionals. We find
that the exchange couplings depend on rather subtle details of the structural
optimization and that only when the insulating state (mediated through spin
polarization) is present in the structural optimization, we do have good
agreement between the calculated and the experimentally determined exchange
couplings. Finally, we discuss the effect of interlayer couplings as well as
longer-ranged couplings in both systems.
