Data-Driven Path Collective Variables.

Identifying optimal collective variables to model transformations using atomic-scale simulations is a long-standing challenge. We propose a new method for the generation, optimization, and comparison of collective variables that can be thought of as a data-driven generalization of the path collective variable concept. It consists of a kernel ridge regression of the committor probability, which encodes a transformation's progress. The resulting collective variable is one-dimensional, interpretable, and differentiable, making it appropriate for enhanced sampling simulations requiring biasing. We demonstrate the validity of the method on two different applications: a precipitation model and the association of Li+ and F- in water. For the former, we show that global descriptors such as the permutation invariant vector allow reaching an accuracy far from the one achieved via simpler, more intuitive variables. For the latter, we show that information correlated with the transformation mechanism is contained in the first solvation shell only and that inertial effects prevent the derivation of optimal collective variables from the atomic positions only.

Inferring free-energy barriers and kinetic rates from molecular dynamics via underdamped Langevin models.

Rare events include many of the most interesting transformation processes in condensed matter, from phase transitions to biomolecular conformational changes to chemical reactions. Access to the corresponding mechanisms, free-energy landscapes and kinetic rates can in principle be obtained by different techniques after projecting the high-dimensional atomic dynamics on one (or a few) collective variable. Even though it is well-known that the projected dynamics approximately follows - in a statistical sense - the generalized, underdamped or overdamped Langevin equations (depending on the time resolution), to date it is nontrivial to parameterize such equations starting from a limited, practically accessible amount of non-ergodic trajectories. In this work we focus on Markovian, underdamped Langevin equations, that arise naturally when considering, e.g., numerous water-solution processes at sub-picosecond resolution. After contrasting the advantages and pitfalls of different numerical approaches, we present an efficient parametrization strategy based on a limited set of molecular dynamics data, including equilibrium trajectories confined to minima and few hundreds transition path sampling-like trajectories. Employing velocity autocorrelation or memory kernel information for learning the friction and likelihood maximization for learning the free-energy landscape, we demonstrate the possibility to reconstruct accurate barriers and rates both for a benchmark system and for the interaction of carbon nanoparticles in water.

CO2 Capture and Release in Amine Solutions: To What Extent Can Molecular Simulations Help Understand the Trends?

Absorption in amine solutions is a well-established advanced technology for CO2 capture. However, the fundamental aspects of the chemical reactions occurring in solution still appear to be unclear. Our previous investigation of aqueous monoethanolamine (MEA) and 2-amino-2-methyl-1,3-propanediol (AMPD), based on ab initio molecular dynamics simulations aided with metadynamics, provided new insights into the reaction mechanisms leading to CO2 capture and release with carbamate formation and dissociation. In particular, the role of water-strongly underestimated in previous computational studies-was established as essential in determining the development of all relevant reactions. In this article, we apply the same simulation protocol to other relevant primary amines, namely, a sterically hindered amine (2-amino-2-methyl-1-propanol (AMP)) and an aromatic amine (benzylamine (BZA)). We also discuss the case of CO2 capture with the formation of bicarbonate. New information is thus obtained that extends our understanding. However, quantitative predictions obtained using molecular simulations suffer from several methodological problems, and comparison among different chemical species is especially demanding. We clarify these problems further with a discussion of previous attempts to explain the different behaviors of AMP and MEA using other types of models and computations.

Optimal Reaction Coordinates and Kinetic Rates from the Projected Dynamics of Transition Paths.

Finding optimal reaction coordinates and predicting accurate kinetic rates for activated processes are two of the foremost challenges of molecular simulations. We introduce an algorithm that tackles the two problems at once: starting from a limited number of reactive molecular dynamics trajectories (transition paths), we automatically generate with a Monte Carlo approach a sequence of different reaction coordinates that progressively reduce the kinetic rate of their projected effective dynamics. Based on a variational principle, the minimal rate accurately approximates the exact one, and it corresponds to the optimal reaction coordinate. After benchmarking the method on an analytic double-well system, we apply it to complex atomistic systems: the interaction of carbon nanoparticles of different sizes in water.

Environmental and Nuclear Quantum Effects on Double Proton Transfer in the Guanine-Cytosine Base Pair.

