Free energies

2021 ◽  
pp. 139-178
Author(s):  
James P. Sethna
Keyword(s):  
Molecular Motors ◽  
Degrees Of Freedom ◽  
Reaction Rates ◽  
Coarse Grained ◽  
Rate Theory ◽  
Free Energies ◽  
Reaction Rate Theory ◽  
The World ◽  
The Cost ◽  
Grand Canonical

Free energies ignore most of a system, to provide the emergent statistical ensemble describing things we care about. Free energies can ignore the external world. The cost of borrowing energy from the world is measured by the temperature, giving us the canonical ensemble and Helmholtz free energy. Similarly, borrowing particles and volume from the world gives us the grand canonical and Gibbs ensembles. Free energies can ignore unimportant internal degrees of freedom. These lead to friction and noise, and theories of chemical reactions and reaction rates. Free energies can be coarse-grained, removing short distances and times. Exercises apply free energies to molecular motors, thermodynamic relations, reaction rate theory, Zipf’s law for word frequencies, zombie outbreaks, and nucleosynthesis.

scholarly journals The Automated Optimisation of a Coarse-Grained Force Field Using Free Energy Data

2020 ◽  
Author(s):  
Javier Caceres-Delpiano ◽  
Lee-Ping Wang ◽  
Jonathan W. Essex
Keyword(s):  
Free Energy ◽  
Force Field ◽  
Degrees Of Freedom ◽  
Coarse Grained ◽  
Free Energies ◽  
Energy Data ◽  
Molecular Systems ◽  
Atomistic Models ◽  
The Cost ◽  
Long Timescales

AbstractAtomistic models provide a detailed representation of molecular systems, but are sometimes inadequate for simulations of large systems over long timescales. Coarse-grained models enable accelerated simulations by reducing the number of degrees of freedom, at the cost of reduced accuracy. New optimisation processes to parameterise these models could improve their quality and range of applicability. We present an automated approach for the optimisation of coarse-grained force fields, by reproducing free energy data derived from atomistic molecular simulations. To illustrate the approach, we implemented hydration free energy gradients as a new target for force field optimisation in ForceBalance and applied it successfully to optimise the un-charged side-chains and the protein backbone in the SIRAH protein coarse-grain force field. The optimised parameters closely reproduced hydration free energies of atomistic models and gave improved agreement with experiment.

Unified Rate Theory of Electrochemistry and Electrocatalysis: Fixed Potential Formulation for General, Electron Transfer, and Proton-Coupled Electron Transfer Reactions

2019 ◽  
Author(s):  
Marko Melander
Keyword(s):  
Electron Transfer ◽  
Electrode Potential ◽  
Canonical Ensemble ◽  
Reaction Rates ◽  
Transfer Reactions ◽  
Rate Theory ◽  
Electron Transfer Reactions ◽  
Proton Coupled Electron Transfer ◽  
Fixed Electrode ◽  
Grand Canonical

<div>Atomistic modeling of electrocatalytic reactions is most naturally conducted within the grand canonical ensemble (GCE) which enables fixed chemical potential calculations. While GCE has been widely adopted for modeling electrochemical and electrocatalytic thermodynamics, the electrochemical reaction rate theory within GCE is lacking. Molecular and condensed phase rate theories are formulated within microcanonical and canonical ensembles, respectively, but electrocatalytic systems described within the GCE require extension of the conventionally used rate theories for computation reaction rates at fixed electrode potentials. In this work, rate theories from (micro)canonical ensemble are generalized to the GCE providing the theoretical basis for the computation reaction rates in electrochemical and electrocatalytic systems. It is shown that all canonical rate theories can be extended to the GCE. From the generalized grand canonical rate theory developed herein, fixed electrode potential rate equations are derived for i) general reactions within the GCE transition state theory (GCE-TST), ii) adiabatic curve-crossing rate theory within the empirical valence bond theory (GCE-EVB), and iii) (non-)adiabatic electron and proton-coupled electron transfer reactions. The rate expressions can be readily combined with ab initio methods to study reaction kinetics reactions at complex electrochemical interfaces as a function of the electrode potential. The theoretical work herein provides a single, unified approach for electrochemical and electrocatalytic kinetics and the inclusion of non-adiabatic and tunneling effects in electrochemical environments widening the scope of reactions amenable to computational studies.</div>

Rate Theory for Electrocatalytic Systems: Fixed Potential Formulation for General, Electron Transfer, and Proton-Coupled Electron Transfer Reactions

