Gibbs free energy of reactions involving SiC, Si3N4, H2, and H2O as a function of temperature and pressure

NASA Technical Reports Server (NTRS)

Isham, M. A.

1992-01-01

Silicon carbide and silicon nitride are considered for application as structural materials and coating in advanced propulsion systems including nuclear thermal. Three-dimensional Gibbs free energy were constructed for reactions involving these materials in H2 and H2/H2O. Free energy plots are functions of temperature and pressure. Calculations used the definition of Gibbs free energy where the spontaneity of reactions is calculated as a function of temperature and pressure. Silicon carbide decomposes to Si and CH4 in pure H2 and forms a SiO2 scale in a wet atmosphere. Silicon nitride remains stable under all conditions. There was no apparent difference in reaction thermodynamics between ideal and Van der Waals treatment of gaseous species.

First-Year University Chemistry Textbooks' Misrepresentation of Gibbs Energy

ERIC Educational Resources Information Center

Quilez, Juan

2012-01-01

This study analyzes the misrepresentation of Gibbs energy by college chemistry textbooks. The article reports the way first-year university chemistry textbooks handle the concepts of spontaneity and equilibrium. Problems with terminology are found; confusion arises in the meaning given to [delta]G, [delta][subscript r]G, [delta]G[degrees], and…

Gibbs energies of transferring triglycine from water into H2O-DMSO solvent

NASA Astrophysics Data System (ADS)

Usacheva, T. R.; Kuz'mina, K. I.; Lan, Pham Thi; Kuz'mina, I. A.; Sharnin, V. A.

2014-08-01

The Gibbs energies of transferring triglycine (3Gly, glycyl-glycyl-glycine) from water into mixtures of water with dimethyl sulfoxide (χDMSO = 0.05, 0.10, and 0.15 mole fractions) at 298.15 K are determined from the interphase distribution. An increased dimethyl sulfoxide (DMSO) concentration in the solvent slightly raises the positive values of Δtr G ○(3Gly), possibly indicating the formation of more stable 3Gly-H2O solvated complexes than ones of 3Gly-DMSO. It is shown that the change in the Gibbs energy of transfer of 3Gly is determined by the enthalpy component. The relationship of 3Gly and 18-crown-6 ether (18C6) solvation's contributions to the change in the Gibbs energy of [3Gly18C6] molecular complex formation in H2O-DMSO solvents is analyzed, and the key role of 3Gly solvation's contribution to the change in the stability of [3Gly18C6] upon moving from H2O to mixtures with DMSO is revealed.

Gibbs free-energy difference between the glass and crystalline phases of a Ni-Zr alloy

NASA Technical Reports Server (NTRS)

Ohsaka, K.; Trinh, E. H.; Holzer, J. C.; Johnson, W. L.

1993-01-01

The heats of eutectic melting and devitrification, and the specific heats of the crystalline, glass, and liquid phases have been measured for a Ni24Zr76 alloy. The data are used to calculate the Gibbs free-energy difference, Delta G(AC), between the real glass and the crystal on an assumption that the liquid-glass transition is second order. The result shows that Delta G(AC) continuously increases as the temperature decreases in contrast to the ideal glass case where Delta G(AC) is assumed to be independent of temperature.

Inference with minimal Gibbs free energy in information field theory.

PubMed

Ensslin, Torsten A; Weig, Cornelius

2010-11-01

Non-linear and non-gaussian signal inference problems are difficult to tackle. Renormalization techniques permit us to construct good estimators for the posterior signal mean within information field theory (IFT), but the approximations and assumptions made are not very obvious. Here we introduce the simple concept of minimal Gibbs free energy to IFT, and show that previous renormalization results emerge naturally. They can be understood as being the gaussian approximation to the full posterior probability, which has maximal cross information with it. We derive optimized estimators for three applications, to illustrate the usage of the framework: (i) reconstruction of a log-normal signal from poissonian data with background counts and point spread function, as it is needed for gamma ray astronomy and for cosmography using photometric galaxy redshifts, (ii) inference of a gaussian signal with unknown spectrum, and (iii) inference of a poissonian log-normal signal with unknown spectrum, the combination of (i) and (ii). Finally we explain how gaussian knowledge states constructed by the minimal Gibbs free energy principle at different temperatures can be combined into a more accurate surrogate of the non-gaussian posterior.

The entropy and Gibbs free energy of formation of the aluminum ion

USGS Publications Warehouse

Hemingway, B.S.; Robie, R.A.

1977-01-01

A reevaluation of the entropy and Gibbs free energy of formation of Al3+(aq) yields -308 ?? 15 J/K??mol and 489.4 ?? 1.4kj/mol for S0298 and ??G0f{hook},298 respectively. The standard electrode potential for aluminum is 1.691 ?? 0.005 volts. ?? 1977.

The Concentration Dependence of the (Delta)s Term in the Gibbs Free Energy Function: Application to Reversible Reactions in Biochemistry

ERIC Educational Resources Information Center

Gary, Ronald K.

2004-01-01

The concentration dependence of (delta)S term in the Gibbs free energy function is described in relation to its application to reversible reactions in biochemistry. An intuitive and non-mathematical argument for the concentration dependence of the (delta)S term in the Gibbs free energy equation is derived and the applicability of the equation to…

Revised values for the Gibbs free energy of formation of [Al(OH)4 aq-], diaspore, boehmite and bayerite at 298.15 K and 1 bar, the thermodynamic properties of kaolinite to 800 K and 1 bar, and the heats of solution of several gibbsite samples

USGS Publications Warehouse

Hemingway, B.S.; Robie, R.A.; Kittrick, J.A.

1978-01-01

Solution calorimetric measurements compared with solubility determinations from the literature for the same samples of gibbsite have provided a direct thermochemical cycle through which the Gibbs free energy of formation of [Al(OH)4 aq-] can be determined. The Gibbs free energy of formation of [Al(OH)4 aq-] at 298.15 K is -1305 ?? 1 kJ/mol. These heat-of-solution results show no significant difference in the thermodynamic properties of gibbsite particles in the range from 50 to 0.05 ??m. The Gibbs free energies of formation at 298.15 K and 1 bar pressure of diaspore, boehmite and bayerite are -9210 ?? 5.0, -918.4 ?? 2.1 and -1153 ?? 2 kJ/mol based upon the Gibbs free energy of [A1(OH)4 aq-] calculated in this paper and the acceptance of -1582.2 ?? 1.3 and -1154.9 ?? 1.2 kJ/mol for the Gibbs free energy of formation of corundum and gibbsite, respectively. Values for the Gibbs free energy formation of [Al(OH)2 aq+] and [AlO2 aq-] were also calculated as -914.2 ?? 2.1 and -830.9 ?? 2.1 kJ/mol, respectively. The use of [AlC2 aq-] as a chemical species is discouraged. A revised Gibbs free energy of formation for [H4SiO4aq0] was recalculated from calorimetric data yielding a value of -1307.5 ?? 1.7 kJ/mol which is in good agreement with the results obtained from several solubility studies. Smoothed values for the thermodynamic functions CP0, ( HT0 - H2980) T, ( GT0 - H2980) T, ST0 - S00, ??Hf{hook},2980 kaolinite are listed at integral temperatures between 298.15 and 800 K. The heat capacity of kaolinite at temperatures between 250 and 800 K may be calculated from the following equation: CP0 = 1430.26 - 0.78850 T + 3.0340 ?? 10-4 T2 -1.85158 ?? 10-4 T2 1 2 + 8.3341 ?? 106 T-2. The thermodynamic properties of most of the geologically important Al-bearing phases have been referenced to the same reference state for Al, namely gibbsite. ?? 1978.

Predicting hydration Gibbs energies of alkyl-aromatics using molecular simulation: a comparison of current force fields and the development of a new parameter set for accurate solvation data.

PubMed

Garrido, Nuno M; Jorge, Miguel; Queimada, António J; Gomes, José R B; Economou, Ioannis G; Macedo, Eugénia A

2011-10-14

The Gibbs energy of hydration is an important quantity to understand the molecular behavior in aqueous systems at constant temperature and pressure. In this work we review the performance of some popular force fields, namely TraPPE, OPLS-AA and Gromos, in reproducing the experimental Gibbs energies of hydration of several alkyl-aromatic compounds--benzene, mono-, di- and tri-substituted alkylbenzenes--using molecular simulation techniques. In the second part of the paper, we report a new model that is able to improve such hydration energy predictions, based on Lennard Jones parameters from the recent TraPPE-EH force field and atomic partial charges obtained from natural population analysis of density functional theory calculations. We apply a scaling factor determined by fitting the experimental hydration energy of only two solutes, and then present a simple rule to generate atomic partial charges for different substituted alkyl-aromatics. This rule has the added advantages of eliminating the unnecessary assumption of fixed charge on every substituted carbon atom and providing a simple guideline for extrapolating the charge assignment to any multi-substituted alkyl-aromatic molecule. The point charges derived here yield excellent predictions of experimental Gibbs energies of hydration, with an overall absolute average deviation of less than 0.6 kJ mol(-1). This new parameter set can also give good predictive performance for other thermodynamic properties and liquid structural information.

Extension of Gibbs-Duhem equation including influences of external fields

NASA Astrophysics Data System (ADS)

Guangze, Han; Jianjia, Meng

2018-03-01

Gibbs-Duhem equation is one of the fundamental equations in thermodynamics, which describes the relation among changes in temperature, pressure and chemical potential. Thermodynamic system can be affected by external field, and this effect should be revealed by thermodynamic equations. Based on energy postulate and the first law of thermodynamics, the differential equation of internal energy is extended to include the properties of external fields. Then, with homogeneous function theorem and a redefinition of Gibbs energy, a generalized Gibbs-Duhem equation with influences of external fields is derived. As a demonstration of the application of this generalized equation, the influences of temperature and external electric field on surface tension, surface adsorption controlled by external electric field, and the derivation of a generalized chemical potential expression are discussed, which show that the extended Gibbs-Duhem equation developed in this paper is capable to capture the influences of external fields on a thermodynamic system.

Temperature-Dependent Estimation of Gibbs Energies Using an Updated Group-Contribution Method.

PubMed

Du, Bin; Zhang, Zhen; Grubner, Sharon; Yurkovich, James T; Palsson, Bernhard O; Zielinski, Daniel C

2018-06-05

Reaction-equilibrium constants determine the metabolite concentrations necessary to drive flux through metabolic pathways. Group-contribution methods offer a way to estimate reaction-equilibrium constants at wide coverage across the metabolic network. Here, we present an updated group-contribution method with 1) additional curated thermodynamic data used in fitting and 2) capabilities to calculate equilibrium constants as a function of temperature. We first collected and curated aqueous thermodynamic data, including reaction-equilibrium constants, enthalpies of reaction, Gibbs free energies of formation, enthalpies of formation, entropy changes of formation of compounds, and proton- and metal-ion-binding constants. Next, we formulated the calculation of equilibrium constants as a function of temperature and calculated the standard entropy change of formation (Δ f S ∘ ) using a model based on molecular properties. The median absolute error in estimating Δ f S ∘ was 0.013 kJ/K/mol. We also estimated magnesium binding constants for 618 compounds using a linear regression model validated against measured data. We demonstrate the improved performance of the current method (8.17 kJ/mol in median absolute residual) over the current state-of-the-art method (11.47 kJ/mol) in estimating the 185 new reactions added in this work. The efforts here fill in gaps for thermodynamic calculations under various conditions, specifically different temperatures and metal-ion concentrations. These, to our knowledge, new capabilities empower the study of thermodynamic driving forces underlying the metabolic function of organisms living under diverse conditions. Copyright © 2018 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Standard Gibbs energy of formation of Mo 3Te 4 by emf measurements

NASA Astrophysics Data System (ADS)

Mallika, C.; Sreedharan, O. M.

1990-03-01

The emf of the galvanic cells Pt, Mo, MoO 2¦8 YSZ¦'FeO', Fe, Pt (I) and Pt, Fe,'FeO' ¦8 YSZ¦MoO 2, Mo 3Te 4, MoTe 2(α), C, Pt (II) were measured over the temperature ranges 837 to 1151 K and 775 to 1196 K, respectively, using 8 mass% yttria-stabilized zirconia (8 YSZ) as the solid electrolyte. From the emf values, the partial molar Gibbs energy of solution of molybdenum in Mo 3Te 4/MoTe 2(α), Δ ḠMo was found to be Δ ḠMo ± 1.19 ( kJ/mol) = -025.08 + 0.00420T(K) . Using the literature data for the Gibbs energy of formation of MoTe 2(α). the expression ΔG° f( Mo3Te4, s) ± 5.97 (kj/mol) = -253.58 + 0.09214 T( K) was derived for the range 775 to 1196 K. A third-law analysis yielded a value of -209 ± 10 kJ/mol for ΔH° f.298o of Mo 3Te 4(s).

PhyloGibbs-MP: Module Prediction and Discriminative Motif-Finding by Gibbs Sampling

PubMed Central

Siddharthan, Rahul

2008-01-01

PhyloGibbs, our recent Gibbs-sampling motif-finder, takes phylogeny into account in detecting binding sites for transcription factors in DNA and assigns posterior probabilities to its predictions obtained by sampling the entire configuration space. Here, in an extension called PhyloGibbs-MP, we widen the scope of the program, addressing two major problems in computational regulatory genomics. First, PhyloGibbs-MP can localise predictions to small, undetermined regions of a large input sequence, thus effectively predicting cis-regulatory modules (CRMs) ab initio while simultaneously predicting binding sites in those modules—tasks that are usually done by two separate programs. PhyloGibbs-MP's performance at such ab initio CRM prediction is comparable with or superior to dedicated module-prediction software that use prior knowledge of previously characterised transcription factors. Second, PhyloGibbs-MP can predict motifs that differentiate between two (or more) different groups of regulatory regions, that is, motifs that occur preferentially in one group over the others. While other “discriminative motif-finders” have been published in the literature, PhyloGibbs-MP's implementation has some unique features and flexibility. Benchmarks on synthetic and actual genomic data show that this algorithm is successful at enhancing predictions of differentiating sites and suppressing predictions of common sites and compares with or outperforms other discriminative motif-finders on actual genomic data. Additional enhancements include significant performance and speed improvements, the ability to use “informative priors” on known transcription factors, and the ability to output annotations in a format that can be visualised with the Generic Genome Browser. In stand-alone motif-finding, PhyloGibbs-MP remains competitive, outperforming PhyloGibbs-1.0 and other programs on benchmark data. PMID:18769735

Using Graphs of Gibbs Energy versus Temperature in General Chemistry Discussions of Phase Changes and Colligative Properties

ERIC Educational Resources Information Center

Hanson, Robert M.; Riley, Patrick; Schwinefus, Jeff; Fischer, Paul J.

2008-01-01

The use of qualitative graphs of Gibbs energy versus temperature is described in the context of chemical demonstrations involving phase changes and colligative properties at the general chemistry level. (Contains 5 figures and 1 note.)

The Gibbs free energy of nukundamite (Cu3.38Fe0.62S4): A correction and implications for phase equilibria

USGS Publications Warehouse

Seal, R.R.; Inan, E.E.; Hemingway, B.S.

2001-01-01

The Gibbs free energy of formation of nukundamite (Cu3.38Fe0.62S4) was calculated from published experimental studies of the reaction 3.25 Cu3.38Fe0.62S4 + S2 = 11 CuS + 2 FeS2 in order to correct an erroneous expression in the published record. The correct expression describing the Gibbs free energy of formation (kJ???mol-1) of nukundamite relative to the elements and ideal S2 gas is ??fG?? nukundamite T(K) = -549.75 + 0.23242 T + 3.1284 T0.5, with an uncertainty of 0.6%. An evaluation of the phase equilibria of nukundamite with associated phases in the system Cu-Fe-S as a function of temperature and sulfur fugacity indicates that nukundamite is stable from 224 to 501??C at high sulfidation states. At its greatest extent, at 434??C, the stability field of nukundamite is only 0.4 log f(S2) units wide, which explains its rarity. Equilibria between nukundamite and bornite, which limit the stability of both phases, involve bornite compositions that deviate significantly from stoichiometric Cu5FeS4. Under equilibrium conditions in the system Cu-Fe-S, nukundamite + chalcopyrite is not a stable assemblage at any temperature.

The use of computational thermodynamics for the determination of surface tension and Gibbs-Thomson coefficient of multicomponent alloys

NASA Astrophysics Data System (ADS)

Ferreira, D. J. S.; Bezerra, B. N.; Collyer, M. N.; Garcia, A.; Ferreira, I. L.

2018-04-01

The simulation of casting processes demands accurate information on the thermophysical properties of the alloy; however, such information is scarce in the literature for multicomponent alloys. Generally, metallic alloys applied in industry have more than three solute components. In the present study, a general solution of Butler's formulation for surface tension is presented for multicomponent alloys and is applied in quaternary Al-Cu-Si-Fe alloys, thus permitting the Gibbs-Thomson coefficient to be determined. Such coefficient is a determining factor to the reliability of predictions furnished by microstructure growth models and by numerical computations of solidification thermal parameters, which will depend on the thermophysical properties assumed in the calculations. The Gibbs-Thomson coefficient for ternary and quaternary alloys is seldom reported in the literature. A numerical model based on Powell's hybrid algorithm and a finite difference Jacobian approximation has been coupled to a Thermo-Calc TCAPI interface to assess the excess Gibbs energy of the liquid phase, permitting liquidus temperature, latent heat, alloy density, surface tension and Gibbs-Thomson coefficient for Al-Cu-Si-Fe hypoeutectic alloys to be calculated, as an example of calculation capabilities for multicomponent alloys of the proposed method. The computed results are compared with thermophysical properties of binary Al-Cu and ternary Al-Cu-Si alloys found in the literature and presented as a function of the Cu solute composition.

Direct measurements of the Gibbs free energy of OH using a CW tunable laser

NASA Technical Reports Server (NTRS)

Killinger, D. K.; Wang, C. C.

1979-01-01

The paper describes an absorption measurement for determining the Gibbs free energy of OH generated in a mixture of water and oxygen vapor. These measurements afford a direct verification of the accuracy of thermochemical data of H2O at high temperatures and pressures. The results indicate that values for the heat capacity of H2O obtained through numerical computations are correct within an experimental uncertainty of 0.15 cal/mole K.

Generalized Gibbs distribution and energy localization in the semiclassical FPU problem

NASA Astrophysics Data System (ADS)

Hipolito, Rafael; Danshita, Ippei; Oganesyan, Vadim; Polkovnikov, Anatoli

2011-03-01

We investigate dynamics of the weakly interacting quantum mechanical Fermi-Pasta-Ulam (qFPU) model in the semiclassical limit below the stochasticity threshold. Within this limit we find that initial quantum fluctuations lead to the damping of FPU oscillations and relaxation of the system to a slowly evolving steady state with energy localized within few momentum modes. We find that in large systems this state can be described by the generalized Gibbs ensemble (GGE), with the Lagrange multipliers being very weak functions of time. This ensembles gives accurate description of the instantaneous correlation functions, both quadratic and quartic. Based on these results we conjecture that GGE generically appears as a prethermalized state in weakly non-integrable systems.

Quantum Gibbs Samplers: The Commuting Case

NASA Astrophysics Data System (ADS)

Kastoryano, Michael J.; Brandão, Fernando G. S. L.

2016-06-01

We analyze the problem of preparing quantum Gibbs states of lattice spin Hamiltonians with local and commuting terms on a quantum computer and in nature. Our central result is an equivalence between the behavior of correlations in the Gibbs state and the mixing time of the semigroup which drives the system to thermal equilibrium (the Gibbs sampler). We introduce a framework for analyzing the correlation and mixing properties of quantum Gibbs states and quantum Gibbs samplers, which is rooted in the theory of non-commutative {mathbb{L}_p} spaces. We consider two distinct classes of Gibbs samplers, one of them being the well-studied Davies generator modelling the dynamics of a system due to weak-coupling with a large Markovian environment. We show that their spectral gap is independent of system size if, and only if, a certain strong form of clustering of correlations holds in the Gibbs state. Therefore every Gibbs state of a commuting Hamiltonian that satisfies clustering of correlations in this strong sense can be prepared efficiently on a quantum computer. As concrete applications of our formalism, we show that for every one-dimensional lattice system, or for systems in lattices of any dimension at temperatures above a certain threshold, the Gibbs samplers of commuting Hamiltonians are always gapped, giving an efficient way of preparing the associated Gibbs states on a quantum computer.

A Gibbs Energy Minimization Approach for Modeling of Chemical Reactions in a Basic Oxygen Furnace

NASA Astrophysics Data System (ADS)

Kruskopf, Ari; Visuri, Ville-Valtteri

2017-12-01

In modern steelmaking, the decarburization of hot metal is converted into steel primarily in converter processes, such as the basic oxygen furnace. The objective of this work was to develop a new mathematical model for top blown steel converter, which accounts for the complex reaction equilibria in the impact zone, also known as the hot spot, as well as the associated mass and heat transport. An in-house computer code of the model has been developed in Matlab. The main assumption of the model is that all reactions take place in a specified reaction zone. The mass transfer between the reaction volume, bulk slag, and metal determine the reaction rates for the species. The thermodynamic equilibrium is calculated using the partitioning of Gibbs energy (PGE) method. The activity model for the liquid metal is the unified interaction parameter model and for the liquid slag the modified quasichemical model (MQM). The MQM was validated by calculating iso-activity lines for the liquid slag components. The PGE method together with the MQM was validated by calculating liquidus lines for solid components. The results were compared with measurements from literature. The full chemical reaction model was validated by comparing the metal and slag compositions to measurements from industrial scale converter. The predictions were found to be in good agreement with the measured values. Furthermore, the accuracy of the model was found to compare favorably with the models proposed in the literature. The real-time capability of the proposed model was confirmed in test calculations.

eQuilibrator--the biochemical thermodynamics calculator.

PubMed

Flamholz, Avi; Noor, Elad; Bar-Even, Arren; Milo, Ron

2012-01-01

The laws of thermodynamics constrain the action of biochemical systems. However, thermodynamic data on biochemical compounds can be difficult to find and is cumbersome to perform calculations with manually. Even simple thermodynamic questions like 'how much Gibbs energy is released by ATP hydrolysis at pH 5?' are complicated excessively by the search for accurate data. To address this problem, eQuilibrator couples a comprehensive and accurate database of thermodynamic properties of biochemical compounds and reactions with a simple and powerful online search and calculation interface. The web interface to eQuilibrator (http://equilibrator.weizmann.ac.il) enables easy calculation of Gibbs energies of compounds and reactions given arbitrary pH, ionic strength and metabolite concentrations. The eQuilibrator code is open-source and all thermodynamic source data are freely downloadable in standard formats. Here we describe the database characteristics and implementation and demonstrate its use.

eQuilibrator—the biochemical thermodynamics calculator

PubMed Central

Flamholz, Avi; Noor, Elad; Bar-Even, Arren; Milo, Ron

2012-01-01

The laws of thermodynamics constrain the action of biochemical systems. However, thermodynamic data on biochemical compounds can be difficult to find and is cumbersome to perform calculations with manually. Even simple thermodynamic questions like ‘how much Gibbs energy is released by ATP hydrolysis at pH 5?’ are complicated excessively by the search for accurate data. To address this problem, eQuilibrator couples a comprehensive and accurate database of thermodynamic properties of biochemical compounds and reactions with a simple and powerful online search and calculation interface. The web interface to eQuilibrator (http://equilibrator.weizmann.ac.il) enables easy calculation of Gibbs energies of compounds and reactions given arbitrary pH, ionic strength and metabolite concentrations. The eQuilibrator code is open-source and all thermodynamic source data are freely downloadable in standard formats. Here we describe the database characteristics and implementation and demonstrate its use. PMID:22064852

Calculating Free Energy Changes in Continuum Solvation Models

DOE PAGES

Ho, Junming; Ertem, Mehmed Z.

2016-02-27

We recently showed for a large dataset of pK as and reduction potentials that free energies calculated directly within the SMD continuum model compares very well with corresponding thermodynamic cycle calculations in both aqueous and organic solvents (Phys. Chem. Chem. Phys. 2015, 17, 2859). In this paper, we significantly expand the scope of our study to examine the suitability of this approach for the calculation of general solution phase kinetics and thermodynamics, in conjunction with several commonly used solvation models (SMDM062X, SMD-HF, CPCM-UAKS, and CPCM-UAHF) for a broad range of systems and reaction types. This includes cluster-continuum schemes for pKmore » a calculations, as well as various neutral, radical and ionic reactions such as enolization, cycloaddition, hydrogen and chlorine atom transfer, and bimolecular SN2 and E2 reactions. On the basis of this benchmarking study, we conclude that the accuracies of both approaches are generally very similar – the mean errors for Gibbs free energy changes of neutral and ionic reactions are approximately 5 kJ mol -1 and 25 kJ mol -1 respectively. In systems where there are significant structural changes due to solvation, as is the case for certain ionic transition states and amino acids, the direct approach generally afford free energy changes that are in better agreement with experiment. The results indicate that when appropriate combinations of electronic structure methods are employed, the direct approach provides a reliable alternative to the thermodynamic cycle calculations of solution phase kinetics and thermodynamics across a broad range of organic reactions.« less

On thermodynamical inconsistency of isotherm equations: Gibbs's thermodynamics.

PubMed

Tóth, József

2003-06-01

It has been proven that all isotherm equations which include the expression 1-Theta contradict the exact Gibbs thermodynamics. These contradictions have been discussed in detail in the case of the Langmuir (L) equation applied to gas/solid (G/S), solid/liquid (S/L), and gas/liquid (G/L) interfaces. In G/S adsorption the L equation can theoretically be applied only at low equilibrium pressures on condition that vg > vs . vg is the molar volume of the adsorbed amount in the gas phase and vs is the same in the Gibbs phase. In S/L and G/L adsorption the L equation is practically applicable only in the domain of very low concentrations. The cause of these contradictions (inconsistencies) is that Gibbs thermodynamics takes excess adsorbed amounts into account; however, the L and other isotherm equations calculate with the absolute adsorbed amount. The two amounts may be practically equal to each other when the limiting conditions mentioned above are fulfilled. It is also discussed how these inconsistent isotherm equations can be transformed into consistent ones.

Size Fluctuations of Near Critical Nuclei and Gibbs Free Energy for Nucleation of BDA on Cu(001)

NASA Astrophysics Data System (ADS)

Schwarz, Daniel; van Gastel, Raoul; Zandvliet, Harold J. W.; Poelsema, Bene

2012-07-01

We present a low-energy electron microscopy study of nucleation and growth of BDA on Cu(001) at low supersaturation. At sufficiently high coverage, a dilute BDA phase coexists with c(8×8) crystallites. The real-time microscopic information allows a direct visualization of near-critical nuclei, determination of the supersaturation and the line tension of the crystallites, and, thus, derivation of the Gibbs free energy for nucleation. The resulting critical nucleus size nicely agrees with the measured value. Nuclei up to 4-6 times larger still decay with finite probability, urging reconsideration of the classic perception of a critical nucleus.

Size fluctuations of near critical nuclei and Gibbs free energy for nucleation of BDA on Cu(001).

PubMed

Schwarz, Daniel; van Gastel, Raoul; Zandvliet, Harold J W; Poelsema, Bene

2012-07-06

We present a low-energy electron microscopy study of nucleation and growth of BDA on Cu(001) at low supersaturation. At sufficiently high coverage, a dilute BDA phase coexists with c(8×8) crystallites. The real-time microscopic information allows a direct visualization of near-critical nuclei, determination of the supersaturation and the line tension of the crystallites, and, thus, derivation of the Gibbs free energy for nucleation. The resulting critical nucleus size nicely agrees with the measured value. Nuclei up to 4-6 times larger still decay with finite probability, urging reconsideration of the classic perception of a critical nucleus.

Chemical Disequilibria and Sources of Gibbs Free Energy Inside Enceladus

NASA Astrophysics Data System (ADS)

Zolotov, M. Y.

2010-12-01

Non-photosynthetic organisms use chemical disequilibria in the environment to gain metabolic energy from enzyme catalyzed oxidation-reduction (redox) reactions. The presence of carbon dioxide, ammonia, formaldehyde, methanol, methane and other hydrocarbons in the eruptive plume of Enceladus [1] implies diverse redox disequilibria in the interior. In the history of the moon, redox disequilibria could have been activated through melting of a volatile-rich ice and following water-rock-organic interactions. Previous and/or present aqueous processes are consistent with the detection of NaCl and Na2CO3/NaHCO3-bearing grains emitted from Enceladus [2]. A low K/Na ratio in the grains [2] and a low upper limit for N2 in the plume [3] indicate low temperature (possibly < 273 K) of aqueous processes. Although many of the energetically favorable redox reactions are sluggish at low temperature, they could be catalyzed by enzymes if organisms were (are) present. The redox conditions in aqueous systems and amounts of available Gibbs free energy should have been affected by the production, consumption and escape of hydrogen. Aqueous oxidation of minerals (Fe-Ni metal, Fe-Ni phosphides, etc.) accreted on Enceladus should have led to H2 production, which is consistent with H2 detection in the plume [1]. Numerical evaluations based on concentrations of plume gases [1] reveal sufficient energy sources available to support metabolically diverse life at a wide range of activities (a) of dissolved H2 (log aH2 from 0 to -10). Formaldehyde, carbon dioxide [c.f. 4], HCN (if it is present), methanol, acetylene and other hydrocarbons have the potential to react with H2 to form methane. Aqueous hydrogenations of acetylene, HCN and formaldehyde to produce methanol are energetically favorable as well. Both favorable hydrogenation and hydration of HCN lead to formation of ammonia. Condensed organic species could also participate in redox reactions. Methane and ammonia are the final products of

Glyoxal and Methylglyoxal Setschenow Salting Constants in Sulfate, Nitrate, and Chloride Solutions: Measurements and Gibbs Energies.

PubMed

Waxman, Eleanor M; Elm, Jonas; Kurtén, Theo; Mikkelsen, Kurt V; Ziemann, Paul J; Volkamer, Rainer

2015-10-06

Knowledge about Setschenow salting constants, KS, the exponential dependence of Henry's Law coefficients on salt concentration, is of particular importance to predict secondary organic aerosol (SOA) formation from soluble species in atmospheric waters with high salt concentrations, such as aerosols. We have measured KS of glyoxal and methylglyoxal for the atmospherically relevant salts (NH4)2SO4, NH4NO3, NaNO3, and NaCl and find that glyoxal consistently "salts-in" (KS of -0.16, -0.06, -0.065, -0.1 molality(-1), respectively) while methylglyoxal "salts-out" (KS of +0.16, +0.075, +0.02, +0.06 molality(-1)). We show that KS values for different salts are additive and present an equation for use in atmospheric models. Additionally, we have performed a series of quantum chemical calculations to determine the interactions between glyoxal/methylglyoxal monohydrate with Cl(-), NO3(-), SO4(2-), Na(+), and NH4(+) and find Gibbs free energies of water displacement of -10.9, -22.0, -22.9, 2.09, and 1.2 kJ/mol for glyoxal monohydrate and -3.1, -10.3, -7.91, 6.11, and 1.6 kJ/mol for methylglyoxal monohydrate with uncertainties of 8 kJ/mol. The quantum chemical calculations support that SO4(2-), NO3(-), and Cl(-) modify partitioning, while cations do not. Other factors such as ion charge or partitioning volume effects likely need to be considered to fully explain salting effects.

Gibbs free energy difference between the undercooled liquid and the beta phase of a Ti-Cr alloy

NASA Technical Reports Server (NTRS)

Ohsaka, K.; Trinh, E. H.; Holzer, J. C.; Johnson, W. L.

1992-01-01

The heat of fusion and the specific heats of the solid and liquid have been experimentally determined for a Ti60Cr40 alloy. The data are used to evaluate the Gibbs free energy difference, delta-G, between the liquid and the beta phase as a function of temperature to verify a reported spontaneous vitrification (SV) of the beta phase in Ti-Cr alloys. The results show that SV of an undistorted beta phase in the Ti60Cr40 alloy at 873 K is not feasible because delta-G is positive at the temperature. However, delta-G may become negative with additional excess free energy to the beta phase in the form of defects.

The Gibbs free energy of homogeneous nucleation: From atomistic nuclei to the planar limit.

PubMed

Cheng, Bingqing; Tribello, Gareth A; Ceriotti, Michele

2017-09-14

In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters (the chemical potential, the interfacial free energy, and a Tolman correction) of a model based on classical nucleation theory can be fitted using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the chemical potentials and the interface energy are pinned to their planar-interface values, more precise estimates for the Tolman length are obtained. Extrapolating the free energy profile obtained from small simulation boxes to larger nuclei is thus more reliable.

Quantum Gibbs ensemble Monte Carlo

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fantoni, Riccardo, E-mail: rfantoni@ts.infn.it; Moroni, Saverio, E-mail: moroni@democritos.it

We present a path integral Monte Carlo method which is the full quantum analogue of the Gibbs ensemble Monte Carlo method of Panagiotopoulos to study the gas-liquid coexistence line of a classical fluid. Unlike previous extensions of Gibbs ensemble Monte Carlo to include quantum effects, our scheme is viable even for systems with strong quantum delocalization in the degenerate regime of temperature. This is demonstrated by an illustrative application to the gas-superfluid transition of {sup 4}He in two dimensions.

Gibbs energy of the resolvation of glycylglycine and its anion in aqueous solutions of dimethylsulfoxide at 298.15 K

NASA Astrophysics Data System (ADS)

Naumov, V. V.; Isaeva, V. A.; Kuzina, E. N.; Sharnin, V. A.

2012-12-01

Gibbs energies for the transfer of glycylglycine and glycylglycinate ions from water to water-dimethylsulfoxide solvents are determined from the interface distribution of substances between immiscible phases in the composition range of 0.00 to 0.20 molar fractions of DMSO at 298.15 K. It is shown that with a rise in the concentration of nonaqueous components in solution, we observe the solvation of dipeptide and its anion, due mainly to the destabilization of the carboxyl group.

Gibbs Ensemble Simulations of the Solvent Swelling of Polymer Films

NASA Astrophysics Data System (ADS)

Gartner, Thomas; Epps, Thomas, III; Jayaraman, Arthi

Solvent vapor annealing (SVA) is a useful technique to tune the morphology of block polymer, polymer blend, and polymer nanocomposite films. Despite SVA's utility, standardized SVA protocols have not been established, partly due to a lack of fundamental knowledge regarding the interplay between the polymer(s), solvent, substrate, and free-surface during solvent annealing and evaporation. An understanding of how to tune polymer film properties in a controllable manner through SVA processes is needed. Herein, the thermodynamic implications of the presence of solvent in the swollen polymer film is explored through two alternative Gibbs ensemble simulation methods that we have developed and extended: Gibbs ensemble molecular dynamics (GEMD) and hybrid Monte Carlo (MC)/molecular dynamics (MD). In this poster, we will describe these simulation methods and demonstrate their application to polystyrene films swollen by toluene and n-hexane. Polymer film swelling experiments, Gibbs ensemble molecular simulations, and polymer reference interaction site model (PRISM) theory are combined to calculate an effective Flory-Huggins χ (χeff) for polymer-solvent mixtures. The effects of solvent chemistry, solvent content, polymer molecular weight, and polymer architecture on χeff are examined, providing a platform to control and understand the thermodynamics of polymer film swelling.

Consideration of some dilute-solution phenomena based on an expression for the Gibbs free energy

NASA Astrophysics Data System (ADS)

Jonah, D. A.

1986-07-01

Rigorous expressions based on the Lennard-Jones (6 12) potential, are presented for the Gibbs and Helmholtz free energy of a dilute mixture. These expressions give the free energy of the mixture in terms of the thermodynamic properties of the pure solvent, thereby providing a convenient means of correlating dilute mixture behavior with that of the pure solvent. Expressions for the following dilute binary solution properties are derived: Henry's constant, limiting activity coefficients with their derivatives, solid solubilities in supercritical gases, and mixed second virial coefficients. The Henry's constant expression suggests a linear temperature dependence; application to solubility data for various gases in methane and water shows a good agreement between theory and experiment. In the thermodynamic modeling of supercritical fluid extraction, we have demonstrated how to predict new solubility-pressure isotherms from a given isotherm, with encouraging results. The mixed second virial coefficient expression has also been applied to experimental data; the agreement with theory is good.

Implementation of a Thermodynamic Solver within a Computer Program for Calculating Fission-Product Release Fractions

NASA Astrophysics Data System (ADS)

Barber, Duncan Henry

During some postulated accidents at nuclear power stations, fuel cooling may be impaired. In such cases, the fuel heats up and the subsequent increased fission-gas release from the fuel to the gap may result in fuel sheath failure. After fuel sheath failure, the barrier between the coolant and the fuel pellets is lost or impaired, gases and vapours from the fuel-to-sheath gap and other open voids in the fuel pellets can be vented. Gases and steam from the coolant can enter the broken fuel sheath and interact with the fuel pellet surfaces and the fission-product inclusion on the fuel surface (including material at the surface of the fuel matrix). The chemistry of this interaction is an important mechanism to model in order to assess fission-product releases from fuel. Starting in 1995, the computer program SOURCE 2.0 was developed by the Canadian nuclear industry to model fission-product release from fuel during such accidents. SOURCE 2.0 has employed an early thermochemical model of irradiated uranium dioxide fuel developed at the Royal Military College of Canada. To overcome the limitations of computers of that time, the implementation of the RMC model employed lookup tables to pre-calculated equilibrium conditions. In the intervening years, the RMC model has been improved, the power of computers has increased significantly, and thermodynamic subroutine libraries have become available. This thesis is the result of extensive work based on these three factors. A prototype computer program (referred to as SC11) has been developed that uses a thermodynamic subroutine library to calculate thermodynamic equilibria using Gibbs energy minimization. The Gibbs energy minimization requires the system temperature (T) and pressure (P), and the inventory of chemical elements (n) in the system. In order to calculate the inventory of chemical elements in the fuel, the list of nuclides and nuclear isomers modelled in SC11 had to be expanded from the list used by SOURCE 2.0. A

Change in the Gibbs energy of 18-crown-6 ether transfer from methanol to methanol-acetonitrile mixtures at 298 K

NASA Astrophysics Data System (ADS)

Kuz'mina, I. A.; Usacheva, T. R.; Kuz'mina, K. I.; Volkova, M. A.; Sharnin, V. A.

2015-01-01

The Gibbs energies of the transfer of 18-crown-6 ether from methanol to its mixtures with acetonitrile (χAN = 0.0-1.0 mole fraction) are determined by means of interphase distribution at 298 K. The effect the solvent composition has on the thermodynamic characteristics of the solvation of 18-crown-6 ether is analyzed. An increase in the content of acetonitrile in the mixed solvent enhances the solvation of crown ether due to changes in the energy of the solution. Resolvation of the macrocycle is assumed to be complete at acetonitrile concentrations higher than 0.6 mole fraction.

Comment on "Inference with minimal Gibbs free energy in information field theory".

PubMed

Iatsenko, D; Stefanovska, A; McClintock, P V E

2012-03-01

Enßlin and Weig [Phys. Rev. E 82, 051112 (2010)] have introduced a "minimum Gibbs free energy" (MGFE) approach for estimation of the mean signal and signal uncertainty in Bayesian inference problems: it aims to combine the maximum a posteriori (MAP) and maximum entropy (ME) principles. We point out, however, that there are some important questions to be clarified before the new approach can be considered fully justified, and therefore able to be used with confidence. In particular, after obtaining a Gaussian approximation to the posterior in terms of the MGFE at some temperature T, this approximation should always be raised to the power of T to yield a reliable estimate. In addition, we show explicitly that MGFE indeed incorporates the MAP principle, as well as the MDI (minimum discrimination information) approach, but not the well-known ME principle of Jaynes [E.T. Jaynes, Phys. Rev. 106, 620 (1957)]. We also illuminate some related issues and resolve apparent discrepancies. Finally, we investigate the performance of MGFE estimation for different values of T, and we discuss the advantages and shortcomings of the approach.

Teaching the Concept of Gibbs Energy Minimization through Its Application to Phase-Equilibrium Calculation

ERIC Educational Resources Information Center

Privat, Romain; Jaubert, Jean-Noe¨l; Berger, Etienne; Coniglio, Lucie; Lemaitre, Ce´cile; Meimaroglou, Dimitrios; Warth, Vale´rie

2016-01-01

Robust and fast methods for chemical or multiphase equilibrium calculation are routinely needed by chemical-process engineers working on sizing or simulation aspects. Yet, while industrial applications essentially require calculation tools capable of discriminating between stable and nonstable states and converging to nontrivial solutions,…

Calculating phase diagrams using PANDAT and panengine

NASA Astrophysics Data System (ADS)

Chen, S.-L.; Zhang, F.; Xie, F.-Y.; Daniel, S.; Yan, X.-Y.; Chang, Y. A.; Schmid-Fetzer, R.; Oates, W. A.

2003-12-01

Knowledge of phase equilibria or phase diagrams and thermodynamic properties is important in alloy design and materials-processing simulation. In principle, stable phase equilibrium is uniquely determined by the thermodynamic properties of the system, such as the Gibbs energy functions of the phases. PANDAT, a new computer software package for multicomponent phase-diagram calculation, was developed under the guidance of this principle.

Comparative study of solute trapping and Gibbs free energy changes at the phase interface during alloy solidification under local nonequilibrium conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sobolev, S. L., E-mail: sobolev@icp.ac.ru

An analytical model has been developed to describe the influence of solute trapping during rapid alloy solidification on the components of the Gibbs free energy change at the phase interface with emphasis on the solute drag energy. For relatively low interface velocity V < V{sub D}, where V{sub D} is the characteristic diffusion velocity, all the components, namely mixing part, local nonequilibrium part, and solute drag, significantly depend on solute diffusion and partitioning. When V ≥ V{sub D}, the local nonequilibrium effects lead to a sharp transition to diffusionless solidification. The transition is accompanied by complete solute trapping and vanishingmore » solute drag energy, i.e. partitionless and “dragless” solidification.« less

Marangoni and Gibbs elasticity of flowing soap films

NASA Astrophysics Data System (ADS)

Kim, Ildoo; Sane, Aakash; Mandre, Shreyas

2017-11-01

A flowing soap film has two elasticities. Marangoni elasticity dynamically stabilizes the film from sudden disturbance, and Gibbs elasticity is an equilibrium property that influences the film's persistence over time. In our experimental investigation, we find that Marangoni elasticity is 22 mN/m independent of the film thickness. On the other hand, Gibbs elasticity depends both on the film thickness and the soap concentration. Interestingly, the soap film made of dilute soap solution has the greater Gibbs elasticity, which is not consistent to the existing theory. Such discrepancy is originated from the flowing nature of our soap films, in which surfactants are continuously replenished.

The Gibbs Phenomenon for Series of Orthogonal Polynomials

ERIC Educational Resources Information Center

Fay, T. H.; Kloppers, P. Hendrik

2006-01-01

This note considers the four classes of orthogonal polynomials--Chebyshev, Hermite, Laguerre, Legendre--and investigates the Gibbs phenomenon at a jump discontinuity for the corresponding orthogonal polynomial series expansions. The perhaps unexpected thing is that the Gibbs constant that arises for each class of polynomials appears to be the same…

Gibbs-Curie-Wulff Theorem in Organic Materials: A Case Study on the Relationship between Surface Energy and Crystal Growth.

PubMed

Li, Rongjin; Zhang, Xiaotao; Dong, Huanli; Li, Qikai; Shuai, Zhigang; Hu, Wenping

2016-02-24

The equilibrium crystal shape and shape evolution of organic crystals are found to follow the Gibbs-Curie-Wulff theorem. Organic crystals are grown by the physical vapor transport technique and exhibit exactly the same shape as predicted by the Gibbs-Curie-Wulff theorem under optimal conditions. This accordance provides concrete proof for the theorem. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Gibbs Free-Energy Gradient along the Path of Glucose Transport through Human Glucose Transporter 3.

PubMed

Liang, Huiyun; Bourdon, Allen K; Chen, Liao Y; Phelix, Clyde F; Perry, George

2018-06-11

Fourteen glucose transporters (GLUTs) play essential roles in human physiology by facilitating glucose diffusion across the cell membrane. Due to its central role in the energy metabolism of the central nervous system, GLUT3 has been thoroughly investigated. However, the Gibbs free-energy gradient (what drives the facilitated diffusion of glucose) has not been mapped out along the transport path. Some fundamental questions remain. Here we present a molecular dynamics study of GLUT3 embedded in a lipid bilayer to quantify the free-energy profile along the entire transport path of attracting a β-d-glucose from the interstitium to the inside of GLUT3 and, from there, releasing it to the cytoplasm by Arrhenius thermal activation. From the free-energy profile, we elucidate the unique Michaelis-Menten characteristics of GLUT3, low K M and high V MAX , specifically suitable for neurons' high and constant demand of energy from their low-glucose environments. We compute GLUT3's binding free energy for β-d-glucose to be -4.6 kcal/mol in agreement with the experimental value of -4.4 kcal/mol ( K M = 1.4 mM). We also compute the hydration energy of β-d-glucose, -18.0 kcal/mol vs the experimental data, -17.8 kcal/mol. In this, we establish a dynamics-based connection from GLUT3's crystal structure to its cellular thermodynamics with quantitative accuracy. We predict equal Arrhenius barriers for glucose uptake and efflux through GLUT3 to be tested in future experiments.

A Gibbs sampler for motif detection in phylogenetically close sequences

NASA Astrophysics Data System (ADS)

Siddharthan, Rahul; van Nimwegen, Erik; Siggia, Eric

2004-03-01

Genes are regulated by transcription factors that bind to DNA upstream of genes and recognize short conserved ``motifs'' in a random intergenic ``background''. Motif-finders such as the Gibbs sampler compare the probability of these short sequences being represented by ``weight matrices'' to the probability of their arising from the background ``null model'', and explore this space (analogous to a free-energy landscape). But closely related species may show conservation not because of functional sites but simply because they have not had sufficient time to diverge, so conventional methods will fail. We introduce a new Gibbs sampler algorithm that accounts for common ancestry when searching for motifs, while requiring minimal ``prior'' assumptions on the number and types of motifs, assessing the significance of detected motifs by ``tracking'' clusters that stay together. We apply this scheme to motif detection in sporulation-cycle genes in the yeast S. cerevisiae, using recent sequences of other closely-related Saccharomyces species.

Reflections on Gibbs: From Critical Phenomena to the Amistad

NASA Astrophysics Data System (ADS)

Kadanoff, Leo P.

2003-03-01

J. Willard Gibbs, the younger was the first American theorist. He was one of the inventors of statistical physics. His introduction and development of the concepts of phase space, phase transitions, and thermodynamic surfaces was remarkably correct and elegant. These three concepts form the basis of different but related areas of physics. The connection among these areas has been a subject of deep reflection from Gibbs' time to our own. I shall talk about these connections by using concepts suggested by the work of Michael Berry and explicitly put forward by the philosopher Robert Batterman. This viewpoint relates theory-connection to the applied mathematics concepts of asymptotic analysis and singular perturbations. J. Willard Gibbs, the younger, had all his achievements concentrated in science. His father, also J. Willard Gibbs, also a Professor at Yale, had one great achievement that remains unmatched in our day. I shall describe it.

Relativistic hydrodynamics from quantum field theory on the basis of the generalized Gibbs ensemble method

NASA Astrophysics Data System (ADS)

Hayata, Tomoya; Hidaka, Yoshimasa; Noumi, Toshifumi; Hongo, Masaru

2015-09-01

We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative and dissipative parts, and analyze their time evolution in detail. Performing the path-integral formulation of the local Gibbs distribution, we microscopically derive the generating functional for the nondissipative hydrodynamics. We also construct a basis to study dissipative corrections. In particular, we derive the first-order dissipative hydrodynamic equations without a choice of frame such as the Landau-Lifshitz or Eckart frame.

Boiling point determination using adiabatic Gibbs ensemble Monte Carlo simulations: Application to metals described by embedded-atom potentials

NASA Astrophysics Data System (ADS)

Gelb, Lev D.; Chakraborty, Somendra Nath

2011-12-01

The normal boiling points are obtained for a series of metals as described by the "quantum-corrected Sutton Chen" (qSC) potentials [S.-N. Luo, T. J. Ahrens, T. Çağın, A. Strachan, W. A. Goddard III, and D. C. Swift, Phys. Rev. B 68, 134206 (2003)]. Instead of conventional Monte Carlo simulations in an isothermal or expanded ensemble, simulations were done in the constant-NPH adabatic variant of the Gibbs ensemble technique as proposed by Kristóf and Liszi [Chem. Phys. Lett. 261, 620 (1996)]. This simulation technique is shown to be a precise tool for direct calculation of boiling temperatures in high-boiling fluids, with results that are almost completely insensitive to system size or other arbitrary parameters as long as the potential truncation is handled correctly. Results obtained were validated using conventional NVT-Gibbs ensemble Monte Carlo simulations. The qSC predictions for boiling temperatures are found to be reasonably accurate, but substantially underestimate the enthalpies of vaporization in all cases. This appears to be largely due to the systematic overestimation of dimer binding energies by this family of potentials, which leads to an unsatisfactory description of the vapor phase.

Reflections on Gibbs: From Statistical Physics to the Amistad V3.0

NASA Astrophysics Data System (ADS)

Kadanoff, Leo P.

2014-07-01

This note is based upon a talk given at an APS meeting in celebration of the achievements of J. Willard Gibbs. J. Willard Gibbs, the younger, was the first American physical sciences theorist. He was one of the inventors of statistical physics. He introduced and developed the concepts of phase space, phase transitions, and thermodynamic surfaces in a remarkably correct and elegant manner. These three concepts form the basis of different areas of physics. The connection among these areas has been a subject of deep reflection from Gibbs' time to our own. This talk therefore celebrated Gibbs by describing modern ideas about how different parts of physics fit together. I finished with a more personal note. Our own J. Willard Gibbs had all his many achievements concentrated in science. His father, also J. Willard Gibbs, also a Professor at Yale, had one great non-academic achievement that remains unmatched in our day. I describe it.

Chemical potential, Gibbs-Duhem equation and quantum gases

NASA Astrophysics Data System (ADS)

Lee, M. Howard

2017-05-01

Thermodynamic relations like the Gibbs-Duhem are valid from the lowest to the highest temperatures. But they cannot by themselves provide any specific temperature behavior of thermodynamic functions like the chemical potential. In this work, we show that if some general conditions are attached to the Gibbs-Duhem equation, it is possible to obtain the low temperature form of the chemical potential for the ideal Fermi and Bose gases very directly.

Gibbs sampling on large lattice with GMRF

NASA Astrophysics Data System (ADS)

Marcotte, Denis; Allard, Denis

2018-02-01

Gibbs sampling is routinely used to sample truncated Gaussian distributions. These distributions naturally occur when associating latent Gaussian fields to category fields obtained by discrete simulation methods like multipoint, sequential indicator simulation and object-based simulation. The latent Gaussians are often used in data assimilation and history matching algorithms. When the Gibbs sampling is applied on a large lattice, the computing cost can become prohibitive. The usual practice of using local neighborhoods is unsatisfying as it can diverge and it does not reproduce exactly the desired covariance. A better approach is to use Gaussian Markov Random Fields (GMRF) which enables to compute the conditional distributions at any point without having to compute and invert the full covariance matrix. As the GMRF is locally defined, it allows simultaneous updating of all points that do not share neighbors (coding sets). We propose a new simultaneous Gibbs updating strategy on coding sets that can be efficiently computed by convolution and applied with an acceptance/rejection method in the truncated case. We study empirically the speed of convergence, the effect of choice of boundary conditions, of the correlation range and of GMRF smoothness. We show that the convergence is slower in the Gaussian case on the torus than for the finite case studied in the literature. However, in the truncated Gaussian case, we show that short scale correlation is quickly restored and the conditioning categories at each lattice point imprint the long scale correlation. Hence our approach enables to realistically apply Gibbs sampling on large 2D or 3D lattice with the desired GMRF covariance.

Levelized Cost of Energy Calculator | Energy Analysis | NREL

Science.gov Websites

Levelized Cost of Energy Calculator Levelized Cost of Energy Calculator Transparent Cost Database Button The levelized cost of energy (LCOE) calculator provides a simple calculator for both utility-scale need to be included for a thorough analysis. To estimate simple cost of energy, use the slider controls

Gibbs Ensembles for Nearly Compatible and Incompatible Conditional Models

PubMed Central

Chen, Shyh-Huei; Wang, Yuchung J.

2010-01-01

Gibbs sampler has been used exclusively for compatible conditionals that converge to a unique invariant joint distribution. However, conditional models are not always compatible. In this paper, a Gibbs sampling-based approach — Gibbs ensemble —is proposed to search for a joint distribution that deviates least from a prescribed set of conditional distributions. The algorithm can be easily scalable such that it can handle large data sets of high dimensionality. Using simulated data, we show that the proposed approach provides joint distributions that are less discrepant from the incompatible conditionals than those obtained by other methods discussed in the literature. The ensemble approach is also applied to a data set regarding geno-polymorphism and response to chemotherapy in patients with metastatic colorectal PMID:21286232

A Gibbs point field model for the spatial pattern of coronary capillaries

NASA Astrophysics Data System (ADS)

Karch, R.; Neumann, M.; Neumann, F.; Ullrich, R.; Neumüller, J.; Schreiner, W.

