In this work, we use first-principles atomistic calculations based on density functional theory to investigate the first phase transition that occurs when pressure and temperature are applied to calcite I, the stable polymorph at standard temperature and pressure. The mechanism of this phase transition is identified as phonon softening, and the specific phonon mode is documented. The phase boundary is computed with the framework of the quasi-harmonic approximation (QHA) and compared to available experiments. The computed phase boundary is sensitive to the approximations adopted to describe electronic exchange and correlation. To explore this sensitivity a range of approximation with the framework of modern density functional theory have been used, namely; global hybrid exchange, the generalized gradient approximation and the inclusion of ad hoc corrections describing van der Waals interactions. The latter prove to be significant in improving the agreement with the available observations of phase stability. The phonon mediated nature of the transition suggests mechanisms for controlling the growth of calcite crystals, for example, via the inclusion of amino acids or partial substitution of ions, to frustrate displacements along the soft phonon modes.