Multithermal-multibaric ensembles from collective-variables-based enhanced sampling methods

Thermodynamic ensembles that exist in nature are usually characterized by some constraint such as having constant energy or temperature. Computer simulations are not only able to reproduce these ensembles but they are also capable of creating new ensembles with different characteristics. Generalized ensembles such as the multicanonical ensemble have been shown to improve the sampling of rugged free energy landscapes and phase transitions. A natural extension is the multithermal-multibaric ensemble in which a large region of the temperature and pressure phase diagram can be sampled in a single simulation. We will discuss two methods to generate multithermal-multibaric ensembles using the potential energy and the volume as collective variables to construct a bias potential. We have employed these algorithms to study the folding of the miniprotein chignolin and to obtain evidence of a liquid-liquid transition in a model of water. Furthermore, we have extended this approach to seamlessly integrate the sampling of a kinetic bottleneck through the addition of one or more collective variables that describe slow modes of the system. We have applied this method successfully to the calculation of liquid-solid phase diagrams in sodium, aluminum, and gallium.