Calculations Of Free Energy Barrier Research Articles

A general relation between the largest nucleus and all nuclei distributions for free energy calculations.

Prediction of nucleation rates in first order phase transitions requires the knowledge of the barrier associated with the free energy profile W. Molecular simulations offer a direct route through W = -kT ln pa, where k is Boltzmann's constant, T is temperature, and pa is the probability distribution of the size of any nucleus. However, in practice, the extremely scarce spontaneous occurrence of large nuclei impedes the full determination of pa, and a numerical bias must be introduced, which is generally done on the size of the largest nucleus in the system, leading to the probability size distribution of the largest nucleus pl. Although pl is known to be system size dependent, unlike pa, it has extensively been used as an approximation for pa. This communication demonstrates an improved relation between pa and pl, which cures this approximation and allows an accurate calculation of free energy barriers from biased simulations.

Calculation of Free-Energy Barriers with TD-DFT: A Case Study on Excited-State Proton Transfer in Indigo

The performance of time-dependent density functional theory (TD-DFT) for the calculation of excited states of molecular systems has been the subject of many benchmark studies. Often, these studies focus on excitation energies or, more recently, excited-state equilibrium geometries. In this work, we take a different angle by instead exploring how well TD-DFT reproduces experimental free-energy barriers of a well-known photochemical reaction: the excited-state proton transfer (ESPT) in indigo. Specifically, by exploiting the possibility of using TD-DFT to locate and compute free energies of first-order saddle points in excited states, we test the performance of several popular density functionals in reproducing recently determined experimental free-energy barriers for ESPT in indigo and in an N-hexyl substituted derivative thereof. Through the calculations, it is found that all of the tested functionals perform quite well, uniformly overestimating the experimental values by 1.4-3.5 (mean error) and 2.5-5.5 kcal mol-1 (maximum error) only. Given that these errors are not larger than those typically observed when barriers for ground-state proton transfer reactions are calculated in ground-state DFT, the results highlight the potential of TD-DFT to enable accurate modeling of ESPT reactions based on free energies and explicit localization of transition states.

Microkinetic modeling in homogeneous catalysis

Computational homogeneous catalysis has focused traditionally on the calculation of free energy barriers, which are ultimately related to rate constants. Experiments do not focus on rate constants, but on reaction rates, which depend also on concentrations. The increasing efficiency of DFT and other electronic structure techniques has led to the development of models that provide quite accurate rate constants, to the extent that improved agreement with experiment requires the introduction of the role of concentration. Microkinetic modeling, consisting in the construction of explicit kinetic reaction networks merging the rate constants provided by calculation and concentration data supplied by experiment, is a simple and elegant way to introduce concentration effects in the computational description of homogeneous catalysis. It has a long history of application in computational heterogeneous catalysis and experimental biochemistry, but its use in computational homogeneous catalysis is still in an early stage. There are a number of situations in homogeneous catalysis where microkinetics have been shown to be critical, such as systems with complex reaction networks and systems where one key species has a concentration orders of magnitude different from the others. Microkinetic modeling, with its low computational cost, is likely to become a standard tool in computational homogeneous catalysis. It is certainly not necessary for all theoretical studies, but the researcher should always be aware of its existence.This article is categorized under: Structure and Mechanism > Reaction Mechanisms and Catalysis

Unsupervised Calculation of Free Energy Barriers in Large Crystalline Systems.

The calculation of free energy differences for thermally activated mechanisms in the solid state are routinely hindered by the inability to define a set of collective variable functions that accurately describe the mechanism under study. Even when possible, the requirement of descriptors for each mechanism under study prevents implementation of free energy calculations in the growing range of automated material simulation schemes. We provide a solution, deriving a path-based, exact expression for free energy differences in the solid state which does not require a converged reaction pathway, collective variable functions, Gram matrix evaluations, or probability flux-based estimators. The generality and efficiency of our method is demonstrated on a complex transformation of C15 interstitial defects in iron and double kink nucleation on a screw dislocation in tungsten, the latter system consisting of more than 120 000 atoms. Both cases exhibit significant anharmonicity under experimentally relevant temperatures.

Reaction Coordinates and Mechanistic Hypothesis Tests.