2006-09-01

We propose a Gibbs point field model for the pattern of coronary capillaries in transverse histologic sections from human hearts, based on the physiology of oxygen supply from capillaries to tissue. To specify the potential energy function of the Gibbs point field, we draw on an analogy between the equation of steady-state oxygen diffusion from an array of parallel capillaries to the surrounding tissue and Poisson's equation for the electrostatic potential of a two-dimensional distribution of identical point charges. The influence of factors other than diffusion is treated as a thermal disturbance. On this basis, we arrive at the well-known two-dimensional one-component plasma, a system of identical point charges exhibiting a weak (logarithmic) repulsive interaction that is completely characterized by a single dimensionless parameter. By variation of this parameter, the model is able to reproduce many characteristics of real capillary patterns.

Boiling point determination using adiabatic Gibbs ensemble Monte Carlo simulations: application to metals described by embedded-atom potentials.

PubMed

Gelb, Lev D; Chakraborty, Somendra Nath

2011-12-14

The normal boiling points are obtained for a series of metals as described by the "quantum-corrected Sutton Chen" (qSC) potentials [S.-N. Luo, T. J. Ahrens, T. Çağın, A. Strachan, W. A. Goddard III, and D. C. Swift, Phys. Rev. B 68, 134206 (2003)]. Instead of conventional Monte Carlo simulations in an isothermal or expanded ensemble, simulations were done in the constant-NPH adabatic variant of the Gibbs ensemble technique as proposed by Kristóf and Liszi [Chem. Phys. Lett. 261, 620 (1996)]. This simulation technique is shown to be a precise tool for direct calculation of boiling temperatures in high-boiling fluids, with results that are almost completely insensitive to system size or other arbitrary parameters as long as the potential truncation is handled correctly. Results obtained were validated using conventional NVT-Gibbs ensemble Monte Carlo simulations. The qSC predictions for boiling temperatures are found to be reasonably accurate, but substantially underestimate the enthalpies of vaporization in all cases. This appears to be largely due to the systematic overestimation of dimer binding energies by this family of potentials, which leads to an unsatisfactory description of the vapor phase. © 2011 American Institute of Physics

Lindeberg theorem for Gibbs-Markov dynamics

NASA Astrophysics Data System (ADS)

Denker, Manfred; Senti, Samuel; Zhang, Xuan

2017-12-01

A dynamical array consists of a family of functions \\{ fn, i: 1≤slant i≤slant k_n, n≥slant 1\\} and a family of initial times \\{τn, i: 1≤slant i≤slant k_n, n≥slant 1\\} . For a dynamical system (X, T) we identify distributional limits for sums of the form for suitable (non-random) constants s_n>0 and an, i\\in { R} . We derive a Lindeberg-type central limit theorem for dynamical arrays. Applications include new central limit theorems for functions which are not locally Lipschitz continuous and central limit theorems for statistical functions of time series obtained from Gibbs-Markov systems. Our results, which hold for more general dynamics, are stated in the context of Gibbs-Markov dynamical systems for convenience.

Revisiting the finite temperature string method for the calculation of reaction tubes and free energies

NASA Astrophysics Data System (ADS)

Vanden-Eijnden, Eric; Venturoli, Maddalena

2009-05-01

An improved and simplified version of the finite temperature string (FTS) method [W. E, W. Ren, and E. Vanden-Eijnden, J. Phys. Chem. B 109, 6688 (2005)] is proposed. Like the original approach, the new method is a scheme to calculate the principal curves associated with the Boltzmann-Gibbs probability distribution of the system, i.e., the curves which are such that their intersection with the hyperplanes perpendicular to themselves coincides with the expected position of the system in these planes (where perpendicular is understood with respect to the appropriate metric). Unlike more standard paths such as the minimum energy path or the minimum free energy path, the location of the principal curve depends on global features of the energy or the free energy landscapes and thereby may remain appropriate in situations where the landscape is rough on the thermal energy scale and/or entropic effects related to the width of the reaction channels matter. Instead of using constrained sampling in hyperplanes as in the original FTS, the new method calculates the principal curve via sampling in the Voronoi tessellation whose generating points are the discretization points along this curve. As shown here, this modification results in greater algorithmic simplicity. As a by-product, it also gives the free energy associated with the Voronoi tessellation. The new method can be applied both in the original Cartesian space of the system or in a set of collective variables. We illustrate FTS on test-case examples and apply it to the study of conformational transitions of the nitrogen regulatory protein C receiver domain using an elastic network model and to the isomerization of solvated alanine dipeptide.

Hybrid Gibbs Sampling and MCMC for CMB Analysis at Small Angular Scales

NASA Technical Reports Server (NTRS)

Jewell, Jeffrey B.; Eriksen, H. K.; Wandelt, B. D.; Gorski, K. M.; Huey, G.; O'Dwyer, I. J.; Dickinson, C.; Banday, A. J.; Lawrence, C. R.

2008-01-01

A) Gibbs Sampling has now been validated as an efficient, statistically exact, and practically useful method for "low-L" (as demonstrated on WMAP temperature polarization data). B) We are extending Gibbs sampling to directly propagate uncertainties in both foreground and instrument models to total uncertainty in cosmological parameters for the entire range of angular scales relevant for Planck. C) Made possible by inclusion of foreground model parameters in Gibbs sampling and hybrid MCMC and Gibbs sampling for the low signal to noise (high-L) regime. D) Future items to be included in the Bayesian framework include: 1) Integration with Hybrid Likelihood (or posterior) code for cosmological parameters; 2) Include other uncertainties in instrumental systematics? (I.e. beam uncertainties, noise estimation, calibration errors, other).

Improved prediction of MHC class I and class II epitopes using a novel Gibbs sampling approach.

PubMed

Nielsen, Morten; Lundegaard, Claus; Worning, Peder; Hvid, Christina Sylvester; Lamberth, Kasper; Buus, Søren; Brunak, Søren; Lund, Ole

2004-06-12

Prediction of which peptides will bind a specific major histocompatibility complex (MHC) constitutes an important step in identifying potential T-cell epitopes suitable as vaccine candidates. MHC class II binding peptides have a broad length distribution complicating such predictions. Thus, identifying the correct alignment is a crucial part of identifying the core of an MHC class II binding motif. In this context, we wish to describe a novel Gibbs motif sampler method ideally suited for recognizing such weak sequence motifs. The method is based on the Gibbs sampling method, and it incorporates novel features optimized for the task of recognizing the binding motif of MHC classes I and II. The method locates the binding motif in a set of sequences and characterizes the motif in terms of a weight-matrix. Subsequently, the weight-matrix can be applied to identifying effectively potential MHC binding peptides and to guiding the process of rational vaccine design. We apply the motif sampler method to the complex problem of MHC class II binding. The input to the method is amino acid peptide sequences extracted from the public databases of SYFPEITHI and MHCPEP and known to bind to the MHC class II complex HLA-DR4(B1*0401). Prior identification of information-rich (anchor) positions in the binding motif is shown to improve the predictive performance of the Gibbs sampler. Similarly, a consensus solution obtained from an ensemble average over suboptimal solutions is shown to outperform the use of a single optimal solution. In a large-scale benchmark calculation, the performance is quantified using relative operating characteristics curve (ROC) plots and we make a detailed comparison of the performance with that of both the TEPITOPE method and a weight-matrix derived using the conventional alignment algorithm of ClustalW. The calculation demonstrates that the predictive performance of the Gibbs sampler is higher than that of ClustalW and in most cases also higher than that of

Dynamical predictive power of the generalized Gibbs ensemble revealed in a second quench.

PubMed

Zhang, J M; Cui, F C; Hu, Jiangping

2012-04-01

We show that a quenched and relaxed completely integrable system is hardly distinguishable from the corresponding generalized Gibbs ensemble in a dynamical sense. To be specific, the response of the quenched and relaxed system to a second quench can be accurately reproduced by using the generalized Gibbs ensemble as a substitute. Remarkably, as demonstrated with the transverse Ising model and the hard-core bosons in one dimension, not only the steady values but even the transient, relaxation dynamics of the physical variables can be accurately reproduced by using the generalized Gibbs ensemble as a pseudoinitial state. This result is an important complement to the previously established result that a quenched and relaxed system is hardly distinguishable from the generalized Gibbs ensemble in a static sense. The relevance of the generalized Gibbs ensemble in the nonequilibrium dynamics of completely integrable systems is then greatly strengthened.

Time-dependent generalized Gibbs ensembles in open quantum systems

NASA Astrophysics Data System (ADS)

Lange, Florian; Lenarčič, Zala; Rosch, Achim

2018-04-01

Generalized Gibbs ensembles have been used as powerful tools to describe the steady state of integrable many-particle quantum systems after a sudden change of the Hamiltonian. Here, we demonstrate numerically that they can be used for a much broader class of problems. We consider integrable systems in the presence of weak perturbations which break both integrability and drive the system to a state far from equilibrium. Under these conditions, we show that the steady state and the time evolution on long timescales can be accurately described by a (truncated) generalized Gibbs ensemble with time-dependent Lagrange parameters, determined from simple rate equations. We compare the numerically exact time evolutions of density matrices for small systems with a theory based on block-diagonal density matrices (diagonal ensemble) and a time-dependent generalized Gibbs ensemble containing only a small number of approximately conserved quantities, using the one-dimensional Heisenberg model with perturbations described by Lindblad operators as an example.

Measuring effective temperatures in a generalized Gibbs ensemble

NASA Astrophysics Data System (ADS)

Foini, Laura; Gambassi, Andrea; Konik, Robert; Cugliandolo, Leticia F.

2017-05-01

The local physical properties of an isolated quantum statistical system in the stationary state reached long after a quench are generically described by the Gibbs ensemble, which involves only its Hamiltonian and the temperature as a parameter. If the system is instead integrable, additional quantities conserved by the dynamics intervene in the description of the stationary state. The resulting generalized Gibbs ensemble involves a number of temperature-like parameters, the determination of which is practically difficult. Here we argue that in a number of simple models these parameters can be effectively determined by using fluctuation-dissipation relationships between response and correlation functions of natural observables, quantities which are accessible in experiments.

Gibbs-Thomson Effect in Planar Nanowires: Orientation and Doping Modulated Growth.

PubMed

Shen, Youde; Chen, Renjie; Yu, Xuechao; Wang, Qijie; Jungjohann, Katherine L; Dayeh, Shadi A; Wu, Tom

2016-07-13

Epitaxy-enabled bottom-up synthesis of self-assembled planar nanowires via the vapor-liquid-solid mechanism is an emerging and promising approach toward large-scale direct integration of nanowire-based devices without postgrowth alignment. Here, by examining large assemblies of indium tin oxide nanowires on yttria-stabilized zirconia substrate, we demonstrate for the first time that the growth dynamics of planar nanowires follows a modified version of the Gibbs-Thomson mechanism, which has been known for the past decades to govern the correlations between thermodynamic supersaturation, growth speed, and nanowire morphology. Furthermore, the substrate orientation strongly influences the growth characteristics of epitaxial planar nanowires as opposed to impact at only the initial nucleation stage in the growth of vertical nanowires. The rich nanowire morphology can be described by a surface-energy-dependent growth model within the Gibbs-Thomson framework, which is further modulated by the tin doping concentration. Our experiments also reveal that the cutoff nanowire diameter depends on the substrate orientation and decreases with increasing tin doping concentration. These results enable a deeper understanding and control over the growth of planar nanowires, and the insights will help advance the fabrication of self-assembled nanowire devices.

Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width.

PubMed

De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher

2015-12-01

Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be exponential in the number of variables. To help understand the behavior of Gibbs sampling, we introduce a new (hyper)graph property, called hierarchy width . We show that under suitable conditions on the weights, bounded hierarchy width ensures polynomial mixing time. Our study of hierarchy width is in part motivated by a class of factor graph templates, hierarchical templates , which have bounded hierarchy width-regardless of the data used to instantiate them. We demonstrate a rich application from natural language processing in which Gibbs sampling provably mixes rapidly and achieves accuracy that exceeds human volunteers.

Rapidly Mixing Gibbs Sampling for a Class of Factor Graphs Using Hierarchy Width

PubMed Central

De Sa, Christopher; Zhang, Ce; Olukotun, Kunle; Ré, Christopher

2016-01-01

Gibbs sampling on factor graphs is a widely used inference technique, which often produces good empirical results. Theoretical guarantees for its performance are weak: even for tree structured graphs, the mixing time of Gibbs may be exponential in the number of variables. To help understand the behavior of Gibbs sampling, we introduce a new (hyper)graph property, called hierarchy width. We show that under suitable conditions on the weights, bounded hierarchy width ensures polynomial mixing time. Our study of hierarchy width is in part motivated by a class of factor graph templates, hierarchical templates, which have bounded hierarchy width—regardless of the data used to instantiate them. We demonstrate a rich application from natural language processing in which Gibbs sampling provably mixes rapidly and achieves accuracy that exceeds human volunteers. PMID:27279724

Measuring effective temperatures in a generalized Gibbs ensemble

DOE PAGES

Foini, Laura; Gambassi, Andrea; Konik, Robert; ...

2017-05-11

The local physical properties of an isolated quantum statistical system in the stationary state reached long after a quench are generically described by the Gibbs ensemble, which involves only its Hamiltonian and the temperature as a parameter. Additional quantities conserved by the dynamics intervene in the description of the stationary state, if the system is instead integrable. The resulting generalized Gibbs ensemble involves a number of temperature-like parameters, the determination of which is practically difficult. We argue that in a number of simple models these parameters can be effectively determined by using fluctuation-dissipation relationships between response and correlation functions ofmore » natural observables, quantities which are accessible in experiments.« less

Theoretical Understanding the Relations of Melting-point Determination Methods from Gibbs Thermodynamic Surface and Applications on Melting Curves of Lower Mantle Minerals

NASA Astrophysics Data System (ADS)

Yin, K.; Belonoshko, A. B.; Zhou, H.; Lu, X.

2016-12-01

The melting temperatures of materials in the interior of the Earth has significant implications in many areas of geophysics. The direct calculations of the melting point by atomic simulations would face substantial hysteresis problem. To overcome the hysteresis encountered in the atomic simulations there are a few different melting-point determination methods available nowadays, which are founded independently, such as the free energy method, the two-phase or coexistence method, and the Z method, etc. In this study, we provide a theoretical understanding the relations of these methods from a geometrical perspective based on a quantitative construction of the volume-entropy-energy thermodynamic surface, a model first proposed by J. Willard Gibbs in 1873. Then combining with an experimental data and/or a previous melting-point determination method, we apply this model to derive the high-pressure melting curves for several lower mantle minerals with less computational efforts relative to using previous methods only. Through this way, some polyatomic minerals at extreme pressures which are almost unsolvable before are calculated fully from first principles now.

A formula for the entropy of the convolution of Gibbs probabilities on the circle

NASA Astrophysics Data System (ADS)

Lopes, Artur O.

2018-07-01

Consider the transformation , such that (mod 1), and where S 1 is the unitary circle. Suppose is Hölder continuous and positive, and moreover that, for any , we have that We say that ρ is a Gibbs probability for the Hölder continuous potential , if where is the Ruelle operator for . We call J the Jacobian of ρ. Suppose is the convolution of two Gibbs probabilities and associated, respectively, to and . We show that ν is also Gibbs and its Jacobian is given by . In this case, the entropy is given by the expression For a fixed we consider differentiable variations , , of on the Banach manifold of Gibbs probabilities, where , and we estimate the derivative of the entropy at t  =  0. We also present an expression for the Jacobian of the convolution of a Gibbs probability ρ with the invariant probability with support on a periodic orbit of period two. This expression is based on the Jacobian of ρ and two Radon–Nidodym derivatives.

Thermodynamic calculations for the liquid systems NaK, KCs and LiPb

NASA Astrophysics Data System (ADS)

Alblas, B. P.; Van Der Lugt, W.; Visser, E. G.; De Hosson, J. Th. M.

1982-06-01

The semi-empirical model for the calculation of the Gibbs free energy of mixing via the entropy of mixing, proposed by Visser et al. [1], is used to determine the activity coefficients and the long-wavelength limit of the structure factor, SCC(0). For the liquid alloys systems NaK and KCs the method leads to fairly accurate results, indicating almost ideal behaviour. For the compound-forming liquid alloys systems LiPb the agreement with experiment is less favourable, but the calculations clearly demonstrate the important influence of the volume contraction on the entropy.

Circular dichroism and UV resonance Raman study of the impact of alcohols on the Gibbs free energy landscape of an α-helical peptide†

PubMed Central

Xiong, Kan; Asher, Sanford A

2010-01-01

We used CD and UV resonance Raman spectroscopy to study the impact of alcohols on the conformational equilibria and relative Gibbs free energy landscapes along the Ramanchandran Ψ-coordinate of a mainly poly-ala peptide, AP of sequence AAAAA(AAARA)3A. 2,2,2-trifluroethanol (TFE) most stabilizes the α-helical-like conformations, followed by ethanol, methanol and pure water. The π-bulge conformation is stabilized more than the α-helix, while the 310-helix is destabilized due to the alcohol increased hydrophobicity. Turns are also stabilized by alcohols. We also found that while TFE induces more α-helices, it favors multiple, shorter helix segments. PMID:20225890

Quantum mechanical calculation of aqueuous uranium complexes: carbonate, phosphate, organic and biomolecular species

PubMed Central

Kubicki, James D; Halada, Gary P; Jha, Prashant; Phillips, Brian L

2009-01-01

Background Quantum mechanical calculations were performed on a variety of uranium species representing U(VI), U(V), U(IV), U-carbonates, U-phosphates, U-oxalates, U-catecholates, U-phosphodiesters, U-phosphorylated N-acetyl-glucosamine (NAG), and U-2-Keto-3-doxyoctanoate (KDO) with explicit solvation by H2O molecules. These models represent major U species in natural waters and complexes on bacterial surfaces. The model results are compared to observed EXAFS, IR, Raman and NMR spectra. Results Agreement between experiment and theory is acceptable in most cases, and the reasons for discrepancies are discussed. Calculated Gibbs free energies are used to constrain which configurations are most likely to be stable under circumneutral pH conditions. Reduction of U(VI) to U(IV) is examined for the U-carbonate and U-catechol complexes. Conclusion Results on the potential energy differences between U(V)- and U(IV)-carbonate complexes suggest that the cause of slower disproportionation in this system is electrostatic repulsion between UO2 [CO3]35- ions that must approach one another to form U(VI) and U(IV) rather than a change in thermodynamic stability. Calculations on U-catechol species are consistent with the observation that UO22+ can oxidize catechol and form quinone-like species. In addition, outer-sphere complexation is predicted to be the most stable for U-catechol interactions based on calculated energies and comparison to 13C NMR spectra. Outer-sphere complexes (i.e., ion pairs bridged by water molecules) are predicted to be comparable in Gibbs free energy to inner-sphere complexes for a model carboxylic acid. Complexation of uranyl to phosphorus-containing groups in extracellular polymeric substances is predicted to favor phosphonate groups, such as that found in phosphorylated NAG, rather than phosphodiesters, such as those in nucleic acids. PMID:19689800

info-gibbs: a motif discovery algorithm that directly optimizes information content during sampling.

PubMed

Defrance, Matthieu; van Helden, Jacques

2009-10-15

Discovering cis-regulatory elements in genome sequence remains a challenging issue. Several methods rely on the optimization of some target scoring function. The information content (IC) or relative entropy of the motif has proven to be a good estimator of transcription factor DNA binding affinity. However, these information-based metrics are usually used as a posteriori statistics rather than during the motif search process itself. We introduce here info-gibbs, a Gibbs sampling algorithm that efficiently optimizes the IC or the log-likelihood ratio (LLR) of the motif while keeping computation time low. The method compares well with existing methods like MEME, BioProspector, Gibbs or GAME on both synthetic and biological datasets. Our study shows that motif discovery techniques can be enhanced by directly focusing the search on the motif IC or the motif LLR. http://rsat.ulb.ac.be/rsat/info-gibbs

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions.

PubMed

Latella, Ivan; Pérez-Madrid, Agustín

2013-10-01

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

Enthalpy of Formation for Cu–Zn–Sn–S (CZTS) Calculated from Surface Binding Energies Experimentally Measured by Ion Sputtering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baryshev, Sergey V.; Thimsen, Elijah

2015-04-14

Herein, we report an analytical procedure to calculate the enthalpy of formation for thin film multinary compounds from sputtering rates measured during ion bombardment. The method is based on Sigmunds sputtering theory and the BornHaber cycle. Using this procedure, an enthalpy of formation for a CZTS film of the composition Cu1.9Zn1.5Sn0.8S4 was measured as -930 +/- 98 kJ mol1. This value is much more negative than the sum of the enthalpies of formation for the constituent binary compounds, meaning the multinary formation reaction is predicted to be exothermic. The measured enthalpy of formation was used to estimate the temperature dependencemore » of the Gibbs free energy of reaction, which appears consistent with many experimental reports in the CZTS processing literature.« less

Calculation of total free energy yield as an alternative approach for predicting the importance of potential chemolithotrophic reactions in geothermal springs.

PubMed

Dodsworth, Jeremy A; McDonald, Austin I; Hedlund, Brian P

2012-08-01

To inform hypotheses regarding the relative importance of chemolithotrophic metabolisms in geothermal environments, we calculated free energy yields of 26 chemical reactions potentially supporting chemolithotrophy in two US Great Basin hot springs, taking into account the effects of changing reactant and product activities on the Gibbs free energy as each reaction progressed. Results ranged from 1.2 × 10(-5) to 3.6 J kg(-1) spring water, or 3.7 × 10(-5) to 11.5 J s(-1) based on measured flow rates, with aerobic oxidation of CH(4) or NH4 + giving the highest average yields. Energy yields calculated without constraining pH were similar to those at constant pH except for reactions where H(+) was consumed, which often had significantly lower yields when pH was unconstrained. In contrast to the commonly used normalization of reaction chemical affinities per mole of electrons transferred, reaction energy yields for a given oxidant varied by several orders of magnitude and were more sensitive to differences in the activities of products and reactants. The high energy yield of aerobic ammonia oxidation is consistent with previous observations of significant ammonia oxidation rates and abundant ammonia-oxidizing archaea in sediments of these springs. This approach offers an additional lens through which to view the thermodynamic landscape of geothermal springs. © 2012 Federation of European Microbiological Societies. Published by Blackwell Publishing Ltd. All rights reserved.

How Does the Gibbs Inequality Condition Affect the Stability and Detachment of Floating Spheres from the Free Surface of Water?

PubMed

Feng, Dong-xia; Nguyen, Anh V

2016-03-01

Floating objects on the air-water interfaces are central to a number of everyday activities, from walking on water by insects to flotation separation of valuable minerals using air bubbles. The available theories show that a fine sphere can float if the force of surface tension and buoyancies can support the sphere at the interface with an apical angle subtended by the circle of contact being larger than the contact angle. Here we show that the pinning of the contact line at the sharp edge, known as the Gibbs inequality condition, also plays a significant role in controlling the stability and detachment of floating spheres. Specifically, we truncated the spheres with different angles and used a force sensor device to measure the force of pushing the truncated spheres from the interface into water. We also developed a theoretical modeling to calculate the pushing force that in combination with experimental results shows different effects of the Gibbs inequality condition on the stability and detachment of the spheres from the water surface. For small angles of truncation, the Gibbs inequality condition does not affect the sphere detachment, and hence the classical theories on the floatability of spheres are valid. For large truncated angles, the Gibbs inequality condition determines the tenacity of the particle-meniscus contact and the stability and detachment of floating spheres. In this case, the classical theories on the floatability of spheres are no longer valid. A critical truncated angle for the transition from the classical to the Gibbs inequality regimes of detachment was also established. The outcomes of this research advance our understanding of the behavior of floating objects, in particular, the flotation separation of valuable minerals, which often contain various sharp edges of their crystal faces.

Development of a group contribution method for estimating free energy of peptides in a dodecane-water system via molecular dynamic simulations.

PubMed

Mora Osorio, Camilo Andrés; González Barrios, Andrés Fernando

2016-12-07

Calculation of the Gibbs free energy changes of biological molecules at the oil-water interface is commonly performed with Molecular Dynamics simulations (MD). It is a process that could be performed repeatedly in order to find some molecules of high stability in this medium. Here, an alternative method of calculation has been proposed: a group contribution method (GCM) for peptides based on MD of the twenty classic amino acids to obtain free energy change during the insertion of any peptide chain in water-dodecane interfaces. Multiple MD of the twenty classic amino acids located at the interface of rectangular simulation boxes with a dodecane-water medium were performed. A GCM to calculate the free energy of entire peptides is then proposed. The method uses the summation of the Gibbs free energy of each amino acid adjusted in function of its presence or absence in the chain as well as its hydrophobic characteristics. Validation of the equation was performed with twenty-one peptides all simulated using MD in dodecane-water rectangular boxes in previous work, obtaining an average relative error of 16%.

Analysis of Gibbs monolayer adsorbed at the toluene/water interface by UV-visible partial internal reflection spectrometry.

PubMed

Moriya, Yoshio; Hasegawa, Takeshi; Okada, Tetsuo; Ogawa, Nobuaki; Kawai, Erika; Abe, Kosuke; Ogasawara, Masataka; Kato, Sumio; Nakata, Shinichi

2006-11-15

Gibbs monolayers of lipophilic tetraphenylporphyrinatomanganese(III) and hydrophilic diacid of meso-tetrakis(4-sulfonatopheny)porphyrin adsorbed at the liquid-liquid interface have been analyzed by UV-visible external reflection (ER) and partial internal reflection (PIR) spectra measured at different angles of incidence. The angle-dependent ER and PIR spectra over the Brewster angles (thetaERB and thetaIRB) have readily been measured at the toluene/water interface. As preliminarily expected in our previous study, the present study has first proved that the reflection-absorbance of UV-visible PIR spectra quantitatively agrees with the theoretical calculations for the Gibbs monolayer over thetaIRB. In addition, it has also been proved that the absorbance of the PIR spectra is greatly enhanced in comparison to that of the ATR spectra. The enhancement is caused by an optical effect in the monolayer sandwiched between two phases of toluene and water that have different but refractive indices close to each other. This optical enhancement requires an optically perfect contact between the phases, which is difficult to prepare for a solid-solid contact. At the liquid/liquid interface, however, an ideal optical contact is easily realized, which makes the enhancement as much as the theoretical expectation. The PIR spectrometry will be recognized to be a new high-sensitive analytical tool to study Gibbs monolayer at the liquid/liquid interface.

Analytic second derivatives of the energy in the fragment molecular orbital method

NASA Astrophysics Data System (ADS)

Nakata, Hiroya; Nagata, Takeshi; Fedorov, Dmitri G.; Yokojima, Satoshi; Kitaura, Kazuo; Nakamura, Shinichiro

2013-04-01

We developed the analytic second derivatives of the energy for the fragment molecular orbital (FMO) method. First we derived the analytic expressions and then introduced some approximations related to the first and second order coupled perturbed Hartree-Fock equations. We developed a parallel program for the FMO Hessian with approximations in GAMESS and used it to calculate infrared (IR) spectra and Gibbs free energies and to locate the transition states in SN2 reactions. The accuracy of the Hessian is demonstrated in comparison to ab initio results for polypeptides and a water cluster. By using the two residues per fragment division, we achieved the accuracy of 3 cm-1 in the reduced mean square deviation of vibrational frequencies from ab initio for all three polyalanine isomers, while the zero point energy had the error not exceeding 0.3 kcal/mol. The role of the secondary structure on IR spectra, zero point energies, and Gibbs free energies is discussed.

Carbohydrates in thermophile metabolism: calculation of the standard molal thermodynamic properties of aqueous pentoses and hexoses at elevated temperatures and pressures

NASA Astrophysics Data System (ADS)

Amend, Jan P.; Plyasunov, Andrey V.

2001-11-01

Experimental thermodynamic data for aqueous organic compounds can be combined with the revised Helgeson-Kirkham-Flowers (HKF) equations of state to generate parameters that can be used to estimate standard molal properties as functions of temperature and pressure. In this study, we regressed thermodynamic data for aqueous carbohydrates at temperatures up to 393 K reported in the literature to permit the calculation of the apparent standard molal Gibbs free energies and enthalpies of formation (ΔGo and ΔHo, respectively) and the standard molal entropies (S2o), heat capacities (CP,2o), and volumes (V2o) to 423 K and several hundred MPa of aqueous C5 aldoses (ribose, arabinose, xylose, lyxose) and C5 ketoses (ribulose, xylulose) as well as C6 aldoses (glucose, mannose, galactose) and C6 ketoses (fructose, sorbose). Values of ΔGo for these 11 aqueous carbohydrates are given as a function of temperature at the saturated water vapor pressure (PSAT) and at 50 MPa. Values of ΔGo for aqueous glucose are then combined with those of other aqueous organic and inorganic compounds to calculate values of the standard molal Gibbs free energies of 13 fermentation and respiration reactions (ΔGro) known or likely to be carried out by thermophilic microorganisms. Finally, values of the overall Gibbs free energies of these reactions (ΔGr) are calculated at the temperature, pressure, and chemical composition that obtain in the hydrothermal fluids of Vulcano Island, southern Italy, a site that is widely known for its tremendous diversity of organisms able to live at high temperatures. At likely activities of aqueous glucose, it is shown that thermophiles in the hot springs of Vulcano at 373 K and ∼0.1 MPa can gain between 400 and 3000 kJ per mole of glucose fermented or respired.

Long-ranged Fermi-Pasta-Ulam systems in thermal contact: Crossover from q-statistics to Boltzmann-Gibbs statistics

NASA Astrophysics Data System (ADS)

Bagchi, Debarshee; Tsallis, Constantino

2017-04-01

The relaxation to equilibrium of two long-range-interacting Fermi-Pasta-Ulam-like models (β type) in thermal contact is numerically studied. These systems, with different sizes and energy densities, are coupled to each other by a few thermal contacts which are short-range harmonic springs. By using the kinetic definition of temperature, we compute the time evolution of temperature and energy density of the two systems. Eventually, for some time t >teq, the temperature and energy density of the coupled system equilibrate to values consistent with standard Boltzmann-Gibbs thermostatistics. The equilibration time teq depends on the system size N as teq ∼Nγ where γ ≃ 1.8. We compute the velocity distribution P (v) of the oscillators of the two systems during the relaxation process. We find that P (v) is non-Gaussian and is remarkably close to a q-Gaussian distribution for all times before thermal equilibrium is reached. During the relaxation process we observe q > 1 while close to t =teq the value of q converges to unity and P (v) approaches a Gaussian. Thus the relaxation phenomenon in long-ranged systems connected by a thermal contact can be generically described as a crossover from q-statistics to Boltzmann-Gibbs statistics.

Landfill Gas Energy Benefits Calculator

EPA Pesticide Factsheets

This page contains the LFG Energy Benefits Calculator to estimate direct, avoided, and total greenhouse gas reductions, as well as environmental and energy benefits, for a landfill gas energy project.

Free-energy calculations using classical molecular simulation: application to the determination of the melting point and chemical potential of a flexible RDX model.

PubMed

Sellers, Michael S; Lísal, Martin; Brennan, John K

2016-03-21

We present an extension of various free-energy methodologies to determine the chemical potential of the solid and liquid phases of a fully-flexible molecule using classical simulation. The methods are applied to the Smith-Bharadwaj atomistic potential representation of cyclotrimethylene trinitramine (RDX), a well-studied energetic material, to accurately determine the solid and liquid phase Gibbs free energies, and the melting point (Tm). We outline an efficient technique to find the absolute chemical potential and melting point of a fully-flexible molecule using one set of simulations to compute the solid absolute chemical potential and one set of simulations to compute the solid-liquid free energy difference. With this combination, only a handful of simulations are needed, whereby the absolute quantities of the chemical potentials are obtained, for use in other property calculations, such as the characterization of crystal polymorphs or the determination of the entropy. Using the LAMMPS molecular simulator, the Frenkel and Ladd and pseudo-supercritical path techniques are adapted to generate 3rd order fits of the solid and liquid chemical potentials. Results yield the thermodynamic melting point Tm = 488.75 K at 1.0 atm. We also validate these calculations and compare this melting point to one obtained from a typical superheated simulation technique.

Pan-STARRS 1 observations of the unusual active Centaur P/2011 S1(Gibbs)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, H. W.; Ip, W. H.; Chen, W. P.

2014-05-01

P/2011 S1 (Gibbs) is an outer solar system comet or active Centaur with a similar orbit to that of the famous 29P/Schwassmann-Wachmann 1. P/2011 S1 (Gibbs) has been observed by the Pan-STARRS 1 (PS1) sky survey from 2010 to 2012. The resulting data allow us to perform multi-color studies of the nucleus and coma of the comet. Analysis of PS1 images reveals that P/2011 S1 (Gibbs) has a small nucleus <4 km radius, with colors g {sub P1} – r {sub P1} = 0.5 ± 0.02, r {sub P1} – i {sub P1} = 0.12 ± 0.02, and i {submore » P1} – z {sub P1} = 0.46 ± 0.03. The comet remained active from 2010 to 2012, with a model-dependent mass-loss rate of ∼100 kg s{sup –1}. The mass-loss rate per unit surface area of P/2011 S1 (Gibbs) is as high as that of 29P/Schwassmann-Wachmann 1, making it one of the most active Centaurs. The mass-loss rate also varies with time from ∼40 kg s{sup –1} to 150 kg s{sup –1}. Due to its rather circular orbit, we propose that P/2011 S1 (Gibbs) has 29P/Schwassmann-Wachmann 1-like outbursts that control the outgassing rate. The results indicate that it may have a similar surface composition to that of 29P/Schwassmann-Wachmann 1. Our numerical simulations show that the future orbital evolution of P/2011 S1 (Gibbs) is more similar to that of the main population of Centaurs than to that of 29P/Schwassmann-Wachmann 1. The results also demonstrate that P/2011 S1 (Gibbs) is dynamically unstable and can only remain near its current orbit for roughly a thousand years.« less

Periodic p-adic Gibbs Measures of q-State Potts Model on Cayley Trees I: The Chaos Implies the Vastness of the Set of p-Adic Gibbs Measures

NASA Astrophysics Data System (ADS)

Ahmad, Mohd Ali Khameini; Liao, Lingmin; Saburov, Mansoor

2018-06-01

We study the set of p-adic Gibbs measures of the q-state Potts model on the Cayley tree of order three. We prove the vastness of the set of the periodic p-adic Gibbs measures for such model by showing the chaotic behavior of the corresponding Potts-Bethe mapping over Q_p for the prime numbers p≡1 (mod 3). In fact, for 0< |θ -1|_p< |q|_p^2 < 1 where θ =\\exp _p(J) and J is a coupling constant, there exists a subsystem that is isometrically conjugate to the full shift on three symbols. Meanwhile, for 0< |q|_p^2 ≤ |θ -1|_p< |q|_p < 1, there exists a subsystem that is isometrically conjugate to a subshift of finite type on r symbols where r ≥ 4. However, these subshifts on r symbols are all topologically conjugate to the full shift on three symbols. The p-adic Gibbs measures of the same model for the prime numbers p=2,3 and the corresponding Potts-Bethe mapping are also discussed. On the other hand, for 0< |θ -1|_p< |q|_p < 1, we remark that the Potts-Bethe mapping is not chaotic when p=3 and p≡ 2 (mod 3) and we could not conclude the vastness of the set of the periodic p-adic Gibbs measures. In a forthcoming paper with the same title, we will treat the case 0< |q|_p ≤ |θ -1|_p < 1 for all prime numbers p.

GibbsCluster: unsupervised clustering and alignment of peptide sequences.

PubMed

Andreatta, Massimo; Alvarez, Bruno; Nielsen, Morten

2017-07-03

Receptor interactions with short linear peptide fragments (ligands) are at the base of many biological signaling processes. Conserved and information-rich amino acid patterns, commonly called sequence motifs, shape and regulate these interactions. Because of the properties of a receptor-ligand system or of the assay used to interrogate it, experimental data often contain multiple sequence motifs. GibbsCluster is a powerful tool for unsupervised motif discovery because it can simultaneously cluster and align peptide data. The GibbsCluster 2.0 presented here is an improved version incorporating insertion and deletions accounting for variations in motif length in the peptide input. In basic terms, the program takes as input a set of peptide sequences and clusters them into meaningful groups. It returns the optimal number of clusters it identified, together with the sequence alignment and sequence motif characterizing each cluster. Several parameters are available to customize cluster analysis, including adjustable penalties for small clusters and overlapping groups and a trash cluster to remove outliers. As an example application, we used the server to deconvolute multiple specificities in large-scale peptidome data generated by mass spectrometry. The server is available at http://www.cbs.dtu.dk/services/GibbsCluster-2.0. © The Author(s) 2017. Published by Oxford University Press on behalf of Nucleic Acids Research.

Modeling adsorption of cationic surfactants at air/water interface without using the Gibbs equation.

PubMed

Phan, Chi M; Le, Thu N; Nguyen, Cuong V; Yusa, Shin-ichi

2013-04-16

The Gibbs adsorption equation has been indispensable in predicting the surfactant adsorption at the interfaces, with many applications in industrial and natural processes. This study uses a new theoretical framework to model surfactant adsorption at the air/water interface without the Gibbs equation. The model was applied to two surfactants, C14TAB and C16TAB, to determine the maximum surface excesses. The obtained values demonstrated a fundamental change, which was verified by simulations, in the molecular arrangement at the interface. The new insights, in combination with recent discoveries in the field, expose the limitations of applying the Gibbs adsorption equation to cationic surfactants at the air/water interface.

Good Practices in Free-energy Calculations

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; Jarzynski, Christopher; Chipot, Christopher

2013-01-01

As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in drug design. Yet, in a number of instances, the reliability of these calculations can be improved significantly if a number of precepts, or good practices are followed. For the most part, the theory upon which these good practices rely has been known for many years, but often overlooked, or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. The current best practices for carrying out free-energy calculations will be reviewed demonstrating that, at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. In energy perturbation and nonequilibrium work methods, monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision. In thermodynamic integration and probability distribution (histogramming) methods, properly designed adaptive techniques yield nearly uniform sampling of the relevant degrees of freedom and, by doing so, could markedly improve efficiency and accuracy of free energy calculations without incurring any additional computational expense.

Scanning sequences after Gibbs sampling to find multiple occurrences of functional elements

PubMed Central

Tharakaraman, Kannan; Mariño-Ramírez, Leonardo; Sheetlin, Sergey L; Landsman, David; Spouge, John L

2006-01-01

Background Many DNA regulatory elements occur as multiple instances within a target promoter. Gibbs sampling programs for finding DNA regulatory elements de novo can be prohibitively slow in locating all instances of such an element in a sequence set. Results We describe an improvement to the A-GLAM computer program, which predicts regulatory elements within DNA sequences with Gibbs sampling. The improvement adds an optional "scanning step" after Gibbs sampling. Gibbs sampling produces a position specific scoring matrix (PSSM). The new scanning step resembles an iterative PSI-BLAST search based on the PSSM. First, it assigns an "individual score" to each subsequence of appropriate length within the input sequences using the initial PSSM. Second, it computes an E-value from each individual score, to assess the agreement between the corresponding subsequence and the PSSM. Third, it permits subsequences with E-values falling below a threshold to contribute to the underlying PSSM, which is then updated using the Bayesian calculus. A-GLAM iterates its scanning step to convergence, at which point no new subsequences contribute to the PSSM. After convergence, A-GLAM reports predicted regulatory elements within each sequence in order of increasing E-values, so users have a statistical evaluation of the predicted elements in a convenient presentation. Thus, although the Gibbs sampling step in A-GLAM finds at most one regulatory element per input sequence, the scanning step can now rapidly locate further instances of the element in each sequence. Conclusion Datasets from experiments determining the binding sites of transcription factors were used to evaluate the improvement to A-GLAM. Typically, the datasets included several sequences containing multiple instances of a regulatory motif. The improvements to A-GLAM permitted it to predict the multiple instances. PMID:16961919

TEA: A Code Calculating Thermochemical Equilibrium Abundances

NASA Astrophysics Data System (ADS)

Blecic, Jasmina; Harrington, Joseph; Bowman, M. Oliver

2016-07-01

We present an open-source Thermochemical Equilibrium Abundances (TEA) code that calculates the abundances of gaseous molecular species. The code is based on the methodology of White et al. and Eriksson. It applies Gibbs free-energy minimization using an iterative, Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature-pressure pairs. We tested the code against the method of Burrows & Sharp, the free thermochemical equilibrium code Chemical Equilibrium with Applications (CEA), and the example given by Burrows & Sharp. Using their thermodynamic data, TEA reproduces their final abundances, but with higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a code document in addition to this theory paper. TEA is available under a reproducible-research, open-source license via https://github.com/dzesmin/TEA.

An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1987-01-01

An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.

Foundations of modeling in cryobiology-I: concentration, Gibbs energy, and chemical potential relationships.

PubMed

Anderson, Daniel M; Benson, James D; Kearsley, Anthony J

2014-12-01

Mathematical modeling plays an enormously important role in understanding the behavior of cells, tissues, and organs undergoing cryopreservation. Uses of these models range from explanation of phenomena, exploration of potential theories of damage or success, development of equipment, and refinement of optimal cryopreservation/cryoablation strategies. Over the last half century there has been a considerable amount of work in bio-heat and mass-transport, and these models and theories have been readily and repeatedly applied to cryobiology with much success. However, there are significant gaps between experimental and theoretical results that suggest missing links in models. One source for these potential gaps is that cryobiology is at the intersection of several very challenging aspects of transport theory: it couples multi-component, moving boundary, multiphase solutions that interact through a semipermeable elastic membrane with multicomponent solutions in a second time-varying domain, during a two-hundred Kelvin temperature change with multi-molar concentration gradients and multi-atmosphere pressure changes. In order to better identify potential sources of error, and to point to future directions in modeling and experimental research, we present a three part series to build from first principles a theory of coupled heat and mass transport in cryobiological systems accounting for all of these effects. The hope of this series is that by presenting and justifying all steps, conclusions may be made about the importance of key assumptions, perhaps pointing to areas of future research or model development, but importantly, lending weight to standard simplification arguments that are often made in heat and mass transport. In this first part, we review concentration variable relationships, their impact on choices for Gibbs energy models, and their impact on chemical potentials. Copyright © 2014 Elsevier Inc. All rights reserved.

Simple Levelized Cost of Energy (LCOE) Calculator Documentation | Energy

Science.gov Websites

Analysis | NREL Simple Levelized Cost of Energy (LCOE) Calculator Documentation Simple Levelized Cost of Energy (LCOE) Calculator Documentation Transparent Cost Database Button This is a simple : 1). Cost and Performance Adjust the sliders to suitable values for each of the cost and performance

An inverse problem for Gibbs fields with hard core potential

NASA Astrophysics Data System (ADS)

Koralov, Leonid

2007-05-01

It is well known that for a regular stable potential of pair interaction and a small value of activity one can define the corresponding Gibbs field (a measure on the space of configurations of points in Rd). In this paper we consider a converse problem. Namely, we show that for a sufficiently small constant ρ¯1 and a sufficiently small function ρ¯2(x), x ∈Rd, that is equal to zero in a neighborhood of the origin, there exist a hard core pair potential and a value of activity such that ρ¯1 is the density and ρ¯2 is the pair correlation function of the corresponding Gibbs field.

Application of the thermorheologically complex nonlinear Adam-Gibbs model for the glass transition to molecular motion in hydrated proteins.

PubMed

Hodge, Ian M

2006-08-01

The nonlinear thermorheologically complex Adam Gibbs (extended "Scherer-Hodge") model for the glass transition is applied to enthalpy relaxation data reported by Sartor, Mayer, and Johari for hydrated methemoglobin. A sensible range in values for the average localized activation energy is obtained (100-200 kJ mol(-1)). The standard deviation in the inferred Gaussian distribution of activation energies, computed from the reported KWW beta-parameter, is approximately 30% of the average, consistent with the suggestion that some relaxation processes in hydrated proteins have exceptionally low activation energies.

A Gibbs sampler for Bayesian analysis of site-occupancy data

USGS Publications Warehouse

Dorazio, Robert M.; Rodriguez, Daniel Taylor

2012-01-01

1. A Bayesian analysis of site-occupancy data containing covariates of species occurrence and species detection probabilities is usually completed using Markov chain Monte Carlo methods in conjunction with software programs that can implement those methods for any statistical model, not just site-occupancy models. Although these software programs are quite flexible, considerable experience is often required to specify a model and to initialize the Markov chain so that summaries of the posterior distribution can be estimated efficiently and accurately. 2. As an alternative to these programs, we develop a Gibbs sampler for Bayesian analysis of site-occupancy data that include covariates of species occurrence and species detection probabilities. This Gibbs sampler is based on a class of site-occupancy models in which probabilities of species occurrence and detection are specified as probit-regression functions of site- and survey-specific covariate measurements. 3. To illustrate the Gibbs sampler, we analyse site-occupancy data of the blue hawker, Aeshna cyanea (Odonata, Aeshnidae), a common dragonfly species in Switzerland. Our analysis includes a comparison of results based on Bayesian and classical (non-Bayesian) methods of inference. We also provide code (based on the R software program) for conducting Bayesian and classical analyses of site-occupancy data.

Computational methods for reactive transport modeling: An extended law of mass-action, xLMA, method for multiphase equilibrium calculations

NASA Astrophysics Data System (ADS)

Leal, Allan M. M.; Kulik, Dmitrii A.; Kosakowski, Georg; Saar, Martin O.

2016-10-01

We present an extended law of mass-action (xLMA) method for multiphase equilibrium calculations and apply it in the context of reactive transport modeling. This extended LMA formulation differs from its conventional counterpart in that (i) it is directly derived from the Gibbs energy minimization (GEM) problem (i.e., the fundamental problem that describes the state of equilibrium of a chemical system under constant temperature and pressure); and (ii) it extends the conventional mass-action equations with Lagrange multipliers from the Gibbs energy minimization problem, which can be interpreted as stability indices of the chemical species. Accounting for these multipliers enables the method to determine all stable phases without presuming their types (e.g., aqueous, gaseous) or their presence in the equilibrium state. Therefore, the here proposed xLMA method inherits traits of Gibbs energy minimization algorithms that allow it to naturally detect the phases present in equilibrium, which can be single-component phases (e.g., pure solids or liquids) or non-ideal multi-component phases (e.g., aqueous, melts, gaseous, solid solutions, adsorption, or ion exchange). Moreover, our xLMA method requires no technique that tentatively adds or removes reactions based on phase stability indices (e.g., saturation indices for minerals), since the extended mass-action equations are valid even when their corresponding reactions involve unstable species. We successfully apply the proposed method to a reactive transport modeling problem in which we use PHREEQC and GEMS as alternative backends for the calculation of thermodynamic properties such as equilibrium constants of reactions, standard chemical potentials of species, and activity coefficients. Our tests show that our algorithm is efficient and robust for demanding applications, such as reactive transport modeling, where it converges within 1-3 iterations in most cases. The proposed xLMA method is implemented in Reaktoro, a

Good practices in free-energy calculations.

PubMed

Pohorille, Andrew; Jarzynski, Christopher; Chipot, Christophe

2010-08-19

As access to computational resources continues to increase, free-energy calculations have emerged as a powerful tool that can play a predictive role in a wide range of research areas. Yet, the reliability of these calculations can often be improved significantly if a number of precepts, or good practices, are followed. Although the theory upon which these good practices rely has largely been known for many years, it is often overlooked or simply ignored. In other cases, the theoretical developments are too recent for their potential to be fully grasped and merged into popular platforms for the computation of free-energy differences. In this contribution, the current best practices for carrying out free-energy calculations using free energy perturbation and nonequilibrium work methods are discussed, demonstrating that at little to no additional cost, free-energy estimates could be markedly improved and bounded by meaningful error estimates. Monitoring the probability distributions that underlie the transformation between the states of interest, performing the calculation bidirectionally, stratifying the reaction pathway, and choosing the most appropriate paradigms and algorithms for transforming between states offer significant gains in both accuracy and precision.

Langmuir-Gibbs Surface Phases and Transitions

NASA Astrophysics Data System (ADS)

Ocko, Benjamin; Sloutskin, Eli; Sapir, Zvi; Tamam, Lilach; Deutsch, Moshe; Bain, Colin

2007-03-01

Recent synchrotron x-ray measurements reveal surface ordering transitions in films of medium-length linear hydrocarbons (alkanes), spread on the water surface. Alkanes longer than hexane do not spread on the free surface of water. However, sub-mM concentrations of some anionic surfactants (e.g. CTAB) induce formation of thermodynamically stable alkane monolayers, through a ``pseudo-partial wetting'' phenomenon[1]. The monolayers, incorporating both water-insoluble alkanes (Langmuir) and water-soluble CTAB molecules (Gibbs) are called Langmuir-Gibbs (LG) films. The films formed by alkanes with n <=17 exhibit ordering transition upon cooling [2], below which the molecules are normal to the water surface and hexagonally packed, with CTAB molecules randomly mixed inside the quasi-2D crystal. Alkanes with n>17 can not form ordered LG monolayers, due to the repulsion from the n=16 tails of CTAB. This repulsion arises from the two chains' length mismatch. A demixing transition occurs upon ordering, with a pure alkane quasi-2D crystal forming on top of disordered alkyl tails of CTAB molecules. [1] K.M. Wilkinson et al., Chem. Phys. Phys. Chem. 6, 547 (2005). [2] E. Sloutskin, Z. Sapir, L. Tamam, B.M. Ocko, C.D. Bain, and M. Deutsch, Thin Solid Films, in press; K.M. Wilkinson, L. Qunfang, and C.D. Bain, Soft Matter 2, 66 (2006).

Effects of Gibbs free energy of interfacial metal oxide on resistive switching characteristics of solution-processed HfOx films

NASA Astrophysics Data System (ADS)

Hsu, Chih-Chieh; Sun, Jhen-Kai; Tsao, Che-Chang; Chuang, Po-Yang

2017-08-01

Effects of bottom electrodes (BEs) of Al, Mo, and Pt on resistive switching characteristics of sol-gel HfOx films were investigated in this work. To avoid influences of plasma or thermal energy on HfOx RS characteristic, the top electrodes were formed by pressing indium balls onto the HfOx surface rather than by using a sputter or an evaporator. When using Mo as the BE, the as-deposited HfOx film can give a forming-free resistive switching behavior with low set/reset voltages of 0.28 V / - 0.54 V. In contrast, non-switching characteristics of the HfOx films were observed when using Al and Pt as the BEs. The HfOx conduction current was found to be highly dependent on the BE. However, when an annealing process at 350 °C in an oxygen ambient was performed to the HfOx films on different BEs, the resistive switching behavior of the HfOx/Mo was absent while it can be found in the HfOx/Al sample. Differences in I-V characteristics of the HfOx films on different BEs were explained by considering Gibbs free energies of interfacial oxide layers. X-ray photoelectron spectroscopy (XPS) depth profile was used to examine the interfacial oxide layer. The resistive switching mechanism was also studied.

Unifying hydrotropy under Gibbs phase rule.

PubMed

Shimizu, Seishi; Matubayasi, Nobuyuki

2017-09-13

The task of elucidating the mechanism of solubility enhancement using hydrotropes has been hampered by the wide variety of phase behaviour that hydrotropes can exhibit, encompassing near-ideal aqueous solution, self-association, micelle formation, and micro-emulsions. Instead of taking a field guide or encyclopedic approach to classify hydrotropes into different molecular classes, we take a rational approach aiming at constructing a unified theory of hydrotropy based upon the first principles of statistical thermodynamics. Achieving this aim can be facilitated by the two key concepts: (1) the Gibbs phase rule as the basis of classifying the hydrotropes in terms of the degrees of freedom and the number of variables to modulate the solvation free energy; (2) the Kirkwood-Buff integrals to quantify the interactions between the species and their relative contributions to the process of solubilization. We demonstrate that the application of the two key concepts can in principle be used to distinguish the different molecular scenarios at work under apparently similar solubility curves observed from experiments. In addition, a generalization of our previous approach to solutes beyond dilution reveals the unified mechanism of hydrotropy, driven by a strong solute-hydrotrope interaction which overcomes the apparent per-hydrotrope inefficiency due to hydrotrope self-clustering.

Exploring Fourier Series and Gibbs Phenomenon Using Mathematica

ERIC Educational Resources Information Center

Ghosh, Jonaki B.

2011-01-01

This article describes a laboratory module on Fourier series and Gibbs phenomenon which was undertaken by 32 Year 12 students. It shows how the use of CAS played the role of an "amplifier" by making higher level mathematical concepts accessible to students of year 12. Using Mathematica students were able to visualise Fourier series of…

The Gibbs Variational Method in Thermodynamics of Equilibrium Plasma: 1. General Conditions of Equilibrium and Stability for One-Component Charged Gas

DTIC Science & Technology

2018-04-01

systems containing ionized gases. 2. Gibbs Method in the Integral Form As per the Gibbs general methodology , based on the concept of heterogeneous...ARL-TR-8348 ● APR 2018 US Army Research Laboratory The Gibbs Variational Method in Thermodynamics of Equilibrium Plasma: 1...ARL-TR-8348 ● APR 2018 US Army Research Laboratory The Gibbs Variational Method in Thermodynamics of Equilibrium Plasma: 1. General

Gibbs measures with memory of length 2 on an arbitrary-order Cayley tree

NASA Astrophysics Data System (ADS)

Akın, Hasan

In this paper, we consider the Ising-Vanniminus model on an arbitrary-order Cayley tree. We generalize the results conjectured by Akın [Chinese J. Phys. 54(4), 635-649 (2016) and Int. J. Mod. Phys. B 31(13), 1750093 (2017)] for an arbitrary-order Cayley tree. We establish the existence and a full classification of translation-invariant Gibbs measures (TIGMs) with a memory of length 2 associated with the model on arbitrary-order Cayley tree. We construct the recurrence equations corresponding to the generalized ANNNI model. We satisfy the Kolmogorov consistency condition. We propose a rigorous measure-theoretical approach to investigate the Gibbs measures with a memory of length 2 for the model. We explain if the number of branches of the tree does not change the number of Gibbs measures. Also, we try to determine when the phase transition does occur.

