Free energy minimization based upon analytical, rather than numerical, derivatives has been applied for the first time to quartz and microporous silica polymorphs. To maximize the efficiency of this method to make the study of large unit cells practical, while maintaining accuracy, a new set of shell model parameters have been derived based on the properties of alpha-quartz which avoid the need for genuine three-body terms. Full minimization of the free energy with respect to both strains and internal degrees of freedom is found to lead to soft modes at about room temperature in the absence of anharmonic corrections, and therefore analytical free energy minimization within the zero static internal stress approximation is found to be the preferred method for quartz and microporous materials. The wider implication is that total free energy minimization in the quasiharmonic approximation of complex chemical systems is likely to fail at relatively modest temperatures and before the classical limit is reached.