In the present letter, we investigate the double proton transfer (DPT) tautomerization process in guanine-cytosine (GC) DNA base pairs. In particular, we study the influence of the biological environment on the mechanism, the kinetics and thermodynamics of such DPT. To this end, we present a molecular dynamics (MD) study in the tight-binding density functional theory framework, and compare the reactivity of the isolated GC dimer with that of the same dimer embedded in a small DNA structure. The impact of nuclear quantum effects (NQEs) is also evaluated using Path Integral based MD. Results show that in the isolated dimer, the DPT occurs via a concerted mechanism, while in the model biological environment, it turns into a stepwise process going through an intermediate structure. One of the water molecules in the vicinity of the proton transfer sites plays an important role as it changes H-bond pattern during the DPT reaction. The inclusion of NQEs has the effect of speeding up the tautomeric-to-canonical reaction, reflecting the destabilization of both the tautomeric and intermediate forms.

Critical comparison of general-purpose collective variables for crystal nucleation.

The nucleation of crystals is a prominent phenomenon in science and technology that still lacks a full atomic-scale understanding. Much work has been devoted to identifying order parameters able to track the process, from the inception of early nuclei to their maturing to critical size until growth of an extended crystal. We critically assess and compare two powerful distance-based collective variables, an effective entropy derived from liquid state theory and the path variable based on permutation invariant vectors using the Kob-Andersen binary mixture and a combination of enhanced-sampling techniques. Our findings reveal a comparable ability to drive nucleation when a bias potential is applied, and comparable free-energy barriers and structural features. Yet, we also found an imperfect correlation with the committor probability on the barrier top which was bypassed by changing the order parameter definition.

Free energy calculations and unbiased molecular dynamics targeting the liquid-liquid transition in water no man's land.

The existence of a first-order phase transition between a low-density liquid (LDL) and a high-density liquid (HDL) form of supercooled water has been a central and highly debated issue of physics and chemistry for the last three decades. We present a computational study that allows us to determine the free-energy landscapes of supercooled water over a wide range of pressure and temperature conditions using the TIP4P/2005 force field. Our approach combines topology-based structural transformation coordinates, state-of-the-art free-energy calculation methods, and extensive unbiased molecular dynamics. All our diverse simulations cannot detect any barrier within the investigated timescales and system size, for a discontinuous transition between the LDL and HDL forms throughout the so-called "no man's land," until the onset of the solid, non-diffusive amorphous forms.

Critical Assessment of Data-Driven versus Heuristic Reaction Coordinates in Solution Chemistry.

Reaction coordinates are an essential ingredient of theoretical studies of rare events in chemistry and physics because they carry information about reaction mechanism and allow the computation of free-energy landscapes and kinetic rates. We present a critical assessment of the merits and disadvantages of heuristic reaction coordinates, largely employed today, with respect to coordinates optimized on the basis of reliable transition-path sampling data. We take as a test bed multinanosecond ab initio molecular dynamics simulations of chloride SN2 substitution on methyl chloride in explicit water. The computational protocol we devise allows the unsupervised optimization of agnostic coordinates able to account for solute and solvent contributions, yielding a free-energy reconstruction of quality comparable to the best heuristic coordinates without requiring chemical intuition.

Combining Machine Learning Approaches and Accurate Ab Initio Enhanced Sampling Methods for Prebiotic Chemical Reactions in Solution.

The study of the thermodynamics, kinetics, and microscopic mechanisms of chemical reactions in solution requires the use of advanced free-energy methods for predictions to be quantitative. This task is however a formidable one for atomistic simulation methods, as the cost of quantum-based ab initio approaches, to obtain statistically meaningful samplings of the relevant chemical spaces and networks, becomes exceedingly heavy. In this work, we critically assess the optimal structure and minimal size of an ab initio training set able to lead to accurate free-energy profiles sampled with neural network potentials. The results allow one to propose an ab initio protocol where the ad hoc inclusion of a machine-learning (ML)-based task can significantly increase the computational efficiency, while keeping the ab initio accuracy and, at the same time, avoiding some of the notorious extrapolation risks in typical atomistic ML approaches. We focus on two representative, and computationally challenging, reaction steps of the classic Strecker-cyanohydrin mechanism for glycine synthesis in water solution, where the main precursors are formaldehyde and hydrogen cyanide. We demonstrate that indistinguishable ab initio quality results are obtained, thanks to the ML subprotocol, at about 1 order of magnitude less of computational load.

Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations.

Simulations with adaptive time-dependent bias enable an efficient exploration of the conformational space of a system. However, the dynamic information is altered by the bias. Infrequent metadynamics recovers the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we use Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the efficiency of collective variables parameter by measuring how efficiently the bias accelerates the transitions. We present approximate analytical expressions of the survival probability, reproducing the barrier-crossing time statistics and enabling the extraction of the unbiased transition rate even for challenging cases. We explore the limits of our method and provide convergence criteria to assess its validity.

Free Energy Landscapes, Diffusion Coefficients, and Kinetic Rates from Transition Paths.

We address the problem of constructing accurate mathematical models of the dynamics of complex systems projected on a collective variable. To this aim we introduce a conceptually simple yet effective algorithm for estimating the parameters of Langevin and Fokker-Planck equations from a set of short, possibly out-of-equilibrium molecular dynamics trajectories, obtained for instance from transition path sampling or as relaxation from high free-energy configurations. The approach maximizes the model likelihood based on any explicit expression of the short-time propagator, hence it can be applied to different evolution equations. We demonstrate the numerical efficiency and robustness of the algorithm on model systems, and we apply it to reconstruct the projected dynamics of pairs of C60 and C240 fullerene molecules in explicit water. Our methodology allows reconstructing the accurate thermodynamics and kinetics of activated processes, namely free energy landscapes, diffusion coefficients, and kinetic rates. Compared to existing enhanced sampling methods, we directly exploit short unbiased trajectories at a competitive computational cost.

Likelihood-based non-Markovian models from molecular dynamics.

SignificanceThe analysis of complex systems with many degrees of freedom generally involves the definition of low-dimensional collective variables more amenable to physical understanding. Their dynamics can be modeled by generalized Langevin equations, whose coefficients have to be estimated from simulations of the initial high-dimensional system. These equations feature a memory kernel describing the mutual influence of the low-dimensional variables and their environment. We introduce and implement an approach where the generalized Langevin equation is designed to maximize the statistical likelihood of the observed data. This provides an efficient way to generate reduced models to study dynamical properties of complex processes such as chemical reactions in solution, conformational changes in biomolecules, or phase transitions in condensed matter systems.

Impurity diffusion in magic-size icosahedral clusters.

Atomic diffusion is at the basis of chemical ordering transformations in nanoalloys. Understanding the diffusion mechanisms at the atomic level is therefore a key issue in the study of the thermodynamic behavior of these systems and, in particular, of their evolution from out-of-equilibrium chemical ordering types often obtained in the experiments. Here, the diffusion is studied in the case of a single-atom impurity of Ag or Au moving within otherwise pure magic-size icosahedral clusters of Cu or Co by means of two different computational techniques, i.e., molecular dynamics and metadynamics. Our simulations reveal unexpected diffusion pathways, in which the displacement of the impurity is coupled with the creation of vacancies in the central part of the cluster. We show that the observed mechanism is quite different from the vacancy-mediated diffusion processes identified so far, and we demonstrate that it can be related to the presence of non-homogeneous compressive stress in the inner part of the icosahedral structure.

Carbon Dioxide under Earth Mantle Conditions: From a Molecular Liquid through a Reactive Fluid to Polymeric Regimes.

In both its gaseous and condensed forms, carbon dioxide has an ever-increasing impact on Earth's chemistry and human life and activities. However, many aspects of its high-pressure phase diagram remain unclear. In this work, we present a complete structural characterization of carbon dioxide fluids under geological conditions using extensive ab initio molecular dynamics simulations throughout a wide pressure and temperature range, corresponding to Earth's lower mantle. We identify and describe four different disordered regimes, including two polymeric forms and two molecular ones, all within the geothermal conditions of the lower mantle. At pressures below 40 GPa, we find that the molecular liquid becomes very reactive above 2000 K: the C-O double bond routinely breaks, resulting in small and transient chains composed of CO2 units and frequently leading to an exchange of oxygen atoms between molecules. At higher pressures, in addition to the polymeric fluid previously reported at 3000 K, we find a polymeric system with glass-like behavior at lower temperatures, suggesting a complex interplay between kinetics and stability.

