  We examine the problem of the collapse and fragmentation of molecular clouds
with a Gaussian density distribution with high resolution, double precision
numerical simulations using the GADGET-2 code. To describe the thermodynamic
properties of the cloud during the collapse -to mimic the rise of temperature
predicted by radiative transfer- we use a barotropic equation of state that
introduces a critical density to separate the isothermal and adiabatic regimes.
We discuss the effects of this critical density in the formation of multiple
systems. We confirm the tendency found for Plummer and Gaussian models that if
the collapse changes from isothermal to adiabatic at earlier times that occurs
for the models with a lower critical density, the collapse is slowed down, and
this enhances the fragments' change to survive. However, this effect happens up
to a threshold density below which single systems tend to form. On the other
hand, by setting a bigger initial perturbation amplitude, the collapse is
faster and in some cases a final single object is formed.