Sulfur mustard gas adsorption on ZnO fullerene-like nanocage: Quantum chemical calculations

NASA Astrophysics Data System (ADS)

Kazemi, Mohammad; Rad, Ali Shokuhi

2017-06-01

In the present study, we used density functional theory calculations (at B3LYP and ωB97XD Levels) to search on the adsorption of Sulfur mustard gas (defined as mustard gas) on the surface of fullerene-like ZnO nanocage as a semiconductor. We found three different configurations of adsorbed gas on the surface of this nanostructure semiconductor. The values of adsorption energy of mustard gas are calculated in the range of -144∼ -200 kJ/mol with enthalpies in the range of -132∼-195 kJ/mol and Gibbs free energies in the range of -88∼-144 kJ/mol (T = 298 K, based on ωB97XD level), which indicate exothermic and spontaneous chemisorption. For all geometries, we calculated geometry parameters by taking into account the charge analysis and frontier molecular orbital study. The result of this study can be a support for next studies to develop new nanomaterials as adsorbent/sensor for mustard gas.

Calculation of phase diagrams for the FeCl2, PbCl2, and ZnCl2 binary systems by using molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Seo, Won-Gap; Matsuura, Hiroyuki; Tsukihashi, Fumitaka

2006-04-01

Recently, molecular dynamics (MD) simulation has been widely employed as a very useful method for the calculation of various physicochemical properties in the molten slags and fluxes. In this study, MD simulation has been applied to calculate the structural, transport, and thermodynamic properties for the FeCl2, PbCl2, and ZnCl2 systems using the Born—Mayer—Huggins type pairwise potential with partial ionic charges. The interatomic potential parameters were determined by fitting the physicochemical properties of iron chloride, lead chloride, and zinc chloride systems with experimentally measured results. The calculated structural, transport, and thermodynamic properties of pure FeCl2, PbCl2, and ZnCl2 showed the same tendency with observed results. Especially, the calculated structural properties of molten ZnCl2 and FeCl2 show the possibility of formation of polymeric network structures based on the ionic complexes of ZnCl{4/2-}, ZnCl{3/-}, FeCl{4/2-}, and FeCl{3/-}, and these calculations have successfully reproduced the measured results. The enthalpy, entropy, and Gibbs energy of mixing for the PbCl2-ZnCl2, FeCl2-PbCl2, and FeCl2-ZnCl2 systems were calculated based on the thermodynamic and structural parameters of each binary system obtained from MD simulation. The phase diagrams of the PbCl2-ZnCl2, FeCl2-PbCl2, and FeCl2-ZnCl2 systems estimated by using the calculated Gibbs energy of mixing reproduced the experimentally measured ones reasonably well.

Chemical potential of carbon in the system UPuCON: Measurements and calculation

NASA Astrophysics Data System (ADS)

Anthonysamy, S.; Ananthasivan, K.; Kahappan, I.; Chandramouli, V.; Vasudeva Rao, P. R.; Mathews, C. K.; Jacob, K. T.

1995-05-01

The carbon potential of (U,Pu) mixed carbides with Pu/(U + Pu) ratios of 0.55 and 0.70 was measured in the temperature range 973 to 1173 K by employing a methane-hydrogen gas equilibration technique. The technique was validated by measuring the Gibbs energy of formation of WC. The compatibility of the mixed carbides with the stainless steel clad was analysed by using the measured carbon potentials. The carbon potentials of mixed carbides of other compositions were calculated theoretically in order to assess their compatibility. The calculations assume ideal solution behavior for all the solid solutions present in the UPuCON system.

TEA: A CODE CALCULATING THERMOCHEMICAL EQUILIBRIUM ABUNDANCES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Blecic, Jasmina; Harrington, Joseph; Bowman, M. Oliver, E-mail: jasmina@physics.ucf.edu

2016-07-01

We present an open-source Thermochemical Equilibrium Abundances (TEA) code that calculates the abundances of gaseous molecular species. The code is based on the methodology of White et al. and Eriksson. It applies Gibbs free-energy minimization using an iterative, Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature–pressure pairs. We tested the code against the method of Burrows and Sharp, the free thermochemical equilibrium code Chemical Equilibrium with Applications (CEA), and the example given by Burrows and Sharp. Using their thermodynamic data, TEA reproduces their final abundances, but withmore » higher precision. We also applied the TEA abundance calculations to models of several hot-Jupiter exoplanets, producing expected results. TEA is written in Python in a modular format. There is a start guide, a user manual, and a code document in addition to this theory paper. TEA is available under a reproducible-research, open-source license via https://github.com/dzesmin/TEA.« less

Bayesian Estimation of the DINA Model with Gibbs Sampling

ERIC Educational Resources Information Center

Culpepper, Steven Andrew

2015-01-01

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

Guidelines for the analysis of free energy calculations.

PubMed

Klimovich, Pavel V; Shirts, Michael R; Mobley, David L

2015-05-01

Free energy calculations based on molecular dynamics simulations show considerable promise for applications ranging from drug discovery to prediction of physical properties and structure-function studies. But these calculations are still difficult and tedious to analyze, and best practices for analysis are not well defined or propagated. Essentially, each group analyzing these calculations needs to decide how to conduct the analysis and, usually, develop its own analysis tools. Here, we review and recommend best practices for analysis yielding reliable free energies from molecular simulations. Additionally, we provide a Python tool, alchemical-analysis.py, freely available on GitHub as part of the pymbar package (located at http://github.com/choderalab/pymbar), that implements the analysis practices reviewed here for several reference simulation packages, which can be adapted to handle data from other packages. Both this review and the tool covers analysis of alchemical calculations generally, including free energy estimates via both thermodynamic integration and free energy perturbation-based estimators. Our Python tool also handles output from multiple types of free energy calculations, including expanded ensemble and Hamiltonian replica exchange, as well as standard fixed ensemble calculations. We also survey a range of statistical and graphical ways of assessing the quality of the data and free energy estimates, and provide prototypes of these in our tool. We hope this tool and discussion will serve as a foundation for more standardization of and agreement on best practices for analysis of free energy calculations.

Guidelines for the analysis of free energy calculations

PubMed Central

Klimovich, Pavel V.; Shirts, Michael R.; Mobley, David L.

2015-01-01

Free energy calculations based on molecular dynamics (MD) simulations show considerable promise for applications ranging from drug discovery to prediction of physical properties and structure-function studies. But these calculations are still difficult and tedious to analyze, and best practices for analysis are not well defined or propagated. Essentially, each group analyzing these calculations needs to decide how to conduct the analysis and, usually, develop its own analysis tools. Here, we review and recommend best practices for analysis yielding reliable free energies from molecular simulations. Additionally, we provide a Python tool, alchemical–analysis.py, freely available on GitHub at https://github.com/choderalab/pymbar–examples, that implements the analysis practices reviewed here for several reference simulation packages, which can be adapted to handle data from other packages. Both this review and the tool covers analysis of alchemical calculations generally, including free energy estimates via both thermodynamic integration and free energy perturbation-based estimators. Our Python tool also handles output from multiple types of free energy calculations, including expanded ensemble and Hamiltonian replica exchange, as well as standard fixed ensemble calculations. We also survey a range of statistical and graphical ways of assessing the quality of the data and free energy estimates, and provide prototypes of these in our tool. We hope these tools and discussion will serve as a foundation for more standardization of and agreement on best practices for analysis of free energy calculations. PMID:25808134

Simultaneous alignment and clustering of peptide data using a Gibbs sampling approach.

PubMed

Andreatta, Massimo; Lund, Ole; Nielsen, Morten

2013-01-01

Proteins recognizing short peptide fragments play a central role in cellular signaling. As a result of high-throughput technologies, peptide-binding protein specificities can be studied using large peptide libraries at dramatically lower cost and time. Interpretation of such large peptide datasets, however, is a complex task, especially when the data contain multiple receptor binding motifs, and/or the motifs are found at different locations within distinct peptides. The algorithm presented in this article, based on Gibbs sampling, identifies multiple specificities in peptide data by performing two essential tasks simultaneously: alignment and clustering of peptide data. We apply the method to de-convolute binding motifs in a panel of peptide datasets with different degrees of complexity spanning from the simplest case of pre-aligned fixed-length peptides to cases of unaligned peptide datasets of variable length. Example applications described in this article include mixtures of binders to different MHC class I and class II alleles, distinct classes of ligands for SH3 domains and sub-specificities of the HLA-A*02:01 molecule. The Gibbs clustering method is available online as a web server at http://www.cbs.dtu.dk/services/GibbsCluster.

Bond-Energy and Surface-Energy Calculations in Metals

ERIC Educational Resources Information Center

Eberhart, James G.; Horner, Steve

2010-01-01

A simple technique appropriate for introductory materials science courses is outlined for the calculation of bond energies in metals from lattice energies. The approach is applied to body-centered cubic (bcc), face-centered cubic (fcc), and hexagonal-closest-packed (hcp) metals. The strength of these bonds is tabulated for a variety metals and is…

New active asteroid 313P/Gibbs

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jewitt, David; Hui, Man-To; Li, Jing

We present initial observations of the newly discovered active asteroid 313P/Gibbs (formerly P/2014 S4), taken to characterize its nucleus and comet-like activity. The central object has a radius ∼0.5 km (geometric albedo 0.05 assumed). We find no evidence for secondary nuclei and set (with qualifications) an upper limit to the radii of such objects near 20 m, assuming the same albedo. Both aperture photometry and a morphological analysis of the ejected dust show that mass-loss is continuous at rates ∼0.2–0.4 kg s{sup −1}, inconsistent with an impact origin. Large dust particles, with radii ∼50–100 μm, dominate the optical appearance. Atmore » 2.4 AU from the Sun, the surface equilibrium temperatures are too low for thermal or desiccation stresses to be responsible for the ejection of dust. No gas is spectroscopically detected (limiting the gas mass-loss rate to <1.8 kg s{sup −1}). However, the protracted emission of dust seen in our data and the detection of another episode of dust release near perihelion, in archival observations from 2003, are highly suggestive of an origin by the sublimation of ice. Coincidentally, the orbit of 313P/Gibbs is similar to those of several active asteroids independently suspected to be ice sublimators, including P/2012 T1, 238P/Read, and 133P/Elst–Pizarro, suggesting that ice is abundant in the outer asteroid belt.« less

GLASS VISCOSITY AS A FUNCTION OF TEMPERATURE AND COMPOSITION: A MODEL BASED ON ADAM-GIBBS EQUATION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hrma, Pavel R.

2008-07-01

Within the temperature range and composition region of processing and product forming, the viscosity of commercial and waste glasses spans over 12 orders of magnitude. This paper shows that a generalized Adam-Gibbs relationship reasonably approximates the real behavior of glasses with four temperature-independent parameters of which two are linear functions of the composition vector. The equation is subjected to two constraints, one requiring that the viscosity-temperature relationship approaches the Arrhenius function at high temperatures with a composition-independent pre-exponential factor and the other that the viscosity value is independent of composition at the glass-transition temperature. Several sets of constant coefficients weremore » obtained by fitting the generalized Adam-Gibbs equation to data of two glass families: float glass and Hanford waste glass. Other equations (the Vogel-Fulcher-Tammann equation, original and modified, the Avramov equation, and the Douglass-Doremus equation) were fitted to float glass data series and compared with the Adam-Gibbs equation, showing that Adam-Gibbs glass appears an excellent approximation of real glasses even as compared with other candidate constitutive relations.« less

Calculating the thermodynamic properties of aqueous solutions of alkali metal carboxylates

NASA Astrophysics Data System (ADS)

Rudakov, A. M.; Sergievskii, V. V.; Zhukova, T. V.

2014-06-01

A modified Robinson-Stokes equation with terms that consider the formation of ionic hydrates and associates is used to describe thermodynamic properties of aqueous solutions of electrolytes. The model is used to describe data on the osmotic coefficients of aqueous solutions of alkali metal carboxylates, and to calculate the mean ionic activity coefficients of salts and excess Gibbs energies. The key contributions from ionic hydration and association to the nonideality of solutions is determined by analyzing the contributions of various factors. Relations that connect the hydration numbers of electrolytes with the parameters of the Pitzer-Mayorga equation and a modified Hückel equation are developed.

Calculating Free Energies Using Average Force

NASA Technical Reports Server (NTRS)

Darve, Eric; Pohorille, Andrew; DeVincenzi, Donald L. (Technical Monitor)

2001-01-01

A new, general formula that connects the derivatives of the free energy along the selected, generalized coordinates of the system with the instantaneous force acting on these coordinates is derived. The instantaneous force is defined as the force acting on the coordinate of interest so that when it is subtracted from the equations of motion the acceleration along this coordinate is zero. The formula applies to simulations in which the selected coordinates are either unconstrained or constrained to fixed values. It is shown that in the latter case the formula reduces to the expression previously derived by den Otter and Briels. If simulations are carried out without constraining the coordinates of interest, the formula leads to a new method for calculating the free energy changes along these coordinates. This method is tested in two examples - rotation around the C-C bond of 1,2-dichloroethane immersed in water and transfer of fluoromethane across the water-hexane interface. The calculated free energies are compared with those obtained by two commonly used methods. One of them relies on determining the probability density function of finding the system at different values of the selected coordinate and the other requires calculating the average force at discrete locations along this coordinate in a series of constrained simulations. The free energies calculated by these three methods are in excellent agreement. The relative advantages of each method are discussed.

Demonstration and resolution of the Gibbs paradox of the first kind

NASA Astrophysics Data System (ADS)

Peters, Hjalmar

2014-01-01

The Gibbs paradox of the first kind (GP1) refers to the false increase in entropy which, in statistical mechanics, is calculated from the process of combining two gas systems S1 and S2 consisting of distinguishable particles. Presented in a somewhat modified form, the GP1 manifests as a contradiction to the second law of thermodynamics. Contrary to popular belief, this contradiction affects not only classical but also quantum statistical mechanics. This paper resolves the GP1 by considering two effects. (i) The uncertainty about which particles are located in S1 and which in S2 contributes to the entropies of S1 and S2. (ii) S1 and S2 are correlated by the fact that if a certain particle is located in one system, it cannot be located in the other. As a consequence, the entropy of the total system consisting of S1 and S2 is not the sum of the entropies of S1 and S2.

Second Order Boltzmann-Gibbs Principle for Polynomial Functions and Applications

NASA Astrophysics Data System (ADS)

Gonçalves, Patrícia; Jara, Milton; Simon, Marielle

2017-01-01

In this paper we give a new proof of the second order Boltzmann-Gibbs principle introduced in Gonçalves and Jara (Arch Ration Mech Anal 212(2):597-644, 2014). The proof does not impose the knowledge on the spectral gap inequality for the underlying model and it relies on a proper decomposition of the antisymmetric part of the current of the system in terms of polynomial functions. In addition, we fully derive the convergence of the equilibrium fluctuations towards (1) a trivial process in case of super-diffusive systems, (2) an Ornstein-Uhlenbeck process or the unique energy solution of the stochastic Burgers equation, as defined in Gubinelli and Jara (SPDEs Anal Comput (1):325-350, 2013) and Gubinelli and Perkowski (Arxiv:1508.07764, 2015), in case of weakly asymmetric diffusive systems. Examples and applications are presented for weakly and partial asymmetric exclusion processes, weakly asymmetric speed change exclusion processes and hamiltonian systems with exponential interactions.

Estimating a Noncompensatory IRT Model Using Metropolis within Gibbs Sampling

ERIC Educational Resources Information Center

Babcock, Ben

2011-01-01

Relatively little research has been conducted with the noncompensatory class of multidimensional item response theory (MIRT) models. A Monte Carlo simulation study was conducted exploring the estimation of a two-parameter noncompensatory item response theory (IRT) model. The estimation method used was a Metropolis-Hastings within Gibbs algorithm…

PHASEGO: A toolkit for automatic calculation and plot of phase diagram

NASA Astrophysics Data System (ADS)

Liu, Zhong-Li

2015-06-01

The PHASEGO package extracts the Helmholtz free energy from the phonon density of states obtained by the first-principles calculations. With the help of equation of states fitting, it reduces the Gibbs free energy as a function of pressure/temperature at fixed temperature/pressure. Based on the quasi-harmonic approximation (QHA), it calculates the possible phase boundaries among all the structures of interest and finally plots the phase diagram automatically. For the single phase analysis, PHASEGO can numerically derive many properties, such as the thermal expansion coefficients, the bulk moduli, the heat capacities, the thermal pressures, the Hugoniot pressure-volume-temperature relations, the Grüneisen parameters, and the Debye temperatures. In order to check its ability of phase transition analysis, I present here two examples: semiconductor GaN and metallic Fe. In the case of GaN, PHASEGO automatically determined and plotted the phase boundaries among the provided zinc blende (ZB), wurtzite (WZ) and rocksalt (RS) structures. In the case of Fe, the results indicate that at high temperature the electronic thermal excitation free energy corrections considerably alter the phase boundaries among the body-centered cubic (bcc), face-centered cubic (fcc) and hexagonal close-packed (hcp) structures.

Discovery of a young asteroid cluster associated with P/2012 F5 (Gibbs)

NASA Astrophysics Data System (ADS)

Novaković, Bojan; Hsieh, Henry H.; Cellino, Alberto; Micheli, Marco; Pedani, Marco

2014-03-01

We present the results of our search for a dynamical family around the active Asteroid P/2012 F5 (Gibbs). By applying the hierarchical clustering method, we discover an extremely compact 9-body cluster associated with P/2012 F5. The statistical significance of this newly discovered Gibbs cluster is estimated to be >99.9%, strongly suggesting that its members share a common origin. The cluster is located in a dynamically cold region of the outer main-belt at a proper semi-major axis of ∼3.005 AU, and all members are found to be dynamically stable over very long timescales. Backward numerical orbital integrations show that the age of the cluster is only 1.5 ± 0.1 Myr. Taxonomic classifications are unavailable for most of the cluster members, but SDSS spectrophotometry available for two cluster members indicate that both appear to be Q-type objects. We also estimate a lower limit of the size of the parent body to be about 10 km, and find that the impact event which produced the Gibbs cluster is intermediate between a cratering and a catastrophic collision. In addition, we search for new main-belt comets in the region of the Gibbs cluster by observing seven asteroids either belonging to the cluster, or being very close in the space of orbital proper elements. However, we do not detect any convincing evidence of the presence of a tail or coma in any our targets. Finally, we obtain optical images of P/2012 F5, and find absolute R-band and V-band magnitudes of HR = 17.0 ± 0.1 mag and HV = 17.4 ± 0.1 mag, respectively, corresponding to an upper limit on the diameter of the P/2012 F5 nucleus of ∼2 km.

Microbial Communities Model Parameter Calculation for TSPA/SR

DOE Office of Scientific and Technical Information (OSTI.GOV)

D. Jolley

2001-07-16

This calculation has several purposes. First the calculation reduces the information contained in ''Committed Materials in Repository Drifts'' (BSC 2001a) to useable parameters required as input to MING V1.O (CRWMS M&O 1998, CSCI 30018 V1.O) for calculation of the effects of potential in-drift microbial communities as part of the microbial communities model. The calculation is intended to replace the parameters found in Attachment II of the current In-Drift Microbial Communities Model revision (CRWMS M&O 2000c) with the exception of Section 11-5.3. Second, this calculation provides the information necessary to supercede the following DTN: M09909SPAMING1.003 and replace it with a newmore » qualified dataset (see Table 6.2-1). The purpose of this calculation is to create the revised qualified parameter input for MING that will allow {Delta}G (Gibbs Free Energy) to be corrected for long-term changes to the temperature of the near-field environment. Calculated herein are the quadratic or second order regression relationships that are used in the energy limiting calculations to potential growth of microbial communities in the in-drift geochemical environment. Third, the calculation performs an impact review of a new DTN: M00012MAJIONIS.000 that is intended to replace the currently cited DTN: GS9809083 12322.008 for water chemistry data used in the current ''In-Drift Microbial Communities Model'' revision (CRWMS M&O 2000c). Finally, the calculation updates the material lifetimes reported on Table 32 in section 6.5.2.3 of the ''In-Drift Microbial Communities'' AMR (CRWMS M&O 2000c) based on the inputs reported in BSC (2001a). Changes include adding new specified materials and updating old materials information that has changed.« less

SPERTI Electric Control Building (PER608). Plan, elevations, and details. Gibbs ...

Library of Congress Historic Buildings Survey, Historic Engineering Record, Historic Landscapes Survey

SPERT-I Electric Control Building (PER-608). Plan, elevations, and details. Gibbs and Hill, Inc. 1087-PER-608-S5. Date: August 1956. INEEL index no. 760-0608-00-312-108328 - Idaho National Engineering Laboratory, SPERT-I & Power Burst Facility Area, Scoville, Butte County, ID

Calculation versus measurement of total energy expenditure.

PubMed

van Lanschot, J J; Feenstra, B W; Vermeij, C G; Bruining, H A

1986-11-01

In acutely ill patients both hypo- and hyperalimentation must be avoided by adjusting caloric intake to total energy expenditure (TEE). We determined the discrepancy between basal energy expenditure (BEE) calculated from the basic Harris-Benedict formula and TEE measured by continuous indirect calorimetry in a heterogeneous group of mechanically ventilated surgical patients. We also compared the accuracy of TEE calculated from the corrected Harris-Benedict formula or estimated by intermittent indirect calorimetry to that of TEE measured by continuous indirect calorimetry. The poor correlation between calculated BEE and measured TEE was significantly (p less than .05) improved by a correction factor based on each patient's clinical condition. The mean absolute difference between calculated TEE and measured TEE was 8.9 +/- 9.6 (SD) %. Calculations were significantly (p less than .05) improved by estimating TEE from two 5-min recording periods, which suggests that continuous indirect calorimetry may not always be necessary to guide caloric replacement.

Atomistic calculations of dislocation core energy in aluminium

DOE PAGES

Zhou, X. W.; Sills, R. B.; Ward, D. K.; ...

2017-02-16

A robust molecular dynamics simulation method for calculating dislocation core energies has been developed. This method has unique advantages: it does not require artificial boundary conditions, is applicable for mixed dislocations, and can yield highly converged results regardless of the atomistic system size. Utilizing a high-fidelity bond order potential, we have applied this method in aluminium to calculate the dislocation core energy as a function of the angle β between the dislocation line and Burgers vector. These calculations show that, for the face-centred-cubic aluminium explored, the dislocation core energy follows the same functional dependence on β as the dislocation elasticmore » energy: Ec = A·sin 2β + B·cos 2β, and this dependence is independent of temperature between 100 and 300 K. By further analysing the energetics of an extended dislocation core, we elucidate the relationship between the core energy and radius of a perfect versus extended dislocation. With our methodology, the dislocation core energy can be accurately accounted for in models of plastic deformation.« less

Atomistic calculations of dislocation core energy in aluminium

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhou, X. W.; Sills, R. B.; Ward, D. K.

A robust molecular dynamics simulation method for calculating dislocation core energies has been developed. This method has unique advantages: it does not require artificial boundary conditions, is applicable for mixed dislocations, and can yield highly converged results regardless of the atomistic system size. Utilizing a high-fidelity bond order potential, we have applied this method in aluminium to calculate the dislocation core energy as a function of the angle β between the dislocation line and Burgers vector. These calculations show that, for the face-centred-cubic aluminium explored, the dislocation core energy follows the same functional dependence on β as the dislocation elasticmore » energy: Ec = A·sin 2β + B·cos 2β, and this dependence is independent of temperature between 100 and 300 K. By further analysing the energetics of an extended dislocation core, we elucidate the relationship between the core energy and radius of a perfect versus extended dislocation. With our methodology, the dislocation core energy can be accurately accounted for in models of plastic deformation.« less

18 CFR 11.13 - Energy gains calculations.

Code of Federal Regulations, 2010 CFR

2010-04-01

... 18 Conservation of Power and Water Resources 1 2010-04-01 2010-04-01 false Energy gains calculations. 11.13 Section 11.13 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY COMMISSION, DEPARTMENT OF ENERGY REGULATIONS UNDER THE FEDERAL POWER ACT ANNUAL CHARGES UNDER PART I OF THE...

18 CFR 11.13 - Energy gains calculations.

Code of Federal Regulations, 2012 CFR

2012-04-01

... 18 Conservation of Power and Water Resources 1 2012-04-01 2012-04-01 false Energy gains calculations. 11.13 Section 11.13 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY COMMISSION, DEPARTMENT OF ENERGY REGULATIONS UNDER THE FEDERAL POWER ACT ANNUAL CHARGES UNDER PART I OF THE...

18 CFR 11.13 - Energy gains calculations.

Code of Federal Regulations, 2011 CFR

2011-04-01

... 18 Conservation of Power and Water Resources 1 2011-04-01 2011-04-01 false Energy gains calculations. 11.13 Section 11.13 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY COMMISSION, DEPARTMENT OF ENERGY REGULATIONS UNDER THE FEDERAL POWER ACT ANNUAL CHARGES UNDER PART I OF THE...

18 CFR 11.13 - Energy gains calculations.

Code of Federal Regulations, 2014 CFR

2014-04-01

... 18 Conservation of Power and Water Resources 1 2014-04-01 2014-04-01 false Energy gains calculations. 11.13 Section 11.13 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY COMMISSION, DEPARTMENT OF ENERGY REGULATIONS UNDER THE FEDERAL POWER ACT ANNUAL CHARGES UNDER PART I OF THE...

18 CFR 11.13 - Energy gains calculations.

Code of Federal Regulations, 2013 CFR

2013-04-01

... 18 Conservation of Power and Water Resources 1 2013-04-01 2013-04-01 false Energy gains calculations. 11.13 Section 11.13 Conservation of Power and Water Resources FEDERAL ENERGY REGULATORY COMMISSION, DEPARTMENT OF ENERGY REGULATIONS UNDER THE FEDERAL POWER ACT ANNUAL CHARGES UNDER PART I OF THE...

An introduction to best practices in free energy calculations.

PubMed

Shirts, Michael R; Mobley, David L

2013-01-01

Free energy calculations are extremely useful for investigating small-molecule biophysical properties such as protein-ligand binding affinities and partition coefficients. However, these calculations are also notoriously difficult to implement correctly. In this chapter, we review standard methods for computing free energy via simulation, discussing current best practices and examining potential pitfalls for computational researchers performing them for the first time. We include a variety of examples and tips for how to set up and conduct these calculations, including applications to relative binding affinities and small-molecule solvation free energies.

Combining the AFLOW GIBBS and elastic libraries to efficiently and robustly screen thermomechanical properties of solids

NASA Astrophysics Data System (ADS)

Toher, Cormac; Oses, Corey; Plata, Jose J.; Hicks, David; Rose, Frisco; Levy, Ohad; de Jong, Maarten; Asta, Mark; Fornari, Marco; Buongiorno Nardelli, Marco; Curtarolo, Stefano

2017-06-01

Thorough characterization of the thermomechanical properties of materials requires difficult and time-consuming experiments. This severely limits the availability of data and is one of the main obstacles for the development of effective accelerated materials design strategies. The rapid screening of new potential materials requires highly integrated, sophisticated, and robust computational approaches. We tackled the challenge by developing an automated, integrated workflow with robust error-correction within the AFLOW framework which combines the newly developed "Automatic Elasticity Library" with the previously implemented GIBBS method. The first extracts the mechanical properties from automatic self-consistent stress-strain calculations, while the latter employs those mechanical properties to evaluate the thermodynamics within the Debye model. This new thermoelastic workflow is benchmarked against a set of 74 experimentally characterized systems to pinpoint a robust computational methodology for the evaluation of bulk and shear moduli, Poisson ratios, Debye temperatures, Grüneisen parameters, and thermal conductivities of a wide variety of materials. The effect of different choices of equations of state and exchange-correlation functionals is examined and the optimum combination of properties for the Leibfried-Schlömann prediction of thermal conductivity is identified, leading to improved agreement with experimental results than the GIBBS-only approach. The framework has been applied to the AFLOW.org data repositories to compute the thermoelastic properties of over 3500 unique materials. The results are now available online by using an expanded version of the REST-API described in the Appendix.

Just Another Gibbs Sampler (JAGS): Flexible Software for MCMC Implementation

ERIC Educational Resources Information Center

Depaoli, Sarah; Clifton, James P.; Cobb, Patrice R.

2016-01-01

A review of the software Just Another Gibbs Sampler (JAGS) is provided. We cover aspects related to history and development and the elements a user needs to know to get started with the program, including (a) definition of the data, (b) definition of the model, (c) compilation of the model, and (d) initialization of the model. An example using a…

Grain-boundary free energy in an assembly of elastic disks.

PubMed

Lusk, Mark T; Beale, Paul D

2004-02-01

Grain-boundary free energy is estimated as a function of misoriention for symmetric tilt boundaries in an assembly of nearly hard disks. Fluctuating cell theory is used to accomplish this since the most common techniques for calculating interfacial free energy cannot be applied to such assemblies. The results are analogous to those obtained using a Leonard-Jones potential, but in this case the interfacial energy is dominated by an entropic contribution. Disk assemblies colorized with free and specific volume elucidate differences between these two characteristics of boundary structure. Profiles are also provided of the Helmholtz and Gibbs free energies as a function of distance from the grain boundaries. Low angle grain boundaries are shown to follow the classical relationship between dislocation orientation/spacing and misorientation angle.

Flory Model of Polymer Crystallization, Kauzmann Paradox and Gibbs-DiMarzio Theory of Glass Transition

NASA Astrophysics Data System (ADS)

Corsi, A.; Gujrati, P. D.

2000-03-01

The Flory model of crystallization of polymers is well known and forms the cornerstone of the Gibbs-DiMarzio theory of glass transition. The model has no known exact solution and the original calculation [1] was shown to be incorrect [2]. Still it is interesting to know the order of the phase transition, if it has one. We have studied the thermodynamics of the model in the limit of infinite molecular weight. We have solved it exactly on a recursive lattice with coordination number q=4, relevant for a tetrahedral lattice. Our results show that there is a continuous, i.e. a second-order, transition at which the entropy of the system is continuous. It is finite at all temperatures and approaches 0 as T goes to 0 so that the system is never completely ordered except at T=0. As the temperature is raised above T=0 the system begins to disorder with a degree of disorder that depends on T, which is in accordance with the analysis of Gujrati and Goldstein [2]. Since there is no first order transition there is no Kauzmann paradox. Similarly there is no possible metastable extension in the model which is central to the Gibbs-DiMarzio conjecture for an ideal glass transition. Thus, our solution does not justify their conjecture. [1] P.J. Flory, Proc. R. Soc. London Ser., A234, 60 (1956) [2] P.D. Gujrati, J. Phys. A: Math. Gen., 13, L437 (1980), P.D. Gujrati, M. Goldstein, J. Chem. Phys., 74(4), 2596 (1981)

Quantitative Boltzmann-Gibbs Principles via Orthogonal Polynomial Duality

NASA Astrophysics Data System (ADS)

Ayala, Mario; Carinci, Gioia; Redig, Frank

2018-06-01

We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann-Gibbs principle. In the context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.

Energy levels and life times calculations of Mo XXXI

NASA Astrophysics Data System (ADS)

Wajid, Abdul; Jabeen, S.; Husain, Abid

2018-05-01

Fine-structure energy levels belonging to 2p63s2, 2p63s3p, 2p63p2 and 2p63p3d for Mo XXXI have been calculated using the multi-configuration Dirac-Fock method including Quantum electrodynamics (QED) corrections. Most of our calculations of energy levels show good agreement with experimental data available on NIST. Lifetimes for excited levels have also been calculated.

Energy deposition calculated by PHITS code in Pb spallation target

NASA Astrophysics Data System (ADS)

Yu, Quanzhi

2016-01-01

Energy deposition in a Pb spallation target irradiated by high energetic protons was calculated by PHITS2.52 code. The validation of the energy deposition and neutron production calculated by PHITS code was performed. Results show good agreements between the simulation results and the experimental data. Detailed comparison shows that for the total energy deposition, PHITS simulation result was about 15% overestimation than that of the experimental data. For the energy deposition along the length of the Pb target, the discrepancy mainly presented at the front part of the Pb target. Calculation indicates that most of the energy deposition comes from the ionizations of the primary protons and the produced secondary particles. With the event generator mode of PHITS, the deposit energy distribution for the particles and the light nulclei is presented for the first time. It indicates that the primary protons with energy more than 100 MeV are the most contributors to the total energy deposition. The energy depositions peaking at 10 MeV and 0.1 MeV, are mainly caused by the electrons, pions, d, t, 3He and also α particles during the cascade process and the evaporation process, respectively. The energy deposition density caused by different proton beam profiles are also calculated and compared. Such calculation and analyses are much helpful for better understanding the physical mechanism of energy deposition in the spallation target, and greatly useful for the thermal hydraulic design of the spallation target.

The importance of the photosynthetic Gibbs effect in the elucidation of the Calvin-Benson-Bassham cycle.

PubMed

Ebenhöh, Oliver; Spelberg, Stephanie

2018-02-19

The photosynthetic carbon reduction cycle, or Calvin-Benson-Bassham (CBB) cycle, is now contained in every standard biochemistry textbook. Although the cycle was already proposed in 1954, it is still the subject of intense research, and even the structure of the cycle, i.e. the exact series of reactions, is still under debate. The controversy about the cycle's structure was fuelled by the findings of Gibbs and Kandler in 1956 and 1957, when they observed that radioactive 14 CO 2 was dynamically incorporated in hexoses in a very atypical and asymmetrical way, a phenomenon later termed the 'photosynthetic Gibbs effect'. Now, it is widely accepted that the photosynthetic Gibbs effect is not in contradiction to the reaction scheme proposed by CBB, but the arguments given have been largely qualitative and hand-waving. To fully appreciate the controversy and to understand the difficulties in interpreting the Gibbs effect, it is illustrative to illuminate the history of the discovery of the CBB cycle. We here give an account of central scientific advances and discoveries, which were essential prerequisites for the elucidation of the cycle. Placing the historic discoveries in the context of the modern textbook pathway scheme illustrates the complexity of the cycle and demonstrates why especially dynamic labelling experiments are far from easy to interpret. We conclude by arguing that it requires sound theoretical approaches to resolve conflicting interpretations and to provide consistent quantitative explanations. © 2018 The Author(s).

Improved modification for the density-functional theory calculation of thermodynamic properties for C-H-O composite compounds.

PubMed

Liu, Min Hsien; Chen, Cheng; Hong, Yaw Shun

2005-02-08

A three-parametric modification equation and the least-squares approach are adopted to calibrating hybrid density-functional theory energies of C(1)-C(10) straight-chain aldehydes, alcohols, and alkoxides to accurate enthalpies of formation DeltaH(f) and Gibbs free energies of formation DeltaG(f), respectively. All calculated energies of the C-H-O composite compounds were obtained based on B3LYP6-311++G(3df,2pd) single-point energies and the related thermal corrections of B3LYP6-31G(d,p) optimized geometries. This investigation revealed that all compounds had 0.05% average absolute relative error (ARE) for the atomization energies, with mean value of absolute error (MAE) of just 2.1 kJ/mol (0.5 kcal/mol) for the DeltaH(f) and 2.4 kJ/mol (0.6 kcal/mol) for the DeltaG(f) of formation.

Light Pipe Energy Savings Calculator

NASA Astrophysics Data System (ADS)

Owens, Erin; Behringer, Ernest R.

2009-04-01

Dependence on fossil fuels is unsustainable and therefore a shift to renewable energy sources such as sunlight is required. Light pipes provide a way to utilize sunlight for interior lighting, and can reduce the need for fossil fuel-generated electrical energy. Because consumers considering light pipe installation may be more strongly motivated by cost considerations than by sustainability arguments, an easy means to examine the corresponding costs and benefits is needed to facilitate informed decision-making. The purpose of this American Physical Society Physics and Society Fellowship project is to create a Web-based calculator to allow users to quantify the possible cost savings for their specific light pipe application. Initial calculations show that the illumination provided by light pipes can replace electric light use during the day, and in many cases can supply greater illumination levels than those typically given by electric lighting. While the installation cost of a light pipe is significantly greater than the avoided cost of electricity over the lifetime of the light pipe at current prices, savings may be realized if electricity prices increase.

Stress versus temperature dependence of activation energies for creep

NASA Technical Reports Server (NTRS)

Freed, A. D.; Raj, S. V.; Walker, K. P.

1992-01-01

The activation energy for creep at low stresses and elevated temperatures is associated with lattice diffusion, where the rate controlling mechanism for deformation is dislocation climb. At higher stresses and intermediate temperatures, the rate controlling mechanism changes from dislocation climb to obstacle-controlled dislocation glide. Along with this change in deformation mechanism occurs a change in the activation energy. When the rate controlling mechanism for deformation is obstacle-controlled dislocation glide, it is shown that a temperature-dependent Gibbs free energy does better than a stress-dependent Gibbs free energy in correlating steady-state creep data for both copper and LiF-22mol percent CaF2 hypereutectic salt.

Generalized Gibbs ensembles for quantum field theories

NASA Astrophysics Data System (ADS)

Essler, F. H. L.; Mussardo, G.; Panfil, M.

2015-05-01

We consider the nonequilibrium dynamics in quantum field theories (QFTs). After being prepared in a density matrix that is not an eigenstate of the Hamiltonian, such systems are expected to relax locally to a stationary state. In the presence of local conservation laws, these stationary states are believed to be described by appropriate generalized Gibbs ensembles. Here we demonstrate that in order to obtain a correct description of the stationary state, it is necessary to take into account conservation laws that are not (ultra)local in the usual sense of QFTs, but fulfill a significantly weaker form of locality. We discuss the implications of our results for integrable QFTs in one spatial dimension.

Stress versus temperature dependent activation energies in creep

NASA Technical Reports Server (NTRS)

Freed, A. D.; Raj, S. V.; Walker, K. P.

1990-01-01

The activation energy for creep at low stresses and elevated temperatures is lattice diffusion, where the rate controlling mechanism for deformation is dislocation climb. At higher stresses and intermediate temperatures, the rate controlling mechanism changes from that of dislocation climb to one of obstacle-controlled dislocation glide. Along with this change, there occurs a change in the activation energy. It is shown that a temperature-dependent Gibbs free energy does a good job of correlating steady-state creep data, while a stress-dependent Gibbs free energy does a less desirable job of correlating the same data. Applications are made to copper and a LiF-22 mol. percent CaF2 hypereutectic salt.

On the dispute between Boltzmann and Gibbs entropy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Buonsante, Pierfrancesco; Franzosi, Roberto, E-mail: roberto.franzosi@ino.it; Smerzi, Augusto

2016-12-15

The validity of the concept of negative temperature has been recently challenged by arguing that the Boltzmann entropy (that allows negative temperatures) is inconsistent from a mathematical and statistical point of view, whereas the Gibbs entropy (that does not admit negative temperatures) provides the correct definition for the microcanonical entropy. Here we prove that the Boltzmann entropy is thermodynamically and mathematically consistent. Analytical results on two systems supporting negative temperatures illustrate the scenario we propose. In addition we numerically study a lattice system to show that negative temperature equilibrium states are accessible and obey standard statistical mechanics prediction.

Recipes for free energy calculations in biomolecular systems.

PubMed

Moradi, Mahmoud; Babin, Volodymyr; Sagui, Celeste; Roland, Christopher

2013-01-01

During the last decade, several methods for sampling phase space and calculating various free energies in biomolecular systems have been devised or refined for molecular dynamics (MD) simulations. Thus, state-of-the-art methodology and the ever increasing computer power allow calculations that were forbidden a decade ago. These calculations, however, are not trivial as they require knowledge of the methods, insight into the system under study, and, quite often, an artful combination of different methodologies in order to avoid the various traps inherent in an unknown free energy landscape. In this chapter, we illustrate some of these concepts with two relatively simple systems, a sugar ring and proline oligopeptides, whose free energy landscapes still offer considerable challenges. In order to explore the configurational space of these systems, and to surmount the various free energy barriers, we combine three complementary methods: a nonequilibrium umbrella sampling method (adaptively biased MD, or ABMD), replica-exchange molecular dynamics (REMD), and steered molecular dynamics (SMD). In particular, ABMD is used to compute the free energy surface of a set of collective variables; REMD is used to improve the performance of ABMD, to carry out sampling in space complementary to the collective variables, and to sample equilibrium configurations directly; and SMD is used to study different transition mechanisms.

A Python tool to set up relative free energy calculations in GROMACS

PubMed Central

Klimovich, Pavel V.; Mobley, David L.

2015-01-01

Free energy calculations based on molecular dynamics (MD) simulations have seen a tremendous growth in the last decade. However, it is still difficult and tedious to set them up in an automated manner, as the majority of the present-day MD simulation packages lack that functionality. Relative free energy calculations are a particular challenge for several reasons, including the problem of finding a common substructure and mapping the transformation to be applied. Here we present a tool, alchemical-setup.py, that automatically generates all the input files needed to perform relative solvation and binding free energy calculations with the MD package GROMACS. When combined with Lead Optimization Mapper [14], recently developed in our group, alchemical-setup.py allows fully automated setup of relative free energy calculations in GROMACS. Taking a graph of the planned calculations and a mapping, both computed by LOMAP, our tool generates the topology and coordinate files needed to perform relative free energy calculations for a given set of molecules, and provides a set of simulation input parameters. The tool was validated by performing relative hydration free energy calculations for a handful of molecules from the SAMPL4 challenge [16]. Good agreement with previously published results and the straightforward way in which free energy calculations can be conducted make alchemical-setup.py a promising tool for automated setup of relative solvation and binding free energy calculations. PMID:26487189

Gibbs paradox of entropy of mixing experimental facts. Its rejection, and the theoretical consequences

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Shu-Kun

1996-12-31

Gibbs paradox statement of entropy of mixing has been regarded as the theoretical foundation of statistical mechanics, quantum theory and biophysics. However, all the relevant chemical experimental observations and logical analyses indicate that the Gibbs paradox statement is false. I prove that this statement is wrong: Gibbs paradox statement implies that entropy decreases with the increase in symmetry (as represented by a symmetry number {sigma}; see any statistical mechanics textbook). From group theory any system has at least a symmetry number {sigma}=1 which is the identity operation for a strictly asymmetric system. It follows that the entropy of a systemmore » is equal to, or less than, zero. However, from either von Neumann-Shannon entropy formula (S(w) =-{Sigma}{sup {omega}} in p{sub 1}) or the Boltzmann entropy formula (S = in w) and the original definition, entropy is non-negative. Therefore, this statement is false. It should not be a surprise that for the first time, many outstanding problems such as the validity of Pauling`s resonance theory, the explanation of second order phase transition phenomena, the biophysical problem of protein folding and the related hydrophobic effect, etc., can be solved. Empirical principles such as Pauli principle (and Hund`s rule) and HSAB principle, etc., can also be given a theoretical explanation.« less

Theoretical study of γ-aminobutyric acid conformers: Intramolecular interactions and ionization energies

NASA Astrophysics Data System (ADS)

Wang, Ke-Dong; Wang, Mei-Ting; Meng, Ju

2014-10-01

Allowing for all combinations of internal single-bond rotamers, 1,296 unique trial structures of γ-Aminobutyric acid (GABA) are obtained. All of these structures are optimized at the M06-2X level of theory and a total of 68 local minimal conformers are found. The nine low-lying conformers are used for further studies. According to the calculated relative Gibbs free energies at M06-2X level of theory, we find that the dispersion is important for the relative energy of GABA. The intramolecular hydrogen bonds and hyperconjugative interaction and their effects on the conformational stability are studied. The results show that both of them have great influence on the conformers. The vertical ionization energies (VIE) are calculated and match the experimental data well. The results show that the neutral GABA in the gas phase is a multi-conformer system and at least four conformations exist.

A Method to Calculate the Surface Tension of a Cylindrical Droplet

ERIC Educational Resources Information Center

Wang, Xiaosong; Zhu, Ruzeng

2010-01-01

The history of Laplace's equations for spherical and cylindrical droplets and the concept of dividing surface in Gibbs' thermodynamic theory of capillary phenomena are briefly reviewed. The existing theories of surface tensions of cylindrical droplets are briefly reviewed too. For cylindrical droplets, a new method to calculate the radius and the…

PDB ligand conformational energies calculated quantum-mechanically.

PubMed

Sitzmann, Markus; Weidlich, Iwona E; Filippov, Igor V; Liao, Chenzhong; Peach, Megan L; Ihlenfeldt, Wolf-Dietrich; Karki, Rajeshri G; Borodina, Yulia V; Cachau, Raul E; Nicklaus, Marc C

2012-03-26

We present here a greatly updated version of an earlier study on the conformational energies of protein-ligand complexes in the Protein Data Bank (PDB) [Nicklaus et al. Bioorg. Med. Chem. 1995, 3, 411-428], with the goal of improving on all possible aspects such as number and selection of ligand instances, energy calculations performed, and additional analyses conducted. Starting from about 357,000 ligand instances deposited in the 2008 version of the Ligand Expo database of the experimental 3D coordinates of all small-molecule instances in the PDB, we created a "high-quality" subset of ligand instances by various filtering steps including application of crystallographic quality criteria and structural unambiguousness. Submission of 640 Gaussian 03 jobs yielded a set of about 415 successfully concluded runs. We used a stepwise optimization of internal degrees of freedom at the DFT level of theory with the B3LYP/6-31G(d) basis set and a single-point energy calculation at B3LYP/6-311++G(3df,2p) after each round of (partial) optimization to separate energy changes due to bond length stretches vs bond angle changes vs torsion changes. Even for the most "conservative" choice of all the possible conformational energies-the energy difference between the conformation in which all internal degrees of freedom except torsions have been optimized and the fully optimized conformer-significant energy values were found. The range of 0 to ~25 kcal/mol was populated quite evenly and independently of the crystallographic resolution. A smaller number of "outliers" of yet higher energies were seen only at resolutions above 1.3 Å. The energies showed some correlation with molecular size and flexibility but not with crystallographic quality metrics such as the Cruickshank diffraction-component precision index (DPI) and R(free)-R, or with the ligand instance-specific metrics such as occupancy-weighted B-factor (OWAB), real-space R factor (RSR), and real-space correlation coefficient

Experimental Pragmatics and What Is Said: A Response to Gibbs and Moise.

ERIC Educational Resources Information Center

Nicolle, Steve; Clark, Billy

1999-01-01

Attempted replication of Gibbs and Moise (1997) experiments regarding the recognition of a distinction between what is said and what is implicated. Results showed that, under certain conditions, subject selected implicatures when asked to select the paraphrase best reflecting what a speaker has said. Suggests that results can be explained with the…

Free energies of binding from large-scale first-principles quantum mechanical calculations: application to ligand hydration energies.

PubMed

Fox, Stephen J; Pittock, Chris; Tautermann, Christofer S; Fox, Thomas; Christ, Clara; Malcolm, N O J; Essex, Jonathan W; Skylaris, Chris-Kriton

2013-08-15

Schemes of increasing sophistication for obtaining free energies of binding have been developed over the years, where configurational sampling is used to include the all-important entropic contributions to the free energies. However, the quality of the results will also depend on the accuracy with which the intermolecular interactions are computed at each molecular configuration. In this context, the energy change associated with the rearrangement of electrons (electronic polarization and charge transfer) upon binding is a very important effect. Classical molecular mechanics force fields do not take this effect into account explicitly, and polarizable force fields and semiempirical quantum or hybrid quantum-classical (QM/MM) calculations are increasingly employed (at higher computational cost) to compute intermolecular interactions in free-energy schemes. In this work, we investigate the use of large-scale quantum mechanical calculations from first-principles as a way of fully taking into account electronic effects in free-energy calculations. We employ a one-step free-energy perturbation (FEP) scheme from a molecular mechanical (MM) potential to a quantum mechanical (QM) potential as a correction to thermodynamic integration calculations within the MM potential. We use this approach to calculate relative free energies of hydration of small aromatic molecules. Our quantum calculations are performed on multiple configurations from classical molecular dynamics simulations. The quantum energy of each configuration is obtained from density functional theory calculations with a near-complete psinc basis set on over 600 atoms using the ONETEP program.

S -matrix calculations of energy levels of sodiumlike ions

DOE PAGES

Sapirstein, J.; Cheng, K. T.

2015-06-24

A recent S -matrix-based QED calculation of energy levels of the lithium isoelectronic sequence is extended to the general case of a valence electron outside an arbitrary filled core. Emphasis is placed on modifications of the lithiumlike formulas required because more than one core state is present, and an unusual feature of the two-photon exchange contribution involving autoionizing states is discussed. Here, the method is illustrated with a calculation of the energy levels of sodiumlike ions, with results for 3s 1/2, 3p 1/2, and 3p 3/2 energies tabulated for the range Z = 30 – 100 . Comparison with experimentmore » and other calculations is given, and prospects for extension of the method to ions with more complex electronic structure discussed.« less

Calculating Potential Energy Curves with Quantum Monte Carlo

NASA Astrophysics Data System (ADS)

Powell, Andrew D.; Dawes, Richard

2014-06-01

Quantum Monte Carlo (QMC) is a computational technique that can be applied to the electronic Schrödinger equation for molecules. QMC methods such as Variational Monte Carlo (VMC) and Diffusion Monte Carlo (DMC) have demonstrated the capability of capturing large fractions of the correlation energy, thus suggesting their possible use for high-accuracy quantum chemistry calculations. QMC methods scale particularly well with respect to parallelization making them an attractive consideration in anticipation of next-generation computing architectures which will involve massive parallelization with millions of cores. Due to the statistical nature of the approach, in contrast to standard quantum chemistry methods, uncertainties (error-bars) are associated with each calculated energy. This study focuses on the cost, feasibility and practical application of calculating potential energy curves for small molecules with QMC methods. Trial wave functions were constructed with the multi-configurational self-consistent field (MCSCF) method from GAMESS-US.[1] The CASINO Monte Carlo quantum chemistry package [2] was used for all of the DMC calculations. An overview of our progress in this direction will be given. References: M. W. Schmidt et al. J. Comput. Chem. 14, 1347 (1993). R. J. Needs et al. J. Phys.: Condensed Matter 22, 023201 (2010).

A Python tool to set up relative free energy calculations in GROMACS.

PubMed

Klimovich, Pavel V; Mobley, David L

2015-11-01

Free energy calculations based on molecular dynamics (MD) simulations have seen a tremendous growth in the last decade. However, it is still difficult and tedious to set them up in an automated manner, as the majority of the present-day MD simulation packages lack that functionality. Relative free energy calculations are a particular challenge for several reasons, including the problem of finding a common substructure and mapping the transformation to be applied. Here we present a tool, alchemical-setup.py, that automatically generates all the input files needed to perform relative solvation and binding free energy calculations with the MD package GROMACS. When combined with Lead Optimization Mapper (LOMAP; Liu et al. in J Comput Aided Mol Des 27(9):755-770, 2013), recently developed in our group, alchemical-setup.py allows fully automated setup of relative free energy calculations in GROMACS. Taking a graph of the planned calculations and a mapping, both computed by LOMAP, our tool generates the topology and coordinate files needed to perform relative free energy calculations for a given set of molecules, and provides a set of simulation input parameters. The tool was validated by performing relative hydration free energy calculations for a handful of molecules from the SAMPL4 challenge (Mobley et al. in J Comput Aided Mol Des 28(4):135-150, 2014). Good agreement with previously published results and the straightforward way in which free energy calculations can be conducted make alchemical-setup.py a promising tool for automated setup of relative solvation and binding free energy calculations.

Quantitative Characterization of Spurious Gibbs Waves in 45 CMIP5 Models

NASA Astrophysics Data System (ADS)

Geil, K. L.; Zeng, X.

2014-12-01

Gibbs oscillations appear in global climate models when representing fields, such as orography, that contain discontinuities or sharp gradients. It has been known for decades that the oscillations are associated with the transformation of the truncated spectral representation of a field to physical space and that the oscillations can also be present in global models that do not use spectral methods. The spurious oscillations are potentially detrimental to model simulations (e.g., over ocean) and this work provides a quantitative characterization of the Gibbs oscillations that appear across the Coupled Model Intercomparison Project Phase 5 (CMIP5) models. An ocean transect running through the South Pacific High toward the Andes is used to characterize the oscillations in ten different variables. These oscillations are found to be stationary and hence are not caused by (physical) waves in the atmosphere. We quantify the oscillation amplitude using the root mean square difference (RMSD) between the transect of a variable and its running mean (rather than the constant mean across the transect). We also compute the RMSD to interannual variability (IAV) ratio, which provides a relative measure of the oscillation amplitude. Of the variables examined, the largest RMSD values exist in the surface pressure field of spectral models, while the smallest RMSD values within the surface pressure field come from models that use finite difference (FD) techniques. Many spectral models have a surface pressure RMSD that is 2 to 15 times greater than IAV over the transect and an RMSD:IAV ratio greater than one for many other variables including surface temperature, incoming shortwave radiation at the surface, incoming longwave radiation at the surface, and total cloud fraction. In general, the FD models out-perform the spectral models, but not all the spectral models have large amplitude oscillations and there are a few FD models where the oscillations do appear. Finally, we present a

Investigation of oxygen self-diffusion in PuO 2 by combining molecular dynamics with thermodynamic calculations

DOE PAGES

Saltas, V.; Chroneos, A.; Cooper, Michael William D.; ...