How natural materials remove heavy metals from water: mechanistic insights from molecular dynamics simulations.

Water pollution by heavy metals is of increasing concern due to its devastating effects on the environment and on human health. For the removal of heavy metals from water sources, natural materials, such as spent-coffee-grains or orange/banana/chestnut peels, appear to offer a potential cheap alternative to more sophisticated and costly technologies currently in use. However, in order to employ them effectively, it is necessary to gain a deeper understanding - at the molecular level - of the heavy metals-bioorganic-water system and exploit the power of computer simulations. As a step in this direction, we investigate via atomistic simulations the capture of lead ions from water by hemicellulose - the latter being representative of the polysaccharides that are common components of vegetables and fruit peels - as well as the reverse process. A series of independent molecular dynamics simulations, both classical and ab initio, reveals a coherent scenario which is consistent with what one would expect of an efficient capture, i.e. that it be fast and irreversible: (i) binding of the metal ions via adsorption is found to happen spontaneously on both carboxylate and hydroxide functional groups; (ii) in contrast, metal ion desorption, leading to solvation in water, involves sizable free-energy barriers.

Stability of a Monoethanolamine-CO2 Zwitterion at the Vapor/Liquid Water Interface: Implications for Low Partial Pressure Carbon Capture Technologies.

The need to chemically convert CO2 at the interface of aqueous amine solutions has become particularly relevant for the development and the broad distribution of cost-effective and near-future devices for direct air capture working at low (e.g., ambient) partial pressure. Here, we have determined the stability of a CO2-monoethanolamine zwitterion and its chemical conversion into carbamate at the vapor/liquid water interface by first-principles molecular dynamics simulations coupled with a recently introduced enhanced sampling technique. Contrary to the bulk water case, our results show that both the zwitterion and carbamate ions are poorly stable at the vapor/amine aqueous interface, further stating the differences between the homogeneous and heterogeneous CO2 chemical conversion. The design of novel and cost-effective capture systems, such as those offered by amine-based scrubbing solutions, working at low (e.g., ambient) CO2 partial pressure should explore the use of novel solvents, different from aqueous mixtures, to overcome the limits of the current absorbents.

Step by Step Strecker Amino Acid Synthesis from Ab Initio Prebiotic Chemistry.

The amino acids synthesis from elementary precursors in abiotic conditions is traditionally described according to the Strecker reaction, thoroughly invoked to justify the observation of amino acids in extraterrestrial samples and their emergence in the primordial Earth. To this day, however, a quantitative microscopic description of the mechanism, thermodynamics, and kinetics of the multistep Strecker reaction is still lacking. In the present work we tackle this study by adopting a state-of-the-art ab initio computational approach, combining an efficient scheme of exploration of the relevant chemical networks with a rigorous determination of the underlying free energy and transition states. We determine the step-by-step chemical pathway from "Strecker precursors" to glycine in solution and calculate the corresponding full free energy landscape. Our results agree well with the scarce available experimental data and complete them, thus providing the first end-to-end study of this complex reaction, a crucial bottleneck for the emergence of life.

Out-of-Equilibrium Polymorph Selection in Nanoparticle Freezing.

The ability to design synthesis processes that are out of equilibrium has opened the possibility of creating nanomaterials with remarkable physicochemical properties, choosing from a much richer palette of possible atomic architectures compared to equilibrium processes in extended systems. In this work, we employ atomistic simulations to demonstrate how to control polymorph selection via the cooling rate during nanoparticle freezing in the case of Ni3Al, a material with a rich structural landscape. State-of-the-art free-energy calculations allow us to rationalize the complex nucleation process, discovering a switch between two kinetic pathways, yielding the equilibrium structure at room temperature and an alternative metastable one at higher temperature. Our findings address the key challenge in the synthesis of nanoalloys for technological applications, i.e., rationally exploiting the competition between kinetics and thermodynamics by designing a treatment history that forces the system into desirable metastable states.

Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems.

Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.