PyRETIS 3: Conquering rare and slow events without boundaries

We present and discuss the advancements made in PyRETIS 3, the third instalment of our Python library for an efficient and user-friendly rare event simulation, focused to execute molecular simulations with replica exchange transition interface sampling (RETIS) and its variations. Apart from a general rewiring of the internal code towards a more modular structure, several recently developed sampling strategies have been implemented. These include recently developed Monte Carlo moves to increase path decorrelation and convergence rate, and new ensemble definitions to handle the challenges of long-lived metastable states and transitions with unbounded reactant and product states. Additionally, the post-analysis software PyVisa is now embedded in the main code, allowing fast use of machine-learning algorithms for clustering and visualising collective variables in the simulation data.

A review of sodium silicate solutions: Structure, gelation, and syneresis

Sodium silicate solutions, also known as waterglass, have been found to have remarkable utility in a variety of applications. The cumulative weight of evidence from 70 years of varied analysis indicates that silicate solutions consist of a wide range of species, from monomers through oligomers, up to colloids. Moreover, the structure and distribution of these species are greatly dependent upon many parameters, such as solute concentrations, silica to alkali ratio, pH, and temperature. The most interesting and characteristic property of silicate solutions is their ability to form silica gels. Overall, despite extensive research using different spectroscopic and scattering techniques, many questions related to sodium silicate's dynamic structure, stability, polymerization, and gelation remain difficult to answer. The multitude of simultaneous reactions which restructure the silicate species at the atomic scale in response to variation in solution and environmental parameters, makes it difficult to investigate the individual events using only experimental data. Molecular modelling provides an alternative way to study the unknown areas in the aqueous silicate and silica gel systems, generating key insights into the chemical reactions at microscopic length scales. However, sufficient sampling remains a challenge for the practical use of molecular simulation for these systems. Based on both experimental and modelling studies, this review provides a detailed discussion over the structure and speciation of sodium silicate solutions, their gelation mechanism and kinetics, and the syneresis phenomenon. The goal is not only to review the current level of understanding of sodium silicate solutions, silica gels and characterization techniques suitable for studying them, but also to identify the gaps in the literature and open up opportunities for advancing knowledge about these complex systems. We believe that the future direction of research should be toward correlating atomistic, molecular, and meso-scale level details of interactions and reactions in silicate solution and establishing a fundamental understanding of its gelation mechanism and kinetics. We believe that this knowledge could eliminate the "trial and error" approach in manufacturing, and improve structural control in the synthesis of important materials derived from these solutions, such as silica gels and zeolites.

The Role of Chloride ion in the Silicate Condensation Reaction from ab Initio Molecular Dynamics Simulations

The comprehension of silicate oligomer formation during the initial stage of zeolite synthesis is of significant importance. In this study, we investigated the effect of chloride ions (Cl-) on silicate oligomerization using ab initio molecular dynamics simulations with explicit water molecules. The results show that the presence of Cl- increases the free energy barriers of all reactions compared to the case without the anion. The formation of the 4-ring structure has the lowest free energy barrier (73 kJ/mol), while the formation of the 3-ring structure has the highest barrier (98 kJ/mol) in the presence of Cl-. These findings suggest that Cl- suppresses the formation of 3-rings and favors the formation of larger oligomers in the process of zeolite synthesis. Our study provides important insights into the directing role of Cl- in silicate oligomerization by regulating thermodynamic and kinetic parameters. An important point to consider is the impact of the anion on aqueous reactions, particularly in altering the hydrogen bond network around reactive species. These results also provide a basis for further studies of the formations of larger silicate oligomers in solution.