2016-01-01

In the present work, the defect properties of oxygen self-diffusion in PuO 2 are investigated over a wide temperature (300–1900 K) and pressure (0–10 GPa) range, by combining molecular dynamics simulations and thermodynamic calculations. Based on the well-established cBΩ thermodynamic model which connects the activation Gibbs free energy of diffusion with the bulk elastic and expansion properties, various point defect parameters such as activation enthalpy, activation entropy, and activation volume were calculated as a function of T and P. Molecular dynamics calculations provided the necessary bulk properties for the proper implementation of the thermodynamic model, in the lack of anymore » relevant experimental data. The estimated compressibility and the thermal expansion coefficient of activation volume are found to be more than one order of magnitude greater than the corresponding values of the bulk plutonia. As a result, the diffusion mechanism is discussed in the context of the temperature and pressure dependence of the activation volume.« less

Simple calculation of ab initio melting curves: Application to aluminum.

PubMed

Robert, Grégory; Legrand, Philippe; Arnault, Philippe; Desbiens, Nicolas; Clérouin, Jean

2015-03-01

We present a simple, fast, and promising method to compute the melting curves of materials with ab initio molecular dynamics. It is based on the two-phase thermodynamic model of Lin et al [J. Chem. Phys. 119, 11792 (2003)] and its improved version given by Desjarlais [Phys. Rev. E 88, 062145 (2013)]. In this model, the velocity autocorrelation function is utilized to calculate the contribution of the nuclei motion to the entropy of the solid and liquid phases. It is then possible to find the thermodynamic conditions of equal Gibbs free energy between these phases, defining the melting curve. The first benchmark on the face-centered cubic melting curve of aluminum from 0 to 300 GPa demonstrates how to obtain an accuracy of 5%-10%, comparable to the most sophisticated methods, for a much lower computational cost.

Lead optimization mapper: automating free energy calculations for lead optimization.

PubMed

Liu, Shuai; Wu, Yujie; Lin, Teng; Abel, Robert; Redmann, Jonathan P; Summa, Christopher M; Jaber, Vivian R; Lim, Nathan M; Mobley, David L

2013-09-01

Alchemical free energy calculations hold increasing promise as an aid to drug discovery efforts. However, applications of these techniques in discovery projects have been relatively few, partly because of the difficulty of planning and setting up calculations. Here, we introduce lead optimization mapper, LOMAP, an automated algorithm to plan efficient relative free energy calculations between potential ligands within a substantial library of perhaps hundreds of compounds. In this approach, ligands are first grouped by structural similarity primarily based on the size of a (loosely defined) maximal common substructure, and then calculations are planned within and between sets of structurally related compounds. An emphasis is placed on ensuring that relative free energies can be obtained between any pair of compounds without combining the results of too many different relative free energy calculations (to avoid accumulation of error) and by providing some redundancy to allow for the possibility of error and consistency checking and provide some insight into when results can be expected to be unreliable. The algorithm is discussed in detail and a Python implementation, based on both Schrödinger's and OpenEye's APIs, has been made available freely under the BSD license.

Free energy calculations of glycosaminoglycan-protein interactions.

PubMed

Gandhi, Neha S; Mancera, Ricardo L

2009-10-01

Glycosaminoglycans (GAGs) are complex highly charged linear polysaccharides that have a variety of roles in biological processes. We report the first use of molecular dynamics (MD) free energy calculations using the MM/PBSA method to investigate the binding of GAGs to protein molecules, namely the platelet endothelial cell adhesion molecule 1 (PECAM-1) and annexin A2. Calculations of the free energy of the binding of heparin fragments of different sizes reveal the existence of a region of low GAG-binding affinity in domains 5-6 of PECAM-1 and a region of high affinity in domains 2-3, consistent with experimental data and ligand-protein docking studies. A conformational hinge movement between domains 2 and 3 was observed, which allows the binding of heparin fragments of increasing size (pentasaccharides to octasaccharides) with an increasingly higher binding affinity. Similar simulations of the binding of a heparin fragment to annexin A2 reveal the optimization of electrostatic and hydrogen bonding interactions with the protein and protein-bound calcium ions. In general, these free energy calculations reveal that the binding of heparin to protein surfaces is dominated by strong electrostatic interactions for longer fragments, with equally important contributions from van der Waals interactions and vibrational entropy changes, against a large unfavorable desolvation penalty due to the high charge density of these molecules.

Comparison of Boltzmann and Gibbs entropies for the analysis of single-chain phase transitions

NASA Astrophysics Data System (ADS)

Shakirov, T.; Zablotskiy, S.; Böker, A.; Ivanov, V.; Paul, W.

2017-03-01

In the last 10 years, flat histogram Monte Carlo simulations have contributed strongly to our understanding of the phase behavior of simple generic models of polymers. These simulations result in an estimate for the density of states of a model system. To connect this result with thermodynamics, one has to relate the density of states to the microcanonical entropy. In a series of publications, Dunkel, Hilbert and Hänggi argued that it would lead to a more consistent thermodynamic description of small systems, when one uses the Gibbs definition of entropy instead of the Boltzmann one. The latter is the logarithm of the density of states at a certain energy, the former is the logarithm of the integral of the density of states over all energies smaller than or equal to this energy. We will compare the predictions using these two definitions for two polymer models, a coarse-grained model of a flexible-semiflexible multiblock copolymer and a coarse-grained model of the protein poly-alanine. Additionally, it is important to note that while Monte Carlo techniques are normally concerned with the configurational energy only, the microcanonical ensemble is defined for the complete energy. We will show how taking the kinetic energy into account alters the predictions from the analysis. Finally, the microcanonical ensemble is supposed to represent a closed mechanical N-particle system. But due to Galilei invariance such a system has two additional conservation laws, in general: momentum and angular momentum. We will also show, how taking these conservation laws into account alters the results.

Using the fast fourier transform in binding free energy calculations.

PubMed

Nguyen, Trung Hai; Zhou, Huan-Xiang; Minh, David D L

2018-04-30

According to implicit ligand theory, the standard binding free energy is an exponential average of the binding potential of mean force (BPMF), an exponential average of the interaction energy between the unbound ligand ensemble and a rigid receptor. Here, we use the fast Fourier transform (FFT) to efficiently evaluate BPMFs by calculating interaction energies when rigid ligand configurations from the unbound ensemble are discretely translated across rigid receptor conformations. Results for standard binding free energies between T4 lysozyme and 141 small organic molecules are in good agreement with previous alchemical calculations based on (1) a flexible complex ( R≈0.9 for 24 systems) and (2) flexible ligand with multiple rigid receptor configurations ( R≈0.8 for 141 systems). While the FFT is routinely used for molecular docking, to our knowledge this is the first time that the algorithm has been used for rigorous binding free energy calculations. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Scalable free energy calculation of proteins via multiscale essential sampling

NASA Astrophysics Data System (ADS)

Moritsugu, Kei; Terada, Tohru; Kidera, Akinori

2010-12-01

A multiscale simulation method, "multiscale essential sampling (MSES)," is proposed for calculating free energy surface of proteins in a sizable dimensional space with good scalability. In MSES, the configurational sampling of a full-dimensional model is enhanced by coupling with the accelerated dynamics of the essential degrees of freedom. Applying the Hamiltonian exchange method to MSES can remove the biasing potential from the coupling term, deriving the free energy surface of the essential degrees of freedom. The form of the coupling term ensures good scalability in the Hamiltonian exchange. As a test application, the free energy surface of the folding process of a miniprotein, chignolin, was calculated in the continuum solvent model. Results agreed with the free energy surface derived from the multicanonical simulation. Significantly improved scalability with the MSES method was clearly shown in the free energy calculation of chignolin in explicit solvent, which was achieved without increasing the number of replicas in the Hamiltonian exchange.

Lipophilicity Assessment of Ruthenium(II)-Arene Complexes by the Means of Reversed-Phase Thin-Layer Chromatography and DFT Calculations

PubMed Central

Shweshein, Khalil Salem A. M.; Andrić, Filip; Radoičić, Aleksandra; Gruden-Pavlović, Maja; Tešić, Živoslav; Milojković-Opsenica, Dušanka

2014-01-01

The lipophilicity of ten ruthenium(II)-arene complexes was assessed by reversed-phase thin-layer chromatography (RP-TLC) on octadecyl silica stationary phase. The binary solvent systems composed of water and acetonitrile were used as mobile phase in order to determine chromatographic descriptors for lipophilicity estimation. Octanol-water partition coefficient, logK OW, of tested complexes was experimentally determined using twenty-eight standard solutes which were analyzed under the same chromatographic conditions as target substances. In addition, ab initio density functional theory (DFT) computational approach was employed to calculate logK OW values from the differences in Gibbs' free solvation energies of the solute transfer from n-octanol to water. A good overall agreement between DFT calculated and experimentally determined logK OW values was established (R 2 = 0.8024–0.9658). PMID:24587761

Biochemical thermodynamics: applications of Mathematica.

PubMed

Alberty, Robert A

2006-01-01

The most efficient way to store thermodynamic data on enzyme-catalyzed reactions is to use matrices of species properties. Since equilibrium in enzyme-catalyzed reactions is reached at specified pH values, the thermodynamics of the reactions is discussed in terms of transformed thermodynamic properties. These transformed thermodynamic properties are complicated functions of temperature, pH, and ionic strength that can be calculated from the matrices of species values. The most important of these transformed thermodynamic properties is the standard transformed Gibbs energy of formation of a reactant (sum of species). It is the most important because when this function of temperature, pH, and ionic strength is known, all the other standard transformed properties can be calculated by taking partial derivatives. The species database in this package contains data matrices for 199 reactants. For 94 of these reactants, standard enthalpies of formation of species are known, and so standard transformed Gibbs energies, standard transformed enthalpies, standard transformed entropies, and average numbers of hydrogen atoms can be calculated as functions of temperature, pH, and ionic strength. For reactions between these 94 reactants, the changes in these properties can be calculated over a range of temperatures, pHs, and ionic strengths, and so can apparent equilibrium constants. For the other 105 reactants, only standard transformed Gibbs energies of formation and average numbers of hydrogen atoms at 298.15 K can be calculated. The loading of this package provides functions of pH and ionic strength at 298.15 K for standard transformed Gibbs energies of formation and average numbers of hydrogen atoms for 199 reactants. It also provides functions of temperature, pH, and ionic strength for the standard transformed Gibbs energies of formation, standard transformed enthalpies of formation, standard transformed entropies of formation, and average numbers of hydrogen atoms for 94

On-line Gibbs learning. II. Application to perceptron and multilayer networks

NASA Astrophysics Data System (ADS)

Kim, J. W.; Sompolinsky, H.

1998-08-01

In the preceding paper (``On-line Gibbs Learning. I. General Theory'') we have presented the on-line Gibbs algorithm (OLGA) and studied analytically its asymptotic convergence. In this paper we apply OLGA to on-line supervised learning in several network architectures: a single-layer perceptron, two-layer committee machine, and a winner-takes-all (WTA) classifier. The behavior of OLGA for a single-layer perceptron is studied both analytically and numerically for a variety of rules: a realizable perceptron rule, a perceptron rule corrupted by output and input noise, and a rule generated by a committee machine. The two-layer committee machine is studied numerically for the cases of learning a realizable rule as well as a rule that is corrupted by output noise. The WTA network is studied numerically for the case of a realizable rule. The asymptotic results reported in this paper agree with the predictions of the general theory of OLGA presented in paper I. In all the studied cases, OLGA converges to a set of weights that minimizes the generalization error. When the learning rate is chosen as a power law with an optimal power, OLGA converges with a power law that is the same as that of batch learning.

Polarizable atomistic calculation of site energy disorder in amorphous Alq3.

PubMed

Nagata, Yuki

2010-02-01

A polarizable molecular dynamics simulation and calculation scheme for site energy disorder is presented in amorphous tris(8-hydroxyquinolinato)aluminum (Alq(3)) by means of the charge response kernel (CRK) method. The CRK fit to the electrostatic potential and the tight-binding approximation are introduced, which enables modeling of the polarizable electrostatic interaction for a large molecule systematically from an ab initio calculation. The site energy disorder for electron and hole transfers is calculated in amorphous Alq(3) and the effect of the polarization on the site energy disorder is discussed.

Performance calculation and simulation system of high energy laser weapon

NASA Astrophysics Data System (ADS)

Wang, Pei; Liu, Min; Su, Yu; Zhang, Ke

2014-12-01

High energy laser weapons are ready for some of today's most challenging military applications. Based on the analysis of the main tactical/technical index and combating process of high energy laser weapon, a performance calculation and simulation system of high energy laser weapon was established. Firstly, the index decomposition and workflow of high energy laser weapon was proposed. The entire system was composed of six parts, including classical target, platform of laser weapon, detect sensor, tracking and pointing control, laser atmosphere propagation and damage assessment module. Then, the index calculation modules were designed. Finally, anti-missile interception simulation was performed. The system can provide reference and basis for the analysis and evaluation of high energy laser weapon efficiency.

Continuous-energy eigenvalue sensitivity coefficient calculations in TSUNAMI-3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perfetti, C. M.; Rearden, B. T.

2013-07-01

Two methods for calculating eigenvalue sensitivity coefficients in continuous-energy Monte Carlo applications were implemented in the KENO code within the SCALE code package. The methods were used to calculate sensitivity coefficients for several test problems and produced sensitivity coefficients that agreed well with both reference sensitivities and multigroup TSUNAMI-3D sensitivity coefficients. The newly developed CLUTCH method was observed to produce sensitivity coefficients with high figures of merit and a low memory footprint, and both continuous-energy sensitivity methods met or exceeded the accuracy of the multigroup TSUNAMI-3D calculations. (authors)

Helmholtz and Gibbs ensembles, thermodynamic limit and bistability in polymer lattice models

NASA Astrophysics Data System (ADS)

Giordano, Stefano

2017-12-01

Representing polymers by random walks on a lattice is a fruitful approach largely exploited to study configurational statistics of polymer chains and to develop efficient Monte Carlo algorithms. Nevertheless, the stretching and the folding/unfolding of polymer chains within the Gibbs (isotensional) and the Helmholtz (isometric) ensembles of the statistical mechanics have not been yet thoroughly analysed by means of the lattice methodology. This topic, motivated by the recent introduction of several single-molecule force spectroscopy techniques, is investigated in the present paper. In particular, we analyse the force-extension curves under the Gibbs and Helmholtz conditions and we give a proof of the ensembles equivalence in the thermodynamic limit for polymers represented by a standard random walk on a lattice. Then, we generalize these concepts for lattice polymers that can undergo conformational transitions or, equivalently, for chains composed of bistable or two-state elements (that can be either folded or unfolded). In this case, the isotensional condition leads to a plateau-like force-extension response, whereas the isometric condition causes a sawtooth-like force-extension curve, as predicted by numerous experiments. The equivalence of the ensembles is finally proved also for lattice polymer systems exhibiting conformational transitions.

Center for the Built Environment: Setpoint Energy Savings Calculator

Science.gov Websites

. Arens, and H. Zhang, 2014. Extending air temperature setpoints: Simulated energy savings and design Near-ZNE Buildings Setpoint Energy Savings Calculator UFAD Case Studies UFAD Cooling Design Tool UFAD Cost Analysis UFAD Design Guide UFAD East End UFAD Energy Modeling UFAD Plenum Performance UFAD

Dissolution kinetics as a function of the Gibbs free energy of reaction: An experimental study based on albite feldspar

NASA Astrophysics Data System (ADS)

Hellmann, Roland; Tisserand, Delphine

2006-01-01

Here we report on an experimental investigation of the relation between the dissolution rate of albite feldspar and the Gibbs free energy of reaction, Δ Gr. The experiments were carried out in a continuously stirred flow-through reactor at 150 °C and pH (150 °C) 9.2. The dissolution rates R are based on steady-state Si and Al concentrations and sample mass loss. The overall relation between Δ Gr and R was determined over a free energy range of -150 < Δ Gr < -15.6 kJ mol -1. The data define a continuous and highly non-linear, sigmoidal relation between R and Δ Gr that is characterized by three distinct free energy regions. The region furthest from equilibrium, delimited by -150 < Δ Gr < -70 kJ mol -1, represents an extensive dissolution rate plateau with an average rate R¯=1.0×10-8molm-2s-1. In this free energy range the rates of dissolution are constant and independent of Δ Gr, as well as [Si] and [Al]. The free energy range delimited by -70 ⩽ Δ Gr ⩽ -25 kJ mol -1, referred to as the 'transition equilibrium' region, is characterized by a sharp decrease in dissolution rates with increasing Δ Gr, indicating a very strong inverse dependence of the rates on free energy. Dissolution nearest equilibrium, defined by Δ Gr > -25 kJ mol -1, represents the 'near equilibrium' region where the rates decrease as chemical equilibrium is approached, but with a much weaker dependence on Δ Gr. The lowest rate measured in this study, R = 6.2 × 10 -11 mol m -2 s -1 at Δ Gr = -16.3 kJ mol -1, is more than two orders of magnitude slower than the plateau rate. The data have been fitted to a rate equation (adapted from Burch et al. [Burch, T. E., Nagy, K. L., Lasaga, A. C., 1993. Free energy dependence of albite dissolution kinetics at 80 °C and pH 8.8. Chem. Geol.105, 137-162]) that represents the sum of two parallel reactions R=k1[1-exp(-ng)]+k2[1-exp(-g)], where k1 and k2 are rate constants that have been determined by regression, with values 1.02 × 10 -8 and 1

Thermodynamic Study of the Nickel Addition in Zinc Hot-Dip Galvanizing Baths

NASA Astrophysics Data System (ADS)

Pistofidis, N.; Vourlias, G.

2010-01-01

A usual practice during zinc hot-dip galvanizing is the addition of nickel in the liquid zinc which is used to inhibit the Sandelin effect. Its action is due to the fact that the ζ (zeta) phase of the Fe-Zn system is replaced by the Τ (tau) phase of the Fe-Zn-Ni system. In the present work an attempt is made to explain the formation of the Τ phase with thermodynamics. For this reason the Gibbs free energy changes for Τ and ζ phases were calculated. The excess free energy for the system was calculated with the Redlich-Kister polyonyme. From this calculation it was deduced that the Gibbs energy change for the tau phase is negative. As a result its formation is spontaneous.

Reactive transport simulation via combination of a multiphase-capable transport code for unstructured meshes with a Gibbs energy minimization solver of geochemical equilibria

NASA Astrophysics Data System (ADS)

Fowler, S. J.; Driesner, T.; Hingerl, F. F.; Kulik, D. A.; Wagner, T.

2011-12-01

We apply a new, C++-based computational model for hydrothermal fluid-rock interaction and scale formation in geothermal reservoirs. The model couples the Complex System Modelling Platform (CSMP++) code for fluid flow in porous and fractured media (Matthai et al., 2007) with the Gibbs energy minimization numerical kernel GEMS3K of the GEM-Selektor (GEMS3) geochemical modelling package (Kulik et al., 2010) in a modular fashion. CSMP++ includes interfaces to commercial file formats, accommodating complex geometry construction using CAD (Rhinoceros) and meshing (ANSYS) software. The CSMP++ approach employs finite element-finite volume spatial discretization, implicit or explicit time discretization, and operator splitting. GEMS3K can calculate complex fluid-mineral equilibria based on a variety of equation of state and activity models. A selection of multi-electrolyte aqueous solution models, such as extended Debye-Huckel, Pitzer (Harvie et al., 1984), EUNIQUAC (Thomsen et al., 1996), and the new ELVIS model (Hingerl et al., this conference), makes it well-suited for application to a wide range of geothermal conditions. An advantage of the GEMS3K solver is simultaneous consideration of complex solid solutions (e.g., clay minerals), gases, fluids, and aqueous solutions. Each coupled simulation results in a thermodynamically-based description of the geochemical and physical state of a hydrothermal system evolving along a complex P-T-X path. The code design allows efficient, flexible incorporation of numerical and thermodynamic database improvements. We demonstrate the coupled code workflow and applicability to compositionally and physically complex natural systems relevant to enhanced geothermal systems, where temporally and spatially varying chemical interactions may take place within diverse lithologies of varying geometry. Engesgaard, P. & Kipp, K. L. (1992). Water Res. Res. 28: 2829-2843. Harvie, C. E.; Møller, N. & Weare, J. H. (1984). Geochim. Cosmochim. Acta 48

Advancing Drug Discovery through Enhanced Free Energy Calculations.

PubMed

Abel, Robert; Wang, Lingle; Harder, Edward D; Berne, B J; Friesner, Richard A

2017-07-18

A principal goal of drug discovery project is to design molecules that can tightly and selectively bind to the target protein receptor. Accurate prediction of protein-ligand binding free energies is therefore of central importance in computational chemistry and computer aided drug design. Multiple recent improvements in computing power, classical force field accuracy, enhanced sampling methods, and simulation setup have enabled accurate and reliable calculations of protein-ligands binding free energies, and position free energy calculations to play a guiding role in small molecule drug discovery. In this Account, we outline the relevant methodological advances, including the REST2 (Replica Exchange with Solute Temperting) enhanced sampling, the incorporation of REST2 sampling with convential FEP (Free Energy Perturbation) through FEP/REST, the OPLS3 force field, and the advanced simulation setup that constitute our FEP+ approach, followed by the presentation of extensive comparisons with experiment, demonstrating sufficient accuracy in potency prediction (better than 1 kcal/mol) to substantially impact lead optimization campaigns. The limitations of the current FEP+ implementation and best practices in drug discovery applications are also discussed followed by the future methodology development plans to address those limitations. We then report results from a recent drug discovery project, in which several thousand FEP+ calculations were successfully deployed to simultaneously optimize potency, selectivity, and solubility, illustrating the power of the approach to solve challenging drug design problems. The capabilities of free energy calculations to accurately predict potency and selectivity have led to the advance of ongoing drug discovery projects, in challenging situations where alternative approaches would have great difficulties. The ability to effectively carry out projects evaluating tens of thousands, or hundreds of thousands, of proposed drug candidates

Structural, electronic, and thermodynamic properties of curium dioxide: Density functional theory calculations

NASA Astrophysics Data System (ADS)

Hou, Ling; Li, Wei-Dong; Wang, Fangwei; Eriksson, Olle; Wang, Bao-Tian

2017-12-01

We present a systematic investigation of the structural, magnetic, electronic, mechanical, and thermodynamic properties of CmO2 with the local density approximation (LDA)+U and the generalized gradient approximation (GGA)+U approaches. The strong Coulomb repulsion and the spin-orbit coupling (SOC) effects on the lattice structures, electronic density of states, and band gaps are carefully studied, and compared with other A O2 (A =U , Np, Pu, and Am). The ferromagnetic configuration with half-metallic character is predicted to be energetically stable while a charge-transfer semiconductor is predicted for the antiferromagnetic configuration. The elastic constants and phonon spectra show that the fluorite structure is mechanically and dynamically stable. Based on the first-principles phonon density of states, the lattice vibrational energy is calculated using the quasiharmonic approximation. Then, the Gibbs free energy, thermal expansion coefficient, specific heat, and entropy are obtained and compared with experimental data. The mode Grüneisen parameters are presented to analyze the anharmonic properties. The Slack relation is applied to obtain the lattice thermal conductivity in temperature range of 300-1600 K. The phonon group velocities are also calculated to investigate the heat transfer. For all these properties, if available, we compare the results of CmO2 with other A O2 .

Density-functional theory computer simulations of CZTS0.25Se0.75 alloy phase diagrams

NASA Astrophysics Data System (ADS)

Chagarov, E.; Sardashti, K.; Haight, R.; Mitzi, D. B.; Kummel, A. C.

2016-08-01

Density-functional theory simulations of CZTS, CZTSe, and CZTS0.25Se0.75 photovoltaic compounds have been performed to investigate the stability of the CZTS0.25Se0.75 alloy vs. decomposition into CZTS, CZTSe, and other secondary compounds. The Gibbs energy for vibrational contributions was estimated by calculating phonon spectra and thermodynamic properties at finite temperatures. It was demonstrated that the CZTS0.25Se0.75 alloy is stabilized not by enthalpy of formation but primarily by the mixing contributions to the Gibbs energy. The Gibbs energy gains/losses for several decomposition reactions were calculated as a function of temperature with/without intermixing and vibration contributions to the Gibbs energy. A set of phase diagrams was built in the multidimensional space of chemical potentials at 300 K and 900 K temperatures to demonstrate alloy stability and boundary compounds at various chemical conditions. It demonstrated for CZTS0.25Se0.75 that the chemical potentials for stability differ between typical processing temperature (˜900 K) and operating temperature (300 K). This implies that as cooling progresses, the flux/concentration of S should be increased in MBE growth to maintain the CZTS0.25Se0.75 in a thermodynamically stable state to minimize phase decomposition.

Thermodynamic properties for bunsenite, NiO, magnetite, Fe3O4, and hematite, Fe2O3, with comments on selected oxygen buffer reactions

USGS Publications Warehouse

Hemingway, B.S.

1990-01-01

Smoothed values of the heat capacities and derived thermodynamic functions are given for bunsenite, magnetite, and hematite for the temperature interval 298.15 to 1800 K. The Gibbs free energy for the reaction Ni + 0.5O2 = NiO is given by the equation ??rG0T = -238.39 + 0.1146T - 3.72 ?? 10-3T ln T and is valid from 298.15 K to 1700 K. The Gibbs free energy (in kJ) of the reaction 2 magnetite + 3 quartz = 3 fayalite + O2 may be calculated from the equation ??rG0T = 474.155 - 0.16120 T in kJ and between 800 and 1400 K. The Gibbs free energy (in kJ) of the reaction 6 hematite = 4 magnetite + O2 may be calculated from the following equations: ??rG0T = 496.215 - 0.27114T, ??rG0T = 514.690 - 0.29753T, ??rG0T = 501.348 - 0.2854T. -from Author

Surfactant Adsorption: A Revised Physical Chemistry Lab

ERIC Educational Resources Information Center

Bresler, Marc R.; Hagen, John P.

2008-01-01

Many physical chemistry lab courses include an experiment in which students measure surface tension as a function of surfactant concentration. In the traditional experiment, the data are fit to the Gibbs isotherm to determine the molar area for the surfactant, and the critical micelle concentration is used to calculate the Gibbs energy of micelle…

Alchemical Free Energy Calculations for Nucleotide Mutations in Protein-DNA Complexes.

PubMed

Gapsys, Vytautas; de Groot, Bert L

2017-12-12

Nucleotide-sequence-dependent interactions between proteins and DNA are responsible for a wide range of gene regulatory functions. Accurate and generalizable methods to evaluate the strength of protein-DNA binding have long been sought. While numerous computational approaches have been developed, most of them require fitting parameters to experimental data to a certain degree, e.g., machine learning algorithms or knowledge-based statistical potentials. Molecular-dynamics-based free energy calculations offer a robust, system-independent, first-principles-based method to calculate free energy differences upon nucleotide mutation. We present an automated procedure to set up alchemical MD-based calculations to evaluate free energy changes occurring as the result of a nucleotide mutation in DNA. We used these methods to perform a large-scale mutation scan comprising 397 nucleotide mutation cases in 16 protein-DNA complexes. The obtained prediction accuracy reaches 5.6 kJ/mol average unsigned deviation from experiment with a correlation coefficient of 0.57 with respect to the experimentally measured free energies. Overall, the first-principles-based approach performed on par with the molecular modeling approaches Rosetta and FoldX. Subsequently, we utilized the MD-based free energy calculations to construct protein-DNA binding profiles for the zinc finger protein Zif268. The calculation results compare remarkably well with the experimentally determined binding profiles. The software automating the structure and topology setup for alchemical calculations is a part of the pmx package; the utilities have also been made available online at http://pmx.mpibpc.mpg.de/dna_webserver.html .

CALCULATION OF GAMMA SPECTRA IN A PLASTIC SCINTILLATOR FOR ENERGY CALIBRATIONAND DOSE COMPUTATION.

PubMed

Kim, Chankyu; Yoo, Hyunjun; Kim, Yewon; Moon, Myungkook; Kim, Jong Yul; Kang, Dong Uk; Lee, Daehee; Kim, Myung Soo; Cho, Minsik; Lee, Eunjoong; Cho, Gyuseong

2016-09-01

Plastic scintillation detectors have practical advantages in the field of dosimetry. Energy calibration of measured gamma spectra is important for dose computation, but it is not simple in the plastic scintillators because of their different characteristics and a finite resolution. In this study, the gamma spectra in a polystyrene scintillator were calculated for the energy calibration and dose computation. Based on the relationship between the energy resolution and estimated energy broadening effect in the calculated spectra, the gamma spectra were simply calculated without many iterations. The calculated spectra were in agreement with the calculation by an existing method and measurements. © The Author 2016. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Low-temperature heat capacity and entropy of chalcopyrite (CuFeS2): estimates of the standard molar enthalpy and Gibbs free energy of formation of chalcopyrite and bornite (Cu5FeS4)

USGS Publications Warehouse

Robie, R.A.; Wiggins, L.B.; Barton, P.B.; Hemingway, B.S.

1985-01-01

The heat capacity of CuFeS2 (chalcopyrite) was measured between 6.3 and 303.5 K. At 298.15 K, Cp,mo and Smo(T) are (95.67??0.14) J??K-1??mol-1 and (124.9??0.2) J??K-1??mol-1, respectively. From a consideration of the results of two sets of equilibrium measurements we conclude that ??fHmo(CuFeS2, cr, 298.15 K) = -(193.6??1.6) kJ??mol-1 and that the recent bomb-calorimetric determination by Johnson and Steele (J. Chem. Thermodynamics 1981, 13, 991) is in error. The standard molar Gibbs free energy of formation of bornite (Cu5FeS4) is -(444.9??2.1) kJ??mol-1 at 748 K. ?? 1985.

Using Bayes' theorem for free energy calculations

NASA Astrophysics Data System (ADS)

Rogers, David M.

Statistical mechanics is fundamentally based on calculating the probabilities of molecular-scale events. Although Bayes' theorem has generally been recognized as providing key guiding principals for setup and analysis of statistical experiments [83], classical frequentist models still predominate in the world of computational experimentation. As a starting point for widespread application of Bayesian methods in statistical mechanics, we investigate the central quantity of free energies from this perspective. This dissertation thus reviews the basics of Bayes' view of probability theory, and the maximum entropy formulation of statistical mechanics before providing examples of its application to several advanced research areas. We first apply Bayes' theorem to a multinomial counting problem in order to determine inner shell and hard sphere solvation free energy components of Quasi-Chemical Theory [140]. We proceed to consider the general problem of free energy calculations from samples of interaction energy distributions. From there, we turn to spline-based estimation of the potential of mean force [142], and empirical modeling of observed dynamics using integrator matching. The results of this research are expected to advance the state of the art in coarse-graining methods, as they allow a systematic connection from high-resolution (atomic) to low-resolution (coarse) structure and dynamics. In total, our work on these problems constitutes a critical starting point for further application of Bayes' theorem in all areas of statistical mechanics. It is hoped that the understanding so gained will allow for improvements in comparisons between theory and experiment.

Non-Equilibrium Properties from Equilibrium Free Energy Calculations

NASA Technical Reports Server (NTRS)

Pohorille, Andrew; Wilson, Michael A.

2012-01-01

Calculating free energy in computer simulations is of central importance in statistical mechanics of condensed media and its applications to chemistry and biology not only because it is the most comprehensive and informative quantity that characterizes the eqUilibrium state, but also because it often provides an efficient route to access dynamic and kinetic properties of a system. Most of applications of equilibrium free energy calculations to non-equilibrium processes rely on a description in which a molecule or an ion diffuses in the potential of mean force. In general case this description is a simplification, but it might be satisfactorily accurate in many instances of practical interest. This hypothesis has been tested in the example of the electrodiffusion equation . Conductance of model ion channels has been calculated directly through counting the number of ion crossing events observed during long molecular dynamics simulations and has been compared with the conductance obtained from solving the generalized Nernst-Plank equation. It has been shown that under relatively modest conditions the agreement between these two approaches is excellent, thus demonstrating the assumptions underlying the diffusion equation are fulfilled. Under these conditions the electrodiffusion equation provides an efficient approach to calculating the full voltage-current dependence routinely measured in electrophysiological experiments.

Zero-point energy constraint in quasi-classical trajectory calculations.

PubMed

Xie, Zhen; Bowman, Joel M

2006-04-27

A method to constrain the zero-point energy in quasi-classical trajectory calculations is proposed and applied to the Henon-Heiles system. The main idea of this method is to smoothly eliminate the coupling terms in the Hamiltonian as the energy of any mode falls below a specified value.

The calculation of band gap energy in zinc oxide films

NASA Astrophysics Data System (ADS)

Arif, Ali; Belahssen, Okba; Gareh, Salim; Benramache, Said

2015-01-01

We investigated the optical properties of undoped zinc oxide thin films as the n-type semiconductor; the thin films were deposited at different precursor molarities by ultrasonic spray and spray pyrolysis techniques. The thin films were deposited at different substrate temperatures ranging between 200 and 500 °C. In this paper, we present a new approach to control the optical gap energy of ZnO thin films by concentration of the ZnO solution and substrate temperatures from experimental data, which were published in international journals. The model proposed to calculate the band gap energy with the Urbach energy was investigated. The relation between the experimental data and theoretical calculation suggests that the band gap energies are predominantly estimated by the Urbach energies, film transparency, and concentration of the ZnO solution and substrate temperatures. The measurements by these proposal models are in qualitative agreements with the experimental data; the correlation coefficient values were varied in the range 0.96-0.99999, indicating high quality representation of data based on Equation (2), so that the relative errors of all calculation are smaller than 4%. Thus, one can suppose that the undoped ZnO thin films are chemically purer and have many fewer defects and less disorder owing to an almost complete chemical decomposition and contained higher optical band gap energy.

Accurate calculation of conformational free energy differences in explicit water: the confinement-solvation free energy approach.

PubMed

Esque, Jeremy; Cecchini, Marco

2015-04-23

The calculation of the free energy of conformation is key to understanding the function of biomolecules and has attracted significant interest in recent years. Here, we present an improvement of the confinement method that was designed for use in the context of explicit solvent MD simulations. The development involves an additional step in which the solvation free energy of the harmonically restrained conformers is accurately determined by multistage free energy perturbation simulations. As a test-case application, the newly introduced confinement/solvation free energy (CSF) approach was used to compute differences in free energy between conformers of the alanine dipeptide in explicit water. The results are in excellent agreement with reference calculations based on both converged molecular dynamics and umbrella sampling. To illustrate the general applicability of the method, conformational equilibria of met-enkephalin (5 aa) and deca-alanine (10 aa) in solution were also analyzed. In both cases, smoothly converged free-energy results were obtained in agreement with equilibrium sampling or literature calculations. These results demonstrate that the CSF method may provide conformational free-energy differences of biomolecules with small statistical errors (below 0.5 kcal/mol) and at a moderate computational cost even with a full representation of the solvent.

Studies on the phase diagram of Pb-Fe-O system and standard molar Gibbs energy of formation of 'PbFe5O8.5' and Pb2Fe2O5

NASA Astrophysics Data System (ADS)

Sahu, Sulata Kumari; Ganesan, Rajesh; Gnanasekaran, T.

2012-07-01

Partial phase diagram of Pb-Fe-O system has been established by phase equilibration studies over a wide temperature range coupled with high temperature solid electrolyte based emf cells. Ternary oxides are found to coexist with liquid lead only at temperatures above 900 K. At temperatures below 900 K, iron oxides coexist with liquid lead. Standard molar Gibbs energy of formation of ternary oxides 'PbFe5O8.5' and Pb2Fe2O5 were determined by measuring equilibrium oxygen partial pressures over relevant phase fields using emf cells and are given by the following expressions: ΔfGmo 'PbFeO'±1.0(kJ mol)=-2208.1+0.6677(T/K) (917⩽T/K⩽1117) ΔfGmo PbFeO±0.8(kJ mol)=-1178.4+0.3724(T/K) (1050⩽T/K⩽1131) .

Progress in calculating the potential energy surface of H3+.

PubMed

Adamowicz, Ludwik; Pavanello, Michele

2012-11-13

The most accurate electronic structure calculations are performed using wave function expansions in terms of basis functions explicitly dependent on the inter-electron distances. In our recent work, we use such basis functions to calculate a highly accurate potential energy surface (PES) for the H(3)(+) ion. The functions are explicitly correlated Gaussians, which include inter-electron distances in the exponent. Key to obtaining the high accuracy in the calculations has been the use of the analytical energy gradient determined with respect to the Gaussian exponential parameters in the minimization of the Rayleigh-Ritz variational energy functional. The effective elimination of linear dependences between the basis functions and the automatic adjustment of the positions of the Gaussian centres to the changing molecular geometry of the system are the keys to the success of the computational procedure. After adiabatic and relativistic corrections are added to the PES and with an effective accounting of the non-adiabatic effects in the calculation of the rotational/vibrational states, the experimental H(3)(+) rovibrational spectrum is reproduced at the 0.1 cm(-1) accuracy level up to 16,600 cm(-1) above the ground state.

Impact of dietary fiber energy on the calculation of food total energy value in the Brazilian Food Composition Database.

PubMed

Menezes, Elizabete Wenzel de; Grande, Fernanda; Giuntini, Eliana Bistriche; Lopes, Tássia do Vale Cardoso; Dan, Milana Cara Tanasov; Prado, Samira Bernardino Ramos do; Franco, Bernadette Dora Gombossy de Melo; Charrondière, U Ruth; Lajolo, Franco Maria

2016-02-15

Dietary fiber (DF) contributes to the energy value of foods and including it in the calculation of total food energy has been recommended for food composition databases. The present study aimed to investigate the impact of including energy provided by the DF fermentation in the calculation of food energy. Total energy values of 1753 foods from the Brazilian Food Composition Database were calculated with or without the inclusion of DF energy. The energy values were compared, through the use of percentage difference (D%), in individual foods and in daily menus. Appreciable energy D% (⩾10) was observed in 321 foods, mainly in the group of vegetables, legumes and fruits. However, in the Brazilian typical menus containing foods from all groups, only D%<3 was observed. In mixed diets, the DF energy may cause slight variations in total energy; on the other hand, there is appreciable energy D% for certain foods, when individually considered. Copyright © 2015 Elsevier Ltd. All rights reserved.

Gibbs-Thomson Law for Singular Step Segments: Thermodynamics Versus Kinetics

NASA Technical Reports Server (NTRS)

Chernov, A. A.

2003-01-01

Classical Burton-Cabrera-Frank theory presumes that thermal fluctuations are so fast that at any time density of kinks on a step is comparable with the reciprocal intermolecular distance, so that the step rate is about isotropic within the crystal plane. Such azimuthal isotropy is, however, often not the case: Kink density may be much lower. In particular, it was recently found on the (010) face of orthorhombic lysozyme that interkink distance may exceed 500-600 intermolecular distances. Under such conditions, Gibbs-Thomson law (GTL) may not be applicable: On a straight step segment between two corners, communication between the comers occurs exclusively by kink exchange. Annihilation between kinks of opposite sign generated at the comers results in the grain in step energy entering GTL. If the step segment length l much greater than D/v, where D and v are the kink diffusivity and propagation rate, respectively, the opposite kinks have practically no chance to annihilate and GTL is not applicable. The opposite condition of the GTL applicability, l much less than D/v, is equivalent to the requirement that relative supersaturation Delta(sub mu)/kT much less than alpha/l, where alpha is molecular size. Thus, GTL may be applied to a segment of 10(exp 3)alpha approx. 3 x 10(exp -5)cm approx 0.3 micron only if supersaturation is less than 0.1%, while practically used driving forces for crystallization are much larger. Relationships alternative to the GTL for different, but low, kink density have been discussed. They confirm experimental evidences that the Burton-Cabrera-Frank theory of spiral growth is growth rates twice as low as compared to the observed figures. Also, application of GTL results in unrealistic step energy while suggested kinetic law give reasonable figures.

Effect of Atomic Charges on Octanol-Water Partition Coefficient Using Alchemical Free Energy Calculation.

PubMed

Ogata, Koji; Hatakeyama, Makoto; Nakamura, Shinichiro

2018-02-15

The octanol-water partition coefficient (log P ow ) is an important index for measuring solubility, membrane permeability, and bioavailability in the drug discovery field. In this paper, the log P ow values of 58 compounds were predicted by alchemical free energy calculation using molecular dynamics simulation. In free energy calculations, the atomic charges of the compounds are always fixed. However, they must be recalculated for each solvent. Therefore, three different sets of atomic charges were tested using quantum chemical calculations, taking into account vacuum, octanol, and water environments. The calculated atomic charges in the different environments do not necessarily influence the correlation between calculated and experimentally measured ∆ G water values. The largest correlation coefficient values of the solvation free energy in water and octanol were 0.93 and 0.90, respectively. On the other hand, the correlation coefficient of log P ow values calculated from free energies, the largest of which was 0.92, was sensitive to the combination of the solvation free energies calculated from the calculated atomic charges. These results reveal that the solvent assumed in the atomic charge calculation is an important factor determining the accuracy of predicted log P ow values.

Efficient free energy calculations of quantum systems through computer simulations

NASA Astrophysics Data System (ADS)

Antonelli, Alex; Ramirez, Rafael; Herrero, Carlos; Hernandez, Eduardo

2009-03-01

In general, the classical limit is assumed in computer simulation calculations of free energy. This approximation, however, is not justifiable for a class of systems in which quantum contributions for the free energy cannot be neglected. The inclusion of quantum effects is important for the determination of reliable phase diagrams of these systems. In this work, we present a new methodology to compute the free energy of many-body quantum systems [1]. This methodology results from the combination of the path integral formulation of statistical mechanics and efficient non-equilibrium methods to estimate free energy, namely, the adiabatic switching and reversible scaling methods. A quantum Einstein crystal is used as a model to show the accuracy and reliability the methodology. This new method is applied to the calculation of solid-liquid coexistence properties of neon. Our findings indicate that quantum contributions to properties such as, melting point, latent heat of fusion, entropy of fusion, and slope of melting line can be up to 10% of the calculated values using the classical approximation. [1] R. M. Ramirez, C. P. Herrero, A. Antonelli, and E. R. Hernández, Journal of Chemical Physics 129, 064110 (2008)

SCALE Continuous-Energy Eigenvalue Sensitivity Coefficient Calculations

DOE PAGES

Perfetti, Christopher M.; Rearden, Bradley T.; Martin, William R.

2016-02-25

Sensitivity coefficients describe the fractional change in a system response that is induced by changes to system parameters and nuclear data. The Tools for Sensitivity and UNcertainty Analysis Methodology Implementation (TSUNAMI) code within the SCALE code system makes use of eigenvalue sensitivity coefficients for an extensive number of criticality safety applications, including quantifying the data-induced uncertainty in the eigenvalue of critical systems, assessing the neutronic similarity between different critical systems, and guiding nuclear data adjustment studies. The need to model geometrically complex systems with improved fidelity and the desire to extend TSUNAMI analysis to advanced applications has motivated the developmentmore » of a methodology for calculating sensitivity coefficients in continuous-energy (CE) Monte Carlo applications. The Contributon-Linked eigenvalue sensitivity/Uncertainty estimation via Tracklength importance CHaracterization (CLUTCH) and Iterated Fission Probability (IFP) eigenvalue sensitivity methods were recently implemented in the CE-KENO framework of the SCALE code system to enable TSUNAMI-3D to perform eigenvalue sensitivity calculations using continuous-energy Monte Carlo methods. This work provides a detailed description of the theory behind the CLUTCH method and describes in detail its implementation. This work explores the improvements in eigenvalue sensitivity coefficient accuracy that can be gained through the use of continuous-energy sensitivity methods and also compares several sensitivity methods in terms of computational efficiency and memory requirements.« less

The Calculation of Accurate Metal-Ligand Bond Energies

NASA Technical Reports Server (NTRS)

Bauschlicher, Charles W.; Partridge, Harry, III; Ricca, Alessandra; Arnold, James O. (Technical Monitor)

1997-01-01

The optimization of the geometry and calculation of zero-point energies are carried out at the B3LYP level of theory. The bond energies are determined at this level, as well as at the CCSD(T) level using very large basis sets. The successive OH bond energies to the first row transition metal cations are reported. For most systems there has been an experimental determination of the first OH. In general, the CCSD(T) values are in good agreement with experiment. The bonding changes from mostly covalent for the early metals to mostly electrostatic for the late transition metal systems.

Correlated natural transition orbital framework for low-scaling excitation energy calculations (CorNFLEx).

PubMed

Baudin, Pablo; Kristensen, Kasper

2017-06-07

We present a new framework for calculating coupled cluster (CC) excitation energies at a reduced computational cost. It relies on correlated natural transition orbitals (NTOs), denoted CIS(D')-NTOs, which are obtained by diagonalizing generalized hole and particle density matrices determined from configuration interaction singles (CIS) information and additional terms that represent correlation effects. A transition-specific reduced orbital space is determined based on the eigenvalues of the CIS(D')-NTOs, and a standard CC excitation energy calculation is then performed in that reduced orbital space. The new method is denoted CorNFLEx (Correlated Natural transition orbital Framework for Low-scaling Excitation energy calculations). We calculate second-order approximate CC singles and doubles (CC2) excitation energies for a test set of organic molecules and demonstrate that CorNFLEx yields excitation energies of CC2 quality at a significantly reduced computational cost, even for relatively small systems and delocalized electronic transitions. In order to illustrate the potential of the method for large molecules, we also apply CorNFLEx to calculate CC2 excitation energies for a series of solvated formamide clusters (up to 4836 basis functions).

Effect of Surface Excess Energy Transport on the Rupture of an Evaporating Film

NASA Astrophysics Data System (ADS)

Luo, Yan; Zhou, Jianqiu; Yang, Xia; Liu, Rong

2018-05-01

In most of existing works on the instabilities of an evaporating film, the energy boundary condition only takes into account contributions of the evaporation latent heat and the heat conduction in the liquid. We use a new generalized energy boundary condition at the evaporating liquid-vapor interface, in which the contribution of the transport of the Gibbs excess energy is included. We have derived the long-wave equations in which the thickness of film and the interfacial temperature are coupled to describe the dynamics of an evaporating thin film. The results of our computation show that the transport of the Gibbs excess internal energy delay the rupture of thin films due to van de Waals force, evaporating effect and vapor recoil.

Modeling Ignition of HMX with the Gibbs Formulation

NASA Astrophysics Data System (ADS)

Lee, Kibaek; Stewart, D. Scott

2017-06-01

We present a HMX model with the Gibbs formulation in which stress tensor and temperature are assumed to be in local equilibrium, but phase/chemical changes are not assumed to be in equilibrium. We assume multi-components for HMX including beta- and delta-phase, liquid, and gas phase of HMX and its gas products. Isotropic small strain solid model, modified Fried Howard liquid EOS, and ideal gas EOS are used for its relevant component. Phase/chemical changes are characterized as reactions and are in individual reaction rate. Maxwell-Stefan model is used for diffusion. Excited gas products in the local domain lead unreacted HMX solid to the ignition event. Density of the mixture, stress, strain, displacement, mass fractions, and temperature are considered in 1D domain with time histories. Office of Naval Research and Air Force Office of Scientific Research.

Ab Initio Prediction of Adsorption Isotherms for Small Molecules in Metal-Organic Frameworks.

PubMed

Kundu, Arpan; Piccini, GiovanniMaria; Sillar, Kaido; Sauer, Joachim

2016-10-26

For CO and N 2 on Mg 2+ sites of the metal-organic framework CPO-27-Mg (Mg-MOF-74), ab initio calculations of Gibbs free energies of adsorption have been performed. Combined with the Bragg-Williams/Langmuir model and taking into account the experimental site availability (76.5%), we obtained adsorption isotherms in close agreement with those in experiment. The remaining deviations in the Gibbs free energy (about 1 kJ/mol) are significantly smaller than the "chemical accuracy" limit of about 4 kJ/mol. The presented approach uses (i) a DFT dispersion method (PBE+D2) to optimize the structure and to calculate anharmonic frequencies for vibrational partition functions and (ii) a "hybrid MP2:(PBE+D2)+ΔCCSD(T)" method to determine electronic energies. With the achieved accuracy (estimated uncertainty ±1.4 kJ/mol), the ab initio energies become useful benchmarks for assessing different DFT + dispersion methods (PBE+D2, B3LYP+D*, and vdW-D2), whereas the ab initio heats, entropies, and Gibbs free energies of adsorption are used to assess the reliability of experimental values derived from fitting isotherms or from variable-temperature IR studies.

Density-functional theory computer simulations of CZTS{sub 0.25}Se{sub 0.75} alloy phase diagrams

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chagarov, E.; Sardashti, K.; Kummel, A. C.

2016-08-14

Density-functional theory simulations of CZTS, CZTSe, and CZTS{sub 0.25}Se{sub 0.75} photovoltaic compounds have been performed to investigate the stability of the CZTS{sub 0.25}Se{sub 0.75} alloy vs. decomposition into CZTS, CZTSe, and other secondary compounds. The Gibbs energy for vibrational contributions was estimated by calculating phonon spectra and thermodynamic properties at finite temperatures. It was demonstrated that the CZTS{sub 0.25}Se{sub 0.75} alloy is stabilized not by enthalpy of formation but primarily by the mixing contributions to the Gibbs energy. The Gibbs energy gains/losses for several decomposition reactions were calculated as a function of temperature with/without intermixing and vibration contributions to themore » Gibbs energy. A set of phase diagrams was built in the multidimensional space of chemical potentials at 300 K and 900 K temperatures to demonstrate alloy stability and boundary compounds at various chemical conditions. It demonstrated for CZTS{sub 0.25}Se{sub 0.75} that the chemical potentials for stability differ between typical processing temperature (∼900 K) and operating temperature (300 K). This implies that as cooling progresses, the flux/concentration of S should be increased in MBE growth to maintain the CZTS{sub 0.25}Se{sub 0.75} in a thermodynamically stable state to minimize phase decomposition.« less

Optimal algorithm to improve the calculation accuracy of energy deposition for betavoltaic MEMS batteries design

NASA Astrophysics Data System (ADS)

Li, Sui-xian; Chen, Haiyang; Sun, Min; Cheng, Zaijun

2009-11-01

Aimed at improving the calculation accuracy when calculating the energy deposition of electrons traveling in solids, a method we call optimal subdivision number searching algorithm is proposed. When treating the energy deposition of electrons traveling in solids, large calculation errors are found, we are conscious of that it is the result of dividing and summing when calculating the integral. Based on the results of former research, we propose a further subdividing and summing method. For β particles with the energy in the entire spectrum span, the energy data is set only to be the integral multiple of keV, and the subdivision number is set to be from 1 to 30, then the energy deposition calculation error collections are obtained. Searching for the minimum error in the collections, we can obtain the corresponding energy and subdivision number pairs, as well as the optimal subdivision number. The method is carried out in four kinds of solid materials, Al, Si, Ni and Au to calculate energy deposition. The result shows that the calculation error is reduced by one order with the improved algorithm.

A new parallel algorithm of MP2 energy calculations.

PubMed

Ishimura, Kazuya; Pulay, Peter; Nagase, Shigeru

2006-03-01

A new parallel algorithm has been developed for second-order Møller-Plesset perturbation theory (MP2) energy calculations. Its main projected applications are for large molecules, for instance, for the calculation of dispersion interaction. Tests on a moderate number of processors (2-16) show that the program has high CPU and parallel efficiency. Timings are presented for two relatively large molecules, taxol (C(47)H(51)NO(14)) and luciferin (C(11)H(8)N(2)O(3)S(2)), the former with the 6-31G* and 6-311G** basis sets (1,032 and 1,484 basis functions, 164 correlated orbitals), and the latter with the aug-cc-pVDZ and aug-cc-pVTZ basis sets (530 and 1,198 basis functions, 46 correlated orbitals). An MP2 energy calculation on C(130)H(10) (1,970 basis functions, 265 correlated orbitals) completed in less than 2 h on 128 processors.

Calculation and Measurement of Low-Energy Radiative Moller Scattering

NASA Astrophysics Data System (ADS)

Epstein, Charles; DarkLight Collaboration

2017-09-01

A number of current nuclear physics experiments have come to rely on precise knowledge of electron-electron (Moller) and positron-electron (Bhabha) scattering. Some of these experiments, having lepton beams on targets containing atomic electrons, use these purely-QED processes as normalization. In other scenarios, with electron beams at low energy and very high intensity, Moller scattering and radiative Moller scattering have such enormous cross-sections that the backgrounds they produce must be understood. In this low-energy regime, the electron mass is also not negligible in the calculation of the cross section. This is important, for example, in the DarkLight experiment (100 MeV). As a result, we have developed a new event generator for the radiative Moller and Bhabha processes, with new calculations that keep all terms of the electron mass. The MIT High Voltage Research Laboratory provides us a unique opportunity to study this process experimentally and compare it with our work, at a low beam energy of 2.5 MeV where the effects of the electron mass are significant. We are preparing a dedicated apparatus consisting of a magnetic spectrometer in order to directly measure this process. An overview of the calculation and the status of the experiment will be presented.

First-principles calculations of the structural, elastic and thermodynamic properties of mackinawite (FeS) and pyrite (FeS2)

NASA Astrophysics Data System (ADS)

Wen, Xiangli; Liang, Yuxuan; Bai, Pengpeng; Luo, Bingwei; Fang, Teng; Yue, Luo; An, Teng; Song, Weiyu; Zheng, Shuqi

2017-11-01

The thermodynamic properties of Fe-S compounds with different crystal structure are very different. In this study, the structural, elastic and thermodynamic properties of mackinawite (FeS) and pyrite (FeS2) were investigated by first-principles calculations. Examination of the electronic density of states shows that mackinawite (FeS) is metallic and that pyrite (FeS2) is a semiconductor with a band gap of Eg = 1.02 eV. Using the stress-strain method, the elastic properties including the bulk modulus and shear modulus were derived from the elastic Cij data. Density functional perturbation theory (DFPT) calculations within the quasi-harmonic approximation (QHA) were used to calculate the thermodynamic properties, and the two Fe-S compounds are found to be dynamically stable. The isothermal bulk modulus, thermal expansion coefficient, heat capacities, Gibbs free energy and entropy of the Fe-S compounds are obtained by first-principles phonon calculations. Furthermore, the temperature of the mackinawite (FeS) ⟶ pyrite (FeS2) phase transition at 0 GPa was predicted. Based on the calculation results, the model for prediction of Fe-S compounds in the Fe-H2S-H2O system was improved.

