  We study the uniform magnetic susceptibility and spin-gap for recently
proposed Heisenberg model Hamiltonians for CaV_4O_9 based on the orbital
ordering scenario of Marini and Khomskii and the LDA calculations of Pickett.
We argue that the experimentally observed uniform susceptibility data is
inconsistent with the weakly coupled dimer picture of Marini and Khomskii. The
model proposed by Pickett can, with appropriate choice of parameters, lead to
an explanation for the observed gap and uniform susceptibility. The resulting
agreement with experiments is of a similar quality to previously studied
models. We argue that this new model is best distinguished from previous ones
by neutron or Raman scattering experiments, via the location of the excitation
minimum in the Brillouin zone and by the possible existence or non-existence of
sharply defined singlet excitations.
