Global Free-Energy Landscapes as a Smoothly Joined Collection of Local Maps.

Enhanced sampling techniques have become an essential tool in computational chemistry and physics, where they are applied to sample activated processes that occur on a time scale that is inaccessible to conventional simulations. Despite their popularity, it is well known that they have constraints that hinder their application to complex problems. The core issue lies in the need to describe the system using a small number of collective variables (CVs). Any slow degree of freedom that is not properly described by the chosen CVs will hinder sampling efficiency. However, the exploration of configuration space is also hampered by including variables that are not relevant for the activated process under study. This paper presents the Adaptive Topography of Landscape for Accelerated Sampling (ATLAS), a new biasing method capable of working with many CVs. The root idea of ATLAS is to apply a divide-and-conquer strategy, where the high-dimensional CVs space is divided into basins, each of which is described by an automatically determined, low-dimensional set of variables. A well-tempered metadynamics-like bias is constructed as a function of these local variables. Indicator functions associated with the basins switch on and off the local biases so that the sampling is performed on a collection of low-dimensional CV spaces that are smoothly combined to generate an effectively high-dimensional bias. The unbiased Boltzmann distribution is recovered through reweighing, making the evaluation of conformational and thermodynamic properties straightforward. The decomposition of the free-energy landscape in local basins can be updated iteratively as the simulation discovers new (meta)stable states.

Iterative Unbiasing of Quasi-Equilibrium Sampling.

Atomistic modeling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an appropriately chosen set of collective variables can significantly accelerate the exploration of phase space, albeit at the price of distorting the distribution of microstates. Efficient reweighting to recover the unbiased distribution can be nontrivial when employing adaptive sampling techniques such as metadynamics, variationally enhanced sampling, or parallel bias metadynamics, in which the system evolves in a quasi-equilibrium manner under a time-dependent bias. We introduce an iterative unbiasing scheme that makes efficient use of all the trajectory data and that does not require the distribution to be evaluated on a grid. The method can thus be used even when the bias has a high dimensionality. We benchmark this approach against some of the existing schemes on model systems with different complexity and dimensionality.

The phase diagram of water at negative pressures: virtual ices.

The phase diagram of water at negative pressures as obtained from computer simulations for two models of water, TIP4P/2005 and TIP5P is presented. Several solid structures with lower densities than ice Ih, so-called virtual ices, were considered as possible candidates to occupy the negative pressure region of the phase diagram of water. In particular the empty hydrate structures sI, sII, and sH and another, recently proposed, low-density ice structure. The relative stabilities of these structures at 0 K was determined using empirical water potentials and density functional theory calculations. By performing free energy calculations and Gibbs-Duhem integration the phase diagram of TIP4P/2005 was determined at negative pressures. The empty hydrates sII and sH appear to be the stable solid phases of water at negative pressures. The phase boundary between ice Ih and sII clathrate occurs at moderate negative pressures, while at large negative pressures sH becomes the most stable phase. This behavior is in reasonable agreement with what is observed in density functional theory calculations.

On thin ice: surface order and disorder during pre-melting.

The effect of temperature on the structure of the ice Ih (0001) surface is considered through a series of molecular dynamics simulations on an ice slab. At relatively low temperatures (200 K) a small fraction of surface self-interstitials (i.e. admolecules) appear that are formed exclusively from molecules leaving the outermost bilayer. At higher temperatures (ca. 250 K), vacancies start to appear in the inner part of the outermost bilayer exposing the underlying bilayer and providing sites with a high concentration of dangling hydrogen bonds. Around 250-260 K aggregates of molecules formed on top of the outermost bilayer from self-interstitials become more mobile and have diffusivities approaching that of liquid water. At approximately 270-280 K the inner bilayer of one surface noticeably destructures and it appears that at above 285 K both surfaces are melting. The observed disparity in the onset of melting between the two sides of the slab is rationalised by considering the relationship between surface energy and the spatial distribution of protons at the surface; thermodynamic stability is conferred on the surface by maximising separations between dangling protons at the crystal exterior. Local hotspots associated with a high dangling proton density are suggested to be susceptible to pre-melting and may be more efficient at trapping species at the external surface than regions with low concentrations of protons thus potentially helping ice particles to catalyse reactions. A preliminary conclusion of this work is that only about 10-20 K below the melting temperature of the particular water potential employed is major disruption of the crystalline lattice noted which could be interpreted as being "liquid", the thickness of this film being about a nanometre.