The calculations of small molecular conformation energy differences by density functional method

NASA Astrophysics Data System (ADS)

Topol, I. A.; Burt, S. K.

1993-03-01

The differences in the conformational energies for the gauche (G) and trans(T) conformers of 1,2-difluoroethane and for myo-and scyllo-conformer of inositol have been calculated by local density functional method (LDF approximation) with geometry optimization using different sets of calculation parameters. It is shown that in the contrast to Hartree—Fock methods, density functional calculations reproduce the correct sign and value of the gauche effect for 1,2-difluoroethane and energy difference for both conformers of inositol. The results of normal vibrational analysis for1,2-difluoroethane showed that harmonic frequencies calculated in LDF approximation agree with experimental data with the accuracy typical for scaled large basis set Hartree—Fock calculations.

Phase Equilibria and Thermodynamic Descriptions of Ag-Ge and Ag-Ge-Ni Systems

NASA Astrophysics Data System (ADS)

Rajkumar, V. B.; Chen, Sinn-Wen

2018-07-01

Gibbs energy modeling of Ag-Ge and Ag-Ge-Ni systems was done using the calculation of the phase diagram method with associated data from this work and relevant literature information. In the Ag-Ge system, the solidus temperatures of Ag-rich alloys are measured using differential thermal analysis, and the energy of mixing for the FCC_A1 phase is calculated using the special quasi-random structures technique. The isothermal sections of the Ag-Ge-Ni system at 1023 K and 673 K are also experimentally determined. These data and findings in the relevant literature are used to model the Gibbs energy of the Ag-Ge and Ag-Ge- Ni systems. A reaction scheme and a liquidus projection of the Ag-Ge-Ni system are determined.

Atomic Radius and Charge Parameter Uncertainty in Biomolecular Solvation Energy Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yang, Xiu; Lei, Huan; Gao, Peiyuan

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a method for quantifying this uncertainty in solvation energies using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many moremore » types of atomic charges; therefore, construction of surrogate models for the charge parameter space required compressed sensing combined with an iterative rotation method to enhance problem sparsity. We present results for the uncertainty in small molecule solvation energies based on these approaches. Additionally, we explore the correlation between uncertainties due to radii and charges which motivates the need for future work in uncertainty quantification methods for high-dimensional parameter spaces.« less

Rigorous Proof of the Boltzmann-Gibbs Distribution of Money on Connected Graphs

NASA Astrophysics Data System (ADS)

Lanchier, Nicolas

2017-04-01

Models in econophysics, i.e., the emerging field of statistical physics that applies the main concepts of traditional physics to economics, typically consist of large systems of economic agents who are characterized by the amount of money they have. In the simplest model, at each time step, one agent gives one dollar to another agent, with both agents being chosen independently and uniformly at random from the system. Numerical simulations of this model suggest that, at least when the number of agents and the average amount of money per agent are large, the distribution of money converges to an exponential distribution reminiscent of the Boltzmann-Gibbs distribution of energy in physics. The main objective of this paper is to give a rigorous proof of this result and show that the convergence to the exponential distribution holds more generally when the economic agents are located on the vertices of a connected graph and interact locally with their neighbors rather than globally with all the other agents. We also study a closely related model where, at each time step, agents buy with a probability proportional to the amount of money they have, and prove that in this case the limiting distribution of money is Poissonian.

Using Density Functional Theory (DFT) for the Calculation of Atomization Energies

NASA Technical Reports Server (NTRS)

Bauschlicher, Charles W., Jr.; Partridge, Harry; Langhoff, Stephen R. (Technical Monitor)

1995-01-01

The calculation of atomization energies using density functional theory (DFT), using the B3LYP hybrid functional, is reported. The sensitivity of the atomization energy to basis set is studied and compared with the coupled cluster singles and doubles approach with a perturbational estimate of the triples (CCSD(T)). Merging the B3LYP results with the G2(MP2) approach is also considered. It is found that replacing the geometry optimization and calculation of the zero-point energy by the analogous quantities computed using the B3LYP approach reduces the maximum error in the G2(MP2) approach. In addition to the 55 G2 atomization energies, some results for transition metal containing systems will also be presented.

Calculations of acceptor ionization energies in GaN

NASA Astrophysics Data System (ADS)

Wang, H.; Chen, A.-B.

2001-03-01

The k.p Hamiltonian and a model potential are used to deduce the acceptor ionization energies in GaN from a systematic study of the chemical trend in GaAs, GaP, and InP. The acceptors studied include Be, Mg, Ca, Zn, and Cd on the cation sites and C, Si, and Ge on the anion sites. Our calculated acceptor ionization energies are estimated to be accurate to better than 10% across the board. The ionization energies of C and Be (152 and 187 meV, respectively) in wurtzite GaN are found to be lower than that of Mg (224 meV). The C was found to behave like the hydrogenic acceptor in all systems and it has the smallest ionization energy among all the acceptors studied.

Multivariate Bayesian analysis of Gaussian, right censored Gaussian, ordered categorical and binary traits using Gibbs sampling

PubMed Central

Korsgaard, Inge Riis; Lund, Mogens Sandø; Sorensen, Daniel; Gianola, Daniel; Madsen, Per; Jensen, Just

2003-01-01

A fully Bayesian analysis using Gibbs sampling and data augmentation in a multivariate model of Gaussian, right censored, and grouped Gaussian traits is described. The grouped Gaussian traits are either ordered categorical traits (with more than two categories) or binary traits, where the grouping is determined via thresholds on the underlying Gaussian scale, the liability scale. Allowances are made for unequal models, unknown covariance matrices and missing data. Having outlined the theory, strategies for implementation are reviewed. These include joint sampling of location parameters; efficient sampling from the fully conditional posterior distribution of augmented data, a multivariate truncated normal distribution; and sampling from the conditional inverse Wishart distribution, the fully conditional posterior distribution of the residual covariance matrix. Finally, a simulated dataset was analysed to illustrate the methodology. This paper concentrates on a model where residuals associated with liabilities of the binary traits are assumed to be independent. A Bayesian analysis using Gibbs sampling is outlined for the model where this assumption is relaxed. PMID:12633531

Removing the barrier to the calculation of activation energies

DOE PAGES

Mesele, Oluwaseun O.; Thompson, Ward H.

2016-10-06

Approaches for directly calculating the activation energy for a chemical reaction from a simulation at a single temperature are explored with applications to both classical and quantum systems. The activation energy is obtained from a time correlation function that can be evaluated from the same molecular dynamics trajectories or quantum dynamics used to evaluate the rate constant itself and thus requires essentially no extra computational work.

AlaScan: A Graphical User Interface for Alanine Scanning Free-Energy Calculations.

PubMed

Ramadoss, Vijayaraj; Dehez, François; Chipot, Christophe

2016-06-27

Computation of the free-energy changes that underlie molecular recognition and association has gained significant importance due to its considerable potential in drug discovery. The massive increase of computational power in recent years substantiates the application of more accurate theoretical methods for the calculation of binding free energies. The impact of such advances is the application of parent approaches, like computational alanine scanning, to investigate in silico the effect of amino-acid replacement in protein-ligand and protein-protein complexes, or probe the thermostability of individual proteins. Because human effort represents a significant cost that precludes the routine use of this form of free-energy calculations, minimizing manual intervention constitutes a stringent prerequisite for any such systematic computation. With this objective in mind, we propose a new plug-in, referred to as AlaScan, developed within the popular visualization program VMD to automate the major steps in alanine-scanning calculations, employing free-energy perturbation as implemented in the widely used molecular dynamics code NAMD. The AlaScan plug-in can be utilized upstream, to prepare input files for selected alanine mutations. It can also be utilized downstream to perform the analysis of different alanine-scanning calculations and to report the free-energy estimates in a user-friendly graphical user interface, allowing favorable mutations to be identified at a glance. The plug-in also assists the end-user in assessing the reliability of the calculation through rapid visual inspection.

Free energies of stable and metastable pores in lipid membranes under tension.

PubMed

den Otter, Wouter K

2009-11-28

The free energy profile of pore formation in a lipid membrane, covering the entire range from a density fluctuation in an intact bilayer to a large tension-stabilized pore, has been calculated by molecular dynamics simulations with a coarse-grained lipid model. Several fixed elongations are used to obtain the Helmholtz free energy as a function of pore size for thermodynamically stable, metastable, and unstable pores, and the system-size dependence of these elongations is discussed. A link to the Gibbs free energy at constant tension, commonly known as the Litster model, is established by a Legendre transformation. The change of genus upon pore formation is exploited to estimate the saddle-splay modulus or Gaussian curvature modulus of the membrane leaflets. Details are provided of the simulation approach, which combines the potential of mean constraint force method with a reaction coordinate based on the local lipid density.

Relative electronic and free energies of octane's unique conformations

NASA Astrophysics Data System (ADS)

Kirschner, Karl N.; Heiden, Wolfgang; Reith, Dirk

2017-06-01

This study reports the geometries and electronic energies of n-octane's unique conformations using perturbation methods that best mimic CCSD(T) results. In total, the fully optimised minima of n-butane (2 conformations), n-pentane (4 conformations), n-hexane (12 conformations) and n-octane (96 conformations) were investigated at several different theory levels and basis sets. We find that DF-MP2.5/aug-cc-pVTZ is in very good agreement with the more expensive CCSD(T) results. At this level, we can clearly confirm the 96 stable minima which were previously found using a reparameterised density functional theory (DFT). Excellent agreement was found between their DFT results and our DF-MP2.5 perturbation results. Subsequent Gibbs free energy calculations, using scaled MP2/aug-cc-pVTZ zero-point vibrational energy and frequencies, indicate a significant temperature dependency of the relative energies, with a change in the predicted global minimum. The results of this work will be important for future computational investigations of fuel-related octane reactions and for optimisation of molecular force fields (e.g. lipids).

Efficient calculation of the energy of a molecule in an arbitrary electric field

NASA Astrophysics Data System (ADS)

Pulay, Peter; Janowski, Tomasz

In thermodynamic (e.g., Monte Carlo) simulations with electronic embedding, the energy of the active site or solute must be calculated for millions of configurations of the environment (solvent or protein matrix) to obtain reliable statistics. This precludes the use of accurate but expensive ab initio and density functional techniques. Except for the immediate neighbors, the effect of the environment is electrostatic. We show that the energy of a molecule in the irregular field of the environment can be determined very efficiently by expanding the electric potential in known functions, and precalculating the first and second order response of the molecule to the components of the potential. These generalized multipole moments and polarizabilities allow the calculation of the energy of the system without further ab initio calculations. Several expansion functions were explored: polynomials, distributed inverse powers, and sine functions. The latter provide the numerically most stable fit but require new types of integrals. Distributed inverse powers can be simulated using dummy atoms, and energies calculated this way provide a very good approximation to the actual energies in the field of the environment.

Development of a SCALE Tool for Continuous-Energy Eigenvalue Sensitivity Coefficient Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perfetti, Christopher M; Rearden, Bradley T

2013-01-01

Two methods for calculating eigenvalue sensitivity coefficients in continuous-energy Monte Carlo applications were implemented in the KENO code within the SCALE code package. The methods were used to calculate sensitivity coefficients for several criticality safety problems and produced sensitivity coefficients that agreed well with both reference sensitivities and multigroup TSUNAMI-3D sensitivity coefficients. The newly developed CLUTCH method was observed to produce sensitivity coefficients with high figures of merit and low memory requirements, and both continuous-energy sensitivity methods met or exceeded the accuracy of the multigroup TSUNAMI-3D calculations.

Development of a quantum mechanics-based free-energy perturbation method: use in the calculation of relative solvation free energies.

PubMed

Reddy, M Rami; Singh, U C; Erion, Mark D

2004-05-26

Free-energy perturbation (FEP) is considered the most accurate computational method for calculating relative solvation and binding free-energy differences. Despite some success in applying FEP methods to both drug design and lead optimization, FEP calculations are rarely used in the pharmaceutical industry. One factor limiting the use of FEP is its low throughput, which is attributed in part to the dependence of conventional methods on the user's ability to develop accurate molecular mechanics (MM) force field parameters for individual drug candidates and the time required to complete the process. In an attempt to find an FEP method that could eventually be automated, we developed a method that uses quantum mechanics (QM) for treating the solute, MM for treating the solute surroundings, and the FEP method for computing free-energy differences. The thread technique was used in all transformations and proved to be essential for the successful completion of the calculations. Relative solvation free energies for 10 structurally diverse molecular pairs were calculated, and the results were in close agreement with both the calculated results generated by conventional FEP methods and the experimentally derived values. While considerably more CPU demanding than conventional FEP methods, this method (QM/MM-based FEP) alleviates the need for development of molecule-specific MM force field parameters and therefore may enable future automation of FEP-based calculations. Moreover, calculation accuracy should be improved over conventional methods, especially for calculations reliant on MM parameters derived in the absence of experimental data.

Observations and Thermochemical Calculations for Hot-Jupiter Atmospheres

NASA Astrophysics Data System (ADS)

Blecic, Jasmina; Harrington, Joseph; Bowman, M. Oliver; Cubillos, Patricio; Stemm, Madison

2015-01-01

I present Spitzer eclipse observations for WASP-14b and WASP-43b, an open source tool for thermochemical equilibrium calculations, and components of an open source tool for atmospheric parameter retrieval from spectroscopic data. WASP-14b is a planet that receives high irradiation from its host star, yet, although theory does not predict it, the planet hosts a thermal inversion. The WASP-43b eclipses have signal-to-noise ratios of ~25, one of the largest among exoplanets. To assess these planets' atmospheric composition and thermal structure, we developed an open-source Bayesian Atmospheric Radiative Transfer (BART) code. My dissertation tasks included developing a Thermochemical Equilibrium Abundances (TEA) code, implementing the eclipse geometry calculation in BART's radiative transfer module, and generating parameterized pressure and temperature profiles so the radiative-transfer module can be driven by the statistical module.To initialize the radiative-transfer calculation in BART, TEA calculates the equilibrium abundances of gaseous molecular species at a given temperature and pressure. It uses the Gibbs-free-energy minimization method with an iterative Lagrangian optimization scheme. Given elemental abundances, TEA calculates molecular abundances for a particular temperature and pressure or a list of temperature-pressure pairs. The code is tested against the original method developed by White at al. (1958), the analytic method developed by Burrows and Sharp (1999), and the Newton-Raphson method implemented in the open-source Chemical Equilibrium with Applications (CEA) code. TEA, written in Python, is modular, documented, and available to the community via the open-source development site GitHub.com.Support for this work was provided by NASA Headquarters under the NASA Earth and Space Science Fellowship Program, grant NNX12AL83H, by NASA through an award issued by JPL/Caltech, and through the Science Mission Directorate's Planetary Atmospheres Program, grant

Application of adjusted data in calculating fission-product decay energies and spectra

NASA Astrophysics Data System (ADS)

George, D. C.; Labauve, R. J.; England, T. R.

1982-06-01

The code ADENA, which approximately calculates fussion-product beta and gamma decay energies and spectra in 19 or fewer energy groups from a mixture of U235 and Pu239 fuels, is described. The calculation uses aggregate, adjusted data derived from a combination of several experiments and summation results based on the ENDF/B-V fission product file. The method used to obtain these adjusted data and the method used by ADENA to calculate fission-product decay energy with an absorption correction are described, and an estimate of the uncertainty of the ADENA results is given. Comparisons of this approximate method are made to experimental measurements, to the ANSI/ANS 5.1-1979 standard, and to other calculational methods. A listing of the complete computer code (ADENA) is contained in an appendix. Included in the listing are data statements containing the adjusted data in the form of parameters to be used in simple analytic functions.

Calculation of Host-Guest Binding Affinities Using a Quantum-Mechanical Energy Model.

PubMed

Muddana, Hari S; Gilson, Michael K

2012-06-12

The prediction of protein-ligand binding affinities is of central interest in computer-aided drug discovery, but it is still difficult to achieve a high degree of accuracy. Recent studies suggesting that available force fields may be a key source of error motivate the present study, which reports the first mining minima (M2) binding affinity calculations based on a quantum mechanical energy model, rather than an empirical force field. We apply a semi-empirical quantum-mechanical energy function, PM6-DH+, coupled with the COSMO solvation model, to 29 host-guest systems with a wide range of measured binding affinities. After correction for a systematic error, which appears to derive from the treatment of polar solvation, the computed absolute binding affinities agree well with experimental measurements, with a mean error 1.6 kcal/mol and a correlation coefficient of 0.91. These calculations also delineate the contributions of various energy components, including solute energy, configurational entropy, and solvation free energy, to the binding free energies of these host-guest complexes. Comparison with our previous calculations, which used empirical force fields, point to significant differences in both the energetic and entropic components of the binding free energy. The present study demonstrates successful combination of a quantum mechanical Hamiltonian with the M2 affinity method.

Phase relations in the system Cu-Gd-O and Gibbs energy of formation of CuGd[sub 2]O[sub 4

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jacob, K.T.; Mathews, T.; Hajra, J.P.

1993-07-01

The phase relations in the system Cu-Gd-O have been determined at 1,273 K by X-ray diffraction, optical microscopy, and electron microprobe analysis of samples equilibrated in quartz ampules and in pure oxygen. Only one ternary compound, CuGd[sub 2]O[sub 4], was found to be stable. The Gibbs free energy of formation of this compound has been measured using the solid-state cell Pt, Cu[sub 2]O + CuGd[sub 2]O[sub 4] + Gd[sub 2]O[sub 3]//(Y[sub 2]O[sub 3])ZrO[sub 2]//CuO + Cu[sub 2]O, Pt in the temperature range of 900 to 1,350 K. For the formation of CuGd[sub 2]O[sub 4] from its binary component oxides, CuOmore » (s) + Gd[sub 2]O[sub 3] (s) [r arrow] CuGd[sub 2]O[sub 4] (s) [Delta]G[degree] = 8230 - 11.2T([plus minus]50)J/mol. Since the formation is endothermic, CuGd[sub 2]O[sub 4] becomes thermodynamically unstable with respect to CuO and Gd[sub 2]O[sub 3] below 735 K. When the oxygen partial pressure over CuGd[sub 2]O[sub 4] is lowered, it decomposes according to the reaction 4CuGd[sub 2]O[sub 4] (s) [r arrow] 4Gd[sub 2]O[sub 3] (s) + 2Cu[sub 2]O (s) + O[sub 2] (g) for which the equilibrium oxygen potential is given by [Delta][mu][sub o][sub 2] = [minus]227,970 + 143.2T([plus minus]500)J/mol. An oxygen potential diagram for the system Cu-Gd-O at 1,273 is presented.« less

Light absorption and excitation energy transfer calculations in primitive photosynthetic bacteria

NASA Astrophysics Data System (ADS)

Komatsu, Yu; Kayanuma, Megumi; Shoji, Mitsuo; Yabana, Kazuhiro; Shiraishi, Kenji; Umemura, Masayuki

2015-06-01

In photosynthetic organisms, light energy is converted into chemical energy through the light absorption and excitation energy transfer (EET) processes. These processes start in light-harvesting complexes, which contain special photosynthetic pigments. The exploration of unique mechanisms in light-harvesting complexes is directly related to studies, such as artificial photosynthesis or biosignatures in astrobiology. We examined, through ab initio calculations, the light absorption and EET processes using cluster models of light-harvesting complexes in purple bacteria (LH2). We evaluated absorption spectra and energy transfer rates using the LH2 monomer and dimer models to reproduce experimental results. After the calibration tests, a LH2 aggregation model, composed of 7 or 19 LH2s aligned in triangle lattice, was examined. We found that the light absorption is red shifted and the energy transfer becomes faster as the system size increases. We also found that EET is accelerated by exchanging the central pigments to lower energy excited pigments. As an astrobiological application, we calculated light absorptions efficiencies of the LH2 in different photoenvironments.

Effects of internal gain assumptions in building energy calculations

NASA Astrophysics Data System (ADS)

Christensen, C.; Perkins, R.

1981-01-01

The utilization of direct solar gains in buildings can be affected by operating profiles, such as schedules for internal gains, thermostat controls, and ventilation rates. Building energy analysis methods use various assumptions about these profiles. The effects of typical internal gain assumptions in energy calculations are described. Heating and cooling loads from simulations using the DOE 2.1 computer code are compared for various internal gain inputs: typical hourly profiles, constant average profiles, and zero gain profiles. Prototype single-family-detached and multifamily-attached residential units are studied with various levels of insulation and infiltration. Small detached commercial buildings and attached zones in large commercial buildings are studied with various levels of internal gains. The results indicate that calculations of annual heating and cooling loads are sensitive to internal gains, but in most cases are relatively insensitive to hourly variations in internal gains.

Surface Segregation Energies of BCC Binaries from Ab Initio and Quantum Approximate Calculations

NASA Technical Reports Server (NTRS)

Good, Brian S.

2003-01-01

We compare dilute-limit segregation energies for selected BCC transition metal binaries computed using ab initio and quantum approximate energy method. Ab initio calculations are carried out using the CASTEP plane-wave pseudopotential computer code, while quantum approximate results are computed using the Bozzolo-Ferrante-Smith (BFS) method with the most recent parameterization. Quantum approximate segregation energies are computed with and without atomistic relaxation. The ab initio calculations are performed without relaxation for the most part, but predicted relaxations from quantum approximate calculations are used in selected cases to compute approximate relaxed ab initio segregation energies. Results are discussed within the context of segregation models driven by strain and bond-breaking effects. We compare our results with other quantum approximate and ab initio theoretical work, and available experimental results.

Unsupervised Calculation of Free Energy Barriers in Large Crystalline Systems

NASA Astrophysics Data System (ADS)

Swinburne, Thomas D.; Marinica, Mihai-Cosmin

2018-03-01

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 C 15 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.

Low energy dipole strength from large scale shell model calculations

NASA Astrophysics Data System (ADS)

Sieja, Kamila

2017-09-01

Low energy enhancement of radiative strength functions has been deduced from experiments in several mass regions of nuclei. Such an enhancement is believed to impact the calculated neutron capture rates which are crucial input for reaction rates of astrophysical interest. Recently, shell model calculations have been performed to explain the upbend of the γ-strength as due to the M1 transitions between close-lying states in the quasi-continuum in Fe and Mo nuclei. Beyond mean-↓eld calculations in Mo suggested, however, a non-negligible role of electric dipole in the low energy enhancement. So far, no calculations of both dipole components within the same theoretical framework have been presented in this context. In this work we present newly developed large scale shell model appraoch that allows to treat on the same footing natural and non-natural parity states. The calculations are performed in a large sd - pf - gds model space, allowing for 1p{1h excitations on the top of the full pf-shell con↓guration mixing. We restrict the discussion to the magnetic part of the dipole strength, however, we calculate for the ↓rst time the magnetic dipole strength between states built of excitations going beyond the classical shell model spaces. Our results corroborate previous ↓ndings for the M1 enhancement for the natural parity states while we observe no enhancement for the 1p{1h contributions. We also discuss in more detail the e↑ects of con↓guration mixing limitations on the enhancement coming out from shell model calculations.

Toward understanding as photosynthetic biosignatures: light harvesting and energy transfer calculation

NASA Astrophysics Data System (ADS)

Komatsu, Y.; Umemura, M.; Shoji, M.; Shiraishi, K.; Kayanuma, M.; Yabana, K.

2014-03-01

Among several proposed biosignatures, red edge is a direct evidence of photosynthetic life if it is detected (Kiang et al 2007). Red edge is a sharp change in reflectance spectra of vegetation in NIR region (about 700-750 nm). The sign of red edge is observed by Earthshine or remote sensing (Wolstencroft & Raven 2002, Woolf et al 2002). But, why around 700-750 nm? The photosynthetic organisms on Earth have evolved to optimize the sunlight condition. However, if we consider about photosynthetic organism on extrasolar planets, they should have developed to utilize the spectra of its principal star. Thus, it is not strange even if it shows different vegetation spectra. In this study, we focused on the light absorption mechanism of photosynthetic organisms on Earth and investigated the fundamental properties of the light harvesting mechanisms, which is the first stage for the light absorption. Light harvesting complexes contain photosynthetic pigments like chlorophylls. Effective light absorption and the energy transfer are accomplished by the electronic excitations of collective photosynthetic pigments. In order to investigate this mechanism, we constructed an energy transfer model by using a dipole-dipole approximation for the interactions between electronic excitations. Transition moments and transition energies of each pigment are calculated at the time-dependent density functional theory (TDDFT) level (Marques & Gross 2004). Quantum dynamics simulation for the excitation energy transfer was calculated by the Liouvelle's equation. We adopted the model to purple bacteria, which has been studied experimentally and known to absorb lower energy. It is meaningful to focus on the mechanism of this bacteria, since in the future mission, M planets will become a important target. We calculated the oscillator strengths in one light harvesting complex and confirmed the validity by comparing to the experimental data. This complex is made of an inner and an outer ring. The

Improvements to the nuclear model code GNASH for cross section calculations at higher energies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Young, P.G.; Chadwick, M.B.

1994-05-01

The nuclear model code GNASH, which in the past has been used predominantly for incident particle energies below 20 MeV, has been modified extensively for calculations at higher energies. The model extensions and improvements are described in this paper, and their significance is illustrated by comparing calculations with experimental data for incident energies up to 160 MeV.

Replica exchange and expanded ensemble simulations as Gibbs sampling: simple improvements for enhanced mixing.

PubMed

Chodera, John D; Shirts, Michael R

2011-11-21

The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in discovering new ways to enhance the phase space mixing of these protocols in order to improve sampling of uncorrelated configurations. Here, we demonstrate how both of these classes of algorithms can be considered as special cases of Gibbs sampling within a Markov chain Monte Carlo framework. Gibbs sampling is a well-studied scheme in the field of statistical inference in which different random variables are alternately updated from conditional distributions. While the update of the conformational degrees of freedom by Metropolis Monte Carlo or molecular dynamics unavoidably generates correlated samples, we show how judicious updating of the thermodynamic state indices--corresponding to thermodynamic parameters such as temperature or alchemical coupling variables--can substantially increase mixing while still sampling from the desired distributions. We show how state update methods in common use can lead to suboptimal mixing, and present some simple, inexpensive alternatives that can increase mixing of the overall Markov chain, reducing simulation times necessary to obtain estimates of the desired precision. These improved schemes are demonstrated for several common applications, including an alchemical expanded ensemble simulation, parallel tempering, and multidimensional replica exchange umbrella sampling.

Free energy and phase equilibria for the restricted primitive model of ionic fluids from Monte Carlo simulations

NASA Astrophysics Data System (ADS)

Orkoulas, Gerassimos; Panagiotopoulos, Athanassios Z.

1994-07-01

In this work, we investigate the liquid-vapor phase transition of the restricted primitive model of ionic fluids. We show that at the low temperatures where the phase transition occurs, the system cannot be studied by conventional molecular simulation methods because convergence to equilibrium is slow. To accelerate convergence, we propose cluster Monte Carlo moves capable of moving more than one particle at a time. We then address the issue of charged particle transfers in grand canonical and Gibbs ensemble Monte Carlo simulations, for which we propose a biased particle insertion/destruction scheme capable of sampling short interparticle distances. We compute the chemical potential for the restricted primitive model as a function of temperature and density from grand canonical Monte Carlo simulations and the phase envelope from Gibbs Monte Carlo simulations. Our calculated phase coexistence curve is in agreement with recent results of Caillol obtained on the four-dimensional hypersphere and our own earlier Gibbs ensemble simulations with single-ion transfers, with the exception of the critical temperature, which is lower in the current calculations. Our best estimates for the critical parameters are T*c=0.053, ρ*c=0.025. We conclude with possible future applications of the biased techniques developed here for phase equilibrium calculations for ionic fluids.

On the GIBBS thermodynamic potential of seawater

NASA Astrophysics Data System (ADS)

Feistel, Rainer; Hagen, Eberhard

Free Enthalpy, the GIBBS thermodynamic potential G(S,t,p) of seawater, has been recomputed including the sound speed equation of DEL GROSSO (1974), temperatures of maximum density (TMD) of CALDWELL (1978), freezing point depression measurements of DOHERTY and KESTER (1974), rederived limiting laws and ice properties, and an extended set of dilution heat data of BROMLEY (1968) and MILLERO, HANSEN and HOFF (1973). As a new reference state, the standard ocean state has been chosen. The resulting average deviations are 0.0006 kg m -3 for pure water density at 1 atm, 0.002 kg m -3 for seawater density at 1 atm, 0.02 m/s for sound speed, 0.01 J kgK -1 for heat capacity at 1 atm, 0.4 kJ kg -1 for dilution heats, 0.002°C for freezing points, and 0.04°C for TMDs. Resulting pressure-dependent freezing points are in good agreement with experiments and UNESCO (1978) formulas. Enthalpy as thermodynamic potential has been explicitly determined for easy computation of potential temperature, potential density, and sound speed. All functions are expressed in the new International Temperature Scale ITS-90.

Binding free energy calculations to rationalize the interactions of huprines with acetylcholinesterase.

PubMed

Nascimento, Érica C M; Oliva, Mónica; Andrés, Juan

2018-05-01

In the present study, the binding free energy of a family of huprines with acetylcholinesterase (AChE) is calculated by means of the free energy perturbation method, based on hybrid quantum mechanics and molecular mechanics potentials. Binding free energy calculations and the analysis of the geometrical parameters highlight the importance of the stereochemistry of huprines in AChE inhibition. Binding isotope effects are calculated to unravel the interactions between ligands and the gorge of AChE. New chemical insights are provided to explain and rationalize the experimental results. A good correlation with the experimental data is found for a family of inhibitors with moderate differences in the enzyme affinity. The analysis of the geometrical parameters and interaction energy per residue reveals that Asp72, Glu199, and His440 contribute significantly to the network of interactions between active site residues, which stabilize the inhibitors in the gorge. It seems that a cooperative effect of the residues of the gorge determines the affinity of the enzyme for these inhibitors, where Asp72, Glu199, and His440 make a prominent contribution.

Binding free energy calculations to rationalize the interactions of huprines with acetylcholinesterase

NASA Astrophysics Data System (ADS)

Nascimento, Érica C. M.; Oliva, Mónica; Andrés, Juan

2018-03-01

In the present study, the binding free energy of a family of huprines with acetylcholinesterase (AChE) is calculated by means of the free energy perturbation method, based on hybrid quantum mechanics and molecular mechanics potentials. Binding free energy calculations and the analysis of the geometrical parameters highlight the importance of the stereochemistry of huprines in AChE inhibition. Binding isotope effects are calculated to unravel the interactions between ligands and the gorge of AChE. New chemical insights are provided to explain and rationalize the experimental results. A good correlation with the experimental data is found for a family of inhibitors with moderate differences in the enzyme affinity. The analysis of the geometrical parameters and interaction energy per residue reveals that Asp72, Glu199, and His440 contribute significantly to the network of interactions between active site residues, which stabilize the inhibitors in the gorge. It seems that a cooperative effect of the residues of the gorge determines the affinity of the enzyme for these inhibitors, where Asp72, Glu199, and His440 make a prominent contribution.

Binding free energy calculations to rationalize the interactions of huprines with acetylcholinesterase

NASA Astrophysics Data System (ADS)

Nascimento, Érica C. M.; Oliva, Mónica; Andrés, Juan

2018-05-01

In the present study, the binding free energy of a family of huprines with acetylcholinesterase (AChE) is calculated by means of the free energy perturbation method, based on hybrid quantum mechanics and molecular mechanics potentials. Binding free energy calculations and the analysis of the geometrical parameters highlight the importance of the stereochemistry of huprines in AChE inhibition. Binding isotope effects are calculated to unravel the interactions between ligands and the gorge of AChE. New chemical insights are provided to explain and rationalize the experimental results. A good correlation with the experimental data is found for a family of inhibitors with moderate differences in the enzyme affinity. The analysis of the geometrical parameters and interaction energy per residue reveals that Asp72, Glu199, and His440 contribute significantly to the network of interactions between active site residues, which stabilize the inhibitors in the gorge. It seems that a cooperative effect of the residues of the gorge determines the affinity of the enzyme for these inhibitors, where Asp72, Glu199, and His440 make a prominent contribution.

Gibbs measures based on 1d (an)harmonic oscillators as mean-field limits

NASA Astrophysics Data System (ADS)

Lewin, Mathieu; Nam, Phan Thành; Rougerie, Nicolas

2018-04-01

We prove that Gibbs measures based on 1D defocusing nonlinear Schrödinger functionals with sub-harmonic trapping can be obtained as the mean-field/large temperature limit of the corresponding grand-canonical ensemble for many bosons. The limit measure is supported on Sobolev spaces of negative regularity, and the corresponding density matrices are not trace-class. The general proof strategy is that of a previous paper of ours, but we have to complement it with Hilbert-Schmidt estimates on reduced density matrices.

4He binding energy calculation including full tensor-force effects

NASA Astrophysics Data System (ADS)

Fonseca, A. C.

1989-09-01

The four-body equations of Alt, Grassberger, and Sandhas are solved in the version where the (2)+(2) subamplitudes are treated exactly by convolution, using one-term separable Yamaguchy nucleon-nucleon potentials in the 1S0 and 3S1-3D1 channels. The resulting jp=1/2+ and (3/2+ three-body subamplitudes are represented in a separable form using the energy-dependent pole expansion. Converged bound-state results are calculated for the first time using the full interaction, and are compared with those obtained from a simplified treatment of the tensor force. The Tjon line that correlates three-nucleon and four-nucleon binding energies is shown using different nucleon-nucleon potentials. In all calculations the Coulomb force has been neglected.

Relativistic calculation of correlational energy for a helium-like atom

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palchikov, V.G.

This paper presents an analytical method for calculating the firstorder correlational energy from the electron interaction, taking account of lag effects. Explicit analytical expressions are obtained for radial matrix elements. The nonrelativistic limit is investigated. The given method may be used to calculate correlation effects in higher orders of perturbation theory (second and higher orders with respect to 1/z) using the Strum expansion for the Coulomb Green's functions.

Calculation of energy costs of composite biomass stirring at biogas stations

NASA Astrophysics Data System (ADS)

Suslov, D. Yu; Temnikov, D. O.

2018-03-01

The paper is devoted to the study of the equipment to produce biogas fuel from organic wastes. The bioreactor equipped with a combined stirring system ensuring mechanical and bubbling stirring is designed. The method of energy cost calculation of the combined stirring system with original design is suggested. The received expressions were used in the calculation of the stirring system installed in the 10 m3 bioreactor: power consumed by the mixer during the start-up period made Nz =9.03 kW, operating power of the mixer made NE =1.406 kW, compressor power for bubbling stirring made NC =18.5 kW. Taking into account the operating mode of single elements of the stirring system, the energy cost made 4.38% of the total energy received by the biogas station.

Transported Geothermal Energy Technoeconomic Screening Tool - Calculation Engine

DOE Data Explorer

Liu, Xiaobing

2016-09-21

This calculation engine estimates technoeconomic feasibility for transported geothermal energy projects. The TGE screening tool (geotool.exe) takes input from input file (input.txt), and list results into output file (output.txt). Both the input and ouput files are in the same folder as the geotool.exe. To use the tool, the input file containing adequate information of the case should be prepared in the format explained below, and the input file should be put into the same folder as geotool.exe. Then the geotool.exe can be executed, which will generate a output.txt file in the same folder containing all key calculation results. The format and content of the output file is explained below as well.

Thermodynamic properties of zeolites: low-temperature heat capacities and thermodynamic functions for phillipsite and clinoptilolite. Estimates of the thermochemical properties of zeolitic water at low temperature.

USGS Publications Warehouse

Hemingway, B.S.; Robie, R.A.

1984-01-01

Measured heat capacities between 15 and 305 K and calculated heat capacities, entropies, enthalpy functions and Gibbs energy functions are reported and analysed for phillipsite and clinoptilolite. - J.A.Z.

Towards accurate free energy calculations in ligand protein-binding studies.

PubMed

Steinbrecher, Thomas; Labahn, Andreas

2010-01-01

Cells contain a multitude of different chemical reaction paths running simultaneously and quite independently next to each other. This amazing feat is enabled by molecular recognition, the ability of biomolecules to form stable and specific complexes with each other and with their substrates. A better understanding of this process, i.e. of the kinetics, structures and thermodynamic properties of biomolecule binding, would be invaluable in the study of biological systems. In addition, as the mode of action of many pharmaceuticals is based upon their inhibition or activation of biomolecule targets, predictive models of small molecule receptor binding are very helpful tools in rational drug design. Since the goal here is normally to design a new compound with a high inhibition strength, one of the most important thermodynamic properties is the binding free energy DeltaG(0). The prediction of binding constants has always been one of the major goals in the field of computational chemistry, because the ability to reliably assess a hypothetical compound's binding properties without having to synthesize it first would save a tremendous amount of work. The different approaches to this question range from fast and simple empirical descriptor methods to elaborate simulation protocols aimed at putting the computation of free energies onto a solid foundation of statistical thermodynamics. While the later methods are still not suited for the screenings of thousands of compounds that are routinely performed in computational drug design studies, they are increasingly put to use for the detailed study of protein ligand interactions. This review will focus on molecular mechanics force field based free energy calculations and their application to the study of protein ligand interactions. After a brief overview of other popular methods for the calculation of free energies, we will describe recent advances in methodology and a variety of exemplary studies of molecular dynamics

A Short Essay on the Uses of Free Energy

ERIC Educational Resources Information Center

Koutandos, Spyridon

2013-01-01

In this article we examine cases of more classical and less classical nature compared to results found by quantum mechanics and attribute a form of Free Energy discontinuity for each case within a boundary layer. The concept of a boundary layer is broadened as to include areas of first or second variations of the Gibbs free energy. It is…

Conformational Transitions and Convergence of Absolute Binding Free Energy Calculations

PubMed Central

Lapelosa, Mauro; Gallicchio, Emilio; Levy, Ronald M.

2011-01-01

The Binding Energy Distribution Analysis Method (BEDAM) is employed to compute the standard binding free energies of a series of ligands to a FK506 binding protein (FKBP12) with implicit solvation. Binding free energy estimates are in reasonably good agreement with experimental affinities. The conformations of the complexes identified by the simulations are in good agreement with crystallographic data, which was not used to restrain ligand orientations. The BEDAM method is based on λ -hopping Hamiltonian parallel Replica Exchange (HREM) molecular dynamics conformational sampling, the OPLS-AA/AGBNP2 effective potential, and multi-state free energy estimators (MBAR). Achieving converged and accurate results depends on all of these elements of the calculation. Convergence of the binding free energy is tied to the level of convergence of binding energy distributions at critical intermediate states where bound and unbound states are at equilibrium, and where the rate of binding/unbinding conformational transitions is maximal. This finding mirrors similar observations in the context of order/disorder transitions as for example in protein folding. Insights concerning the physical mechanism of ligand binding and unbinding are obtained. Convergence for the largest FK506 ligand is achieved only after imposing strict conformational restraints, which however require accurate prior structural knowledge of the structure of the complex. The analytical AGBNP2 model is found to underestimate the magnitude of the hydrophobic driving force towards binding in these systems characterized by loosely packed protein-ligand binding interfaces. Rescoring of the binding energies using a numerical surface area model corrects this deficiency. This study illustrates the complex interplay between energy models, exploration of conformational space, and free energy estimators needed to obtain robust estimates from binding free energy calculations. PMID:22368530

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion.

PubMed

Ryham, Rolf J; Klotz, Thomas S; Yao, Lihan; Cohen, Fredric S

2016-03-08

We use continuum mechanics to calculate an entire least energy pathway of membrane fusion, from stalk formation, to pore creation, and through fusion pore enlargement. The model assumes that each structure in the pathway is axially symmetric. The static continuum stalk structure agrees quantitatively with experimental stalk architecture. Calculations show that in a stalk, the distal monolayer is stretched and the stored stretching energy is significantly less than the tilt energy of an unstretched distal monolayer. The string method is used to determine the energy of the transition barriers that separate intermediate states and the dynamics of two bilayers as they pass through them. Hemifusion requires a small amount of energy independently of lipid composition, while direct transition from a stalk to a fusion pore without a hemifusion intermediate is highly improbable. Hemifusion diaphragm expansion is spontaneous for distal monolayers containing at least two lipid components, given sufficiently negative diaphragm spontaneous curvature. Conversely, diaphragms formed from single-component distal monolayers do not expand without the continual injection of energy. We identify a diaphragm radius, below which central pore expansion is spontaneous. For larger diaphragms, prior studies have shown that pore expansion is not axisymmetric, and here our calculations supply an upper bound for the energy of the barrier against pore formation. The major energy-requiring deformations in the steps of fusion are: widening of a hydrophobic fissure in bilayers for stalk formation, splay within the expanding hemifusion diaphragm, and fissure widening initiating pore formation in a hemifusion diaphragm. Copyright © 2016 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion

PubMed Central

Ryham, Rolf J.; Klotz, Thomas S.; Yao, Lihan; Cohen, Fredric S.

2016-01-01

We use continuum mechanics to calculate an entire least energy pathway of membrane fusion, from stalk formation, to pore creation, and through fusion pore enlargement. The model assumes that each structure in the pathway is axially symmetric. The static continuum stalk structure agrees quantitatively with experimental stalk architecture. Calculations show that in a stalk, the distal monolayer is stretched and the stored stretching energy is significantly less than the tilt energy of an unstretched distal monolayer. The string method is used to determine the energy of the transition barriers that separate intermediate states and the dynamics of two bilayers as they pass through them. Hemifusion requires a small amount of energy independently of lipid composition, while direct transition from a stalk to a fusion pore without a hemifusion intermediate is highly improbable. Hemifusion diaphragm expansion is spontaneous for distal monolayers containing at least two lipid components, given sufficiently negative diaphragm spontaneous curvature. Conversely, diaphragms formed from single-component distal monolayers do not expand without the continual injection of energy. We identify a diaphragm radius, below which central pore expansion is spontaneous. For larger diaphragms, prior studies have shown that pore expansion is not axisymmetric, and here our calculations supply an upper bound for the energy of the barrier against pore formation. The major energy-requiring deformations in the steps of fusion are: widening of a hydrophobic fissure in bilayers for stalk formation, splay within the expanding hemifusion diaphragm, and fissure widening initiating pore formation in a hemifusion diaphragm. PMID:26958888

A Multidimensional Item Response Model: Constrained Latent Class Analysis Using the Gibbs Sampler and Posterior Predictive Checks.

ERIC Educational Resources Information Center

Hoijtink, Herbert; Molenaar, Ivo W.

1997-01-01

This paper shows that a certain class of constrained latent class models may be interpreted as a special case of nonparametric multidimensional item response models. Parameters of this latent class model are estimated using an application of the Gibbs sampler, and model fit is investigated using posterior predictive checks. (SLD)

Molecular structures and thermodynamic properties of monohydrated gaseous iodine compounds: Modelling for severe accident simulation

NASA Astrophysics Data System (ADS)

Sudolská, Mária; Cantrel, Laurent; Budzák, Šimon; Černušák, Ivan

2014-03-01

Monohydrated complexes of iodine species (I, I2, HI, and HOI) have been studied by correlated ab initio calculations. The standard enthalpies of formation, Gibbs free energy and the temperature dependence of the heat capacities at constant pressure were calculated. The values obtained have been implemented in ASTEC nuclear accident simulation software to check the thermodynamic stability of hydrated iodine compounds in the reactor coolant system and in the nuclear containment building of a pressurised water reactor during a severe accident. It can be concluded that iodine complexes are thermodynamically unstable by means of positive Gibbs free energies and would be represented by trace level concentrations in severe accident conditions; thus it is well justified to only consider pure iodine species and not hydrated forms.

Structural, electronic, elastic, thermoelectric and thermodynamic properties of the NbMSb half heusler (M=Fe, Ru, Os) compounds with first principle calculations

NASA Astrophysics Data System (ADS)

Abid, O. Miloud; Menouer, S.; Yakoubi, A.; Khachai, H.; Omran, S. Bin; Murtaza, G.; Prakash, Deo; Khenata, R.; Verma, K. D.

2016-05-01

The structural, electronic, elastic, thermoelectric and thermodynamic properties of NbMSb (M = Fe, Ru, Os) half heusler compounds are reported. The full-potential linearized augmented plane wave (FP-LAPW) plus local orbital (lo) method, based on the density functional theory (DFT) was employed for the present study. The equilibrium lattice parameter results are in good compliance with the available experimental measurements. The electronic band structure and Boltzmann transport calculations indicated a narrow indirect energy band gap for the compound having electronic structure favorable for thermoelectric performance as well as with substantial thermopowers at temperature ranges from 300 K to 800 K. Furthermore, good potential for thermoelectric performance (thermopower S ≥ 500 μeV) was found at higher temperature. In addition, the analysis of the charge density, partial and total densities of states (DOS) of three compounds demonstrate their semiconducting, ionic and covalent characters. Conversely, the calculated values of the Poisson's ratio and the B/G ratio indicate their ductile makeup. The thermal properties of the compounds were calculated by quasi-harmonic Debye model as implemented in the GIBBS code.

Calculating Free Energies Using Scaled-Force Molecular Dynamics Algorithm

NASA Technical Reports Server (NTRS)

Darve, Eric; Wilson, Micahel A.; Pohorille, Andrew

2000-01-01

One common objective of molecular simulations in chemistry and biology is to calculate the free energy difference between different states of the system of interest. Examples of problems that have such an objective are calculations of receptor-ligand or protein-drug interactions, associations of molecules in response to hydrophobic, and electrostatic interactions or partition of molecules between immiscible liquids. Another common objective is to describe evolution of the system towards a low energy (possibly the global minimum energy), 'native' state. Perhaps the best example of such a problem is folding of proteins or short RNA molecules. Both types of problems share the same difficulty. Often, different states of the system are separated by high energy barriers, which implies that transitions between these states are rare events. This, in turn, can greatly impede exploration of phase space. In some instances this can lead to 'quasi non-ergodicity', whereby a part of phase space is inaccessible on timescales of the simulation. A host of strategies has been developed to improve efficiency of sampling the phase space. For example, some Monte Carlo techniques involve large steps which move the system between low-energy regions in phase space without the need for sampling the configurations corresponding to energy barriers (J-walking). Most strategies, however, rely on modifying probabilities of sampling low and high-energy regions in phase space such that transitions between states of interest are encouraged. Perhaps the simplest implementation of this strategy is to increase the temperature of the system. This approach was successfully used to identify denaturation pathways in several proteins, but it is clearly not applicable to protein folding. It is also not a successful method for determining free energy differences. Finally, the approach is likely to fail for systems with co-existing phases, such as water-membrane systems, because it may lead to spontaneous

Revised values for the thermodynamic properties of boehmite, AlO(OH) , and related species and phases in the system Al-H-O

USGS Publications Warehouse

Hemingway, B.S.; Robie, R.A.; Apps, J.A.

1991-01-01

Heat capacity measurements are reported for a well-characterized boehmite that differ significantly from results reported earlier by Shomate and Cook (1946) for a monohydrate of alumina. It is suggested that the earlier measurements were made on a sample that was a mixture of phases and that use of that heat-capacity and derived thermodynamic data be discontinued. The entropy of boehmite derived in this study is 37.19 ?? 0.10 J/(mol.K) at 298.15 K. Based on our value for the entropy and accepting the recommended Gibbs free energy for Al(OH)-4, the Gibbs free energy and enthalpy of formation of boehmite are calculated to be -918.4 ?? 2.1 and -996.4 ?? 2.2 kJ/mol, respectively, from solubility data for boehmite. The Gibbs energy for boehmite is unchanged from that given by Hemingway et al. (1978). -from Authors

A study of the Boltzmann and Gibbs entropies in the context of a stochastic toy model

NASA Astrophysics Data System (ADS)

Malgieri, Massimiliano; Onorato, Pasquale; De Ambrosis, Anna

2018-05-01

In this article we reconsider a stochastic toy model of thermal contact, first introduced in Onorato et al (2017 Eur. J. Phys. 38 045102), showing its educational potential for clarifying some current issues in the foundations of thermodynamics. The toy model can be realized in practice using dice and coins, and can be seen as representing thermal coupling of two subsystems with energy bounded from above. The system is used as a playground for studying the different behaviours of the Boltzmann and Gibbs temperatures and entropies in the approach to steady state. The process that models thermal contact between the two subsystems can be proved to be an ergodic, reversible Markov chain; thus the dynamics produces an equilibrium distribution in which the weight of each state is proportional to its multiplicity in terms of microstates. Each one of the two subsystems, taken separately, is formally equivalent to an Ising spin system in the non-interacting limit. The model is intended for educational purposes, and the level of readership of the article is aimed at advanced undergraduates.

Graphical Calculation of Estimated Energy Expenditure in Burn Patients.

PubMed

Egro, Francesco M; Manders, Ernest C; Manders, Ernest K

2018-03-01

Historically, estimated energy expenditure (EEE) has been related to the percent of body surface area burned. Subsequent evaluations of these estimates have indicated that the earlier formulas may overestimate the amount of caloric support necessary for burn-injured patients. Ireton-Jones et al derived 2 equations for determining the EEE required to support burn patients, 1 for ventilator-dependent patients and 1 for spontaneously breathing patients. Evidence has proved their reliability, but they remain challenging to apply in a clinical setting given the difficult and cumbersome mathematics involved. This study aims to introduce a graphical calculation of EEE in burn patients that can be easily used in the clinical setting. The multivariant linear regression analysis from Ireton-Jones et al yielded equations that were rearranged into the form of a simple linear equation of the type y = mx + b. By choosing an energy expenditure and the age of the subject, the weight was calculated. The endpoints were then calculated, and a graph was mapped by means of Adobe FrameMaker. A graphical representation of Ireton-Jones et al's equations was obtained by plotting the weight (kg) on the y axis, the age (years) on the x axis, and a series of parallel lines representing the EEE in burn patients. The EEE has been displayed graphically on a grid to allow rapid determination of the EEE needed for a given patient of a designated weight and age. Two graphs were plotted: 1 for ventilator-dependent patients and 1 for spontaneously breathing patients. Correction factors for sex, the presence of additional trauma, and obesity are indicated on the graphical calculators. We propose a graphical tool to calculate caloric requirements in a fast, easy, and portable manner.

A Comparison of the ab Initio Calculated and Experimental Conformational Energies of Alkylcyclohexanes

NASA Astrophysics Data System (ADS)

Freeman, Fillmore; Tsegai, Zufan M.; Kasner, Marc L.; Hehre, Warren J.

2000-05-01

Ab initio 6-31G(d) and MP2/6-31G(d)//6-31G(d) methods were used to calculate the energies of the rotamers of the chair conformers of alkylcyclohexanes and trimethylsilylcyclohexane. The MP2/6-31G(d)//6-31G(d) calculated conformational energies ( ? or A values, in kcal/mol) of the alkylcyclohexanes (Me = 1.96; Et = 1.80; Pr = 1.73 iso-Pr = 1.60; t-Bu = 5.45; neo-pent = 1.32) and trimethylsilylcyclohexane (SiMe3 = 2.69) are similar to the experimental values. Plots of the calculated conformational energies for the alkylcyclohexanes and trimethylsilylcyclohexane versus their experimental values are linear (slope = 1.253 and r = .993 for 6-31G(d) and slope = 1.114 and r = .982 for MP2/6-31G(d)//6-31G(d)). The conformational energies are determined primarily by steric effects which include gauche (synclinal) interactions and repulsive nonbonded interactions in both the axial and equatorial conformers.

Comparison of approximations in density functional theory calculations: Energetics and structure of binary oxides

NASA Astrophysics Data System (ADS)

Hinuma, Yoyo; Hayashi, Hiroyuki; Kumagai, Yu; Tanaka, Isao; Oba, Fumiyasu

2017-09-01

High-throughput first-principles calculations based on density functional theory (DFT) are a powerful tool in data-oriented materials research. The choice of approximation to the exchange-correlation functional is crucial as it strongly affects the accuracy of DFT calculations. This study compares performance of seven approximations, six of which are based on Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) with and without Hubbard U and van der Waals corrections (PBE, PBE+U, PBED3, PBED3+U, PBEsol, and PBEsol+U), and the strongly constrained and appropriately normed (SCAN) meta-GGA on the energetics and crystal structure of elementary substances and binary oxides. For the latter, only those with closed-shell electronic structures are considered, examples of which include C u2O , A g2O , MgO, ZnO, CdO, SnO, PbO, A l2O3 , G a2O3 , I n2O3 , L a2O3 , B i2O3 , Si O2 , Sn O2 , Pb O2 , Ti O2 , Zr O2 , Hf O2 , V2O5 , N b2O5 , T a2O5 , Mo O3 , and W O3 . Prototype crystal structures are selected from the Inorganic Crystal Structure Database (ICSD) and cation substitution is used to make a set of existing and hypothetical oxides. Two indices are proposed to quantify the extent of lattice and internal coordinate relaxation during a calculation. The former is based on the second invariant and determinant of the transformation matrix of basis vectors from before relaxation to after relaxation, and the latter is derived from shifts of internal coordinates of atoms in the unit cell. PBED3, PBEsol, and SCAN reproduce experimental lattice parameters of elementary substances and oxides well with few outliers. Notably, PBEsol and SCAN predict the lattice parameters of low dimensional structures comparably well with PBED3, even though these two functionals do not explicitly treat van der Waals interactions. SCAN gives formation enthalpies and Gibbs free energies closest to experimental data, with mean errors (MEs) of 0.01 and -0.04 eV, respectively, and root

Sustainable manufacturing by calculating the energy demand during turning of AISI 1045 steel

NASA Astrophysics Data System (ADS)

Nur, R.; Nasrullah, B.; Suyuti, M. A.; Apollo

2018-01-01

Sustainable development will become important issues for many fields, including production, industry, and manufacturing. In order to achieve sustainable development, industry should be able to perform of sustainable production processes and environmentally friendly. Therefore, there is need to minimize the energy demand in the machining process. This paper presents a calculation method of energy consumption in the machining process, especially turning process which calculated by summing the number of energy consumption, such as the electric energy consumed during the machining preparation, the electrical energy during the cutting processes, and the electrical energy to produce a cutting tool. A case study was performed on dry turning of mild carbon steel using coated carbide. This approach can be used to determine the total amount of electrical energy consumed in the specific machining process. It concluded that the energy consumption will be an increase for using the high cutting speed as well as for the feed rate was increased.