Insight into the role of excess hydroxide ions in silicate condensation reactions

The formation of silicate oligomers in the early stages is key to zeolite synthesis. The pH and the presence of hydroxide ions are important in regulating the reaction rate and the dominant species in solutions. This paper describes the formation of silicate species, from dimers to 4-membered rings, using ab initio molecular dynamics simulations in explicit water molecules with an excess hydroxide ion. The thermodynamic integration method was used to calculate the free energy profile of the condensation reactions. The hydroxide group's role is not only to control the pH of the environment, but also to actively participate in the condensation reaction. The results show that the most favorable reactions are linear-tetramer and 4-membered-ring formation, with overall barriers of 71 kJ mol^-1 and 73 kJ mol^-1, respectively. The formation of trimeric silicate, with the largest free-energy barrier of 102 kJ mol^-1, is the rate-limiting step under these conditions. The excess hydroxide ion aids in the stabilization of the 4-membered-ring structure over the 3-membered-ring structure. Due to a relatively high free-energy barrier, the 4-membered ring is the most difficult of the small silicate structures to dissolve in the backward reaction. This study is consistent with the experimental observation that silicate growth in zeolite synthesis is slower in a very-high-pH environment.

Understanding formation thermodynamics of structurally diverse zeolite oligomers with first principles calculations

The mechanisms of many zeolitic processes, including nucleation and interzeolite transformation, are not fully understood owing to complex growth mixtures that obfuscate in situ monitoring of molecular events. In this work, we provide insights into zeolite chemistry by investigating the formation thermodynamics of small zeolitic species using first principles calculations. We systematically study how formation energies of pure-silicate and aluminosilicate species differ by structure type and size, temperature, and the presence of alkali or alkaline earth metal cations (Na⁺, K⁺, and Ca²⁺). Highly condensed (cage-like) species are found to be strongly preferred to simple rings in the pure-silicate system, and this thermodynamic preference increases with temperature. Introducing aluminum leads to more favorable formation thermodynamics for all species. Moreover, for species with a low Si/Al ratio (≤2), a thermodynamic preference does not exist among structure types; instead, a pool of diverse aluminosilicate structures compete in formation. Metal cation effects strongly depend on the presence of aluminum, cage size, cation type, and location, since each of these factors can alter electrostatic interactions between cations and zeolitic species. We reveal that confined metal cations may destabilize pure-silicate cages due to localized interactions; conversely, they stabilize aluminosilicates due to strong cation-framework attractions in sufficiently large cages. Importantly, this work rationalizes a series of experimental observations and can potentially guide efforts for controlling zeolite nucleation/crystallization processes.

Enhanced path sampling using subtrajectory Monte Carlo moves

Path sampling allows the study of rare events, such as chemical reactions, nucleation, and protein folding, via a Monte Carlo (MC) exploration in path space. Instead of configuration points, this method samples short molecular dynamics (MD) trajectories with specific start- and end-conditions. As in configuration MC, its efficiency highly depends on the types of MC moves. Since the last two decades, the central MC move for path sampling has been the so-called shooting move in which a perturbed phase point of the old path is propagated backward and forward in time to generate a new path. Recently, we proposed the subtrajectory moves, stone-skipping (SS) and web-throwing, that are demonstrably more efficient. However, the one-step crossing requirement makes them somewhat more difficult to implement in combination with external MD programs or when the order parameter determination is expensive. In this article, we present strategies to address the issue. The most generic solution is a new member of subtrajectory moves, wire fencing (WF), that is less thrifty than the SS but more versatile. This makes it easier to link path sampling codes with external MD packages and provides a practical solution for cases where the calculation of the order parameter is expensive or not a simple function of geometry. We demonstrate the WF move in a double-well Langevin model, a thin film breaking transition based on classical force fields, and a smaller ruthenium redox reaction at the ab initio level in which the order parameter explicitly depends on the electron density.

Elucidating the role of catalytic amino acid residues in the peptide-mediated silica oligomerization reaction mechanism

Understanding the detailed mechanism by which the proteins of marine diatoms such as silaffins are able to control the morphology of silica oligomers has eluded synthetic chemists and materials scientists for decades. In this study, we use DFT calculations to determine how individual amino acid residues of silaffin catalyze silica dimerization. The reaction network for formation of a silica dimer was explored using several different small molecules, including water, guanidinium ions, and methylammonium ions, the latter two molecules representing analogs of arginine and lysine, both of which are known to play critical roles in enabling the catalytic function of naturally occurring protein and synthetic analogs of silaffin. It was found that the lysine analog selectively lowers the energy of a direct water removal pathway for silicate dimerization. Comparing the energy landscapes and mechanisms for various catalysts for this reaction provides direct evidence for the role of lysine side chains of silaffins in the oligmerization of silica.

