  We have performed an {\it ab initio} study of the electronic structure of two
isostructural quantum spin systems, KCuCl$_{3}$ and TlCuCl$_{3}$, which have
recently attracted much attention due to their unconventional magnetic
properties. Our first-principles analysis shows unambiguously the role of Tl,
as opposed to structural differences between the two compounds, in making
TlCuCl$_{3}$ a {\it strongly} coupled s=1/2 dimer system compared to
KCuCl$_{3}$ which shows a {\it weakly} coupled s=1/2 dimer behavior. Good
agreement with the existing analysis of inelastic neutron scattering results
has been observed.
