  We study the structural, electronic, and magnetic properties of Co$_2$ZAl
compounds employing a pseudopotential electronic bandstructure method. The
stability of the compounds is established through the formation and cohesive
energy calculations. The effect of the lattice parameter variation on the
electronic and magnetic properties of the compounds is investigated and
meticulous explanation is provided for the observed behavior. The variation of
the individual spin magnetic moments and the stability of the total spin
magnetic moment during the expansion and contraction of the lattice parameter
is observed and an attempt is made to understand the obtained behavior.
Finally, we implement DFT+U to examine its consequences on the electronic and
magnetic properties of the Co$_2$ZAl compounds. We find that the use of DFT+U
is not justified for these compounds and in some cases like Co$_2$MnAl it
produces unrealistic properties. The exception is Co2FeAl where the desired
half-metallicity is restored after the inclusion of on-site correlations. We
explain why the on-site correlations might be important for Co$_2$FeAl by
comparing it with other Heusler alloys where the correlation was found to be
meaningful to explain the observed magnetic moments.