2019 ◽  
Author(s):  
Marko Melander
Keyword(s):  
Electron Transfer ◽  
Electrode Potential ◽  
Canonical Ensemble ◽  
Reaction Rates ◽  
Transfer Reactions ◽  
Rate Theory ◽  
Electron Transfer Reactions ◽  
Proton Coupled Electron Transfer ◽  
Fixed Electrode ◽  
Grand Canonical

<div>Atomistic modeling of electrocatalytic reactions is most naturally conducted within the grand canonical ensemble (GCE) which enables fixed chemical potential calculations. While GCE has been widely adopted for modeling electrochemical and electrocatalytic thermodynamics, the electrochemical reaction rate theory within GCE is lacking. Molecular and condensed phase rate theories are formulated within microcanonical and canonical ensembles, respectively, but electrocatalytic systems described within the GCE require extension of the conventionally used rate theories for computation reaction rates at fixed electrode potentials. In this work, rate theories from (micro) canonical ensemble are generalized to the GCE providing the theoretical basis for the computation reaction rates in electrochemical systems. It is shown that all canonical rate theories can be extended to the GCE. From the generalized grand canonical rate theory developed herein, fixed electrode potential rate equations are derived for i) general reactions within the GCE transition state theory (GCE-TST), ii) adiabatic curve-crossing rate theory within the empirical valence bond theory (GCE-EVB), and iii) (non-) adiabatic electron and proton-coupled electron transfer reactions. The rate expressions can be readily combined with ab initio methods to study reaction kinetics reactions at complex electrochemical interfaces as a function of the electrode potential. The theoretical work herein provides the basis for treating electrochemical kinetics and the inclusion of non-adiabatic and tunneling effects in electrochemical environments widening the scope of reactions amenable to computational studies.</div>

scholarly journals Unified Rate Theory of Electrochemistry and Electrocatalysis: Fixed Potential Formulation for General, Electron Transfer, and Proton-Coupled Electron Transfer Reactions

2019 ◽  
Author(s):  
Marko Melander
Keyword(s):  
Electron Transfer ◽  
Electrode Potential ◽  
Canonical Ensemble ◽  
Reaction Rates ◽  
Transfer Reactions ◽  
Rate Theory ◽  
Electron Transfer Reactions ◽  
Proton Coupled Electron Transfer ◽  
Fixed Electrode ◽  
Grand Canonical

<div>Atomistic modeling of electrocatalytic reactions is most naturally conducted within the grand canonical ensemble (GCE) which enables fixed chemical potential calculations. While GCE has been widely adopted for modeling electrochemical and electrocatalytic thermodynamics, the electrochemical reaction rate theory within GCE is lacking. Molecular and condensed phase rate theories are formulated within microcanonical and canonical ensembles, respectively, but electrocatalytic systems described within the GCE require extension of the conventionally used rate theories for computation reaction rates at fixed electrode potentials. In this work, rate theories from (micro)canonical ensemble are generalized to the GCE providing the theoretical basis for the computation reaction rates in electrochemical and electrocatalytic systems. It is shown that all canonical rate theories can be extended to the GCE. From the generalized grand canonical rate theory developed herein, fixed electrode potential rate equations are derived for i) general reactions within the GCE transition state theory (GCE-TST), ii) adiabatic curve-crossing rate theory within the empirical valence bond theory (GCE-EVB), and iii) (non-)adiabatic electron and proton-coupled electron transfer reactions. The rate expressions can be readily combined with ab initio methods to study reaction kinetics reactions at complex electrochemical interfaces as a function of the electrode potential. The theoretical work herein provides a single, unified approach for electrochemical and electrocatalytic kinetics and the inclusion of non-adiabatic and tunneling effects in electrochemical environments widening the scope of reactions amenable to computational studies.</div>

On the interpretation of dislocation-loop growth during in-situ high-voltage Electron Microscopy

1990 ◽  
Vol 48 (4) ◽  
pp. 532-533
Author(s):  
E. Holzäpfel ◽  
F. Phillipp ◽  
M. Wilkens
Keyword(s):  
Point Defect ◽  
Rate Equations ◽  
Rate Theory ◽  
Dislocation Loops ◽  
High Voltage Electron Microscopy ◽  
Vacancy Migration ◽  
Voltage Electron ◽  
Reaction Rate Theory ◽  
Defect Reactions

