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The possible existence of a metastable liquid–liquid transition (LLT) and a corresponding liquid–liquid critical point (LLCP) in supercooled liquid water remains a topic of much debate. An LLT has been rigorously proved in three empirically parametrized molecular models of water, and evidence consistent with an LLT has been reported for several other such models. In contrast, experimental proof of this phenomenon has been elusive due to rapid ice nucleation under deeply supercooled conditions. In this work, we combined density functional theory (DFT), machine learning, and molecular simulations to shed additional light on the possible existence of an LLT in water. We trained a deep neural network (DNN) model to represent the ab initio potential energy surface of water from DFT calculations using the Strongly Constrained and Appropriately Normed (SCAN) functional. We then used advanced sampling simulations in the multithermal–multibaric ensemble to efficiently explore the thermophysical properties of the DNN model. The simulation results are consistent with the existence of an LLCP, although they do not constitute a rigorous proof thereof. We fit the simulation data to a two-state equation of state to provide an estimate of the LLCP’s location. These combined results—obtained from a purely first-principles approach with no empirical parameters—are strongly suggestive of the existence of an LLT, bolstering the hypothesis that water can separate into two distinct liquid forms.

We introduce a computational method to discover polymorphs in molecular crystals at finite temperature. The method is based on reproducing the crystallization process starting from the liquid and letting the system discover the relevant polymorphs. This idea, however, conflicts with the fact that crystallization has a time scale much longer than that of molecular simulations. In order to bring the process within affordable simulation time, we enhance the fluctuations of a collective variable by constructing a bias potential with well tempered metadynamics. We use as collective variable an entropy surrogate based on an extended pair correlation function that includes the correlation between the orientation of pairs of molecules. We also propose a similarity metric between configurations based on the extended pair correlation function and a generalized Kullback-Leibler divergence. In this way, we automatically classify the configurations as belonging to a given polymorph using our metric and a hierarchical clustering algorithm. We find all relevant polymorphs for both substances and we predict new polymorphs. One of them is stabilized at finite temperature by entropic effects.Polymorphism is the ability that substances have to crystallize into different structures. A paradigmatic example is carbon that in its two main polymorphs, graphite and diamond, exhibits amazingly different properties. Polymorphism is also important from a practical point of view since controlling which crystal structure forms is of the utmost importance in many manufacturing processes. The pharmaceutical industry suffers in particular the consequences of polymorphism 1,2 . Active pharmaceutical ingredients are usually small, organic molecules that frequently exist in a plethora of crystalline forms. Different polymorphs can be patented separately and usually lead to different drug performances. Therefore a comprehensive screening of polymorphs is crucial to avoid a rival company from releasing to the market the same molecule in a different polymorph 3 , and to anticipate the transformation of one polymorph into another during the manufacturing process or the shelf life 4 .The screening of polymorphs was traditionally performed experimentally in spite of the large costs involved 2 . In the last 15 years the increase in computer power and the development of algorithms able to screen a large number of polymorphs has lead to a very significant successes in polymorph prediction 5-9 . Such methods are based on the search of local minima on the potential energy surface. The minima are ordered by energy and typically corrected for thermal effects using the harmonic approximation. However no method can claim to be able to scan exhaustively all the relevant low-lying minima. In addition, entropic effects beyond the harmonic approximation can be significant. Not only they a) Electronic mail: parrinello@phys.chem.ethz.ch can alter the delicate energetic balance between the different polymorphs but even stabilize structures that are not local minima of t...

Crystallization is a process of great practical relevance in which rare but crucial fluctuations lead to the formation of a solid phase starting from the liquid. As in all first order first transitions, there is an interplay between enthalpy and entropy. Based on this idea, in order to drive crystallization in molecular simulations, we introduce two collective variables, one enthalpic and the other entropic. Defined in this way, these collective variables do not prejudge the structure into which the system is going to crystallize. We show the usefulness of this approach by studying the cases of sodium and aluminum that crystallize in the bcc and fcc crystalline structures, respectively. Using these two generic collective variables, we perform variationally enhanced sampling and well tempered metadynamics simulations and find that the systems transform spontaneously and reversibly between the liquid and the solid phases.