The formation of ice in the troposphere is one of the major open problems in atmospheric physics. Ice generation from supercooled droplets mostly occurs in the presence of specific aerosols called ice-nucleating particles. However, experimental observations in cold clouds show that ice particle concentrations exceed those of atmospheric ice-nucleating particles by several orders of magnitude, a phenomenon known as ice multiplication. Recent theoretical and experimental work has suggested an alternative hypothesis that freezing can be triggered by extreme negative pressures in supercooled water. We explore this hypothesis, modeling supercooled water droplet-to-ice phase transitions by extending a Diffuse Interface model proposed by Gránásy, embedding supercooled water and hexagonal ice thermodynamics using IAPWS multiparametric equations of state. This framework, combined with the Simplified String Method—a rare-event technique—allows us to find ice nuclei profiles along the Minimum Energy Path and to compute ice nucleation rates across different temperature and pressure conditions. Results show excellent agreement with experimental and Molecular Dynamics data. A key result is that negative pressures dramatically reduce the nucleation barrier, making ice formation orders of magnitude more likely. Through a complementary study, we show that such tensile states arise naturally during droplet coalescence: the nanometric curvature of the neck between merging droplets generates pressures on the order of -100 MPa, potentially triggering ice multiplication. This work establishes a reliable computational framework for predicting ice nucleation rates from physical principles, bridging the gap between molecular-scale physics and atmospheric processes. The methodology developed here lays the groundwork for future investigations of ice formation in atmospheric clouds.