CONTINUOUS-ENERGY MONTE CARLO METHODS FOR CALCULATING GENERALIZED RESPONSE SENSITIVITIES USING TSUNAMI-3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perfetti, Christopher M; Rearden, Bradley T

2014-01-01

This work introduces a new approach for calculating sensitivity coefficients for generalized neutronic responses to nuclear data uncertainties using continuous-energy Monte Carlo methods. The approach presented in this paper, known as the GEAR-MC method, allows for the calculation of generalized sensitivity coefficients for multiple responses in a single Monte Carlo calculation with no nuclear data perturbations or knowledge of nuclear covariance data. The theory behind the GEAR-MC method is presented here, and proof of principle is demonstrated by using the GEAR-MC method to calculate sensitivity coefficients for responses in several 3D, continuous-energy Monte Carlo applications.

Some aspects of multicomponent excess free energy models with subregular binaries

NASA Astrophysics Data System (ADS)

Cheng, Weiji; Ganguly, Jibamitra

1994-09-01

We have shown that two of the most commonly used multicomponent formulations of excess Gibbs free energy of mixing, those by WOHL (1946, 1953) and REDLICH and KISTER (1948), are formally equivalent if the binaries are constrained to have subregular properties, and also that other subregular multicomponent formulations developed in the mineralogical and geochemical literature are equivalent to, or higher order extensions of, these formulations. We have also presented a compact derivation of a multicomponent subregular solution leading to the same expression as derived by HELFFRICH and WOOD (1989). It is shown that Wohl's multicomponent formulation involves combination of binary excess free energies, which are calculated at compositions obtained by normal projection of the multicomponent composition onto the bounding binary joins, and is, thus, equivalent to the formulation developed by MUGGIANU et al. (1975). Finally, following the lead of HILLERT (1980), we have explored the limiting behavior of regular and subregular ternary solutions when a pair of components become energetically equivalent, and have, thus, derived an expression for calculating the ternary interaction parameter in a ternary solution from a knowledge of the properties of the bounding binaries, when one of these binaries is nearly ideal.

Free-Energy Calculations. A Mathematical Perspective

NASA Technical Reports Server (NTRS)

Pohorille, Andrzej

2015-01-01

conductance, defined as the ratio of ionic current through the channel to applied voltage, can be calculated in MD simulations by way of applying an external electric field to the system and counting the number of ions that traverse the channel per unit time. If the current is small, a voltage significantly higher than the experimental one needs to be applied to collect sufficient statistics of ion crossing events. Then, the calculated conductance has to be extrapolated to the experimental voltage using procedures of unknown accuracy. Instead, we propose an alternative approach that applies if ion transport through channels can be described with sufficient accuracy by the one-dimensional diffusion equation in the potential given by the free energy profile and applied voltage. Then, it is possible to test the assumptions of the equation, recover the full voltage/current dependence, determine the reliability of the calculated conductance and reconstruct the underlying (equilibrium) free energy profile, all from MD simulations at a single voltage. We will present the underlying theory, model calculations that test this theory and simulations on ion conductance through a channel that has been extensively studied experimentally. To our knowledge this is the first case in which the complete, experimentally measured dependence of the current on applied voltage has been reconstructed from MD simulations.

Recommendations for terminology and databases for biochemical thermodynamics.

PubMed

Alberty, Robert A; Cornish-Bowden, Athel; Goldberg, Robert N; Hammes, Gordon G; Tipton, Keith; Westerhoff, Hans V

2011-05-01

Chemical equations are normally written in terms of specific ionic and elemental species and balance atoms of elements and electric charge. However, in a biochemical context it is usually better to write them with ionic reactants expressed as totals of species in equilibrium with each other. This implies that atoms of elements assumed to be at fixed concentrations, such as hydrogen at a specified pH, should not be balanced in a biochemical equation used for thermodynamic analysis. However, both kinds of equations are needed in biochemistry. The apparent equilibrium constant K' for a biochemical reaction is written in terms of such sums of species and can be used to calculate standard transformed Gibbs energies of reaction Δ(r)G'°. This property for a biochemical reaction can be calculated from the standard transformed Gibbs energies of formation Δ(f)G(i)'° of reactants, which can be calculated from the standard Gibbs energies of formation of species Δ(f)G(j)° and measured apparent equilibrium constants of enzyme-catalyzed reactions. Tables of Δ(r)G'° of reactions and Δ(f)G(i)'° of reactants as functions of pH and temperature are available on the web, as are functions for calculating these properties. Biochemical thermodynamics is also important in enzyme kinetics because apparent equilibrium constant K' can be calculated from experimentally determined kinetic parameters when initial velocities have been determined for both forward and reverse reactions. Specific recommendations are made for reporting experimental results in the literature. Copyright © 2011 Elsevier B.V. All rights reserved.

Torsional energy levels of CH₃OH⁺/CH₃OD⁺/CD₃OD⁺ studied by zero-kinetic energy photoelectron spectroscopy and theoretical calculations.

PubMed

Dai, Zuyang; Gao, Shuming; Wang, Jia; Mo, Yuxiang

2014-10-14

The torsional energy levels of CH3OH(+), CH3OD(+), and CD3OD(+) have been determined for the first time using one-photon zero kinetic energy photoelectron spectroscopy. The adiabatic ionization energies for CH3OH, CH3OD, and CD3OD are determined as 10.8396, 10.8455, and 10.8732 eV with uncertainties of 0.0005 eV, respectively. Theoretical calculations have also been performed to obtain the torsional energy levels for the three isotopologues using a one-dimensional model with approximate zero-point energy corrections of the torsional potential energy curves. The calculated values are in good agreement with the experimental data. The barrier height of the torsional potential energy without zero-point energy correction was calculated as 157 cm(-1), which is about half of that of the neutral (340 cm(-1)). The calculations showed that the cation has eclipsed conformation at the energy minimum and staggered one at the saddle point, which is the opposite of what is observed in the neutral molecule. The fundamental C-O stretch vibrational energy level for CD3OD(+) has also been determined. The energy levels for the combinational excitation of the torsional vibration and the fundamental C-O stretch vibration indicate a strong torsion-vibration coupling.

Surface energy of talc and chlorite: Comparison between electronegativity calculation and immersion results.

PubMed

Douillard, Jean-Marc; Salles, Fabrice; Henry, Marc; Malandrini, Harold; Clauss, Frédéric

2007-01-15

The surface energies of talc and chlorite is computed using a simple model, which uses the calculation of the electrostatic energy of the crystal. It is necessary to calculate the atomic charges. We have chosen to follow Henry's model of determination of partial charges using scales of electronegativity and hardness. The results are in correct agreement with a determination of the surface energy obtained from an analysis of the heat of immersion data. Both results indicate that the surface energy of talc is lower than the surface energy of chlorite, in agreement with observed behavior of wettability. The influence of Al and Fe on this phenomenon is discussed. Surface energy of this type of solids seems to depend more strongly on the geometry of the crystal than on the type of atoms pointing out of the surface; i.e., the surface energy depends more on the physics of the system than on its chemistry.

Classical and quantum Reissner-Nordström black hole thermodynamics and first order phase transition

NASA Astrophysics Data System (ADS)

Ghaffarnejad, Hossein

2016-01-01

First we consider classical Reissner-Nordström black hole (CRNBH) metric which is obtained by solving Einstein-Maxwell metric equation for a point electric charge e inside of a spherical static body with mass M. It has 2 interior and exterior horizons. Using Bekenstein-Hawking entropy theorem we calculate interior and exterior entropy, temperature, Gibbs free energy and heat capacity at constant electric charge. We calculate first derivative of the Gibbs free energy with respect to temperature which become a singular function having a singularity at critical point Mc=2|e|/√{3} with corresponding temperature Tc=1/24π√{3|e|}. Hence we claim first order phase transition is happened there. Temperature same as Gibbs free energy takes absolutely positive (negative) values on the exterior (interior) horizon. The Gibbs free energy takes two different positive values synchronously for 0< T< Tc but not for negative values which means the system is made from two subsystem. For negative temperatures entropy reaches to zero value at Tto-∞ and so takes Bose-Einstein condensation single state. Entropy increases monotonically in case 0< T< Tc. Regarding results of the work presented at Wang and Huang (Phys. Rev. D 63:124014, 2001) we calculate again the mentioned thermodynamical variables for remnant stable final state of evaporating quantum Reissner-Nordström black hole (QRNBH) and obtained results same as one in case of the CRNBH. Finally, we solve mass loss equation of QRNBH against advance Eddington-Finkelstein time coordinate and derive luminosity function. We obtain switching off of QRNBH evaporation before than the mass completely vanishes. It reaches to a could Lukewarm type of RN black hole which its final remnant mass is m_{final}=|e| in geometrical units. Its temperature and luminosity vanish but not in Schwarzschild case of evaporation. Our calculations can be take some acceptable statements about information loss paradox (ILP).

Solubility and dissolution thermodynamics of tetranitroglycoluril in organic solvents at 295-318 K

NASA Astrophysics Data System (ADS)

Zheng, Zhihua; Wang, Jianlong; Hu, Zhiyan; Du, Hongbin

2017-08-01

The solubility data of tetranitroglycoluril in acetone, methanol, ethanol, ethyl acetate, nitromethane and chloroform at temperatures ranging from 295-318 K were measured by gravimetric method. The solubility data of tetranitroglycoluril were fitted with Apelblat semiempirical equation. The dissolution enthalpy, entropy and Gibbs energy of tetranitroglycoluril were calculated using the Van't Hoff and Gibbs equations. The results showed that the Apelblat semiempirical equation was significantly correlated with solubility data. The dissolving process was endothermic, entropy-driven, and nonspontaneous.

A novel method for calculating relative free energy of similar molecules in two environments

NASA Astrophysics Data System (ADS)

Farhi, Asaf; Singh, Bipin

2017-03-01

Calculating relative free energies is a topic of substantial interest and has many applications including solvation and binding free energies, which are used in computational drug discovery. However, there remain the challenges of accuracy, simple implementation, robustness and efficiency, which prevent the calculations from being automated and limit their use. Here we present an exact and complete decoupling analysis in which the partition functions of the compared systems decompose into the partition functions of the common and different subsystems. This decoupling analysis is applicable to submolecules with coupled degrees of freedom such as the methyl group and to any potential function (including the typical dihedral potentials), enabling to remove less terms in the transformation which results in a more efficient calculation. Then we show mathematically, in the context of partition function decoupling, that the two compared systems can be simulated separately, eliminating the need to design a composite system. We demonstrate the decoupling analysis and the separate transformations in a relative free energy calculation using MD simulations for a general force field and compare to another calculation and to experimental results. We present a unified soft-core technique that ensures the monotonicity of the numerically integrated function (analytical proof) which is important for the selection of intermediates. We show mathematically that in this soft-core technique the numerically integrated function can be non-steep only when we transform the systems separately, which can simplify the numerical integration. Finally, we show that when the systems have rugged energy landscape they can be equilibrated without introducing another sampling dimension which can also enable to use the simulation results for other free energy calculations.

Monte Carlo calculations of initial energies of electrons in water irradiated by photons with energies up to 1GeV.

PubMed

Todo, A S; Hiromoto, G; Turner, J E; Hamm, R N; Wright, H A

1982-12-01

Previous calculations of the initial energies of electrons produced in water irradiated by photons are extended to 1 GeV by including pair and triplet production. Calculations were performed with the Monte Carlo computer code PHOEL-3, which replaces the earlier code, PHOEL-2. Tables of initial electron energies are presented for single interactions of monoenergetic photons at a number of energies from 10 keV to 1 GeV. These tables can be used to compute kerma in water irradiated by photons with arbitrary energy spectra to 1 GeV. In addition, separate tables of Compton-and pair-electron spectra are given over this energy range. The code PHOEL-3 is available from the Radiation Shielding Information Center, Oak Ridge National Laboratory, Oak Ridge, TN 37830.

Metadyn View: Fast web-based viewer of free energy surfaces calculated by metadynamics

NASA Astrophysics Data System (ADS)

Hošek, Petr; Spiwok, Vojtěch

2016-01-01

Metadynamics is a highly successful enhanced sampling technique for simulation of molecular processes and prediction of their free energy surfaces. An in-depth analysis of data obtained by this method is as important as the simulation itself. Although there are several tools to compute free energy surfaces from metadynamics data, they usually lack user friendliness and a build-in visualization part. Here we introduce Metadyn View as a fast and user friendly viewer of bias potential/free energy surfaces calculated by metadynamics in Plumed package. It is based on modern web technologies including HTML5, JavaScript and Cascade Style Sheets (CSS). It can be used by visiting the web site and uploading a HILLS file. It calculates the bias potential/free energy surface on the client-side, so it can run online or offline without necessity to install additional web engines. Moreover, it includes tools for measurement of free energies and free energy differences and data/image export.

How to deal with multiple binding poses in alchemical relative protein-ligand binding free energy calculations.

PubMed

Kaus, Joseph W; Harder, Edward; Lin, Teng; Abel, Robert; McCammon, J Andrew; Wang, Lingle

2015-06-09

Recent advances in improved force fields and sampling methods have made it possible for the accurate calculation of protein–ligand binding free energies. Alchemical free energy perturbation (FEP) using an explicit solvent model is one of the most rigorous methods to calculate relative binding free energies. However, for cases where there are high energy barriers separating the relevant conformations that are important for ligand binding, the calculated free energy may depend on the initial conformation used in the simulation due to the lack of complete sampling of all the important regions in phase space. This is particularly true for ligands with multiple possible binding modes separated by high energy barriers, making it difficult to sample all relevant binding modes even with modern enhanced sampling methods. In this paper, we apply a previously developed method that provides a corrected binding free energy for ligands with multiple binding modes by combining the free energy results from multiple alchemical FEP calculations starting from all enumerated poses, and the results are compared with Glide docking and MM-GBSA calculations. From these calculations, the dominant ligand binding mode can also be predicted. We apply this method to a series of ligands that bind to c-Jun N-terminal kinase-1 (JNK1) and obtain improved free energy results. The dominant ligand binding modes predicted by this method agree with the available crystallography, while both Glide docking and MM-GBSA calculations incorrectly predict the binding modes for some ligands. The method also helps separate the force field error from the ligand sampling error, such that deviations in the predicted binding free energy from the experimental values likely indicate possible inaccuracies in the force field. An error in the force field for a subset of the ligands studied was identified using this method, and improved free energy results were obtained by correcting the partial charges assigned to the

How To Deal with Multiple Binding Poses in Alchemical Relative Protein–Ligand Binding Free Energy Calculations

PubMed Central

2016-01-01

Recent advances in improved force fields and sampling methods have made it possible for the accurate calculation of protein–ligand binding free energies. Alchemical free energy perturbation (FEP) using an explicit solvent model is one of the most rigorous methods to calculate relative binding free energies. However, for cases where there are high energy barriers separating the relevant conformations that are important for ligand binding, the calculated free energy may depend on the initial conformation used in the simulation due to the lack of complete sampling of all the important regions in phase space. This is particularly true for ligands with multiple possible binding modes separated by high energy barriers, making it difficult to sample all relevant binding modes even with modern enhanced sampling methods. In this paper, we apply a previously developed method that provides a corrected binding free energy for ligands with multiple binding modes by combining the free energy results from multiple alchemical FEP calculations starting from all enumerated poses, and the results are compared with Glide docking and MM-GBSA calculations. From these calculations, the dominant ligand binding mode can also be predicted. We apply this method to a series of ligands that bind to c-Jun N-terminal kinase-1 (JNK1) and obtain improved free energy results. The dominant ligand binding modes predicted by this method agree with the available crystallography, while both Glide docking and MM-GBSA calculations incorrectly predict the binding modes for some ligands. The method also helps separate the force field error from the ligand sampling error, such that deviations in the predicted binding free energy from the experimental values likely indicate possible inaccuracies in the force field. An error in the force field for a subset of the ligands studied was identified using this method, and improved free energy results were obtained by correcting the partial charges assigned to the

Impact of domain knowledge on blinded predictions of binding energies by alchemical free energy calculations

NASA Astrophysics Data System (ADS)

Mey, Antonia S. J. S.; Jiménez, Jordi Juárez; Michel, Julien

2018-01-01

The Drug Design Data Resource (D3R) consortium organises blinded challenges to address the latest advances in computational methods for ligand pose prediction, affinity ranking, and free energy calculations. Within the context of the second D3R Grand Challenge several blinded binding free energies predictions were made for two congeneric series of Farsenoid X Receptor (FXR) inhibitors with a semi-automated alchemical free energy calculation workflow featuring FESetup and SOMD software tools. Reasonable performance was observed in retrospective analyses of literature datasets. Nevertheless, blinded predictions on the full D3R datasets were poor due to difficulties encountered with the ranking of compounds that vary in their net-charge. Performance increased for predictions that were restricted to subsets of compounds carrying the same net-charge. Disclosure of X-ray crystallography derived binding modes maintained or improved the correlation with experiment in a subsequent rounds of predictions. The best performing protocols on D3R set1 and set2 were comparable or superior to predictions made on the basis of analysis of literature structure activity relationships (SAR)s only, and comparable or slightly inferior, to the best submissions from other groups.

Free Energies of Formation Measurements on Solid-State Electrochemical Cells

ERIC Educational Resources Information Center

Rollino, J. A.; Aronson, S.

1972-01-01

A simple experiment is proposed that can provide the student with some insight into the chemical properties of solids. It also demonstrates the relationship between the Gibbs free energy of formation of an ionic solid and the emf of an electrochemical cell. (DF)

Contribution of thermal energy to initial ion production in matrix-assisted laser desorption/ionization observed with 2,4,6-trihydroxyacetophenone.

PubMed

Lai, Yin-Hung; Chen, Bo-Gaun; Lee, Yuan Tseh; Wang, Yi-Sheng; Lin, Sheng Hsien

2014-08-15

Although several reaction models have been proposed in the literature to explain matrix-assisted laser desorption/ionization (MALDI), further study is still necessary to explore the important ionization pathways that occur under the high-temperature environment of MALDI. 2,4,6-Trihydroxyacetophenone (THAP) is an ideal compound for evaluating the contribution of thermal energy to an initial reaction with minimum side reactions. Desorbed neutral THAP and ions were measured using a crossed-molecular beam machine and commercial MALDI-TOF instrument, respectively. A quantitative model incorporating an Arrhenius-type desorption rate derived from transition state theory was proposed. Reaction enthalpy was calculated using GAUSSIAN 03 software with dielectric effect. Additional evidence of thermal-induced proton disproportionation was given by the indirect ionization of THAP embedded in excess fullerene molecules excited by a 450 nm laser. The quantitative model predicted that proton disproportionation of THAP would be achieved by thermal energy converted from a commonly used single UV laser photon. The dielectric effect reduced the reaction Gibbs free energy considerably even when the dielectric constant was reduced under high-temperature MALDI conditions. With minimum fitting parameters, observations of pure THAP and THAP mixed with fullerene both agreed with predictions. Proton disproportionation of solid THAP was energetically favorable with a single UV laser photon. The quantitative model revealed an important initial ionization pathway induced by the abrupt heating of matrix crystals. In the matrix crystals, the dielectric effect reduced reaction Gibbs free energy under typical MALDI conditions. The result suggested that thermal energy plays an important role in the initial ionization reaction of THAP. Copyright © 2014 John Wiley & Sons, Ltd.

On the accuracy of density functional theory and wave function methods for calculating vertical ionization energies

DOE Office of Scientific and Technical Information (OSTI.GOV)

McKechnie, Scott; Booth, George H.; Cohen, Aron J.

The best practice in computational methods for determining vertical ionization energies (VIEs) is assessed, via reference to experimentally determined VIEs that are corroborated by highly accurate coupled-cluster calculations. These reference values are used to benchmark the performance of density-functional theory (DFT) and wave function methods: Hartree-Fock theory (HF), second-order Møller-Plesset perturbation theory (MP2) and Electron Propagator Theory (EPT). The core test set consists of 147 small molecules. An extended set of six larger molecules, from benzene to hexacene, is also considered to investigate the dependence of the results on molecule size. The closest agreement with experiment is found for ionizationmore » energies obtained from total energy diff calculations. In particular, DFT calculations using exchange-correlation functionals with either a large amount of exact exchange or long-range correction perform best. The results from these functionals are also the least sensitive to an increase in molecule size. In general, ionization energies calculated directly from the orbital energies of the neutral species are less accurate and more sensitive to an increase in molecule size. For the single-calculation approach, the EPT calculations are in closest agreement for both sets of molecules. For the orbital energies from DFT functionals, only those with long-range correction give quantitative agreement with dramatic failing for all other functionals considered. The results offer a practical hierarchy of approximations for the calculation of vertical ionization energies. In addition, the experimental and computational reference values can be used as a standardized set of benchmarks, against which other approximate methods can be compared.« less

Heterogeneous nucleation on rough surfaces: Generalized Gibbs' approach.

PubMed

Abyzov, Alexander S; Schmelzer, Jürn W P; Davydov, Leonid N

2017-12-07

Heterogeneous nucleation (condensation) of liquid droplets from vapor (gas) on a defective solid surface is considered. The vapor is described by the van der Waals equation of state. The dependence of nucleating droplet parameters on droplet size is accounted for within the generalized Gibbs approach. As a surface defect, a conic void is taken. This choice allows us to simplify the analysis and at the same time to follow the main aspects of the influence of the surface roughness on the nucleation process. Similar to condensation on ideal planar surfaces, the contact angle and catalytic factor for heterogeneous nucleation on a rough surface depend on the degree of vapor overcooling. In the case of droplet formation on a hydrophilic surface of a conic void, the nucleation rate considerably increases in comparison with the condensation on a planar interface. In fact, the presence of a defect on the hydrophilic surface leads to a considerable shift of the spinodal towards lower supersaturation in comparison with heterogeneous nucleation on a planar interface. With the decrease in the void cone angle, the heterogeneous spinodal approaches the binodal, and the region of metastability is diminished at the expense of the instability region.

Mesohysteresis model for ferromagnetic materials by minimization of the micromagnetic free energy

NASA Astrophysics Data System (ADS)

van den Berg, A.; Dupré, L.; Van de Wiele, B.; Crevecoeur, G.

2009-04-01

To study the connection between macroscopic hysteretic behavior and the microstructural properties, this paper presents and validates a new material dependent three-dimensional mesoscopic magnetic hysteresis model. In the presented mesoscopic description, the different micromagnetic energy terms are reformulated on the space scale of the magnetic domains. The sample is discretized in cubic cells, each with a local stress state, local bcc crystallographic axes, etc. The magnetization is assumed to align with one of the three crystallographic axes, in positive or negative sense, defining six volume fractions within each cell. The micromagnetic Gibbs free energy is described in terms of these volume fractions. Hysteresis loops are computed by minimizing the mesoscopic Gibbs free energy using a modified gradient search for a sequence of external applied fields. To validate the mesohysteresis model, we studied the magnetic memory properties. Numerical experiments reveal that (1) minor hysteresis loops are indeed closed and (2) the closed minor loops are erased from the memory.

Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review

PubMed Central

Miao, Yinglong; McCammon, J. Andrew

2016-01-01

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations. PMID:27453631

Unconstrained Enhanced Sampling for Free Energy Calculations of Biomolecules: A Review.

PubMed

Miao, Yinglong; McCammon, J Andrew

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.

Enhanced calculation of eigen-stress field and elastic energy in atomistic interdiffusion of alloys

NASA Astrophysics Data System (ADS)

Cecilia, José M.; Hernández-Díaz, A. M.; Castrillo, Pedro; Jiménez-Alonso, J. F.

2017-02-01

The structural evolution of alloys is affected by the elastic energy associated to eigen-stress fields. However, efficient calculations of the elastic energy in evolving geometries are actually a great challenge in promising atomistic simulation techniques such as Kinetic Monte Carlo (KMC) methods. In this paper, we report two complementary algorithms to calculate the eigen-stress field by linear superposition (a.k.a. LSA, Lineal Superposition Algorithm) and the elastic energy modification in atomistic interdiffusion of alloys (the Atom Exchange Elastic Energy Evaluation (AE4) Algorithm). LSA is shown to be appropriated for fast incremental stress calculation in highly nanostructured materials, whereas AE4 provides the required input for KMC and, additionally, it can be used to evaluate the accuracy of the eigen-stress field calculated by LSA. Consequently, they are suitable to be used on-the-fly with KMC. Both algorithms are massively parallel by their definition and thus well-suited for their parallelization on modern Graphics Processing Units (GPUs). Our computational studies confirm that we can obtain significant improvements compared to conventional Finite Element Methods, and the utilization of GPUs opens up new possibilities for the development of these methods in atomistic simulation of materials.

Enhanced Ligand Sampling for Relative Protein–Ligand Binding Free Energy Calculations

PubMed Central

2016-01-01

Free energy calculations are used to study how strongly potential drug molecules interact with their target receptors. The accuracy of these calculations depends on the accuracy of the molecular dynamics (MD) force field as well as proper sampling of the major conformations of each molecule. However, proper sampling of ligand conformations can be difficult when there are large barriers separating the major ligand conformations. An example of this is for ligands with an asymmetrically substituted phenyl ring, where the presence of protein loops hinders the proper sampling of the different ring conformations. These ring conformations become more difficult to sample when the size of the functional groups attached to the ring increases. The Adaptive Integration Method (AIM) has been developed, which adaptively changes the alchemical coupling parameter λ during the MD simulation so that conformations sampled at one λ can aid sampling at the other λ values. The Accelerated Adaptive Integration Method (AcclAIM) builds on AIM by lowering potential barriers for specific degrees of freedom at intermediate λ values. However, these methods may not work when there are very large barriers separating the major ligand conformations. In this work, we describe a modification to AIM that improves sampling of the different ring conformations, even when there is a very large barrier between them. This method combines AIM with conformational Monte Carlo sampling, giving improved convergence of ring populations and the resulting free energy. This method, called AIM/MC, is applied to study the relative binding free energy for a pair of ligands that bind to thrombin and a different pair of ligands that bind to aspartyl protease β-APP cleaving enzyme 1 (BACE1). These protein–ligand binding free energy calculations illustrate the improvements in conformational sampling and the convergence of the free energy compared to both AIM and AcclAIM. PMID:25906170

Exploring the folding free energy landscape of a β-hairpin miniprotein, chignolin, using multiscale free energy landscape calculation method.

PubMed

Harada, Ryuhei; Kitao, Akio

2011-07-14

The folding process for a β-hairpin miniprotein, chignolin, was investigated by free energy landscape (FEL) calculations using the recently proposed multiscale free energy landscape calculation method (MSFEL). First, coarse-grained molecular dynamics simulations searched a broad conformational space, then multiple independent, all-atom molecular dynamics simulations with explicit solvent determined the detailed local FEL using massively distributed computing. The combination of the two models enabled efficient calculation of the free energy landscapes. The MSFEL analysis showed that chignolin has an intermediate state as well as a misfolded state. The folding process is initiated by the formation of a β-hairpin turn, followed by the formation of contacts in the hydrophobic core between Tyr2 and Trp9. Furthermore, mutation of Tyr2 shifts the population to the misfolded conformation. The results indicate that the hydrophobic core plays an important role in stabilizing the native state of chignolin. © 2011 American Chemical Society

Predicting relative binding affinities of non-peptide HIV protease inhibitors with free energy perturbation calculations

NASA Astrophysics Data System (ADS)

McCarrick, Margaret A.; Kollman, Peter A.

1999-03-01

The relative binding free energies in HIV protease of haloperidol thioketal (THK) and three of its derivatives were examined with free energy calculations. THK is a weak inhibitor (IC50 = 15 μM) for which two cocrystal structures with HIV type 1 proteases have been solved [Rutenber, E. et al., J. Biol. Chem., 268 (1993) 15343]. A THK derivative with a phenyl group on C2 of the piperidine ring was expected to be a poor inhibitor based on experiments with haloperidol ketal and its 2- phenyl derivative (Caldera, P., personal communication). Our calculations predict that a 5-phenyl THK derivative, suggested based on examination of the crystal structure, will bind significantly better than THK. Although there are large error bars as estimated from hysteresis, the calculations predict that the 5-phenyl substituent is clearly favored over the 2-phenyl derivative as well as the parent compound. The unfavorable free energies of solvation of both phenyl THK derivatives relative to the parent compound contributed to their predicted binding free energies. In a third simulation, the change in binding free energy for 5-benzyl THK relative to THK was calculated. Although this derivative has a lower free energy in the protein, its decreased free energy of solvation increases the predicted ΔΔG(bind) to the same range as that of the 2-phenyl derivative.

Leveraging Gibbs Ensemble Molecular Dynamics and Hybrid Monte Carlo/Molecular Dynamics for Efficient Study of Phase Equilibria.

PubMed

Gartner, Thomas E; Epps, Thomas H; Jayaraman, Arthi

2016-11-08

We describe an extension of the Gibbs ensemble molecular dynamics (GEMD) method for studying phase equilibria. Our modifications to GEMD allow for direct control over particle transfer between phases and improve the method's numerical stability. Additionally, we found that the modified GEMD approach had advantages in computational efficiency in comparison to a hybrid Monte Carlo (MC)/MD Gibbs ensemble scheme in the context of the single component Lennard-Jones fluid. We note that this increase in computational efficiency does not compromise the close agreement of phase equilibrium results between the two methods. However, numerical instabilities in the GEMD scheme hamper GEMD's use near the critical point. We propose that the computationally efficient GEMD simulations can be used to map out the majority of the phase window, with hybrid MC/MD used as a follow up for conditions under which GEMD may be unstable (e.g., near-critical behavior). In this manner, we can capitalize on the contrasting strengths of these two methods to enable the efficient study of phase equilibria for systems that present challenges for a purely stochastic GEMC method, such as dense or low temperature systems, and/or those with complex molecular topologies.

An empirical formula to calculate the full energy peak efficiency of scintillation detectors.

PubMed

Badawi, Mohamed S; Abd-Elzaher, Mohamed; Thabet, Abouzeid A; El-khatib, Ahmed M

2013-04-01

This work provides an empirical formula to calculate the FEPE for different detectors using the effective solid angle ratio derived from experimental measurements. The full energy peak efficiency (FEPE) curves of the (2″(*)2″) NaI(Tl) detector at different seven axial distances from the detector were depicted in a wide energy range from 59.53 to 1408keV using standard point sources. The distinction was based on the effects of the source energy and the source-to-detector distance. A good agreement was noticed between the measured and calculated efficiency values for the source-to-detector distances at 20, 25, 30, 35, 40, 45 and 50cm. Copyright © 2012 Elsevier Ltd. All rights reserved.

New more accurate calculations of the ground state potential energy surface of H(3) (+).

PubMed

Pavanello, Michele; Tung, Wei-Cheng; Leonarski, Filip; Adamowicz, Ludwik

2009-02-21

Explicitly correlated Gaussian functions with floating centers have been employed to recalculate the ground state potential energy surface (PES) of the H(3) (+) ion with much higher accuracy than it was done before. The nonlinear parameters of the Gaussians (i.e., the exponents and the centers) have been variationally optimized with a procedure employing the analytical gradient of the energy with respect to these parameters. The basis sets for calculating new PES points were guessed from the points already calculated. This allowed us to considerably speed up the calculations and achieve very high accuracy of the results.

Wind Energy Finance (WEF): An Online Calculator for Economic Analysis of Wind Projects

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

2004-02-01

This brochure provides an overview of Wind Energy Finance (WEF), a free online cost of energy calculator developed by the National Renewable Energy Laboratory that provides quick, detailed economic evaluation of potential utility-scale wind energy projects. The brochure lists the features of the tool, the inputs and outputs that a user can expect, visuals of the screens and a Cash Flow Results table, and contact information.

Extended wave-packet model to calculate energy-loss moments of protons in matter

NASA Astrophysics Data System (ADS)

Archubi, C. D.; Arista, N. R.

2017-12-01

In this work we introduce modifications to the wave-packet method proposed by Kaneko to calculate the energy-loss moments of a projectile traversing a target which is represented in terms of Gaussian functions for the momentum distributions of electrons in the atomic shells. These modifications are introduced using the Levine and Louie technique to take into account the energy gaps corresponding to the different atomic levels of the target. We use the extended wave-packet model to evaluate the stopping power, the energy straggling, the inverse mean free path, and the ionization cross sections for protons in several targets, obtaining good agreements for all these quantities on an extensive energy range that covers low-, intermediate-, and high-energy regions. The extended wave-packet model proposed here provides a method to calculate in a very straightforward way all the significant terms of the inelastic interaction of light ions with any element of the periodic table.

Potential energy surface interpolation with neural networks for instanton rate calculations

NASA Astrophysics Data System (ADS)

Cooper, April M.; Hallmen, Philipp P.; Kästner, Johannes

2018-03-01

Artificial neural networks are used to fit a potential energy surface (PES). We demonstrate the benefits of using not only energies but also their first and second derivatives as training data for the neural network. This ensures smooth and accurate Hessian surfaces, which are required for rate constant calculations using instanton theory. Our aim was a local, accurate fit rather than a global PES because instanton theory requires information on the potential only in the close vicinity of the main tunneling path. Elongations along vibrational normal modes at the transition state are used as coordinates for the neural network. The method is applied to the hydrogen abstraction reaction from methanol, calculated on a coupled-cluster level of theory. The reaction is essential in astrochemistry to explain the deuteration of methanol in the interstellar medium.

Automated calculation of surface energy fluxes with high-frequency lake buoy data

USGS Publications Warehouse

Woolway, R. Iestyn; Jones, Ian D; Hamilton, David P.; Maberly, Stephen C; Muroaka, Kohji; Read, Jordan S.; Smyth, Robyn L; Winslow, Luke A.

2015-01-01

Lake Heat Flux Analyzer is a program used for calculating the surface energy fluxes in lakes according to established literature methodologies. The program was developed in MATLAB for the rapid analysis of high-frequency data from instrumented lake buoys in support of the emerging field of aquatic sensor network science. To calculate the surface energy fluxes, the program requires a number of input variables, such as air and water temperature, relative humidity, wind speed, and short-wave radiation. Available outputs for Lake Heat Flux Analyzer include the surface fluxes of momentum, sensible heat and latent heat and their corresponding transfer coefficients, incoming and outgoing long-wave radiation. Lake Heat Flux Analyzer is open source and can be used to process data from multiple lakes rapidly. It provides a means of calculating the surface fluxes using a consistent method, thereby facilitating global comparisons of high-frequency data from lake buoys.

Calculation of Quasi-Particle Energies of Aromatic Self-Assembled Monolayers on Au(111).

PubMed

Li, Yan; Lu, Deyu; Galli, Giulia

2009-04-14

We present many-body perturbation theory calculations of the electronic properties of phenylene diisocyanide self-assembled monolayers (SAMs) on a gold surface. Using structural models obtained within density functional theory (DFT), we have investigated how the SAM molecular energies are modified by self-energy corrections and how they are affected by the presence of the surface. We have employed a combination of GW (G = Green's function; W = screened Coulomb interaction) calculations of the SAM quasi-particle energies and a semiclassical image potential model to account for surface polarization effects. We find that it is essential to include both quasi-particle corrections and surface screening in order to provide a reasonable estimate of the energy level alignment at a SAM-metal interface. In particular, our results show that within the GW approximation the energy distance between phenylene diisocyanide SAM energy levels and the gold surface Fermi level is much larger than that found within DFT, e.g., more than double in the case of low packing densities of the SAM.

Excited state free energy calculations of Cy3 in different environments

NASA Astrophysics Data System (ADS)

Sawangsang, Pilailuk; Buranachai, Chittanon; Punwong, Chutintorn

2015-05-01

Cy3, a cyanine dye, is one of the most widely used dyes in investigating the structure and dynamics of biomolecules by means of fluorescence methods. However, Cy3 fluorescence emission is strongly competed by trans-cis isomerization, whose efficiency is dictated by the isomerization energy barrier and the environment of Cy3. The fluorescence quantum yield of Cy3 is very low when the dye is free in homogeneous solution but it is considerably enhanced in an environment that rigidifies the structure, e.g. when it is attached to a DNA strand. In this work, the barriers for isomerization on the excited state of free Cy3, and Cy3 attached to single- and double-stranded DNA in methanol, are presented. The free energy and subsequently the isomerization barrier calculations are performed using the umbrella sampling technique with the weighted histogram analysis method. The hybrid quantum mechanics/molecular mechanics (QM/MM) approach is employed to provide the potential energy surfaces for the excited state dynamics simulations in umbrella sampling. The semiempirical floating occupation molecular orbital configuration interaction method is used for electronic excited state calculations of the QM region (Cy3). From the free energy calculations, the barrier of Cy3 attached to the single-stranded DNA is highest, in agreement with previously reported experimental results. This is likely due to the stacking interaction between Cy3 and DNA. Such a stacking interaction is likely associated with steric hindrance that prevents the rotation around the conjugated bonds of Cy3. If Cy3 experiences high steric hindrance, it has a higher isomerization barrier and thus the efficiency of fluorescence emission increases.

Site energies and charge transfer rates near pentacene grain boundaries from first-principles calculations

NASA Astrophysics Data System (ADS)

Kobayashi, Hajime; Tokita, Yuichi

2015-03-01

Charge transfer rates near pentacene grain boundaries are derived by calculating the site energies and transfer integrals of 37 pentacene molecules using first-principles calculations. The site energies decrease considerably near the grain boundaries, and electron traps of up to 300 meV and hole barriers of up to 400 meV are generated. The charge transfer rates across the grain boundaries are found to be reduced by three to five orders of magnitude with a grain boundary gap of 4 Å because of the reduction in the transfer integrals. The electron traps and hole barriers also reduce the electron and hole transfer rates by factors of up to 10 and 50, respectively. It is essential to take the site energies into consideration to determine charge transport near the grain boundaries. We show that the complex site energy distributions near the grain boundaries can be represented by an equivalent site energy difference, which is a constant for any charge transfer pass. When equivalent site energy differences are obtained for various grain boundary structures by first-principles calculations, the effects of the grain boundaries on the charge transfer rates are introduced exactly into charge transport simulations, such as the kinetic Monte Carlo method.

Nitrogen in chromium-manganese stainless steels: a review on the evaluation of stacking fault energy by computational thermodynamics.

PubMed

Mosecker, Linda; Saeed-Akbari, Alireza

2013-06-01

Nitrogen in austenitic stainless steels and its effect on the stacking fault energy (SFE) has been the subject of intense discussions in the literature. Until today, no generally accepted method for the SFE calculation exists that can be applied to a wide range of chemical compositions in these systems. Besides different types of models that are used from first-principle to thermodynamics-based approaches, one main reason is the general lack of experimentally measured SFE values for these steels. Moreover, in the respective studies, not only different alloying systems but also different domains of nitrogen contents were analyzed resulting in contrary conclusions on the effect of nitrogen on the SFE. This work gives a review on the current state of SFE calculation by computational thermodynamics for the Fe-Cr-Mn-N system. An assessment of the thermodynamic effective Gibbs free energy, [Formula: see text], model for the [Formula: see text] phase transformation considering existing data from different literature and commercial databases is given. Furthermore, we introduce the application of a non-constant composition-dependent interfacial energy, б γ / ε , required to consider the effect of nitrogen on SFE in these systems.

Nitrogen in chromium–manganese stainless steels: a review on the evaluation of stacking fault energy by computational thermodynamics

PubMed Central

Mosecker, Linda; Saeed-Akbari, Alireza

2013-01-01

Nitrogen in austenitic stainless steels and its effect on the stacking fault energy (SFE) has been the subject of intense discussions in the literature. Until today, no generally accepted method for the SFE calculation exists that can be applied to a wide range of chemical compositions in these systems. Besides different types of models that are used from first-principle to thermodynamics-based approaches, one main reason is the general lack of experimentally measured SFE values for these steels. Moreover, in the respective studies, not only different alloying systems but also different domains of nitrogen contents were analyzed resulting in contrary conclusions on the effect of nitrogen on the SFE. This work gives a review on the current state of SFE calculation by computational thermodynamics for the Fe–Cr–Mn–N system. An assessment of the thermodynamic effective Gibbs free energy, , model for the phase transformation considering existing data from different literature and commercial databases is given. Furthermore, we introduce the application of a non-constant composition-dependent interfacial energy, бγ/ε, required to consider the effect of nitrogen on SFE in these systems. PMID:27877573

Calculation of intensity of high energy muon groups observed deep underground

NASA Technical Reports Server (NTRS)

Vavilov, Y. N.; Dedenko, L. G.

1985-01-01

The intensity of narrow muon groups observed in Kolar Gold Field (KGF) at the depth of 3375 m.w.e. was calculated in terms of quark-gluon strings model for high energy hadron - air nuclei interactions by the method of direct modeling of nuclear cascade in the air and muon propagation in the ground for normal primary cosmic ray composition. The calculated intensity has been found to be approx. 10 to the 4 times less than one observed experimentally.

Biogas - the calculable energy

NASA Astrophysics Data System (ADS)

Kith, Károly; Nagy, Orsolya; Balla, Zoltán; Tamás, András

2015-04-01

EU actions against climate change are rising energy prices, both have emphasized the use of renewable energy,increase investments and energy efficiency. A number of objectives formulated in the EC decree no. 29/2009 by 2020. This document is based on the share of renewable energies in energy consumption should be increased to 20% (EC, 2009). The EU average is 20% but the share of renewables vary from one member state to another. In Hungary in 2020, 14.65% renewable energy share is planned to be achieved. According to the latest Eurostat data, the share of renewable energy in energy consumption of the EU average was 14.1%, while in Hungary, this share was 9.6% in 2012. (EUROSTAT, 2014). The use of renewable energy plant level is influenced by several factors. The most important of these is the cost savings and efficiency gains. Hungarian investments in renewable energy production usually have high associated costs and the payback period is substantially more than five years, depending on the support rate. For example, the payback period is also influenced by the green electricity generated feed prices, which is one of the lowest in Hungary compared the Member States of the European Union. Consequently, it is important to increase the production of green energy. Nowadays, predictable biogas energy is an outstanding type of decentralized energy production. It follows directly that agricultural by-products can be used to produce energy and they also create jobs by the construction of a biogas plant. It is important to dispose of and destroy hazardous and noxious substances in energy production. It follows from this that the construction of biogas plants have a positive impact, in addition to green energy which is prepared to reduce the load on the environment. The production of biogas and green electricity is one of the most environment friendly forms of energy production. Biogas production also has other important ecological effects, such as the substitution of

X-alpha calculation of transition energies in multiply ionized atoms

NASA Technical Reports Server (NTRS)

Ringers, D. A.; Chen, M. H.

1974-01-01

It is shown that the accuracy of calculations can be improved if appropriate (different) values of alpha are used for each configuration. Alternatively, the Slater Transition state can be used, wherein a total energy difference is related to a difference in single electron eigenvalues. By a series expansion, the value of alpha for an excited configuration can be related to its value for the ground state configuration. The terms Delta alpha (delta Epsilon/delta alpha) exhibit a similar dependence on atomic number as the ground state values of alpha. Results of sample calculations are reported and compared with experiment.

Basis sets for the calculation of core-electron binding energies

NASA Astrophysics Data System (ADS)

Hanson-Heine, Magnus W. D.; George, Michael W.; Besley, Nicholas A.

2018-05-01

Core-electron binding energies (CEBEs) computed within a Δ self-consistent field approach require large basis sets to achieve convergence with respect to the basis set limit. It is shown that supplementing a basis set with basis functions from the corresponding basis set for the element with the next highest nuclear charge (Z + 1) provides basis sets that give CEBEs close to the basis set limit. This simple procedure provides relatively small basis sets that are well suited for calculations where the description of a core-ionised state is important, such as time-dependent density functional theory calculations of X-ray emission spectroscopy.

The importance of geospatial data to calculate the optimal distribution of renewable energies

NASA Astrophysics Data System (ADS)

Díaz, Paula; Masó, Joan

2013-04-01

Specially during last three years, the renewable energies are revolutionizing the international trade while they are geographically diversifying markets. Renewables are experiencing a rapid growth in power generation. According to REN21 (2012), during last six years, the total renewables capacity installed grew at record rates. In 2011, the EU raised its share of global new renewables capacity till 44%. The BRICS nations (Brazil, Russia, India and China) accounted for about 26% of the total global. Moreover, almost twenty countries in the Middle East, North Africa, and sub-Saharan Africa have currently active markets in renewables. The energy return ratios are commonly used to calculate the efficiency of the traditional energy sources. The Energy Return On Investment (EROI) compares the energy returned for a certain source and the energy used to get it (explore, find, develop, produce, extract, transform, harvest, grow, process, etc.). These energy return ratios have demonstrated a general decrease of efficiency of the fossil fuels and gas. When considering the limitations of the quantity of energy produced by some sources, the energy invested to obtain them and the difficulties of finding optimal locations for the establishment of renewables farms (e.g. due to an ever increasing scarce of appropriate land) the EROI becomes relevant in renewables. A spatialized EROI, which uses variables with spatial distribution, enables the optimal position in terms of both energy production and associated costs. It is important to note that the spatialized EROI can be mathematically formalized and calculated the same way for different locations in a reproducible way. This means that having established a concrete EROI methodology it is possible to generate a continuous map that will highlight the best productive zones for renewable energies in terms of maximum energy return at minimum cost. Relevant variables to calculate the real energy invested are the grid connections between

Calculation of the Local Free Energy Landscape in the Restricted Region by the Modified Tomographic Method.

PubMed

Chen, Changjun

2016-03-31

The free energy landscape is the most important information in the study of the reaction mechanisms of the molecules. However, it is difficult to calculate. In a large collective variable space, a molecule must take a long time to obtain the sufficient sampling during the simulation. To save the calculation quantity, decreasing the sampling region and constructing the local free energy landscape is required in practice. However, the restricted region in the collective variable space may have an irregular shape. Simply restricting one or more collective variables of the molecule cannot satisfy the requirement. In this paper, we propose a modified tomographic method to perform the simulation. First, it divides the restricted region by some hyperplanes and connects the centers of hyperplanes together by a curve. Second, it forces the molecule to sample on the curve and the hyperplanes in the simulation and calculates the free energy data on them. Finally, all the free energy data are combined together to form the local free energy landscape. Without consideration of the area outside the restricted region, this free energy calculation can be more efficient. By this method, one can further optimize the path quickly in the collective variable space.

Microhydration of caesium compounds: Cs, CsOH, CsI and Cs₂I₂ complexes with one to three H₂O molecules of nuclear safety interest.

PubMed

Sudolská, Mária; Cantrel, Laurent; Cernušák, Ivan

2014-04-01

Structure and thermodynamic properties (standard enthalpies of formation and Gibbs free energies) of hydrated caesium species of nuclear safety interest, Cs, CsOH, CsI and its dimer Cs₂I₂, with one up to three water molecules, are calculated to assess their possible existence in severe accident occurring to a pressurized water reactor. The calculations were performed using the coupled cluster theory including single, double and non-iterative triple substitutions (CCSD(T)) in conjunction with the basis sets (ANO-RCC) developed for scalar relativistic calculations. The second-order spin-free Douglas-Kroll-Hess Hamiltonian was used to account for the scalar relativistic effects. Thermodynamic properties obtained by these correlated ab initio calculations (entropies and thermal capacities at constant pressure as a function of temperature) are used in nuclear accident simulations using ASTEC/SOPHAEROS software. Interaction energies, standard enthalpies and Gibbs free energies of successive water molecules addition determine the ordering of the complexes. CsOH forms the most hydrated stable complexes followed by CsI, Cs₂I₂, and Cs. CsOH still exists in steam atmosphere even at quite high temperature, up to around 1100 K.

Monte Carlo calculations of energy deposition distributions of electrons below 20 keV in protein.

PubMed

Tan, Zhenyu; Liu, Wei

2014-05-01

The distributions of energy depositions of electrons in semi-infinite bulk protein and the radial dose distributions of point-isotropic mono-energetic electron sources [i.e., the so-called dose point kernel (DPK)] in protein have been systematically calculated in the energy range below 20 keV, based on Monte Carlo methods. The ranges of electrons have been evaluated by extrapolating two calculated distributions, respectively, and the evaluated ranges of electrons are compared with the electron mean path length in protein which has been calculated by using electron inelastic cross sections described in this work in the continuous-slowing-down approximation. It has been found that for a given energy, the electron mean path length is smaller than the electron range evaluated from DPK, but it is large compared to the electron range obtained from the energy deposition distributions of electrons in semi-infinite bulk protein. The energy dependences of the extrapolated electron ranges based on the two investigated distributions are given, respectively, in a power-law form. In addition, the DPK in protein has also been compared with that in liquid water. An evident difference between the two DPKs is observed. The calculations presented in this work may be useful in studies of radiation effects on proteins.

Boosting association rule mining in large datasets via Gibbs sampling.

PubMed

Qian, Guoqi; Rao, Calyampudi Radhakrishna; Sun, Xiaoying; Wu, Yuehua

2016-05-03

Current algorithms for association rule mining from transaction data are mostly deterministic and enumerative. They can be computationally intractable even for mining a dataset containing just a few hundred transaction items, if no action is taken to constrain the search space. In this paper, we develop a Gibbs-sampling-induced stochastic search procedure to randomly sample association rules from the itemset space, and perform rule mining from the reduced transaction dataset generated by the sample. Also a general rule importance measure is proposed to direct the stochastic search so that, as a result of the randomly generated association rules constituting an ergodic Markov chain, the overall most important rules in the itemset space can be uncovered from the reduced dataset with probability 1 in the limit. In the simulation study and a real genomic data example, we show how to boost association rule mining by an integrated use of the stochastic search and the Apriori algorithm.

Quasiclassical trajectory calculations to evaluate a kinematic constraint on internal energy in suprathreshold collision energy abstraction reactions

NASA Astrophysics Data System (ADS)

Shuman, Nicholas S.; Mihok, Morgan; Fistik, Margaret; Valentini, James J.

2005-08-01

Experimentally observed product quantum state distributions across a wide range of abstraction reactions at suprathreshold collision energies have shown a strong bias against product internal energy. Only a fraction, sometimes quite a small fraction, of the energetically accessible product quantum states are populated. Picconatto et al. [J. Chem. Phys. 114, 1663 (2001)] noted a simple mathematical relationship between the highest-energy rovibrational states observed and the kinematics of the reaction system. They proposed a reaction model based on reaction kinematics that quantitatively explains this behavior. The model is in excellent agreement with measured quantum state distributions. The assumptions of the model invoke detailed characteristics of reactive trajectories at suprathreshold collision energies. Here we test those assumptions using quasiclassical trajectory calculations for the abstraction reactions H +HCl→H2+Cl, D +HCl→HD+Cl, and H +DCl→HD+Cl. Trajectories were run on a potential-energy surface calculated with a London-Eyring-Polyani-Sato function with a localized 3-center term (LEPS-3C) previously shown to accurately reproduce experimentally observed product state distributions for the H +HCl abstraction reaction. The trajectories sample collision energies near threshold and also substantially above it. Although the trajectories demonstrate some aspects of the model, they show that it is not valid. However, the inadequacy of the proposed model does not invalidate the apparent kinematic basis of the observed energy constraint. The present results show that there must be some other molecular behavior rooted in the reaction kinematics that is the explanation and the source of the constraint.

Alternative definitions of the frozen energy in energy decomposition analysis of density functional theory calculations.

PubMed

Horn, Paul R; Head-Gordon, Martin

2016-02-28

In energy decomposition analysis (EDA) of intermolecular interactions calculated via density functional theory, the initial supersystem wavefunction defines the so-called "frozen energy" including contributions such as permanent electrostatics, steric repulsions, and dispersion. This work explores the consequences of the choices that must be made to define the frozen energy. The critical choice is whether the energy should be minimized subject to the constraint of fixed density. Numerical results for Ne2, (H2O)2, BH3-NH3, and ethane dissociation show that there can be a large energy lowering associated with constant density orbital relaxation. By far the most important contribution is constant density inter-fragment relaxation, corresponding to charge transfer (CT). This is unwanted in an EDA that attempts to separate CT effects, but it may be useful in other contexts such as force field development. An algorithm is presented for minimizing single determinant energies at constant density both with and without CT by employing a penalty function that approximately enforces the density constraint.

Free Energy Minimization Calculation of Complex Chemical Equilibria. Reduction of Silicon Dioxide with Carbon at High Temperature.

ERIC Educational Resources Information Center

Wai, C. M.; Hutchinson, S. G.

