  Despite the simplicity of its molecular unit, water is a challenging system
because of its uniquely rich polymorphism and predicted but yet unconfirmed
features. Introducing a novel space of generalized coordinates that capture
changes in the topology of the interatomic network, we are able to
systematically track transitions among liquid, amorphous and crystalline forms
throughout the whole phase diagram of water, including the nucleation of
crystals above and below the melting point. Our approach, based on molecular
dynamics and enhanced sampling / free energy calculation techniques, is not
specific to water and could be applied to very different structural phase
transitions, paving the way towards the prediction of kinetic routes connecting
polymorphic structures in a range of materials.