Reaction coordinates are integral to several classic rate theories that can (a) predict kinetic trends across conditions and homologous reactions, (b) extract activation parameters with a clear physical interpretation from experimental rates, and (c) enable efficient calculations of free energy barriers and rates. New trajectory-based rare events methods can provide rates directly from dynamical trajectories without a reaction coordinate. Trajectory-based frameworks can also generate ideal (but abstract) reaction coordinates such as committors and eigenfunctions of the master equation. However, rates and mechanistic insights obtained from trajectory-based methods and abstract coordinates are not readily generalized across simulation conditions or reaction families. We discuss methods for identifying physically meaningful reaction coordinates, including committor analysis, variational transition state theory, Kramers-Langer-Berezhkovskii-Szabo theory, and statistical inference methods that can use path sampling data to screen, mix, and optimize thousands of trial coordinates. Special focus is given to likelihood maximization and inertial likelihood maximization approaches.

Path Sampling Methods for Enzymatic Quantum Particle Transfer Reactions.

The mechanisms of enzymatic reactions are studied via a host of computational techniques. While previous methods have been used successfully, many fail to incorporate the full dynamical properties of enzymatic systems. This can lead to misleading results in cases where enzyme motion plays a significant role in the reaction coordinate, which is especially relevant in particle transfer reactions where nuclear tunneling may occur. In this chapter, we outline previous methods, as well as discuss newly developed dynamical methods to interrogate mechanisms of enzymatic particle transfer reactions. These new methods allow for the calculation of free energy barriers and kinetic isotope effects (KIEs) with the incorporation of quantum effects through centroid molecular dynamics (CMD) and the full complement of enzyme dynamics through transition path sampling (TPS). Recent work, summarized in this chapter, applied the method for calculation of free energy barriers to reaction in lactate dehydrogenase (LDH) and yeast alcohol dehydrogenase (YADH). We found that tunneling plays an insignificant role in YADH but plays a more significant role in LDH, though not dominant over classical transfer. Additionally, we summarize the application of a TPS algorithm for the calculation of reaction rates in tandem with CMD to calculate the primary H/D KIE of YADH from first principles. We found that the computationally obtained KIE is within the margin of error of experimentally determined KIEs and corresponds to the KIE of particle transfer in the enzyme. These methods provide new ways to investigate enzyme mechanism with the inclusion of protein and quantum dynamics.

Graph representation of protein free energy landscape

The thermodynamics and kinetics of protein folding and protein conformational changes are governed by the underlying free energy landscape. However, the multidimensional nature of the free energy landscape makes it difficult to describe. We propose to use a weighted-graph approach to depict the free energy landscape with the nodes on the graph representing the conformational states and the edge weights reflecting the free energy barriers between the states. Our graph is constructed from a molecular dynamics trajectory and does not involve projecting the multi-dimensional free energy landscape onto a low-dimensional space defined by a few order parameters. The calculation of free energy barriers was based on transition-path theory using the MSMBuilder2 package. We compare our graph with the widely used transition disconnectivity graph (TRDG) which is constructed from the same trajectory and show that our approach gives more accurate description of the free energy landscape than the TRDG approach even though the latter can be organized into a simple tree representation. The weighted-graph is a general approach and can be used on any complex system.

Fully quantum mechanical calculation of the diffusivity of hydrogen in iron using the tight-binding approximation and path integral theory

We present calculations of free energy barriers and diffusivities as functions of temperature for the diffusion of hydrogen in bcc-Fe. This is a fully quantum mechanical approach since the total energy landscape is computed using a new self consistent, transferable tight binding model for interstitial impurities in magnetic iron. Also the hydrogen nucleus is treated quantum mechanically and we compare here two approaches in the literature both based in the Feynman path integral formulation of statistical mechanics. We find that the quantum transition state theory which admits greater freedom for the proton to explore phase space gives result in better agreement with experiment than the alternative which is based on fixed centroid calculations of the free energy barrier. We also find results in better agreement compared to recent centroid molecular dynamics (CMD) calculations of the diffusivity which employed a classical interatomic potential rather than our quantum mechanical tight binding theory. In particular we find first that quantum effects persist to higher temperatures than previously thought, and conversely that the low temperature diffusivity is smaller than predicted in CMD calculations and larger than predicted by classical transition state theory. This will have impact on future modeling and simulation of hydrogen trapping and diffusion.

