  Mass loss forms an important aspect of the evolution of massive stars, as
well as for the enrichment of the surrounding ISM. Our goal is to predict
accurate mass-loss rates and terminal wind velocities. These quantities can be
compared to empirical values, thereby testing radiation-driven wind models. One
specific issue is that of the "weak-wind problem", where empirically derived
mass-loss rates fall orders of magnitude short of predicted values. We employ
an established Monte Carlo model and a recently suggested new line acceleration
formalism to solve the wind dynamics consistently. We provide a new grid of
mass-loss rates and terminal wind velocities of O stars, and compare the values
to empirical results. Our models fail to provide mass-loss rates for
main-sequence stars below a luminosity of log(L/Lsun) = 5.2, where we run into
a fundamental limit. At luminosities below this critical value there is
insufficient momentum transferred in the region below the sonic point to
kick-start the acceleration. This problem occurs at the location of the onset
of the weak-wind problem. For O dwarfs, the boundary between being able to
start a wind, and failing to do so, is at spectral type O6/O6.5. The direct
cause of this failure is a combination of the lower luminosity and a lack of Fe
V lines at the wind base. This might indicate that another mechanism is
required to provide the necessary driving to initiate the wind. For stars more
luminous than log(L/Lsun) = 5.2, our new mass-loss rates are in excellent
agreement with the mass-loss prescription by Vink et al. 2000. This implies
that the main assumption entering the method of the Vink et al. prescriptions -
i.e. that the momentum equation is not explicitly solved for - does not
compromise the reliability of the Vink et al. results for this part of
parameter space (Abridged).
