First principles calculations of the total energy of Imma states have found instabilities in states near the β-Sn phase and in states near the simple hexagonal (sh) phase of Si crystal. In agreement with experiment the two instability ranges narrow the stable range between them and also in agreement with experiment the instabilities force first-order transitions to both the β-Sn and sh phases when the pressure is held constant, the experimental condition. The transition pressures to the β-Sn and sh phases for a non-vibrating crystal model are found to be 96 and 110 kbar respectively. These pressure values are considerably lower than the experimental values, but we show that lattice vibrations will increase the equilibrium-state pressures. We find widespread occurrence of instability in the equilibrium states of the three phases and show the presence of three kinds of instability. Near and up to the sh phase structure we find the unusual case of stability at constant volume, but, as observed, instability at constant pressure p. Two special computational procedures are discussed, which locate the unstable ranges of structure. One is based on finding phases from minima of total energy E at constant V and the other finds phases from minima of the Gibbs free energy G at constant p. When the minima cease to exist the Imma phase is unstable. © 2011 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.