During in-situ radiation damage experiments aiming on the investigation of vacancy-migration properties interstitial-type dislocation loops are used as probes monitoring the development of the point defect concentrations. The temperature dependence of the loop-growth rate v is analyzed in terms of reaction-rate theory yielding information on the vacancy migration enthalpy. The relation between v and the point-defect production rate P provides a critical test of such a treatment since it is sensitive to the defect reactions which are dominant. If mutual recombination of vacancies and interstitials is the dominant reaction, vαP0.5 holds. If, however, annihilation of the defects at unsaturable sinks determines the concentrations, a linear relationship vαP is expected.Detailed studies in pure bcc-metals yielded vαPx with 0.7≾×≾1.0 showing that besides recombination of vacancies and interstitials annihilation at sinks plays an important role in the concentration development which has properly to be incorporated into the rate equations.

Understanding Conformational Entropy in Small Molecules

2020 ◽  
Author(s):  
Lucian Chan ◽  
Garrett Morris ◽  
Geoffrey Hutchison
Keyword(s):  
Small Molecules ◽  
Degrees Of Freedom ◽  
Absolute Error ◽  
Low Energy ◽  
Standard Entropy ◽  
Free Energies ◽  
Conformational Entropy ◽  
Wide Range ◽  
High Degree ◽  
Empirical Corrections

The calculation of the entropy of flexible molecules can be challenging, since the number of possible conformers grows exponentially with molecule size and many low-energy conformers may be thermally accessible. Different methods have been proposed to approximate the contribution of conformational entropy to the molecular standard entropy, including performing thermochemistry calculations with all possible stable conformations, and developing empirical corrections from experimental data. We have performed conformer sampling on over 120,000 small molecules generating some 12 million conformers, to develop models to predict conformational entropy across a wide range of molecules. Using insight into the nature of conformational disorder, our cross-validated physically-motivated statistical model can outperform common machine learning and deep learning methods, with a mean absolute error ≈4.8 J/mol•K, or under 0.4 kcal/mol at 300 K. Beyond predicting molecular entropies and free energies, the model implies a high degree of correlation between torsions in most molecules, often as- sumed to be independent. While individual dihedral rotations may have low energetic barriers, the shape and chemical functionality of most molecules necessarily correlate their torsional degrees of freedom, and hence restrict the number of low-energy conformations immensely. Our simple models capture these correlations, and advance our understanding of small molecule conformational entropy.

Thermal Decomposition Kinetics of Glyphosate (GP) and its Metabolite Aminomethylphosphonic Acid (AMPA)

2019 ◽  
Author(s):  
Milad Narimani ◽  
Gabriel da Silva
Keyword(s):  
Thermal Decomposition ◽  
Reaction Rate ◽  
Decomposition Kinetics ◽  
Rate Theory ◽  
Thermal Decomposition Mechanism ◽  
Treatment Processes ◽  
Aminomethylphosphonic Acid ◽  
Reaction Rate Theory ◽  
Decomposition Chemistry ◽  
Kinetics Of

Glyphosate (GP) is a widely used herbicide worldwide, yet accumulation of GP and its main byproduct, aminomethylphosphonic acid (AMPA), in soil and water has raised concerns about its potential effects to human health. Thermal treatment processes are one option for decontaminating material containing GP and AMPA, yet the thermal decomposition chemistry of these compounds remains poorly understood. Here, we have revealed the thermal decomposition mechanism of GP and AMPA by applying computational chemistry and reaction rate theory methods. <br>

Glembotskaya G.T., Eremin S.Yu. Scientific and practical approach to optimizing costs on development and promotion of drugs

2019 ◽  
Vol 2019 (3) ◽  
pp. 47-53
Author(s):  
Галина Глембоцкая ◽  
Galina Glembockaya ◽  
Станислав Еремин ◽  
Stanislav Eremin
Keyword(s):  
Scientific Literature ◽  
Pharmacological Action ◽  
Pharmaceutical Market ◽  
Pharmaceutical Companies ◽  
Strategic Development ◽  
The World ◽  
The Russian Federation ◽  
The Cost ◽  
Further Development ◽  
Registration Phase