Exploration of the Mechanism of the Dimerization of Hydroxymethylsilanetriol Using Electronic Structure Methods

Hydroxymethylsilanetriol undergoes condensation reactions to form new structures with an organic part in the formed bridges. As a first step to explore the formation of these bridges, we studied the corresponding mechanisms using simple models and theoretical methods. Three mechanisms were studied for the formation of dimers of hydroxymethylsilanetriol with bridges: Si-O-C-Si, Si-O-Si, and Si-C-O-C-Si. Energies are calculated using M06/6-311+G(d,p) single-point calculations on B3LYP-optimized geometries in solution and including B3LYP thermodynamic corrections. The first mechanism for the formation of the Si-O-C-Si bridge consists of one step. The second mechanism for the formation of the Si-O-Si bridge consists of two steps. The barrier for the last mechanism for the formation of the Si-C-O-C-Si bridge is too high and cannot occur at room temperature. The energy barriers are 31.8, 27.6, and 65.9 kcal mol^-1 for the first, second, and third mechanisms, respectively. When adding one explicit water molecule, these energies are 25.9, 22.9, and 80.3 kcal mol^-1, respectively. The first and second mechanisms can occur at room temperature, which is in agreement with the experimental results.

Theoretical Studies on the Oligomerization of Silicate Species in Basic Solution

The possible reaction pathways of silicate species to linear- and ring-structure oligomers up to silicate hexamers in the basic medium have been studied using the density functional theory. The calculations were performed at the ωB97XD/6-31+G(d,p) level, and the integral equation formalism polarizable continuum model was employed to simulate the solvent effects, and it was found that they are appropriate in exploring the reaction mechanism of silicate species condensation. There are two steps in the anionic silicate condensation reactions: the SiO-Si bond formation step and the dehydration step. Moreover, the latter is the rate-limiting step for most of the reaction pathways except for the cyclization reaction of the linear pentamer to the 5-ring. The short linear oligomers would be likely formed from the reaction between monomers and oligomers, while the longer ones are easily formed through the reactions between short oligomers. The 4-ring and branched 5-ring oligomers are found to be formed very favorable both in kinetic and thermodynamic and could have great influences on the initial stage of zeolite synthesis. The intramolecular and intermolecular hydrogen bond effect of silicate species is an important factor affecting the reaction mechanism.

Chemistrees: Data-Driven Identification of Reaction Pathways via Machine Learning

We propose to analyze molecular dynamics (MD) output via a supervised machine learning (ML) algorithm, the decision tree. The approach aims to identify the predominant geometric features which correlate with trajectories that transition between two arbitrarily defined states. The data-driven algorithm aims to identify these features without the bias of human “chemical intuition”. We demonstrate the method by analyzing the proton exchange reactions in formic acid solvated in small water clusters. The simulations were performed with ab initio MD combined with a method to efficiently sample the rare event, path sampling. Our ML analysis identified relevant geometric variables involved in the proton transfer reaction and how they may change as the number of solvating water molecules changes.

The Promoter Role of Amines in the Condensation of Silicic Acid: A First-Principles Investigation

Though well-recognized, the molecular-level understanding of the multifunctional roles of amines in the condensation of polysilicic acids, which is one of the key processes in hydrothermal synthesis of zeolites, is still limited. Taking ethylamine as a prototype, we investigated the mechanism of polysilicic acid condensation in the existence of organic amines in aqueous solution with extensive first-principles-based calculations. Because of the high proton affinity, ethylamine exists as amine silicates and alters the subsequent condensation mechanisms from a 1-step lateral attack mechanism accompanied with simultaneous intermolecular proton transfer in neutral aqueous solution to a 2-step SN2-like mechanism. Specifically, the 5-coordinated Si species that were not observed on pathways of condensation in neutral solution are effectively stabilized by the ethylamine cations as intermediates, and the barriers for condensation of ortho-silicic acid are significantly reduced from 133 kJ/mol in neutral solution to 58 and 63 kJ/mol for formation of the 5-coordinated Si intermediate and proton transfer for water release, respectively. Similar variations of mechanisms and barriers for condensation were also observed in the formation of cyclic trimers as well as linear and cyclic tetramers of ortho-silicic acids. Based on these, it was proposed that apart from acting as structure-directing agents, pore fillers, and pH adjusters, organic amines can also function as promoters in the condensation of polysilicic acids.

