  We investigate the ground-state properties of the ultracold gases of bosonic
microwave-shielded polar molecules. To account for the large shielding core of
the inter-molecular potential, we adopt a variational ansatz incorporating the
Jastrow correlation factor. We show that the system is always stable and
supports a self-bound gas phase and an expanding gas phase. We also calculate
the condensate fraction which is significantly reduced when the size of the
shielding core of the two-body potential becomes comparable to the
inter-molecular distance. Our studies distinguish the molecular condensates
from the atomic ones and invalidate the application of the Gross-Pitaevskii
equation to the microwave-shielded molecular gases. Our work paves the way for
studying the Bose-Einstein condensations of ultracold gases of
microwave-shielded polar molecules.
