  Using the effective potential approach for composite operators, we have
formulated a general method of calculation of the truly nonperturbative
Yang-Mills vacuum energy density in the covariant gauge QCD ground state
quantum models. It is defined as an integration of the truly nonperturbative
part of the full gluon propagator over the deep infrared region (soft momentum
region). A nontrivial minimization procedure makes it possible to determine the
value of the soft cutoff in terms of the corresponding nonperturbative scale
parameter, which is inevitably present in any nonperturbative model for the
full gluon propagator. We have shown for specific models of the full gluon
propagator explicitly that the use of the infrared enhanced and finite gluon
propagators lead to the vacuum energy density which is finite, always negative
and it has no imaginary part (stable vacuum), while the infrared vanishing
propagators lead to unstable vacuum and therefore they are physically
unacceptable.