1989-01-01

Discusses the calculation of free energy in reactions between silicon dioxide and carbon. Describes several computer programs for calculating the free energy minimization and their uses in chemistry classrooms. Lists 16 references. (YP)

Using force-based adaptive resolution simulations to calculate solvation free energies of amino acid sidechain analogues

NASA Astrophysics Data System (ADS)

Fiorentini, Raffaele; Kremer, Kurt; Potestio, Raffaello; Fogarty, Aoife C.

2017-06-01

The calculation of free energy differences is a crucial step in the characterization and understanding of the physical properties of biological molecules. In the development of efficient methods to compute these quantities, a promising strategy is that of employing a dual-resolution representation of the solvent, specifically using an accurate model in the proximity of a molecule of interest and a simplified description elsewhere. One such concurrent multi-resolution simulation method is the Adaptive Resolution Scheme (AdResS), in which particles smoothly change their resolution on-the-fly as they move between different subregions. Before using this approach in the context of free energy calculations, however, it is necessary to make sure that the dual-resolution treatment of the solvent does not cause undesired effects on the computed quantities. Here, we show how AdResS can be used to calculate solvation free energies of small polar solutes using Thermodynamic Integration (TI). We discuss how the potential-energy-based TI approach combines with the force-based AdResS methodology, in which no global Hamiltonian is defined. The AdResS free energy values agree with those calculated from fully atomistic simulations to within a fraction of kBT. This is true even for small atomistic regions whose size is on the order of the correlation length, or when the properties of the coarse-grained region are extremely different from those of the atomistic region. These accurate free energy calculations are possible because AdResS allows the sampling of solvation shell configurations which are equivalent to those of fully atomistic simulations. The results of the present work thus demonstrate the viability of the use of adaptive resolution simulation methods to perform free energy calculations and pave the way for large-scale applications where a substantial computational gain can be attained.

Thermodynamic and energy efficiency analysis of power generation from natural salinity gradients by pressure retarded osmosis.

PubMed

Yip, Ngai Yin; Elimelech, Menachem

2012-05-01

The Gibbs free energy of mixing dissipated when fresh river water flows into the sea can be harnessed for sustainable power generation. Pressure retarded osmosis (PRO) is one of the methods proposed to generate power from natural salinity gradients. In this study, we carry out a thermodynamic and energy efficiency analysis of PRO work extraction. First, we present a reversible thermodynamic model for PRO and verify that the theoretical maximum extractable work in a reversible PRO process is identical to the Gibbs free energy of mixing. Work extraction in an irreversible constant-pressure PRO process is then examined. We derive an expression for the maximum extractable work in a constant-pressure PRO process and show that it is less than the ideal work (i.e., Gibbs free energy of mixing) due to inefficiencies intrinsic to the process. These inherent inefficiencies are attributed to (i) frictional losses required to overcome hydraulic resistance and drive water permeation and (ii) unutilized energy due to the discontinuation of water permeation when the osmotic pressure difference becomes equal to the applied hydraulic pressure. The highest extractable work in constant-pressure PRO with a seawater draw solution and river water feed solution is 0.75 kWh/m(3) while the free energy of mixing is 0.81 kWh/m(3)-a thermodynamic extraction efficiency of 91.1%. Our analysis further reveals that the operational objective to achieve high power density in a practical PRO process is inconsistent with the goal of maximum energy extraction. This study demonstrates thermodynamic and energetic approaches for PRO and offers insights on actual energy accessible for utilization in PRO power generation through salinity gradients. © 2012 American Chemical Society

Calculation of positron binding energies using the generalized any particle propagator theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Romero, Jonathan; Charry, Jorge A.; Flores-Moreno, Roberto

2014-09-21

We recently extended the electron propagator theory to any type of quantum species based in the framework of the Any-Particle Molecular Orbital (APMO) approach [J. Romero, E. Posada, R. Flores-Moreno, and A. Reyes, J. Chem. Phys. 137, 074105 (2012)]. The generalized any particle molecular orbital propagator theory (APMO/PT) was implemented in its quasiparticle second order version in the LOWDIN code and was applied to calculate nuclear quantum effects in electron binding energies and proton binding energies in molecular systems [M. Díaz-Tinoco, J. Romero, J. V. Ortiz, A. Reyes, and R. Flores-Moreno, J. Chem. Phys. 138, 194108 (2013)]. In this work,more » we present the derivation of third order quasiparticle APMO/PT methods and we apply them to calculate positron binding energies (PBEs) of atoms and molecules. We calculated the PBEs of anions and some diatomic molecules using the second order, third order, and renormalized third order quasiparticle APMO/PT approaches and compared our results with those previously calculated employing configuration interaction (CI), explicitly correlated and quantum Montecarlo methodologies. We found that renormalized APMO/PT methods can achieve accuracies of ∼0.35 eV for anionic systems, compared to Full-CI results, and provide a quantitative description of positron binding to anionic and highly polar species. Third order APMO/PT approaches display considerable potential to study positron binding to large molecules because of the fifth power scaling with respect to the number of basis sets. In this regard, we present additional PBE calculations of some small polar organic molecules, amino acids and DNA nucleobases. We complement our numerical assessment with formal and numerical analyses of the treatment of electron-positron correlation within the quasiparticle propagator approach.« less

An ab initio potential energy surface for the formic acid dimer: zero-point energy, selected anharmonic fundamental energies, and ground-state tunneling splitting calculated in relaxed 1-4-mode subspaces.

PubMed

Qu, Chen; Bowman, Joel M

2016-09-14

We report a full-dimensional, permutationally invariant potential energy surface (PES) for the cyclic formic acid dimer. This PES is a least-squares fit to 13475 CCSD(T)-F12a/haTZ (VTZ for H and aVTZ for C and O) energies. The energy-weighted, root-mean-square fitting error is 11 cm -1 and the barrier for the double-proton transfer on the PES is 2848 cm -1 , in good agreement with the directly-calculated ab initio value of 2853 cm -1 . The zero-point vibrational energy of 15 337 ± 7 cm -1 is obtained from diffusion Monte Carlo calculations. Energies of fundamentals of fifteen modes are calculated using the vibrational self-consistent field and virtual-state configuration interaction method. The ground-state tunneling splitting is computed using a reduced-dimensional Hamiltonian with relaxed potentials. The highest-level, four-mode coupled calculation gives a tunneling splitting of 0.037 cm -1 , which is roughly twice the experimental value. The tunneling splittings of (DCOOH) 2 and (DCOOD) 2 from one to three mode calculations are, as expected, smaller than that for (HCOOH) 2 and consistent with experiment.

Efficient calculation of the polarizability: a simplified effective-energy technique

NASA Astrophysics Data System (ADS)

Berger, J. A.; Reining, L.; Sottile, F.

2012-09-01

In a recent publication [J.A. Berger, L. Reining, F. Sottile, Phys. Rev. B 82, 041103(R) (2010)] we introduced the effective-energy technique to calculate in an accurate and numerically efficient manner the GW self-energy as well as the polarizability, which is required to evaluate the screened Coulomb interaction W. In this work we show that the effective-energy technique can be used to further simplify the expression for the polarizability without a significant loss of accuracy. In contrast to standard sum-over-state methods where huge summations over empty states are required, our approach only requires summations over occupied states. The three simplest approximations we obtain for the polarizability are explicit functionals of an independent- or quasi-particle one-body reduced density matrix. We provide evidence of the numerical accuracy of this simplified effective-energy technique as well as an analysis of our method.

Absolute binding free energies between T4 lysozyme and 141 small molecules: calculations based on multiple rigid receptor configurations

PubMed Central

Xie, Bing; Nguyen, Trung Hai; Minh, David D. L.

2017-01-01

We demonstrate the feasibility of estimating protein-ligand binding free energies using multiple rigid receptor configurations. Based on T4 lysozyme snapshots extracted from six alchemical binding free energy calculations with a flexible receptor, binding free energies were estimated for a total of 141 ligands. For 24 ligands, the calculations reproduced flexible-receptor estimates with a correlation coefficient of 0.90 and a root mean square error of 1.59 kcal/mol. The accuracy of calculations based on Poisson-Boltzmann/Surface Area implicit solvent was comparable to previously reported free energy calculations. PMID:28430432

Time-reversal imaging for classification of submerged elastic targets via Gibbs sampling and the Relevance Vector Machine.

PubMed

Dasgupta, Nilanjan; Carin, Lawrence

2005-04-01

Time-reversal imaging (TRI) is analogous to matched-field processing, although TRI is typically very wideband and is appropriate for subsequent target classification (in addition to localization). Time-reversal techniques, as applied to acoustic target classification, are highly sensitive to channel mismatch. Hence, it is crucial to estimate the channel parameters before time-reversal imaging is performed. The channel-parameter statistics are estimated here by applying a geoacoustic inversion technique based on Gibbs sampling. The maximum a posteriori (MAP) estimate of the channel parameters are then used to perform time-reversal imaging. Time-reversal implementation requires a fast forward model, implemented here by a normal-mode framework. In addition to imaging, extraction of features from the time-reversed images is explored, with these applied to subsequent target classification. The classification of time-reversed signatures is performed by the relevance vector machine (RVM). The efficacy of the technique is analyzed on simulated in-channel data generated by a free-field finite element method (FEM) code, in conjunction with a channel propagation model, wherein the final classification performance is demonstrated to be relatively insensitive to the associated channel parameters. The underlying theory of Gibbs sampling and TRI are presented along with the feature extraction and target classification via the RVM.

Computational scheme for pH-dependent binding free energy calculation with explicit solvent.

PubMed

Lee, Juyong; Miller, Benjamin T; Brooks, Bernard R

2016-01-01

We present a computational scheme to compute the pH-dependence of binding free energy with explicit solvent. Despite the importance of pH, the effect of pH has been generally neglected in binding free energy calculations because of a lack of accurate methods to model it. To address this limitation, we use a constant-pH methodology to obtain a true ensemble of multiple protonation states of a titratable system at a given pH and analyze the ensemble using the Bennett acceptance ratio (BAR) method. The constant pH method is based on the combination of enveloping distribution sampling (EDS) with the Hamiltonian replica exchange method (HREM), which yields an accurate semi-grand canonical ensemble of a titratable system. By considering the free energy change of constraining multiple protonation states to a single state or releasing a single protonation state to multiple states, the pH dependent binding free energy profile can be obtained. We perform benchmark simulations of a host-guest system: cucurbit[7]uril (CB[7]) and benzimidazole (BZ). BZ experiences a large pKa shift upon complex formation. The pH-dependent binding free energy profiles of the benchmark system are obtained with three different long-range interaction calculation schemes: a cutoff, the particle mesh Ewald (PME), and the isotropic periodic sum (IPS) method. Our scheme captures the pH-dependent behavior of binding free energy successfully. Absolute binding free energy values obtained with the PME and IPS methods are consistent, while cutoff method results are off by 2 kcal mol(-1) . We also discuss the characteristics of three long-range interaction calculation methods for constant-pH simulations. © 2015 The Protein Society.

Strong correlations between the exponent α and the particle number for a Renyi monoatomic gas in Gibbs' statistical mechanics.

PubMed

Plastino, A; Rocca, M C

2017-06-01

Appealing to the 1902 Gibbs formalism for classical statistical mechanics (SM)-the first SM axiomatic theory ever that successfully explained equilibrium thermodynamics-we show that already at the classical level there is a strong correlation between Renyi's exponent α and the number of particles for very simple systems. No reference to heat baths is needed for such a purpose.

Molecular dynamics simulation of cytochrome c3: studying the reduction processes using free energy calculations.

PubMed Central

Soares, C M; Martel, P J; Mendes, J; Carrondo, M A

1998-01-01

The tetraheme cytochrome c3 from Desulfovibrio vulgaris Hildenborough is studied using molecular dynamics simulation studies in explicit solvent. The high heme content of the protein, which has its core almost entirely made up of c-type heme, presents specific problems in the simulation. Instability in the structure is observed in long simulations above 1 ns, something that does not occur in a monoheme cytochrome, suggesting problems in heme parametrization. Given these stability problems, a partially restrained model, which avoids destruction of the structure, was created with the objective of performing free energy calculations of heme reduction, studies that require long simulations. With this model, the free energy of reduction of each individual heme was calculated. A correction in the long-range electrostatic interactions of charge groups belonging to the redox centers had to be made in order to make the system physically meaningful. Correlation is obtained between the calculated free energies and the experimental data for three of four hemes. However, the relative scale of the calculated energies is different from the scale of the experimental free energies. Reasons for this are discussed. In addition to the free energy calculations, this model allows the study of conformational changes upon reduction. Even if the precise details of the structural changes that take place in this system upon individual heme reduction are probably out of the reach of this study, it appears that these structural changes are small, similarly to what is observed for other redox proteins. This does not mean that their effect is minor, and one example is the conformational change observed in propionate D from heme I when heme II becomes reduced. A motion of this kind could be the basis of the experimentally observed cooperativity effects between heme reduction, namely positive cooperativity. PMID:9545034

SU-E-T-510: Calculation of High Resolution and Material-Specific Photon Energy Deposition Kernels.

PubMed

Huang, J; Childress, N; Kry, S

2012-06-01

To calculate photon energy deposition kernels (EDKs) used for convolution/superposition dose calculation at a higher resolution than the original Mackie et al. 1988 kernels and to calculate material-specific kernels that describe how energy is transported and deposited by secondary particles when the incident photon interacts in a material other than water. The high resolution EDKs for various incident photon energies were generated using the EGSnrc user-code EDKnrc, which forces incident photons to interact at the center of a 60 cm radius sphere of water. The simulation geometry is essentially the same as the original Mackie calculation but with a greater number of scoring voxels (48 radial, 144 angular bins). For the material-specific EDKs, incident photons were forced to interact at the center of a 1 mm radius sphere of material (lung, cortical bone, silver, or titanium) surrounded by a 60 cm radius water sphere, using the original scoring voxel geometry implemented by Mackie et al. 1988 (24 radial, 48 angular bins). Our Monte Carlo-calculated high resolution EDKs showed excellent agreement with the Mackie kernels, with our kernels providing more information about energy deposition close to the interaction site. Furthermore, our EDKs resulted in smoother dose deposition functions due to the finer resolution and greater number of simulation histories. The material-specific EDK results show that the angular distribution of energy deposition is different for incident photons interacting in different materials. Calculated from the angular dose distribution for 300 keV incident photons, the expected polar angle for dose deposition () is 28.6° for water, 33.3° for lung, 36.0° for cortical bone, 44.6° for titanium, and 58.1° for silver, showing a dependence on the material in which the primary photon interacts. These high resolution and material-specific EDKs have implications for convolution/superposition dose calculations in heterogeneous patient

Recent advances in QM/MM free energy calculations using reference potentials.

PubMed

Duarte, Fernanda; Amrein, Beat A; Blaha-Nelson, David; Kamerlin, Shina C L

2015-05-01

Recent years have seen enormous progress in the development of methods for modeling (bio)molecular systems. This has allowed for the simulation of ever larger and more complex systems. However, as such complexity increases, the requirements needed for these models to be accurate and physically meaningful become more and more difficult to fulfill. The use of simplified models to describe complex biological systems has long been shown to be an effective way to overcome some of the limitations associated with this computational cost in a rational way. Hybrid QM/MM approaches have rapidly become one of the most popular computational tools for studying chemical reactivity in biomolecular systems. However, the high cost involved in performing high-level QM calculations has limited the applicability of these approaches when calculating free energies of chemical processes. In this review, we present some of the advances in using reference potentials and mean field approximations to accelerate high-level QM/MM calculations. We present illustrative applications of these approaches and discuss challenges and future perspectives for the field. The use of physically-based simplifications has shown to effectively reduce the cost of high-level QM/MM calculations. In particular, lower-level reference potentials enable one to reduce the cost of expensive free energy calculations, thus expanding the scope of problems that can be addressed. As was already demonstrated 40 years ago, the usage of simplified models still allows one to obtain cutting edge results with substantially reduced computational cost. This article is part of a Special Issue entitled Recent developments of molecular dynamics. Copyright © 2014. Published by Elsevier B.V.

Recent advances in QM/MM free energy calculations using reference potentials☆

PubMed Central

Duarte, Fernanda; Amrein, Beat A.; Blaha-Nelson, David; Kamerlin, Shina C.L.

2015-01-01

Background Recent years have seen enormous progress in the development of methods for modeling (bio)molecular systems. This has allowed for the simulation of ever larger and more complex systems. However, as such complexity increases, the requirements needed for these models to be accurate and physically meaningful become more and more difficult to fulfill. The use of simplified models to describe complex biological systems has long been shown to be an effective way to overcome some of the limitations associated with this computational cost in a rational way. Scope of review Hybrid QM/MM approaches have rapidly become one of the most popular computational tools for studying chemical reactivity in biomolecular systems. However, the high cost involved in performing high-level QM calculations has limited the applicability of these approaches when calculating free energies of chemical processes. In this review, we present some of the advances in using reference potentials and mean field approximations to accelerate high-level QM/MM calculations. We present illustrative applications of these approaches and discuss challenges and future perspectives for the field. Major conclusions The use of physically-based simplifications has shown to effectively reduce the cost of high-level QM/MM calculations. In particular, lower-level reference potentials enable one to reduce the cost of expensive free energy calculations, thus expanding the scope of problems that can be addressed. General significance As was already demonstrated 40 years ago, the usage of simplified models still allows one to obtain cutting edge results with substantially reduced computational cost. This article is part of a Special Issue entitled Recent developments of molecular dynamics. PMID:25038480

Relations between dissipated work and Rényi divergences in the generalized Gibbs ensemble

NASA Astrophysics Data System (ADS)

Wei, Bo-Bo

2018-04-01

In this work, we show that the dissipation in a many-body system under an arbitrary nonequilibrium process is related to the Rényi divergences between two states along the forward and reversed dynamics under a very general family of initial conditions. This relation generalizes the links between dissipated work and Rényi divergences to quantum systems with conserved quantities whose equilibrium state is described by the generalized Gibbs ensemble. The relation is applicable for quantum systems with conserved quantities and can be applied to protocols driving the system between integrable and chaotic regimes. We demonstrate our ideas by considering the one-dimensional transverse quantum Ising model and the Jaynes-Cummings model which are driven out of equilibrium.

Ab initio calculation of reaction energies. III. Basis set dependence of relative energies on the FH2 and H2CO potential energy surfaces

NASA Astrophysics Data System (ADS)

Frisch, Michael J.; Binkley, J. Stephen; Schaefer, Henry F., III

1984-08-01

The relative energies of the stationary points on the FH2 and H2CO nuclear potential energy surfaces relevant to the hydrogen atom abstraction, H2 elimination and 1,2-hydrogen shift reactions have been examined using fourth-order Møller-Plesset perturbation theory and a variety of basis sets. The theoretical absolute zero activation energy for the F+H2→FH+H reaction is in better agreement with experiment than previous theoretical studies, and part of the disagreement between earlier theoretical calculations and experiment is found to result from the use of assumed rather than calculated zero-point vibrational energies. The fourth-order reaction energy for the elimination of hydrogen from formaldehyde is within 2 kcal mol-1 of the experimental value using the largest basis set considered. The qualitative features of the H2CO surface are unchanged by expansion of the basis set beyond the polarized triple-zeta level, but diffuse functions and several sets of polarization functions are found to be necessary for quantitative accuracy in predicted reaction and activation energies. Basis sets and levels of perturbation theory which represent good compromises between computational efficiency and accuracy are recommended.

Calculation of Energy Diagram of Asymmetric Graded-Band-Gap Semiconductor Superlattices.

PubMed

Monastyrskii, Liubomyr S; Sokolovskii, Bogdan S; Alekseichyk, Mariya P

2017-12-01

The paper theoretically investigates the peculiarities of energy diagram of asymmetric graded-band-gap superlattices with linear coordinate dependences of band gap and electron affinity. For calculating the energy diagram of asymmetric graded-band-gap superlattices, linearized Poisson's equation has been solved for the two layers forming a period of the superlattice. The obtained coordinate dependences of edges of the conduction and valence bands demonstrate substantial transformation of the shape of the energy diagram at changing the period of the lattice and the ratio of width of the adjacent layers. The most marked changes in the energy diagram take place when the period of lattice is comparable with the Debye screening length. In the case when the lattice period is much smaller that the Debye screening length, the energy diagram has the shape of a sawtooth-like pattern.

Free energy calculations: an efficient adaptive biasing potential method.

PubMed

Dickson, Bradley M; Legoll, Frédéric; Lelièvre, Tony; Stoltz, Gabriel; Fleurat-Lessard, Paul

2010-05-06

We develop an efficient sampling and free energy calculation technique within the adaptive biasing potential (ABP) framework. By mollifying the density of states we obtain an approximate free energy and an adaptive bias potential that is computed directly from the population along the coordinates of the free energy. Because of the mollifier, the bias potential is "nonlocal", and its gradient admits a simple analytic expression. A single observation of the reaction coordinate can thus be used to update the approximate free energy at every point within a neighborhood of the observation. This greatly reduces the equilibration time of the adaptive bias potential. This approximation introduces two parameters: strength of mollification and the zero of energy of the bias potential. While we observe that the approximate free energy is a very good estimate of the actual free energy for a large range of mollification strength, we demonstrate that the errors associated with the mollification may be removed via deconvolution. The zero of energy of the bias potential, which is easy to choose, influences the speed of convergence but not the limiting accuracy. This method is simple to apply to free energy or mean force computation in multiple dimensions and does not involve second derivatives of the reaction coordinates, matrix manipulations nor on-the-fly adaptation of parameters. For the alanine dipeptide test case, the new method is found to gain as much as a factor of 10 in efficiency as compared to two basic implementations of the adaptive biasing force methods, and it is shown to be as efficient as well-tempered metadynamics with the postprocess deconvolution giving a clear advantage to the mollified density of states method.

SU-F-T-376: The Efficiency of Calculating Photonuclear Reaction On High-Energy Photon Therapy by Monte Carlo Method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hirayama, S; Fujibuchi, T

Purpose: Secondary-neutrons having harmful influences to a human body are generated by photonuclear reaction on high-energy photon therapy. Their characteristics are not known in detail since the calculation to evaluate them takes very long time. PHITS(Particle and Heavy Ion Transport code System) Monte Carlo code since versions 2.80 has the new parameter “pnimul” raising the probability of occurring photonuclear reaction forcibly to make the efficiency of calculation. We investigated the optimum value of “pnimul” on high-energy photon therapy. Methods: The geometry of accelerator head based on the specification of a Varian Clinac 21EX was used for PHITS ver. 2.80. Themore » phantom (30 cm * 30 cm * 30 cm) filled the composition defined by ICRU(International Commission on Radiation Units) was placed at source-surface distance 100 cm. We calculated the neutron energy spectra in the surface of ICRU phantom with “pnimal” setting 1, 10, 100, 1000, 10000 and compared the total calculation time and the behavior of photon using PDD(Percentage Depth Dose) and OCR(Off-Center Ratio). Next, the cutoff energy of photon, electron and positron were investigated for the calculation efficiency with 4, 5, 6 and 7 MeV. Results: The calculation total time until the errors of neutron fluence become within 1% decreased as increasing “pnimul”. PDD and OCR showed no differences by the parameter. The calculation time setting the cutoff energy like 4, 5, 6 and 7 MeV decreased as increasing the cutoff energy. However, the errors of photon become within 1% did not decrease by the cutoff energy. Conclusion: The optimum values of “pnimul” and the cutoff energy were investigated on high-energy photon therapy. It is suggest that using the optimum “pnimul” makes the calculation efficiency. The study of the cutoff energy need more investigation.« less

Weather data for simplified energy calculation methods. Volume IV. United States: WYEC data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olsen, A.R.; Moreno, S.; Deringer, J.

The objective of this report is to provide a source of weather data for direct use with a number of simplified energy calculation methods available today. Complete weather data for a number of cities in the United States are provided for use in the following methods: degree hour, modified degree hour, bin, modified bin, and variable degree day. This report contains sets of weather data for 23 cities using Weather Year for Energy Calculations (WYEC) source weather data. Considerable overlap is present in cities (21) covered by both the TRY and WYEC data. The weather data at each city hasmore » been summarized in a number of ways to provide differing levels of detail necessary for alternative simplified energy calculation methods. Weather variables summarized include dry bulb and wet bulb temperature, percent relative humidity, humidity ratio, wind speed, percent possible sunshine, percent diffuse solar radiation, total solar radiation on horizontal and vertical surfaces, and solar heat gain through standard DSA glass. Monthly and annual summaries, in some cases by time of day, are available. These summaries are produced in a series of nine computer generated tables.« less

Accurate, robust and reliable calculations of Poisson-Boltzmann binding energies

PubMed Central

Nguyen, Duc D.; Wang, Bao

2017-01-01

Poisson-Boltzmann (PB) model is one of the most popular implicit solvent models in biophysical modeling and computation. The ability of providing accurate and reliable PB estimation of electrostatic solvation free energy, ΔGel, and binding free energy, ΔΔGel, is important to computational biophysics and biochemistry. In this work, we investigate the grid dependence of our PB solver (MIBPB) with SESs for estimating both electrostatic solvation free energies and electrostatic binding free energies. It is found that the relative absolute error of ΔGel obtained at the grid spacing of 1.0 Å compared to ΔGel at 0.2 Å averaged over 153 molecules is less than 0.2%. Our results indicate that the use of grid spacing 0.6 Å ensures accuracy and reliability in ΔΔGel calculation. In fact, the grid spacing of 1.1 Å appears to deliver adequate accuracy for high throughput screening. PMID:28211071

Quantum algorithms for Gibbs sampling and hitting-time estimation

DOE PAGES

Chowdhury, Anirban Narayan; Somma, Rolando D.

2017-02-01

In this paper, we present quantum algorithms for solving two problems regarding stochastic processes. The first algorithm prepares the thermal Gibbs state of a quantum system and runs in time almost linear in √Nβ/Ζ and polynomial in log(1/ϵ), where N is the Hilbert space dimension, β is the inverse temperature, Ζ is the partition function, and ϵ is the desired precision of the output state. Our quantum algorithm exponentially improves the dependence on 1/ϵ and quadratically improves the dependence on β of known quantum algorithms for this problem. The second algorithm estimates the hitting time of a Markov chain. Formore » a sparse stochastic matrix Ρ, it runs in time almost linear in 1/(ϵΔ 3/2), where ϵ is the absolute precision in the estimation and Δ is a parameter determined by Ρ, and whose inverse is an upper bound of the hitting time. Our quantum algorithm quadratically improves the dependence on 1/ϵ and 1/Δ of the analog classical algorithm for hitting-time estimation. Finally, both algorithms use tools recently developed in the context of Hamiltonian simulation, spectral gap amplification, and solving linear systems of equations.« less

On the importance of full-dimensionality in low-energy molecular scattering calculations

PubMed Central

Faure, Alexandre; Jankowski, Piotr; Stoecklin, Thierry; Szalewicz, Krzysztof

2016-01-01

Scattering of H2 on CO is of great importance in astrophysics and also is a benchmark system for comparing theory to experiment. We present here a new 6-dimensional potential energy surface for the ground electronic state of H2-CO with an estimated uncertainty of about 0.6 cm−1 in the global minimum region, several times smaller than achieved earlier. This potential has been used in nearly exact 6-dimensional quantum scattering calculations to compute state-to-state cross-sections measured in low-energy crossed-beam experiments. Excellent agreement between theory and experiment has been achieved in all cases. We also show that the fully 6-dimensional approach is not needed with the current accuracy of experimental data since an equally good agreement with experiment was obtained using only a 4-dimensional treatment, which validates the rigid-rotor approach widely used in scattering calculations. This finding, which disagrees with some literature statements, is important since for larger systems full-dimensional scattering calculations are currently not possible. PMID:27333870

Development of a calculation method for estimating specific energy distribution in complex radiation fields.

PubMed

Sato, Tatsuhiko; Watanabe, Ritsuko; Niita, Koji

2006-01-01

Estimation of the specific energy distribution in a human body exposed to complex radiation fields is of great importance in the planning of long-term space missions and heavy ion cancer therapies. With the aim of developing a tool for this estimation, the specific energy distributions in liquid water around the tracks of several HZE particles with energies up to 100 GeV n(-1) were calculated by performing track structure simulation with the Monte Carlo technique. In the simulation, the targets were assumed to be spherical sites with diameters from 1 nm to 1 microm. An analytical function to reproduce the simulation results was developed in order to predict the distributions of all kinds of heavy ions over a wide energy range. The incorporation of this function into the Particle and Heavy Ion Transport code System (PHITS) enables us to calculate the specific energy distributions in complex radiation fields in a short computational time.

Quantum mechanical electronic structure calculation reveals orientation dependence of hydrogen bond energy in proteins.

PubMed

Mondal, Abhisek; Datta, Saumen

2017-06-01

Hydrogen bond plays a unique role in governing macromolecular interactions with exquisite specificity. These interactions govern the fundamental biological processes like protein folding, enzymatic catalysis, molecular recognition. Despite extensive research work, till date there is no proper report available about the hydrogen bond's energy surface with respect to its geometric parameters, directly derived from proteins. Herein, we have deciphered the potential energy landscape of hydrogen bond directly from the macromolecular coordinates obtained from Protein Data Bank using quantum mechanical electronic structure calculations. The findings unravel the hydrogen bonding energies of proteins in parametric space. These data can be used to understand the energies of such directional interactions involved in biological molecules. Quantitative characterization has also been performed using Shannon entropic calculations for atoms participating in hydrogen bond. Collectively, our results constitute an improved way of understanding hydrogen bond energies in case of proteins and complement the knowledge-based potential. Proteins 2017; 85:1046-1055. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Preliminary Energy Deposition Calculations for GRIST-2 Tests in the TREAT Upgrade

DOE Office of Scientific and Technical Information (OSTI.GOV)

Olson, W. O.

1978-03-01

Preliminary studies have been made to estimate the energy deposition in GRIST-2 tests irradiated in the proposed TREAT Upgrade reactor. The objective of the GRIST-2 project is to test GCFR (gas cooled fast reactor) fuel under conditions of hypothetical core disruptive accidents (HCDA). Test requirements are (1) an energy deposition in the test of approximately 2500 J/g or higher, (2) a pin-to-pin variation in energy deposition of less than 10% and (3) the variation in the energy deposition across any pin (at a given axial position) should be less than 10%. Calculations performed by EG&G Idaho were made for 7more » and 37-pin tests using one-dimensional transport theory. These yield average energy deposition rates in the test at the axial peak which are in the 5000-5500 J/g range for the 37-pin test and are in the 8500-9000 J/g range for the 7-pin test. These values are obtained with a cadmium thermal neutron filter (TNF) surrounding the test. This hardens the flux to meet the third requirement. The central test pin is fully enriched UO{sub 2}, with the outer pins having lower enrichments to satisfy requirement 2. Addition of the TNF reduces the energy deposition by about 10%. The results in the above calculations are also compared with the Monte Carlo results computed by ANL-West personnel.« less

Effects of Differing Energy Dependences in Three Level-Density Models on Calculated Cross Sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fu, C.Y.

2000-07-15

Three level-density formalisms commonly used for cross-section calculations are examined. Residual nuclides in neutron interaction with {sup 58}Ni are chosen to quantify the well-known differences in the energy dependences of the three formalisms. Level-density parameters for the Gilbert and Cameron model are determined from experimental information. Parameters for the back-shifted Fermi-gas and generalized superfluid models are obtained by fitting their level densities at two selected energies for each nuclide to those of the Gilbert and Cameron model, forcing the level densities of the three models to be as close as physically allowed. The remaining differences are in their energy dependencesmore » that, it is shown, can change the calculated cross sections and particle emission spectra significantly, in some cases or energy ranges by a factor of 2.« less

Robust identification of transcriptional regulatory networks using a Gibbs sampler on outlier sum statistic.

PubMed

Gu, Jinghua; Xuan, Jianhua; Riggins, Rebecca B; Chen, Li; Wang, Yue; Clarke, Robert

2012-08-01

Identification of transcriptional regulatory networks (TRNs) is of significant importance in computational biology for cancer research, providing a critical building block to unravel disease pathways. However, existing methods for TRN identification suffer from the inclusion of excessive 'noise' in microarray data and false-positives in binding data, especially when applied to human tumor-derived cell line studies. More robust methods that can counteract the imperfection of data sources are therefore needed for reliable identification of TRNs in this context. In this article, we propose to establish a link between the quality of one target gene to represent its regulator and the uncertainty of its expression to represent other target genes. Specifically, an outlier sum statistic was used to measure the aggregated evidence for regulation events between target genes and their corresponding transcription factors. A Gibbs sampling method was then developed to estimate the marginal distribution of the outlier sum statistic, hence, to uncover underlying regulatory relationships. To evaluate the effectiveness of our proposed method, we compared its performance with that of an existing sampling-based method using both simulation data and yeast cell cycle data. The experimental results show that our method consistently outperforms the competing method in different settings of signal-to-noise ratio and network topology, indicating its robustness for biological applications. Finally, we applied our method to breast cancer cell line data and demonstrated its ability to extract biologically meaningful regulatory modules related to estrogen signaling and action in breast cancer. The Gibbs sampler MATLAB package is freely available at http://www.cbil.ece.vt.edu/software.htm. xuan@vt.edu Supplementary data are available at Bioinformatics online.

Simulation of Reversible Protein–Protein Binding and Calculation of Binding Free Energies Using Perturbed Distance Restraints

PubMed Central

2017-01-01

Virtually all biological processes depend on the interaction between proteins at some point. The correct prediction of biomolecular binding free-energies has many interesting applications in both basic and applied pharmaceutical research. While recent advances in the field of molecular dynamics (MD) simulations have proven the feasibility of the calculation of protein–protein binding free energies, the large conformational freedom of proteins and complex free energy landscapes of binding processes make such calculations a difficult task. Moreover, convergence and reversibility of resulting free-energy values remain poorly described. In this work, an easy-to-use, yet robust approach for the calculation of standard-state protein–protein binding free energies using perturbed distance restraints is described. In the binding process the conformations of the proteins were restrained, as suggested earlier. Two approaches to avoid end-state problems upon release of the conformational restraints were compared. The method was evaluated by practical application to a small model complex of ubiquitin and the very flexible ubiquitin-binding domain of human DNA polymerase ι (UBM2). All computed free energy differences were closely monitored for convergence, and the calculated binding free energies had a mean unsigned deviation of only 1.4 or 2.5 kJ·mol–1 from experimental values. Statistical error estimates were in the order of thermal noise. We conclude that the presented method has promising potential for broad applicability to quantitatively describe protein–protein and various other kinds of complex formation. PMID:28898077

Limitations in the application of the Gibbs equation to anionic surfactants at the air/water surface: sodium dodecylsulfate and sodium dodecylmonooxyethylenesulfate above and below the CMC.

PubMed

Xu, Hui; Li, Pei Xun; Ma, Kun; Thomas, Robert K; Penfold, Jeffrey; Lu, Jian Ren

2013-07-30

This is a second paper responding to recent papers by Menger et al. and the ensuing discussion about the application of the Gibbs equation to surface tension (ST) data. Using new neutron reflection (NR) measurements on sodium dodecylsulfate (SDS) and sodium dodecylmonooxyethylene sulfate (SLES) above and below their CMCs and with and without added NaCl, in conjunction with the previous ST measurements on SDS by Elworthy and Mysels (EM), we conclude that (i) ST measurements are often seriously compromised by traces of divalent ions, (ii) adsorption does not generally reach saturation at the CMC, making it difficult to obtain the limiting Gibbs slope, and (iii) the significant width of micellization may make it impossible to apply the Gibbs equation in a significant range of concentration below the CMC. Menger et al. proposed ii as a reason for the difficulty of applying the Gibbs equation to ST data. Conclusions i and iii now further emphasize the failings of the ST-Gibbs analysis for determining the limiting coverage at the CMC, especially for SDS. For SDS, adsorption increases above the CMC to a value of 10 × CMC, which is about 25% greater than at the CMC and about the same as at the CMC in the presence of 0.1 M NaCl. In contrast, the adsorption of SLES reaches a limit at the CMC with no further increase up to 10 × CMC, but the addition of 0.1 M NaCl increases the surface excess by 20-25%. The results for SDS are combined with earlier NR results to generate an adsorption isotherm from 2 to 100 mM. The NR results for SDS are compared to the definitive surface tension (ST) measurements of EM, and the surface excesses agree over the range where they can safely be compared, from 2 to 6 mM. This confirms that the anomalous decrease in the slope of EM's σ - ln c curve between 6 mM and the CMC at 8.2 mM results from changes in activity associated with a significant width of micellization. This anomaly shows that it is impossible to apply the Gibbs equation usefully

Self-energy matrices for electron transport calculations within the real-space finite-difference formalism

NASA Astrophysics Data System (ADS)

Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji; Blügel, Stefan

2017-03-01

The self-energy term used in transport calculations, which describes the coupling between electrode and transition regions, is able to be evaluated only from a limited number of the propagating and evanescent waves of a bulk electrode. This obviously contributes toward the reduction of the computational expenses in transport calculations. In this paper, we present a mathematical formula for reducing the computational expenses further without using any approximation and without losing accuracy. So far, the self-energy term has been handled as a matrix with the same dimension as the Hamiltonian submatrix representing the interaction between an electrode and a transition region. In this work, through the singular-value decomposition of the submatrix, the self-energy matrix is handled as a smaller matrix, whose dimension is the rank number of the Hamiltonian submatrix. This procedure is practical in the case of using the pseudopotentials in a separable form, and the computational expenses for determining the self-energy matrix are reduced by 90% when employing a code based on the real-space finite-difference formalism and projector-augmented wave method. In addition, this technique is applicable to the transport calculations using atomic or localized basis sets. Adopting the self-energy matrices obtained from this procedure, we present the calculation of the electron transport properties of C20 molecular junctions. The application demonstrates that the electron transmissions are sensitive to the orientation of the molecule with respect to the electrode surface. In addition, channel decomposition of the scattering wave functions reveals that some unoccupied C20 molecular orbitals mainly contribute to the electron conduction through the molecular junction.

Extended calculations of energies, transition rates, and lifetimes for F-like Kr XXVIII

NASA Astrophysics Data System (ADS)

Zhang, C. Y.; Si, R.; Yao, K.; Gu, M. F.; Wang, K.; Chen, C. Y.

2018-02-01

The excitation energies, lifetimes, wavelengths and E1, E2, M1 and M2 transition rates for the lowest 389 levels of the 2l7, 2l63l‧, 2l64l‧, and 2l65l‧ configurations from second-order many-body perturbation theory (MBPT) calculations, and the results for the lowest 200 states of the 2l7, 2l63l‧, and 2l64l‧ configurations from multi-configuration Dirac-Hartree-Fock (MCDHF) calculations in F-like Kr XXVIII are presented in this work. The relative differences between our two sets of level energies are mostly within 0.005% for the lowest 200 levels. Comparisons are made with experimental and other available theoretical results to assess the reliability and accuracy of the present calculations. We believe them to be the most complete and accurate results for Kr XXVIII at present.

Electron propagator calculations on the ionization energies of CrH -, MnH - and FeH -

NASA Astrophysics Data System (ADS)

Lin, Jyh-Shing; Ortiz, J. V.

1990-08-01

Electron propagator calculations with unrestricted Hartree-Fock reference states yield the ionization energies of the title anions. Spin contamination in the anionic reference state is small, enabling the use of second-and third-order self-energies in the Dyson equation. Feynman-Dyson amplitudes for these ionizations are essentially identical to canonical spin-orbitals. For most of the final states, these consist of an antibonding combination of an sp metal hybrid, polarized away from the hydrogen, and hydroegen s functions. In one case, the Feynman-Dyson amplitude consists of nonbonding d functions. Calculated ionization energies are within 0.5 eV of experiment.

Small Changes in the Primary Structure of Transportan 10 Alter the Thermodynamics and Kinetics of its Interaction with Phospholipid Vesicles

PubMed Central

2008-01-01

The kinetics and thermodynamics of binding of transportan 10 (tp10) and four of its variants to phospholipid vesicles, and the kinetics of peptide-induced dye efflux, were compared. Tp10 is a 21-residue, amphipathic, cationic, cell-penetrating peptide similar to helical antimicrobial peptides. The tp10 variants examined include amidated and free peptides, and replacements of tyrosine by tryptophan. Carboxy-terminal amidation or substitution of tryptophan for tyrosine enhance binding and activity. The Gibbs energies of peptide binding to membranes determined experimentally and calculated from the interfacial hydrophobicity scale are in good agreement. The Gibbs energy for insertion into the bilayer core was calculated using hydrophobicity scales of residue transfer from water to octanol and to the membrane/water interface. Peptide-induced efflux becomes faster as the Gibbs energies for binding and insertion of the tp10 variants decrease. If anionic lipids are included, binding and efflux rate increase, as expected because all tp10 variants are cationic and an electrostatic component is added. Whether the most important effect of peptide amidation is the change in charge or an enhancement of helical structure, however, still needs to be established. Nevertheless, it is clear that the changes in efflux rate reflect the differences in the thermodynamics of binding and insertion of the free and amidated peptide groups. PMID:18260641

Carbon deposition thresholds on nickel-based solid oxide fuel cell anodes II. Steam:carbon ratio and current density

NASA Astrophysics Data System (ADS)

Kuhn, J.; Kesler, O.

2015-03-01

For the second part of a two part publication, coking thresholds with respect to molar steam:carbon ratio (SC) and current density in nickel-based solid oxide fuel cells were determined. Anode-supported button cell samples were exposed to 2-component and 5-component gas mixtures with 1 ≤ SC ≤ 2 and zero fuel utilization for 10 h, followed by measurement of the resulting carbon mass. The effect of current density was explored by measuring carbon mass under conditions known to be prone to coking while increasing the current density until the cell was carbon-free. The SC coking thresholds were measured to be ∼1.04 and ∼1.18 at 600 and 700 °C, respectively. Current density experiments validated the thresholds measured with respect to fuel utilization and steam:carbon ratio. Coking thresholds at 600 °C could be predicted with thermodynamic equilibrium calculations when the Gibbs free energy of carbon was appropriately modified. Here, the Gibbs free energy of carbon on nickel-based anode support cermets was measured to be -6.91 ± 0.08 kJ mol-1. The results of this two part publication show that thermodynamic equilibrium calculations with appropriate modification to the Gibbs free energy of solid-phase carbon can be used to predict coking thresholds on nickel-based anodes at 600-700 °C.

Absolute surface energy calculations of Wurtzite (0001)/(000-1): a study of ZnO and GaN

NASA Astrophysics Data System (ADS)

Zhang, Jingzhao; Zhang, Yiou; Tse, Kinfai; Deng, Bei; Xu, Hu; Zhu, Junyi

The accurate absolute surface energies of (0001)/(000-1) surfaces of wurtzite structures are crucial in determining the thin film growth mode of important energy materials. However, the surface energies still remain to be solved due to the intrinsic difficulty of calculating dangling bond energy of asymmetrically bonded surface atoms. We used a pseudo-hydrogen passivation method to estimate the dangling bond energy and calculate the polar surfaces of ZnO and GaN. The calculations were based on the pseudo chemical potentials obtained from a set of tetrahedral clusters or simple pseudo-molecules, using density functional theory approaches, for both GGA and HSE. And the surface energies of (0001)/(000-1) surfaces of wurtzite ZnO and GaN we obtained showed relatively high self-consistencies. A wedge structure calculation with a new bottom surface passivation scheme of group I and group VII elements was also proposed and performed to show converged absolute surface energy of wurtzite ZnO polar surfaces. Part of the computing resources was provided by the High Performance Cluster Computing Centre, Hong Kong Baptist University. This work was supported by the start-up funding and direct Grant with the Project code of 4053134 at CUHK.

An efficient parallel algorithm for the calculation of canonical MP2 energies.

PubMed

Baker, Jon; Pulay, Peter

2002-09-01

We present the parallel version of a previous serial algorithm for the efficient calculation of canonical MP2 energies (Pulay, P.; Saebo, S.; Wolinski, K. Chem Phys Lett 2001, 344, 543). It is based on the Saebo-Almlöf direct-integral transformation, coupled with an efficient prescreening of the AO integrals. The parallel algorithm avoids synchronization delays by spawning a second set of slaves during the bin-sort prior to the second half-transformation. Results are presented for systems with up to 2000 basis functions. MP2 energies for molecules with 400-500 basis functions can be routinely calculated to microhartree accuracy on a small number of processors (6-8) in a matter of minutes with modern PC-based parallel computers. Copyright 2002 Wiley Periodicals, Inc. J Comput Chem 23: 1150-1156, 2002

MULTIMODE quantum calculations of vibrational energies and IR spectrum of the NO⁺(H₂O) cluster using accurate potential energy and dipole moment surfaces.

PubMed

Homayoon, Zahra

2014-09-28

A new, full (nine)-dimensional potential energy surface and dipole moment surface to describe the NO(+)(H2O) cluster is reported. The PES is based on fitting of roughly 32,000 CCSD(T)-F12/aug-cc-pVTZ electronic energies. The surface is a linear least-squares fit using a permutationally invariant basis with Morse-type variables. The PES is used in a Diffusion Monte Carlo study of the zero-point energy and wavefunction of the NO(+)(H2O) and NO(+)(D2O) complexes. Using the calculated ZPE the dissociation energies of the clusters are reported. Vibrational configuration interaction calculations of NO(+)(H2O) and NO(+)(D2O) using the MULTIMODE program are performed. The fundamental, a number of overtone, and combination states of the clusters are reported. The IR spectrum of the NO(+)(H2O) cluster is calculated using 4, 5, 7, and 8 modes VSCF/CI calculations. The anharmonic, coupled vibrational calculations, and IR spectrum show very good agreement with experiment. Mode coupling of the water "antisymmetric" stretching mode with the low-frequency intermolecular modes results in intensity borrowing.

MULTIMODE quantum calculations of vibrational energies and IR spectrum of the NO+(H2O) cluster using accurate potential energy and dipole moment surfaces

NASA Astrophysics Data System (ADS)

Homayoon, Zahra

2014-09-01

A new, full (nine)-dimensional potential energy surface and dipole moment surface to describe the NO+(H2O) cluster is reported. The PES is based on fitting of roughly 32 000 CCSD(T)-F12/aug-cc-pVTZ electronic energies. The surface is a linear least-squares fit using a permutationally invariant basis with Morse-type variables. The PES is used in a Diffusion Monte Carlo study of the zero-point energy and wavefunction of the NO+(H2O) and NO+(D2O) complexes. Using the calculated ZPE the dissociation energies of the clusters are reported. Vibrational configuration interaction calculations of NO+(H2O) and NO+(D2O) using the MULTIMODE program are performed. The fundamental, a number of overtone, and combination states of the clusters are reported. The IR spectrum of the NO+(H2O) cluster is calculated using 4, 5, 7, and 8 modes VSCF/CI calculations. The anharmonic, coupled vibrational calculations, and IR spectrum show very good agreement with experiment. Mode coupling of the water "antisymmetric" stretching mode with the low-frequency intermolecular modes results in intensity borrowing.

A local framework for calculating coupled cluster singles and doubles excitation energies (LoFEx-CCSD)

DOE PAGES

Baudin, Pablo; Bykov, Dmytro; Liakh, Dmitry I.; ...

2017-02-22

Here, the recently developed Local Framework for calculating Excitation energies (LoFEx) is extended to the coupled cluster singles and doubles (CCSD) model. In the new scheme, a standard CCSD excitation energy calculation is carried out within a reduced excitation orbital space (XOS), which is composed of localised molecular orbitals and natural transition orbitals determined from time-dependent Hartree–Fock theory. The presented algorithm uses a series of reduced second-order approximate coupled cluster singles and doubles (CC2) calculations to optimise the XOS in a black-box manner. This ensures that the requested CCSD excitation energies have been determined to a predefined accuracy compared tomore » a conventional CCSD calculation. We present numerical LoFEx-CCSD results for a set of medium-sized organic molecules, which illustrate the black-box nature of the approach and the computational savings obtained for transitions that are local compared to the size of the molecule. In fact, for such local transitions, the LoFEx-CCSD scheme can be applied to molecular systems where a conventional CCSD implementation is intractable.« less

A virtual photon energy fluence model for Monte Carlo dose calculation.

PubMed

Fippel, Matthias; Haryanto, Freddy; Dohm, Oliver; Nüsslin, Fridtjof; Kriesen, Stephan

2003-03-01

The presented virtual energy fluence (VEF) model of the patient-independent part of the medical linear accelerator heads, consists of two Gaussian-shaped photon sources and one uniform electron source. The planar photon sources are located close to the bremsstrahlung target (primary source) and to the flattening filter (secondary source), respectively. The electron contamination source is located in the plane defining the lower end of the filter. The standard deviations or widths and the relative weights of each source are free parameters. Five other parameters correct for fluence variations, i.e., the horn or central depression effect. If these parameters and the field widths in the X and Y directions are given, the corresponding energy fluence distribution can be calculated analytically and compared to measured dose distributions in air. This provides a method of fitting the free parameters using the measurements for various square and rectangular fields and a fixed number of monitor units. The next step in generating the whole set of base data is to calculate monoenergetic central axis depth dose distributions in water which are used to derive the energy spectrum by deconvolving the measured depth dose curves. This spectrum is also corrected to take the off-axis softening into account. The VEF model is implemented together with geometry modules for the patient specific part of the treatment head (jaws, multileaf collimator) into the XVMC dose calculation engine. The implementation into other Monte Carlo codes is possible based on the information in this paper. Experiments are performed to verify the model by comparing measured and calculated dose distributions and output factors in water. It is demonstrated that open photon beams of linear accelerators from two different vendors are accurately simulated using the VEF model. The commissioning procedure of the VEF model is clinically feasible because it is based on standard measurements in air and water. It is

Density functional calculations on structural materials for nuclear energy applications and functional materials for photovoltaic energy applications (abstract only).

PubMed

Domain, C; Olsson, P; Becquart, C S; Legris, A; Guillemoles, J F

2008-02-13

Ab initio density functional theory calculations are carried out in order to predict the evolution of structural materials under aggressive working conditions such as cases with exposure to corrosion and irradiation, as well as to predict and investigate the properties of functional materials for photovoltaic energy applications. Structural metallic materials used in nuclear facilities are subjected to irradiation which induces the creation of large amounts of point defects. These defects interact with each other as well as with the different elements constituting the alloys, which leads to modifications of the microstructure and the mechanical properties. VASP (Vienna Ab initio Simulation Package) has been used to determine the properties of point defect clusters and also those of extended defects such as dislocations. The resulting quantities, such as interaction energies and migration energies, are used in larger scale simulation methods in order to build predictive tools. For photovoltaic energy applications, ab initio calculations are used in order to search for new semiconductors and possible element substitutions for existing ones in order to improve their efficiency.

Calculation of Cyclodextrin Binding Affinities: Energy, Entropy, and Implications for Drug Design

PubMed Central

Chen, Wei; Chang, Chia-En; Gilson, Michael K.

2004-01-01

The second generation Mining Minima method yields binding affinities accurate to within 0.8 kcal/mol for the associations of α-, β-, and γ-cyclodextrin with benzene, resorcinol, flurbiprofen, naproxen, and nabumetone. These calculations require hours to a day on a commodity computer. The calculations also indicate that the changes in configurational entropy upon binding oppose association by as much as 24 kcal/mol and result primarily from a narrowing of energy wells in the bound versus the free state, rather than from a drop in the number of distinct low-energy conformations on binding. Also, the configurational entropy is found to vary substantially among the bound conformations of a given cyclodextrin-guest complex. This result suggests that the configurational entropy must be accounted for to reliably rank docked conformations in both host-guest and ligand-protein complexes. In close analogy with the common experimental observation of entropy-enthalpy compensation, the computed entropy changes show a near-linear relationship with the changes in mean potential plus solvation energy. PMID:15339804

Are electrostatic potentials between regions of different chemical composition measurable? The Gibbs-Guggenheim Principle reconsidered, extended and its consequences revisited.

PubMed

Pethica, Brian A

2007-12-21

As indicated by Gibbs and made explicit by Guggenheim, the electrical potential difference between two regions of different chemical composition cannot be measured. The Gibbs-Guggenheim Principle restricts the use of classical electrostatics in electrochemical theories as thermodynamically unsound with some few approximate exceptions, notably for dilute electrolyte solutions and concomitant low potentials where the linear limit for the exponential of the relevant Boltzmann distribution applies. The Principle invalidates the widespread use of forms of the Poisson-Boltzmann equation which do not include the non-electrostatic components of the chemical potentials of the ions. From a thermodynamic analysis of the parallel plate electrical condenser, employing only measurable electrical quantities and taking into account the chemical potentials of the components of the dielectric and their adsorption at the surfaces of the condenser plates, an experimental procedure to provide exceptions to the Principle has been proposed. This procedure is now reconsidered and rejected. No other related experimental procedures circumvent the Principle. Widely-used theoretical descriptions of electrolyte solutions, charged surfaces and colloid dispersions which neglect the Principle are briefly discussed. MD methods avoid the limitations of the Poisson-Bolzmann equation. Theoretical models which include the non-electrostatic components of the inter-ion and ion-surface interactions in solutions and colloid systems assume the additivity of dispersion and electrostatic forces. An experimental procedure to test this assumption is identified from the thermodynamics of condensers at microscopic plate separations. The available experimental data from Kelvin probe studies are preliminary, but tend against additivity. A corollary to the Gibbs-Guggenheim Principle is enunciated, and the Principle is restated that for any charged species, neither the difference in electrostatic potential nor the

A Method for Calculating Fermi Energy and Carrier Concentrations in Semiconducts

ERIC Educational Resources Information Center

Gaylord, T. K.; Linxwiler, J. N., Jr.