In order to identify promising strategic development possibilities for the pharmaceutical industry in the Russian Federation, a pilot study was conducted, which has analyzed the main trends in the development of innovative medicines. As a result of the content analysis of available sources of scientific literature, the characteristics of options used in the world practice for increasing the innovative activity of individual subjects and the pharmaceutical market as a whole are presented. Possible reserves for the further development of the innovative component of the pharmaceutical market within the framework of the concept of personalized medicine according to the P4 principle (predictive - personalized - preventive - participatory) are identified and structured. The results of use by individual pharmaceutical companies of scientifically and practically justified approaches to optimizing the costs of development and promoting drugs are presented. The advantages and real prospects of a generally accepted method to reduce the cost of development by «expanding the pharmacological effect» (label expansion) of already existing drugs with a known safety profile in the world practice are shown. A scientific generalization and structuring of the goals and results of the post-registration phase of clinical trials to expand the pharmacological action of a number of drugs already existed at the market have been carried out.

scholarly journals Quantum information probes of charge fractionalization in large-N gauge theories

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Brandon S. DiNunno ◽  
Niko Jokela ◽  
Juan F. Pedraza ◽  
Arttu Pönni
Keyword(s):  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
Strongly Coupled ◽  
Information Theoretic ◽  
Large N ◽  
Wide Range ◽  
Charge Fractionalization ◽  
Electric Flux

Abstract We study in detail various information theoretic quantities with the intent of distinguishing between different charged sectors in fractionalized states of large-N gauge theories. For concreteness, we focus on a simple holographic (2 + 1)-dimensional strongly coupled electron fluid whose charged states organize themselves into fractionalized and coherent patterns at sufficiently low temperatures. However, we expect that our results are quite generic and applicable to a wide range of systems, including non-holographic. The probes we consider include the entanglement entropy, mutual information, entanglement of purification and the butterfly velocity. The latter turns out to be particularly useful, given the universal connection between momentum and charge diffusion in the vicinity of a black hole horizon. The RT surfaces used to compute the above quantities, though, are largely insensitive to the electric flux in the bulk. To address this deficiency, we propose a generalized entanglement functional that is motivated through the Iyer-Wald formalism, applied to a gravity theory coupled to a U(1) gauge field. We argue that this functional gives rise to a coarse grained measure of entanglement in the boundary theory which is obtained by tracing over (part) of the fractionalized and cohesive charge degrees of freedom. Based on the above, we construct a candidate for an entropic c-function that accounts for the existence of bulk charges. We explore some of its general properties and their significance, and discuss how it can be used to efficiently account for charged degrees of freedom across different energy scales.

scholarly journals Punishment Strategies across Societies: Conventional Wisdoms Reconsidered

Games ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 63
Author(s):  
Ramzi Suleiman ◽  
Yuval Samid
Keyword(s):  
Public Goods ◽  
Strong Predictor ◽  
Social Environments ◽  
Public Goods Game ◽  
The Public ◽  
Free Riders ◽  
The World ◽  
Emergence Of Cooperation ◽  
Using Data ◽  
The Cost

Experiments using the public goods game have repeatedly shown that in cooperative social environments, punishment makes cooperation flourish, and withholding punishment makes cooperation collapse. In less cooperative social environments, where antisocial punishment has been detected, punishment was detrimental to cooperation. The success of punishment in enhancing cooperation was explained as deterrence of free riders by cooperative strong reciprocators, who were willing to pay the cost of punishing them, whereas in environments in which punishment diminished cooperation, antisocial punishment was explained as revenge by low cooperators against high cooperators suspected of punishing them in previous rounds. The present paper reconsiders the generality of both explanations. Using data from a public goods experiment with punishment, conducted by the authors on Israeli subjects (Study 1), and from a study published in Science using sixteen participant pools from cities around the world (Study 2), we found that: 1. The effect of punishment on the emergence of cooperation was mainly due to contributors increasing their cooperation, rather than from free riders being deterred. 2. Participants adhered to different contribution and punishment strategies. Some cooperated and did not punish (‘cooperators’); others cooperated and punished free riders (‘strong reciprocators’); a third subgroup punished upward and downward relative to their own contribution (‘norm-keepers’); and a small sub-group punished only cooperators (‘antisocial punishers’). 3. Clear societal differences emerged in the mix of the four participant types, with high-contributing pools characterized by higher ratios of ‘strong reciprocators’, and ‘cooperators’, and low-contributing pools characterized by a higher ratio of ‘norm keepers’. 4. The fraction of ‘strong reciprocators’ out of the total punishers emerged as a strong predictor of the groups’ level of cooperation and success in providing the public goods.

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