Impact of Organic Templates on the Selective Formation of Zeolite Oligomers

Zeolites are essential materials to industry due to their adsorption and catalytic properties. The best current approach to prepare a targeted zeolite still relies on trial and error's synthetic procedures since a rational understanding of the impact of synthesis variables on the final structures is still missing. To discern the role of a variety of organic templates, we perform simulations of the early stages of condensation of silica oligomers by combining DFT, Brønsted-Evans-Polanyi relationships and kinetic Monte Carlo simulations. We investigate an extended reaction path mechanism including 258 equilibrium reactions and 242 chemical species up to silica octamers, comparing the computed concentrations of Si oligomers with ²⁹ SI NMR experimental data. The effect of the templating agent is linked to the modification of the intramolecular H-bond network in the growing oligomer, which produces higher concentration of 4-membered ring intermediates, precursors of the key double-four ring building blocks present on more than 39 known zeolite topologies.

Elucidating the Role of Tetraethylammonium in the Silicate Condensation Reaction from Ab Initio Molecular Dynamics Simulations

The understanding of the formation of silicate oligomers in the initial stage of zeolite synthesis is important. The use of organic structure-directing agents (OSDAs) is known to be a key factor in the formation of different silicate species and the final zeolite structure. For example, tetraethylammonium ion (TEA⁺) is a commonly used organic template for zeolite synthesis. In this study, ab initio molecular dynamics (AIMD) simulation is used to provide an understanding of the role of TEA⁺ in the formation of various silicate oligomers, ranging from dimer to 4-ring. Calculated free-energy profiles of the reaction pathways show that the formation of a 4-ring structure has the highest energy barrier (97 kJ/mol). The formation of smaller oligomers such as dimer, trimer, and 3-ring has lower activation barriers. The TEA⁺ ion plays an important role in regulating the predominant species in solution via its coordination with silicate structures during the condensation process. The kinetics and thermodynamics of the oligomerization reaction indicate a more favorable formation of the 3-ring over the 4-ring structure. The results from AIMD simulations are in line with the experimental observation that TEA⁺ favors the 3-ring and double 3-ring in solution. The results of this study imply that the role of OSDAs is not only important for the host-guest interaction but also crucial for controlling the reactivity of different silicate oligomers during the initial stage of zeolite formation.

Path sampling for atmospheric reactions: formic acid catalysed conversion of SO3 + H2O to H2SO4

Atmospheric reactions, hitherto studied computationally mainly with static computations in conjunction with transition state theories, can be further described via path sampling calculations. Here we report on an exploratory study of the formic acid catalysed hydrolysis of SO3 to produce H2SO4. We demonstrate that precise measurements of rate coefficients can be obtained in principle for such reactions with an acceptable expenditure of computational resources, and that new insights into the reaction can be obtained by the analysis of the path space explored via path sampling techniques.

Fast Decorrelating Monte Carlo Moves for Efficient Path Sampling

Many relevant processes in chemistry, physics, and biology are rare events from a computational perspective as they take place beyond the accessible time scale of molecular dynamics (MD). Examples are chemical reactions, nucleation, and conformational changes of biomolecules. Path sampling is an approach to break this time scale limit via a Monte Carlo (MC) sampling of MD trajectories. Still, many trajectories are needed for accurately predicting rate constants. To improve the speed of convergence, we propose two new MC moves, stone skipping and web throwing. In these moves, trajectories are constructed via a sequence of subpaths obeying superdetailed balance. By a reweighting procedure, almost all paths can be accepted. Whereas the generation of a single trajectory becomes more expensive, the reduced correlation results in a significant speedup. For a study on DNA denaturation, the increase was found to be a factor 12.