An algorithm to find minimum free-energy paths using umbrella integration

The calculation of free-energy barriers by umbrella sampling and many other methods is hampered by the necessity for an a priori choice of the reaction coordinate along which to sample. We avoid this problem by providing a method to search for saddle points on the free-energy surface in many coordinates. The necessary gradients and Hessians of the free energy are obtained by multidimensional umbrella integration. We construct the minimum free-energy path by following the gradient down to minima on the free-energy surface. The change of free energy along the path is obtained by integrating out all coordinates orthogonal to the path. While we expect the method to be applicable to large systems, we test it on the alanine dipeptide in vacuum. The minima, transition states, and free-energy barriers agree well with those obtained previously with other methods.

Calculations of free energy barriers for local mechanisms of hydrogen diffusion in alanates

Brute force histogram calculation and a recently developed method to efficiently reconstruct the free energy profile of complex systems (the single-sweep method) are combined with ab initio molecular dynamics to study possible local mechanisms for the diffusion of hydrogen in sodium alanates. These compounds may help to understand key properties of solid state hydrogen storage materials. In this work, the identity of a mobile species observed in experiments characterizing the first dissociation reaction of sodium alanates is investigated. The activation barrier of two suggested processes for hydrogen diffusion in Na3AlH6 is evaluated and, by comparing our results with available experimental information, we are able to discriminate among them and to show that one is compatible with the observed signal while the other is not.

Calculation of Free Energy Barriers to the Fusion of Small Vesicles

The fusion of small vesicles, either with a planar bilayer or with one another, is studied using a microscopic model in which the bilayers are composed of hexagonal- and lamellar-forming amphiphiles. The free energy of the system is obtained within the self-consistent field approximation. We find that the free energy barrier to form the initial stalk is hardly affected by the radius of the vesicle, but that the barrier to expand the hemifusion diaphragm and form a fusion pore decreases rapidly as the radius decreases. As a consequence, once the initial barrier to stalk formation is overcome, one which we estimate at 13 k B T for biological membranes, fusion involving small vesicles should proceed with little or no further input of energy.

A thermodynamic approach for determining the contact angle hysteresis for superhydrophobic surfaces

Contact angle hysteresis (CAH) is critical to superhydrophobicity of a surface. This study proposes a free energy thermodynamic analysis (of a 2-D model surface) that significantly simplifies calculations of free energy barrier associated with CAH phenomena. A microtextured surface with pillar structure, typical of one used in experimental studies, is used as an example. We demonstrate that the predicted CAH and equilibrium contact angles are consistent with experimental observations and predictions of Wenzel's and Cassie's equations, respectively. We also establish a criterion for transition between noncomposite and composite wetting states. The results and methodology presented can potentially be used for designing superhydrophobic surfaces.

Density functional approaches to the dynamics of phase transitions

Density functional approaches have become well known in applications of equilibrium statistical mechanics to phase diagrams, interfacial structures, and free energies. This paper describes how these methods can be extended to the dynamics of phase transitions. Two aspects are emphasized: the calculation of free-energy barriers in nucleation and of growth velocities for crystallization from the melt. Significant deviations from classical nucleation theory and from diffusion-based theories of crystal growth are found. The continuum density functional approach is effective in describing the dynamics of collective-mode fluctuations, which dominate single-particle dynamics in these cases. The role of body-centred ordering at the interface between a face-centred crystal and the melt is described.

Ab Initio Calculations of Free Energy Barriers for Chemical Reactions in Solution

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTAb Initio Calculations of Free Energy Barriers for Chemical Reactions in SolutionRichard P. Muller and Arieh WarshelCite this: J. Phys. Chem. 1995, 99, 49, 17516–17524Publication Date (Print):December 1, 1995Publication History Published online1 May 2002Published inissue 1 December 1995https://doi.org/10.1021/j100049a009RIGHTS & PERMISSIONSArticle Views876Altmetric-Citations167LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (1 MB) Get e-Alerts

Relative stability of f.c.c. and b.c.c. structures for model systems at high temperatures

Free-energy, entropy and volume differences between face-centered and body-centered cubic structures have been evaluated for model rare gas and alkali metal crystals by using the method of overlapping distributions. Stable phases are predicted in agreement with the behaviour of real materials in the regions of validity of classical mechanics and in agreement with the results of previous dynamical-simulation studies of crystal nucleation from the melt and of polymorphic transformations. The existence of a stable b.c.c. phase at high pressure and temperatures is predicted in this way for Lennard-Jones solids, while no high-pressure f.c.c. phase is expected for model Rb and Cs systems. We also show the possibility of making calculations of free-energy barriers to displacive crystalline transformations along a prescribed trajectory in configuration space.