1976-01-01

An efficient numerical method for calculating the Fermi energy, the free electron and free hole concentrations, and the ionized impurity conductors in a semiconductor material is described. The method allows freedom with respect to type of material, temperature, and amount and type of donor and acceptor impurities. (Author/CP)

Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation.

PubMed

Miao, Yinglong; Feher, Victoria A; McCammon, J Andrew

2015-08-11

A Gaussian accelerated molecular dynamics (GaMD) approach for simultaneous enhanced sampling and free energy calculation of biomolecules is presented. By constructing a boost potential that follows Gaussian distribution, accurate reweighting of the GaMD simulations is achieved using cumulant expansion to the second order. Here, GaMD is demonstrated on three biomolecular model systems: alanine dipeptide, chignolin folding, and ligand binding to the T4-lysozyme. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of these biomolecules. Furthermore, the free energy profiles obtained from reweighting of the GaMD simulations allow us to identify distinct low-energy states of the biomolecules and characterize the protein-folding and ligand-binding pathways quantitatively.

Size Reduction of Hamiltonian Matrix for Large-Scale Energy Band Calculations Using Plane Wave Bases

NASA Astrophysics Data System (ADS)

Morifuji, Masato

2018-01-01

We present a method of reducing the size of a Hamiltonian matrix used in calculations of electronic states. In the electronic states calculations using plane wave basis functions, a large number of plane waves are often required to obtain precise results. Even using state-of-the-art techniques, the Hamiltonian matrix often becomes very large. The large computational time and memory necessary for diagonalization limit the widespread use of band calculations. We show a procedure of deriving a reduced Hamiltonian constructed using a small number of low-energy bases by renormalizing high-energy bases. We demonstrate numerically that the significant speedup of eigenstates evaluation is achieved without losing accuracy.

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

NASA Astrophysics Data System (ADS)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Comparison of Measured Dark Current Distributions with Calculated Damage Energy Distributions in HgCdTe

NASA Technical Reports Server (NTRS)

Marshall, C. J.; Marshall, P. W.; Howe, C. L.; Reed, R. A.; Weller, R. A.; Mendenhall, M.; Waczynski, A.; Ladbury, R.; Jordan, T. M.

2007-01-01

This paper presents a combined Monte Carlo and analytic approach to the calculation of the pixel-to-pixel distribution of proton-induced damage in a HgCdTe sensor array and compares the results to measured dark current distributions after damage by 63 MeV protons. The moments of the Coulombic, nuclear elastic and nuclear inelastic damage distributions were extracted from Monte Carlo simulations and combined to form a damage distribution using the analytic techniques first described in [1]. The calculations show that the high energy recoils from the nuclear inelastic reactions (calculated using the Monte Carlo code MCNPX [2]) produce a pronounced skewing of the damage energy distribution. While the nuclear elastic component (also calculated using the MCNPX) contributes only a small fraction of the total nonionizing damage energy, its inclusion in the shape of the damage across the array is significant. The Coulombic contribution was calculated using MRED [3-5], a Geant4 [4,6] application. The comparison with the dark current distribution strongly suggests that mechanisms which are not linearly correlated with nonionizing damage produced according to collision kinematics are responsible for the observed dark current increases. This has important implications for the process of predicting the on-orbit dark current response of the HgCdTe sensor array.

CALCULATION OF ELECTRON AFFINITIES OF POLYCYCLIC AROMATIC HYDROCARBONS AND SOVATION ENERGIES OF THEIR ANIONS

EPA Science Inventory

Electron affinities (EAs) and free energies for electron attachment have been calculated for 42 polynuclear aromatic hydrocarbons and related molecules by a variety of theoretical models, including Koopmans' theorem methods and the L1E method from differences in energy between th...

Molecular Gibbs Surface Excess and CO2-Hydrate Density Determine the Strong Temperature- and Pressure-Dependent Supercritical CO2-Brine Interfacial Tension.

PubMed

Ji, Jiayuan; Zhao, Lingling; Tao, Lu; Lin, Shangchao

2017-06-29

In CO 2 geological storage, the interfacial tension (IFT) between supercritical CO 2 and brine is critical for the storage capacitance design to prevent CO 2 leakage. IFT relies not only on the interfacial molecule properties but also on the environmental conditions at different storage sites. In this paper, supercritical CO 2 -NaCl solution systems are modeled at 343-373 K and 6-35 MPa under the salinity of 1.89 mol/L using molecular dynamics simulations. After computing and comparing the molecular density profile across the interface, the atomic radial distribution function, the molecular orientation distribution, the molecular Gibbs surface excess (derived from the molecular density profile), and the CO 2 -hydrate number density under the above environmental conditions, we confirm that only the molecular Gibbs surface excess of CO 2 molecules and the CO 2 -hydrate number density correlate strongly with the temperature- and pressure-dependent IFTs. We also compute the populations of two distinct CO 2 -hydrate structures (T-type and H-type) and attribute the observed dependence of IFTs to the dominance of the more stable, surfactant-like T-type CO 2 -hydrates at the interface. On the basis of these new molecular mechanisms behind IFT variations, this study could guide the rational design of suitable injecting environmental pressure and temperature conditions. We believe that the above two molecular-level metrics (Gibbs surface excess and hydrate number density) are of great fundamental importance for understanding the supercritical CO 2 -water interface and engineering applications in geological CO 2 storage.

CC2 oscillator strengths within the local framework for calculating excitation energies (LoFEx).

PubMed

Baudin, Pablo; Kjærgaard, Thomas; Kristensen, Kasper

2017-04-14

In a recent work [P. Baudin and K. Kristensen, J. Chem. Phys. 144, 224106 (2016)], we introduced a local framework for calculating excitation energies (LoFEx), based on second-order approximated coupled cluster (CC2) linear-response theory. LoFEx is a black-box method in which a reduced excitation orbital space (XOS) is optimized to provide coupled cluster (CC) excitation energies at a reduced computational cost. In this article, we present an extension of the LoFEx algorithm to the calculation of CC2 oscillator strengths. Two different strategies are suggested, in which the size of the XOS is determined based on the excitation energy or the oscillator strength of the targeted transitions. The two strategies are applied to a set of medium-sized organic molecules in order to assess both the accuracy and the computational cost of the methods. The results show that CC2 excitation energies and oscillator strengths can be calculated at a reduced computational cost, provided that the targeted transitions are local compared to the size of the molecule. To illustrate the potential of LoFEx for large molecules, both strategies have been successfully applied to the lowest transition of the bivalirudin molecule (4255 basis functions) and compared with time-dependent density functional theory.

Improving the Efficiency of Free Energy Calculations in the Amber Molecular Dynamics Package.

PubMed

Kaus, Joseph W; Pierce, Levi T; Walker, Ross C; McCammont, J Andrew

2013-09-10

Alchemical transformations are widely used methods to calculate free energies. Amber has traditionally included support for alchemical transformations as part of the sander molecular dynamics (MD) engine. Here we describe the implementation of a more efficient approach to alchemical transformations in the Amber MD package. Specifically we have implemented this new approach within the more computational efficient and scalable pmemd MD engine that is included with the Amber MD package. The majority of the gain in efficiency comes from the improved design of the calculation, which includes better parallel scaling and reduction in the calculation of redundant terms. This new implementation is able to reproduce results from equivalent simulations run with the existing functionality, but at 2.5 times greater computational efficiency. This new implementation is also able to run softcore simulations at the λ end states making direct calculation of free energies more accurate, compared to the extrapolation required in the existing implementation. The updated alchemical transformation functionality will be included in the next major release of Amber (scheduled for release in Q1 2014) and will be available at http://ambermd.org, under the Amber license.

Improving the Efficiency of Free Energy Calculations in the Amber Molecular Dynamics Package

PubMed Central

Pierce, Levi T.; Walker, Ross C.; McCammont, J. Andrew

2013-01-01

Alchemical transformations are widely used methods to calculate free energies. Amber has traditionally included support for alchemical transformations as part of the sander molecular dynamics (MD) engine. Here we describe the implementation of a more efficient approach to alchemical transformations in the Amber MD package. Specifically we have implemented this new approach within the more computational efficient and scalable pmemd MD engine that is included with the Amber MD package. The majority of the gain in efficiency comes from the improved design of the calculation, which includes better parallel scaling and reduction in the calculation of redundant terms. This new implementation is able to reproduce results from equivalent simulations run with the existing functionality, but at 2.5 times greater computational efficiency. This new implementation is also able to run softcore simulations at the λ end states making direct calculation of free energies more accurate, compared to the extrapolation required in the existing implementation. The updated alchemical transformation functionality will be included in the next major release of Amber (scheduled for release in Q1 2014) and will be available at http://ambermd.org, under the Amber license. PMID:24185531

Calculating the sensitivity and robustness of binding free energy calculations to force field parameters

PubMed Central

Rocklin, Gabriel J.; Mobley, David L.; Dill, Ken A.

2013-01-01

Binding free energy calculations offer a thermodynamically rigorous method to compute protein-ligand binding, and they depend on empirical force fields with hundreds of parameters. We examined the sensitivity of computed binding free energies to the ligand’s electrostatic and van der Waals parameters. Dielectric screening and cancellation of effects between ligand-protein and ligand-solvent interactions reduce the parameter sensitivity of binding affinity by 65%, compared with interaction strengths computed in the gas-phase. However, multiple changes to parameters combine additively on average, which can lead to large changes in overall affinity from many small changes to parameters. Using these results, we estimate that random, uncorrelated errors in force field nonbonded parameters must be smaller than 0.02 e per charge, 0.06 Å per radius, and 0.01 kcal/mol per well depth in order to obtain 68% (one standard deviation) confidence that a computed affinity for a moderately-sized lead compound will fall within 1 kcal/mol of the true affinity, if these are the only sources of error considered. PMID:24015114

Use of SCALE Continuous-Energy Monte Carlo Tools for Eigenvalue Sensitivity Coefficient Calculations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perfetti, Christopher M; Rearden, Bradley T

2013-01-01

The TSUNAMI code within the SCALE code system makes use of eigenvalue sensitivity coefficients for an extensive number of criticality safety applications, such as quantifying the data-induced uncertainty in the eigenvalue of critical systems, assessing the neutronic similarity between different critical systems, and guiding nuclear data adjustment studies. The need to model geometrically complex systems with improved fidelity and the desire to extend TSUNAMI analysis to advanced applications has motivated the development of a methodology for calculating sensitivity coefficients in continuous-energy (CE) Monte Carlo applications. The CLUTCH and Iterated Fission Probability (IFP) eigenvalue sensitivity methods were recently implemented in themore » CE KENO framework to generate the capability for TSUNAMI-3D to perform eigenvalue sensitivity calculations in continuous-energy applications. This work explores the improvements in accuracy that can be gained in eigenvalue and eigenvalue sensitivity calculations through the use of the SCALE CE KENO and CE TSUNAMI continuous-energy Monte Carlo tools as compared to multigroup tools. The CE KENO and CE TSUNAMI tools were used to analyze two difficult models of critical benchmarks, and produced eigenvalue and eigenvalue sensitivity coefficient results that showed a marked improvement in accuracy. The CLUTCH sensitivity method in particular excelled in terms of efficiency and computational memory requirements.« less

Numerical renormalization group calculation of impurity internal energy and specific heat of quantum impurity models

NASA Astrophysics Data System (ADS)

Merker, L.; Costi, T. A.

2012-08-01

We introduce a method to obtain the specific heat of quantum impurity models via a direct calculation of the impurity internal energy requiring only the evaluation of local quantities within a single numerical renormalization group (NRG) calculation for the total system. For the Anderson impurity model we show that the impurity internal energy can be expressed as a sum of purely local static correlation functions and a term that involves also the impurity Green function. The temperature dependence of the latter can be neglected in many cases, thereby allowing the impurity specific heat Cimp to be calculated accurately from local static correlation functions; specifically via Cimp=(∂Eionic)/(∂T)+(1)/(2)(∂Ehyb)/(∂T), where Eionic and Ehyb are the energies of the (embedded) impurity and the hybridization energy, respectively. The term involving the Green function can also be evaluated in cases where its temperature dependence is non-negligible, adding an extra term to Cimp. For the nondegenerate Anderson impurity model, we show by comparison with exact Bethe ansatz calculations that the results recover accurately both the Kondo induced peak in the specific heat at low temperatures as well as the high-temperature peak due to the resonant level. The approach applies to multiorbital and multichannel Anderson impurity models with arbitrary local Coulomb interactions. An application to the Ohmic two-state system and the anisotropic Kondo model is also given, with comparisons to Bethe ansatz calculations. The approach could also be of interest within other impurity solvers, for example, within quantum Monte Carlo techniques.

Efficient multidimensional free energy calculations for ab initio molecular dynamics using classical bias potentials

NASA Astrophysics Data System (ADS)

VandeVondele, Joost; Rothlisberger, Ursula

2000-09-01

We present a method for calculating multidimensional free energy surfaces within the limited time scale of a first-principles molecular dynamics scheme. The sampling efficiency is enhanced using selected terms of a classical force field as a bias potential. This simple procedure yields a very substantial increase in sampling accuracy while retaining the high quality of the underlying ab initio potential surface and can thus be used for a parameter free calculation of free energy surfaces. The success of the method is demonstrated by the applications to two gas phase molecules, ethane and peroxynitrous acid, as test case systems. A statistical analysis of the results shows that the entire free energy landscape is well converged within a 40 ps simulation at 500 K, even for a system with barriers as high as 15 kcal/mol.

Variationally Optimized Free-Energy Flooding for Rate Calculation.

PubMed

McCarty, James; Valsson, Omar; Tiwary, Pratyush; Parrinello, Michele

2015-08-14

We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to construct a bias potential as a function of several collective variables that is designed to flood the associated free energy surface up to a predefined level. The resulting bias potential effectively accelerates transitions between metastable free energy minima while ensuring bias-free transition states, thus allowing accurate kinetic rates to be obtained. We test the method on a few illustrative systems for which we obtain an order of magnitude improvement in efficiency relative to previous approaches and several orders of magnitude relative to unbiased molecular dynamics. We expect an even larger improvement in more complex systems. This and the ability of the variational approach to deal efficiently with a large number of collective variables will greatly enhance the scope of these calculations. This work is a vindication of the potential that the variational principle has if applied in innovative ways.

A Simple Approach for the Calculation of Energy Levels of Light Atoms

ERIC Educational Resources Information Center

Woodyard, Jack R., Sr.

1972-01-01

Describes a method for direct calculation of energy levels by using elementary techniques. Describes the limitations of the approach but also claims that with a minimum amount of labor a student can get greater understanding of atomic physics problems. (PS)

Gaussian Accelerated Molecular Dynamics: Unconstrained Enhanced Sampling and Free Energy Calculation

PubMed Central

2016-01-01

A Gaussian accelerated molecular dynamics (GaMD) approach for simultaneous enhanced sampling and free energy calculation of biomolecules is presented. By constructing a boost potential that follows Gaussian distribution, accurate reweighting of the GaMD simulations is achieved using cumulant expansion to the second order. Here, GaMD is demonstrated on three biomolecular model systems: alanine dipeptide, chignolin folding, and ligand binding to the T4-lysozyme. Without the need to set predefined reaction coordinates, GaMD enables unconstrained enhanced sampling of these biomolecules. Furthermore, the free energy profiles obtained from reweighting of the GaMD simulations allow us to identify distinct low-energy states of the biomolecules and characterize the protein-folding and ligand-binding pathways quantitatively. PMID:26300708

Robust identification of transcriptional regulatory networks using a Gibbs sampler on outlier sum statistic

PubMed Central

Gu, Jinghua; Xuan, Jianhua; Riggins, Rebecca B.; Chen, Li; Wang, Yue; Clarke, Robert

2012-01-01

Motivation: Identification of transcriptional regulatory networks (TRNs) is of significant importance in computational biology for cancer research, providing a critical building block to unravel disease pathways. However, existing methods for TRN identification suffer from the inclusion of excessive ‘noise’ in microarray data and false-positives in binding data, especially when applied to human tumor-derived cell line studies. More robust methods that can counteract the imperfection of data sources are therefore needed for reliable identification of TRNs in this context. Results: In this article, we propose to establish a link between the quality of one target gene to represent its regulator and the uncertainty of its expression to represent other target genes. Specifically, an outlier sum statistic was used to measure the aggregated evidence for regulation events between target genes and their corresponding transcription factors. A Gibbs sampling method was then developed to estimate the marginal distribution of the outlier sum statistic, hence, to uncover underlying regulatory relationships. To evaluate the effectiveness of our proposed method, we compared its performance with that of an existing sampling-based method using both simulation data and yeast cell cycle data. The experimental results show that our method consistently outperforms the competing method in different settings of signal-to-noise ratio and network topology, indicating its robustness for biological applications. Finally, we applied our method to breast cancer cell line data and demonstrated its ability to extract biologically meaningful regulatory modules related to estrogen signaling and action in breast cancer. Availability and implementation: The Gibbs sampler MATLAB package is freely available at http://www.cbil.ece.vt.edu/software.htm. Contact: xuan@vt.edu Supplementary information: Supplementary data are available at Bioinformatics online. PMID:22595208

Density functional calculation of activation energies for lattice and grain boundary diffusion in alumina

NASA Astrophysics Data System (ADS)

Lei, Yinkai; Gong, Yu; Duan, Zhiyao; Wang, Guofeng

2013-06-01

To acquire knowledge on the lattice and grain boundary diffusion processes in alumina, we have determined the activation energies of elementary O and Al diffusive jumps in the bulk crystal, Σ3(0001) grain boundaries, and Σ3(101¯0) grain boundaries of α-Al2O3 using the first-principles density functional theory method. Specifically, we calculated the activation energies for four elementary jumps of both O and Al lattice diffusion in alumina. It was predicted that the activation energy of O lattice diffusion varied from 3.58 to 5.03 eV, while the activation energy of Al lattice diffusion ranged from 1.80 to 3.17 eV. As compared with experimental measurements, the theoretical predictions of the activation energy for lattice diffusion were lower and thus implied that there might be other high-energy diffusive jumps in the experimental alumina samples. Moreover, our results suggested that the Al lattice diffusion was faster than the O lattice diffusion in alumina, in agreement with experiment observations. Furthermore, it was found from our calculations for α-Al2O3 that the activation energies of O and Al grain boundary diffusion in the high-energy Σ3(0001) grain boundaries were significantly lower than those of the lattice diffusion. In contrast, the activation energies of O and Al grain boundary diffusion in the low-energy Σ3(101¯0) grain boundaries could be even higher than those of the lattice diffusion.

Calculating the True and Observed Rates of Complex Heterogeneous Catalytic Reactions

NASA Astrophysics Data System (ADS)

Avetisov, A. K.; Zyskin, A. G.

2018-06-01

Equations of the theory of steady-state complex reactions are considered in matrix form. A set of stage stationarity equations is given, and an algorithm is described for deriving the canonic set of stationarity equations with appropriate corrections for the existence of fast stages in a mechanism. A formula for calculating the number of key compounds is presented. The applicability of the Gibbs rule to estimating the number of independent compounds in a complex reaction is analyzed. Some matrix equations relating the rates of dependent and key substances are derived. They are used as a basis to determine the general diffusion stoichiometry relationships between temperature, the concentrations of dependent reaction participants, and the concentrations of key reaction participants in a catalyst grain. An algorithm is described for calculating heat and mass transfer in a catalyst grain with respect to arbitrary complex heterogeneous catalytic reactions.

A new potential energy surface for vibration-vibration coupling in HF-HF collisions. Formulation and quantal scattering calculations

NASA Astrophysics Data System (ADS)

Schwenke, David W.; Truhlar, Donald G.

1988-04-01

We present new ab initio calculations of the HF-HF interaction potential for the case where both molecules are simultaneously displaced from their equilibrium internuclear distance. These and previous ab initio calculations are then fit to a new analytic representation which is designed to be efficient to evaluate and to provide an especially faithful account of the forces along the vibrational coordinates. We use the new potential for two sets of quantal scattering calculations for collisions in three dimensions with total angular momentum zero. First we test that the angular harmonic representation of the anisotropy is adequate by comparing quantal rigid rotator calculations to those carried out for potentials involving higher angular harmonics and for which the expansion in angular harmonics is systematically increased to convergence. Then we carry out large-scale quantal calculations of vibration-vibration energy transfer including the coupling of both sets of vibrational and rotational coordinates. These calculations indicate that significant rotational energy transfer accompanies the vibration-to-vibration energy transfer process.

Multiple scattering calculations of relativistic electron energy loss spectra

NASA Astrophysics Data System (ADS)

Jorissen, K.; Rehr, J. J.; Verbeeck, J.

2010-04-01

A generalization of the real-space Green’s-function approach is presented for ab initio calculations of relativistic electron energy loss spectra (EELS) which are particularly important in anisotropic materials. The approach incorporates relativistic effects in terms of the transition tensor within the dipole-selection rule. In particular, the method accounts for relativistic corrections to the magic angle in orientation resolved EELS experiments. The approach is validated by a study of the graphite CK edge, for which we present an accurate magic angle measurement consistent with the predicted value.

Calculation of the Ti(C y N1- y )-Ti4C2S2-MnS-austenite equilibrium in Ti-bearing steels

NASA Astrophysics Data System (ADS)

Liu, W. J.; Jonas, J. J.

1989-08-01

A thermodynamic model is presented for the equilibria among various precipitates (Ti(C y N1- y ), Ti4C2S2, and MnS) and austenite containing six alloying elements (C, Mn, N, S, Si, and Ti). This model is applied to four microalloyed steels with Ti levels of 0.05, 0.11, 0.18, and 0.25 pct. The calculations show that the Ti in these steels cannot be completely dissolved over the austenite temperature range. However, the compositions of the undissolved Ti carbonitrides differ significantly from pure TiN, as 10 to 40 pct of the nitrogen is replaced by carbon. An expression for the Gibbs energy for the formation of Ti4C2S2 in austenite is estimated. The present predictions are compared with those of the Hudd, Jones, and Kale (HJK) model; considerable differences are observed at temperatures below 1250°C.

About the choice of Gibbs' potential for modelling of FCC ↔ HCP transformation in FeMnSi-based shape memory alloys

NASA Astrophysics Data System (ADS)

Evard, Margarita E.; Volkov, Aleksandr E.; Belyaev, Fedor S.; Ignatova, Anna D.

2018-05-01

The choice of Gibbs' potential for microstructural modeling of FCC ↔ HCP martensitic transformation in FeMn-based shape memory alloys is discussed. Threefold symmetry of the HCP phase is taken into account on specifying internal variables characterizing volume fractions of martensite variants. Constraints imposed on model constants by thermodynamic equilibrium conditions are formulated.

Relative Binding Free Energy Calculations in Drug Discovery: Recent Advances and Practical Considerations.

PubMed

Cournia, Zoe; Allen, Bryce; Sherman, Woody

2017-12-26

Accurate in silico prediction of protein-ligand binding affinities has been a primary objective of structure-based drug design for decades due to the putative value it would bring to the drug discovery process. However, computational methods have historically failed to deliver value in real-world drug discovery applications due to a variety of scientific, technical, and practical challenges. Recently, a family of approaches commonly referred to as relative binding free energy (RBFE) calculations, which rely on physics-based molecular simulations and statistical mechanics, have shown promise in reliably generating accurate predictions in the context of drug discovery projects. This advance arises from accumulating developments in the underlying scientific methods (decades of research on force fields and sampling algorithms) coupled with vast increases in computational resources (graphics processing units and cloud infrastructures). Mounting evidence from retrospective validation studies, blind challenge predictions, and prospective applications suggests that RBFE simulations can now predict the affinity differences for congeneric ligands with sufficient accuracy and throughput to deliver considerable value in hit-to-lead and lead optimization efforts. Here, we present an overview of current RBFE implementations, highlighting recent advances and remaining challenges, along with examples that emphasize practical considerations for obtaining reliable RBFE results. We focus specifically on relative binding free energies because the calculations are less computationally intensive than absolute binding free energy (ABFE) calculations and map directly onto the hit-to-lead and lead optimization processes, where the prediction of relative binding energies between a reference molecule and new ideas (virtual molecules) can be used to prioritize molecules for synthesis. We describe the critical aspects of running RBFE calculations, from both theoretical and applied perspectives

Generalized Gibbs ensemble in integrable lattice models

NASA Astrophysics Data System (ADS)

Vidmar, Lev; Rigol, Marcos

2016-06-01

The generalized Gibbs ensemble (GGE) was introduced ten years ago to describe observables in isolated integrable quantum systems after equilibration. Since then, the GGE has been demonstrated to be a powerful tool to predict the outcome of the relaxation dynamics of few-body observables in a variety of integrable models, a process we call generalized thermalization. This review discusses several fundamental aspects of the GGE and generalized thermalization in integrable systems. In particular, we focus on questions such as: which observables equilibrate to the GGE predictions and who should play the role of the bath; what conserved quantities can be used to construct the GGE; what are the differences between generalized thermalization in noninteracting systems and in interacting systems mappable to noninteracting ones; why is it that the GGE works when traditional ensembles of statistical mechanics fail. Despite a lot of interest in these questions in recent years, no definite answers have been given. We review results for the XX model and for the transverse field Ising model. For the latter model, we also report original results and show that the GGE describes spin-spin correlations over the entire system. This makes apparent that there is no need to trace out a part of the system in real space for equilibration to occur and for the GGE to apply. In the past, a spectral decomposition of the weights of various statistical ensembles revealed that generalized eigenstate thermalization occurs in the XX model (hard-core bosons). Namely, eigenstates of the Hamiltonian with similar distributions of conserved quantities have similar expectation values of few-spin observables. Here we show that generalized eigenstate thermalization also occurs in the transverse field Ising model.

A Method for the Calculation of Lattice Energies of Complex Crystals with Application to the Oxides of Molybdenum

NASA Technical Reports Server (NTRS)

Chaney, William S.

1961-01-01

A theoretical study has been made of molybdenum dioxide and molybdenum trioxide in order to extend the knowledge of factors Involved in the oxidation of molybdenum. New methods were developed for calculating the lattice energies based on electrostatic valence theory, and the coulombic, polarization, Van der Waals, and repulsion energie's were calculated. The crystal structure was examined and structure details were correlated with lattice energy.

On Detecting Biospheres from Chemical Thermodynamic Disequilibrium in Planetary Atmospheres.

PubMed

Krissansen-Totton, Joshua; Bergsman, David S; Catling, David C

2016-01-01

Atmospheric chemical disequilibrium has been proposed as a method for detecting extraterrestrial biospheres from exoplanet observations. Chemical disequilibrium is potentially a generalized biosignature since it makes no assumptions about particular biogenic gases or metabolisms. Here, we present the first rigorous calculations of the thermodynamic chemical disequilibrium in Solar System atmospheres, in which we quantify the available Gibbs energy: the Gibbs free energy of an observed atmosphere minus that of atmospheric gases reacted to equilibrium. The purely gas phase disequilibrium in Earth's atmosphere is mostly attributable to O2 and CH4. The available Gibbs energy is not unusual compared to other Solar System atmospheres and smaller than that of Mars. However, Earth's fluid envelope contains an ocean, allowing gases to react with water and requiring a multiphase calculation with aqueous species. The disequilibrium in Earth's atmosphere-ocean system (in joules per mole of atmosphere) ranges from ∼20 to 2 × 10(6) times larger than the disequilibria of other atmospheres in the Solar System, where Mars is second to Earth. Only on Earth is the chemical disequilibrium energy comparable to the thermal energy per mole of atmosphere (excluding comparison to Titan with lakes, where quantification is precluded because the mean lake composition is unknown). Earth's disequilibrium is biogenic, mainly caused by the coexistence of N2, O2, and liquid water instead of more stable nitrate. In comparison, the O2-CH4 disequilibrium is minor, although kinetics requires a large CH4 flux into the atmosphere. We identify abiotic processes that cause disequilibrium in the other atmospheres. Our metric requires minimal assumptions and could potentially be calculated from observations of exoplanet atmospheres. However, further work is needed to establish whether thermodynamic disequilibrium is a practical exoplanet biosignature, requiring an assessment of false positives, noisy

Methods for calculating dietary energy density in a nationally representative sample

PubMed Central

Vernarelli, Jacqueline A.; Mitchell, Diane C.; Rolls, Barbara J.; Hartman, Terryl J.

2013-01-01

There has been a growing interest in examining dietary energy density (ED, kcal/g) as it relates to various health outcomes. Consuming a diet low in ED has been recommended in the 2010 Dietary Guidelines, as well as by other agencies, as a dietary approach for disease prevention. Translating this recommendation into practice; however, is difficult. Currently there is no standardized method for calculating dietary ED; as dietary ED can be calculated with foods alone, or with a combination of foods and beverages. Certain items may be defined as either a food or a beverage (e.g., meal replacement shakes) and require special attention. National survey data are an excellent resource for evaluating factors that are important to dietary ED calculation. The National Health and Nutrition Examination Survey (NHANES) nutrient and food database does not include an ED variable, thus researchers must independently calculate ED. The objective of this study was to provide information that will inform the selection of a standardized ED calculation method by comparing and contrasting methods for ED calculation. The present study evaluates all consumed items and defines foods and beverages based on both USDA food codes and how the item was consumed. Results are presented as mean EDs for the different calculation methods stratified by population demographics (e.g. age, sex). Using United State Department of Agriculture (USDA) food codes in the 2005–2008 NHANES, a standardized method for calculating dietary ED can be derived. This method can then be adapted by other researchers for consistency across studies. PMID:24432201

Factors influencing the mechanism of surfactant catalyzed reaction of vitamin C-ferric chloride hexahydrate system

NASA Astrophysics Data System (ADS)

Farrukh, Muhammad Akhyar; Kauser, Robina; Adnan, Rohana

2013-09-01

The kinetics of vitamin C by ferric chloride hexahydrate has been investigated in the aqueous ethanol solution of basic surfactant viz. octadecylamine (ODA) under pseudo-first order conditions. The critical micelle concentration (CMC) of surfactant was determined by surface tension measurement. The effect of pH (2.5-4.5) and temperature (15-35°C) in the presence and absence of surfactant were investigated. Activation parameters, Δ E a, Δ H #, Δ S #, Δ G ≠, for the reaction were calculated by using Arrhenius and Eyring plot. Surface excess concentration (Γmax), minimum area per surfactant molecule ( A min), average area occupied by each molecule of surfactant ( a), surface pressure at the CMC (Πmax), Gibb's energy of micellization (Δ G M°), Gibb's energy of adsorption (Δ G ad°), were calculated. It was found that the reaction in the presence of surfactant showed faster oxidation rate than the aqueous ethanol solution. Reaction mechanism has been deduced in the presence and absence of surfactant.

Fine-structure calculations of energy levels, oscillator strengths, and transition probabilities for sulfur-like iron, Fe XI

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abou El-Maaref, A., E-mail: aahmh@hotmail.com; Ahmad, Mahmoud; Allam, S.H.

Energy levels, oscillator strengths, and transition probabilities for transitions among the 14 LS states belonging to configurations of sulfur-like iron, Fe XI, have been calculated. These states are represented by configuration interaction wavefunctions and have configurations 3s{sup 2}3p{sup 4}, 3s3p{sup 5}, 3s{sup 2}3p{sup 3}3d, 3s{sup 2}3p{sup 3}4s, 3s{sup 2}3p{sup 3}4p, and 3s{sup 2}3p{sup 3}4d, which give rise to 123 fine-structure energy levels. Extensive configuration interaction calculations using the CIV3 code have been performed. To assess the importance of relativistic effects, the intermediate coupling scheme by means of the Breit–Pauli Hamiltonian terms, such as the one-body mass correction and Darwin term,more » and spin–orbit, spin–other-orbit, and spin–spin corrections, are incorporated within the code. These incorporations adjusted the energy levels, therefore the calculated values are close to the available experimental data. Comparisons between the present calculated energy levels as well as oscillator strengths and both experimental and theoretical data have been performed. Our results show good agreement with earlier works, and they might be useful in thermonuclear fusion research and astrophysical applications. -- Highlights: •Accurate atomic data of iron ions are needed for identification of solar corona. •Extensive configuration interaction wavefunctions including 123 fine-structure levels have been calculated. •The relativistic effects by means of the Breit–Pauli Hamiltonian terms are incorporated. •This incorporation adjusts the energy levels, therefore the calculated values are close to experimental values.« less

Ab initio SCF calculations on the potential energy surface of potassium cyanide (KCN)

NASA Astrophysics Data System (ADS)

Wormer, Paul E. S.; Tennyson, Jonathan

1981-08-01

The potential energy surface of KCN has been generated by ab initio SCF calculations in the region of equilibrium bond distances. An analytic representation of the surface is presented. The calculations show that the bonding between K and CN is ionic, and that the structure of KCN is triangular, which confirms recent experimental findings. The computed geometry is &KCN = 62.4°, rCK = 5.492a0, and rCN = 2.186a0.

Employment of Gibbs-Donnan-based concepts for interpretation of the properties of linear polyelectrolyte solutions

USGS Publications Warehouse

Marinsky, J.A.; Reddy, M.M.

1991-01-01

Earlier research has shown that the acid dissociation and metal ion complexation equilibria of linear, weak-acid polyelectrolytes and their cross-linked gel analogues are similarly sensitive to the counterion concentration levels of their solutions. Gibbs-Donnan-based concepts, applicable to the gel, are equally applicable to the linear polyelectrolyte for the accommodation of this sensitivity to ionic strength. This result is presumed to indicate that the linear polyelectrolyte in solution develops counterion-concentrating regions that closely resemble the gel phase of their analogues. Advantage has been taken of this description of linear polyelectrolytes to estimate the solvent uptake by these regions. ?? 1991 American Chemical Society.

The Gibbs paradox and the physical criteria for indistinguishability of identical particles

NASA Astrophysics Data System (ADS)

Unnikrishnan, C. S.

2016-08-01

Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits quantum theory for enabling indistinguishability of identical particles to solve the problem. We argue that indistinguishability of identical particles is already a feature in classical mechanics and this is clearly brought out when the problem is treated in the language of information and associated entropy. We pinpoint the physical criteria for indistinguishability that is crucial for the treatment of the Gibbs’ problem and the consistency of its solution with conventional thermodynamics. Quantum mechanics provides a quantitative criterion, not possible in the classical picture, for the degree of indistinguishability in terms of visibility of quantum interference, or overlap of the states as pointed out by von Neumann, thereby endowing the entropy expression with mathematical continuity and physical reasonableness.

Study of thermodynamic and transport properties of binary liquid mixture of diesel with biodiesel at 298.15K

NASA Astrophysics Data System (ADS)

Suthar, Shyam Sunder; Purohit, Suresh

2018-05-01

Properties of diesel and biodiesel (produced from corn oil) are used. Densities and viscosities of binary mixture of diesel with biodiesel (produced from corn oil) have been computed by using liquid binary mixture law over the entire range of compositions at T=298.15K and atmospheric pressure. From the computed values of density and viscosities, viscosity deviation (Δη), the excess molar volume (VE) and excess Gibbs energy of activation of viscous flow (ΔG#E) have been calculated. The results of excess volume, excess Gibbs energy of activation of viscous flow and viscosity deviation have been fitted to Redlich -Kister models to estimate the binary coefficients. The results are communicated in terms of the molecular interactions and the best suited composition has been found.

Free Energy Calculations using a Swarm-Enhanced Sampling Molecular Dynamics Approach.

PubMed

Burusco, Kepa K; Bruce, Neil J; Alibay, Irfan; Bryce, Richard A

2015-10-26

Free energy simulations are an established computational tool in modelling chemical change in the condensed phase. However, sampling of kinetically distinct substates remains a challenge to these approaches. As a route to addressing this, we link the methods of thermodynamic integration (TI) and swarm-enhanced sampling molecular dynamics (sesMD), where simulation replicas interact cooperatively to aid transitions over energy barriers. We illustrate the approach by using alchemical alkane transformations in solution, comparing them with the multiple independent trajectory TI (IT-TI) method. Free energy changes for transitions computed by using IT-TI grew increasingly inaccurate as the intramolecular barrier was heightened. By contrast, swarm-enhanced sampling TI (sesTI) calculations showed clear improvements in sampling efficiency, leading to more accurate computed free energy differences, even in the case of the highest barrier height. The sesTI approach, therefore, has potential in addressing chemical change in systems where conformations exist in slow exchange. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

LoFEx - A local framework for calculating excitation energies: Illustrations using RI-CC2 linear response theory.

PubMed

Baudin, Pablo; Kristensen, Kasper

2016-06-14

We present a local framework for the calculation of coupled cluster excitation energies of large molecules (LoFEx). The method utilizes time-dependent Hartree-Fock information about the transitions of interest through the concept of natural transition orbitals (NTOs). The NTOs are used in combination with localized occupied and virtual Hartree-Fock orbitals to generate a reduced excitation orbital space (XOS) specific to each transition where a standard coupled cluster calculation is carried out. Each XOS is optimized to ensure that the excitation energies are determined to a predefined precision. We apply LoFEx in combination with the RI-CC2 model to calculate the lowest excitation energies of a set of medium-sized organic molecules. The results demonstrate the black-box nature of the LoFEx approach and show that significant computational savings can be gained without affecting the accuracy of CC2 excitation energies.

Characterization of racemic species of chiral drugs using thermal analysis, thermodynamic calculation, and structural studies.

PubMed

Li, Z J; Zell, M T; Munson, E J; Grant, D J

1999-03-01

The identification of the racemic species, as a racemic compound, a racemic conglomerate, or a racemic solid solution (pseudoracemate), is crucial for rationalizing the potential for resolution of racemates by crystallization. The melting points and enthalpies of fusion of a number of chiral drugs and their salts were measured by differential scanning calorimetry. Based on a thermodynamic cycle involving the solid and liquid phases of the enantiomers and racemic species, the enthalpy, entropy and Gibbs free energy of the racemic species were derived from the thermal data. The Gibbs free energy of formation, is always negative for a racemic compound, if it can exist, and the contribution from the entropy of mixing in the liquid state to the free energy of formation is the driving force for the process. For a racemic conglomerate, the entropy of mixing in the liquid state is close to the ideal value of R ln 2 (1.38 cal.mol-1. K-1). Pseudoracemates behave differently from the other two types of racemic species. When the melting points of the racemic species is about 30 K below that of the homochiral species, is approximately zero, indicating that the racemic compound and racemic conglomerate possess similar relative stabilities. The powder X-ray diffraction patterns and 13C solid-state nuclear magnetic resonance spectra are valuable for revealing structural differences between a racemic compound and a racemic conglomerate. Thermodynamic prediction, thermal analysis, and structural study are in excellent agreement for identifying the nature of the racemic species.

Fast and flexible gpu accelerated binding free energy calculations within the amber molecular dynamics package.

PubMed

Mermelstein, Daniel J; Lin, Charles; Nelson, Gard; Kretsch, Rachael; McCammon, J Andrew; Walker, Ross C

2018-07-15

Alchemical free energy (AFE) calculations based on molecular dynamics (MD) simulations are key tools in both improving our understanding of a wide variety of biological processes and accelerating the design and optimization of therapeutics for numerous diseases. Computing power and theory have, however, long been insufficient to enable AFE calculations to be routinely applied in early stage drug discovery. One of the major difficulties in performing AFE calculations is the length of time required for calculations to converge to an ensemble average. CPU implementations of MD-based free energy algorithms can effectively only reach tens of nanoseconds per day for systems on the order of 50,000 atoms, even running on massively parallel supercomputers. Therefore, converged free energy calculations on large numbers of potential lead compounds are often untenable, preventing researchers from gaining crucial insight into molecular recognition, potential druggability and other crucial areas of interest. Graphics Processing Units (GPUs) can help address this. We present here a seamless GPU implementation, within the PMEMD module of the AMBER molecular dynamics package, of thermodynamic integration (TI) capable of reaching speeds of >140 ns/day for a 44,907-atom system, with accuracy equivalent to the existing CPU implementation in AMBER. The implementation described here is currently part of the AMBER 18 beta code and will be an integral part of the upcoming version 18 release of AMBER. © 2018 Wiley Periodicals, Inc. © 2018 Wiley Periodicals, Inc.

Energy-level alignment in organic dye-sensitized TiO2 from GW calculations.

PubMed

Umari, P; Giacomazzi, L; De Angelis, F; Pastore, M; Baroni, Stefano

2013-07-07

The electronic energy levels of some representative isolated and oxide-supported organic dyes, relevant for photovoltaic applications, are investigated using many-body perturbation theory within the GW approximation. We consider a set of all-organic dyes (denominated L0, L2, L3, and L4) featuring the same donor and anchor groups and differing for the linker moieties. We first calculate the energy levels of the isolated molecules, thus allowing us to address the effects of the different linker groups, and resulting in good agreement with photo-electron spectroscopic and electrochemical data. We then consider the L0 dye adsorbed on the (101) surface of anatase-TiO2. We find a density of occupied states in agreement with experimental photo-electron data. The HOMO-LUMO energy gap of the L0 dye is found to be reduced by ~1 eV upon adsorption. Our results validate the reliability of GW calculations for photovoltaic applications and point to their potential as a powerful tool for the screening and rational design of new components of electrochemical solar cells.

The self-consistent calculation of pseudo-molecule energy levels, construction of energy level correlation diagrams and an automated computation system for SCF-X(Alpha)-SW calculations

NASA Technical Reports Server (NTRS)

Schlosser, H.

1981-01-01

The self consistent calculation of the electronic energy levels of noble gas pseudomolecules formed when a metal surface is bombarded by noble gas ions is discussed along with the construction of energy level correlation diagrams as a function of interatomic spacing. The self consistent field x alpha scattered wave (SCF-Xalpha-SW) method is utilized. Preliminary results on the Ne-Mg system are given. An interactive x alpha programming system, implemented on the LeRC IBM 370 computer, is described in detail. This automated system makes use of special PROCDEFS (procedure definitions) to minimize the data to be entered manually at a remote terminal. Listings of the special PROCDEFS and of typical input data are given.

Free energy calculations, enhanced by a Gaussian ansatz, for the "chemical work" distribution.

PubMed

Boulougouris, Georgios C

2014-05-15

The evaluation of the free energy is essential in molecular simulation because it is intimately related with the existence of multiphase equilibrium. Recently, it was demonstrated that it is possible to evaluate the Helmholtz free energy using a single statistical ensemble along an entire isotherm by accounting for the "chemical work" of transforming each molecule, from an interacting one, to an ideal gas. In this work, we show that it is possible to perform such a free energy perturbation over a liquid vapor phase transition. Furthermore, we investigate the link between a general free energy perturbation scheme and the novel nonequilibrium theories of Crook's and Jarzinsky. We find that for finite systems away from the thermodynamic limit the second law of thermodynamics will always be an inequality for isothermal free energy perturbations, resulting always to a dissipated work that may tend to zero only in the thermodynamic limit. The work, the heat, and the entropy produced during a thermodynamic free energy perturbation can be viewed in the context of the Crooks and Jarzinsky formalism, revealing that for a given value of the ensemble average of the "irreversible" work, the minimum entropy production corresponded to a Gaussian distribution for the histogram of the work. We propose the evaluation of the free energy difference in any free energy perturbation based scheme on the average irreversible "chemical work" minus the dissipated work that can be calculated from the variance of the distribution of the logarithm of the work histogram, within the Gaussian approximation. As a consequence, using the Gaussian ansatz for the distribution of the "chemical work," accurate estimates for the chemical potential and the free energy of the system can be performed using much shorter simulations and avoiding the necessity of sampling the computational costly tails of the "chemical work." For a more general free energy perturbation scheme that the Gaussian ansatz may not be

Lattice model calculation of the strain energy density and other properties of crystalline LiCoO{sub 2}

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hart, F.X.; Bates, J.B.

1998-06-01

The strain energy densities for various crystalline planes of LiCoO{sub 2} were calculated from the stiffness tensors obtained from lattice model calculations using the program GULP. In addition to Coulomb and Buckingham potentials, it was necessary to include shell models for the oxygen and cobalt ions in order to obtain acceptable agreement between the observed and calculated structural parameters and high frequency dielectric constant. The strain energy densities u due to differential thermal expansion were calculated using the theoretical stiffness tensors and estimated values for the thermal expansion coefficients of LiCoO{sub 2}. For a temperature change of 675thinsp{degree}C, these rangedmore » from 0.5 to 1.3{times}10{sup 8}thinsperg/cm{sup 3} or 5 to 13thinspJ/m{sup 2} for 1-{mu}m-thick films on alumina substrates. In particular, the energies for the (003), (101), and (104) planes were ordered as u(003){gt}u(104){gt}u(101). This suggests that the strong (101) preferred orientation of LiCoO{sub 2} films ({ge}1thinsp{mu}m thick) is due to the tendency to minimize volume strain energy that arises from differential thermal expansion between the film and the substrate. Additional properties obtained from the GULP calculations include the free energy, heat capacity, and the k=0 vibrational modes. thinsp« less

On the Gibbs phenomenon 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function

NASA Technical Reports Server (NTRS)

Gottlieb, David; Shu, Chi-Wang; Solomonoff, Alex; Vandeven, Herve

1992-01-01

It is well known that the Fourier series of an analytic or periodic function, truncated after 2N+1 terms, converges exponentially with N, even in the maximum norm, although the function is still analytic. This is known as the Gibbs phenomenon. Here, we show that the first 2N+1 Fourier coefficients contain enough information about the function, so that an exponentially convergent approximation (in the maximum norm) can be constructed.

Ab initio calculations of the structural, electronic, thermodynamic and thermal properties of BaSe1-x Te x alloys

NASA Astrophysics Data System (ADS)

Drablia, S.; Boukhris, N.; Boulechfar, R.; Meradji, H.; Ghemid, S.; Ahmed, R.; Omran, S. Bin; El Haj Hassan, F.; Khenata, R.

2017-10-01

The alkaline earth metal chalcogenides are being intensively investigated because of their advanced technological applications, for example in photoluminescent devices. In this study, the structural, electronic, thermodynamic and thermal properties of the BaSe1-x Te x alloys at alloying composition x = 0, 0.25, 0.50, 0.75 and 1 are investigated. The full potential linearized augmented plane wave plus local orbital method designed within the density functional theory was used to perform the total energy calculations. In this research work the effect of the composition on the results of the parameters and bulk modulus as well as on the band gap energy is analyzed. From our results, we found a deviation of the obtained results for the lattice constants from Vegard’s law as well as a deviation of the value of the bulk modulus from the linear concentration dependence. We also carried out a microscopic analysis of the origin of the band gap energy bowing parameter. Furthermore, the thermodynamic stability of the considered alloys was explored through the measurement of the miscibility critical temperature. The quasi-harmonic Debye model, as implemented in the Gibbs code, was used to predict the thermal properties of the BaSe1-x Te x alloys, and these investigations comprise our first theoretical predictions concerning the BaSe1-x Te x alloys.

Towards solar energy storage in the photochromic dihydroazulene-vinylheptafulvene system.

PubMed

Cacciarini, Martina; Skov, Anders B; Jevric, Martyn; Hansen, Anne S; Elm, Jonas; Kjaergaard, Henrik G; Mikkelsen, Kurt V; Brøndsted Nielsen, Mogens

2015-05-11

One key challenge in the field of exploitation of solar energy is to store the energy and make it available on demand. One possibility is to use photochromic molecules that undergo light-induced isomerization to metastable isomers. Here we present efforts to develop solar thermal energy storage systems based on the dihydroazulene (DHA)/vinylheptafulvene (VHF) photo/thermoswitch. New DHA derivatives with one electron-withdrawing cyano group at position 1 and one or two phenyl substituents in the five-membered ring were prepared by using different synthetic routes. In particular, a diastereoselective reductive removal of one cyano group from DHAs incorporating two cyano groups at position 1 turned out to be most effective. Quantum chemical calculations reveal that the structural modifications provide two benefits relative to DHAs with two cyano groups at position 1: 1) The DHA-VHF energy difference is increased (i.e., higher energy capacity of metastable VHF isomer); 2) the Gibbs free energy of activation is increased for the energy-releasing VHF to DHA back-reaction. In fact, experimentally, these new derivatives were so reluctant to undergo the back-reaction at room temperature that they practically behaved as DHA to VHF one-way switches. Although lifetimes of years are at first attractive, which offers the ultimate control of energy release, for a real device it must of course be possible to trigger the back-reaction, which calls for further iterations in the future. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Bimodality emerges from transport model calculations of heavy ion collisions at intermediate energy

NASA Astrophysics Data System (ADS)

Mallik, S.; Das Gupta, S.; Chaudhuri, G.

2016-04-01

This work is a continuation of our effort [S. Mallik, S. Das Gupta, and G. Chaudhuri, Phys. Rev. C 91, 034616 (2015)], 10.1103/PhysRevC.91.034616 to examine if signatures of a phase transition can be extracted from transport model calculations of heavy ion collisions at intermediate energy. A signature of first-order phase transition is the appearance of a bimodal distribution in Pm(k ) in finite systems. Here Pm(k ) is the probability that the maximum of the multiplicity distribution occurs at mass number k . Using a well-known model for event generation [Botzmann-Uehling-Uhlenbeck (BUU) plus fluctuation], we study two cases of central collision: mass 40 on mass 40 and mass 120 on mass 120. Bimodality is seen in both the cases. The results are quite similar to those obtained in statistical model calculations. An intriguing feature is seen. We observe that at the energy where bimodality occurs, other phase-transition-like signatures appear. There are breaks in certain first-order derivatives. We then examine if such breaks appear in standard BUU calculations without fluctuations. They do. The implication is interesting. If first-order phase transition occurs, it may be possible to recognize that from ordinary BUU calculations. Probably the reason this has not been seen already is because this aspect was not investigated before.

The Calculation of Potential Energy Curves of Diatomic Molecules: The RKR Method.

ERIC Educational Resources Information Center

Castano, F.; And Others

1983-01-01

The RKR method for determining accurate potential energy curves is described. Advantages of using the method (compared to Morse procedure) and a TRS-80 computer program which calculates the classical turning points by an RKR method are also described. The computer program is available from the author upon request. (Author/JN)

Comparison of Measured Leakage Current Distributions with Calculated Damage Energy Distributions in HgCdTe

NASA Technical Reports Server (NTRS)

Marshall, C. J.; Ladbury, R.; Marshall, P. W.; Reed, R. A.; Howe, C.; Weller, B.; Mendenhall, M.; Waczynski, A.; Jordan, T. M.; Fodness, B.

2006-01-01

This paper presents a combined Monte Carlo and analytic approach to the calculation of the pixel-to-pixel distribution of proton-induced damage in a HgCdTe sensor array and compares the results to measured dark current distributions after damage by 63 MeV protons. The moments of the Coulombic, nuclear elastic and nuclear inelastic damage distribution were extracted from Monte Carlo simulations and combined to form a damage distribution using the analytic techniques first described in [I]. The calculations show that the high energy recoils from the nuclear inelastic reactions (calculated using the Monte Car10 code MCNPX [2]) produce a pronounced skewing of the damage energy distribution. The nuclear elastic component (also calculated using the MCNPX) has a negligible effect on the shape of the damage distribution. The Coulombic contribution was calculated using MRED [3,4], a Geant4 [4,5] application. The comparison with the dark current distribution strongly suggests that mechanisms which are not linearly correlated with nonionizing damage produced according to collision kinematics are responsible for the observed dark current increases. This has important implications for the process of predicting the on-orbit dark current response of the HgCdTe sensor array.

Ab initio calculation of the G peak intensity of graphene: Laser-energy and Fermi-energy dependence and importance of quantum interference effects

NASA Astrophysics Data System (ADS)

Reichardt, Sven; Wirtz, Ludger

2017-05-01

We present the results of a diagrammatic, fully ab initio calculation of the G peak intensity of graphene. The flexibility and generality of our approach enables us to go beyond the previous analytical calculations in the low-energy regime. We study the laser and Fermi energy dependence of the G peak intensity and analyze the contributions from resonant and nonresonant electronic transitions. In particular, we explicitly demonstrate the importance of quantum interference and nonresonant states for the G peak process. Our method of analysis and computational concept is completely general and can easily be applied to study other materials as well.

Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble

NASA Astrophysics Data System (ADS)

Mestyán, M.; Pozsgay, B.; Takács, G.; Werner, M. A.

2015-04-01

Following our previous work (Pozsgay et al 2014 Phys. Rev. Lett. 113 117203) we present here a detailed comparison of the quench action approach and the predictions of the generalized Gibbs ensemble, with the result that while the quench action formalism correctly captures the steady state, the GGE does not give a correct description of local short-distance correlation functions. We extend our studies to include another initial state, the so-called q-dimer state. We present important details of our construction, including new results concerning exact overlaps for the dimer and q-dimer states, and we also give an exact solution of the quench-action-based overlap-TBA for the q-dimer. Furthermore, we extend our computations to include the xx spin correlations besides the zz correlations treated previously, and give a detailed discussion of the underlying reasons for the failure of the GGE, especially in the light of new developments.

Star sub-pixel centroid calculation based on multi-step minimum energy difference method

NASA Astrophysics Data System (ADS)

Wang, Duo; Han, YanLi; Sun, Tengfei

2013-09-01

The star's centroid plays a vital role in celestial navigation, star images which be gotten during daytime, due to the strong sky background, have a low SNR, and the star objectives are nearly submerged in the background, takes a great trouble to the centroid localization. Traditional methods, such as a moment method, weighted centroid calculation method is simple but has a big error, especially in the condition of a low SNR. Gaussian method has a high positioning accuracy, but the computational complexity. Analysis of the energy distribution in star image, a location method for star target centroids based on multi-step minimum energy difference is proposed. This method uses the linear superposition to narrow the centroid area, in the certain narrow area uses a certain number of interpolation to pixels for the pixels' segmentation, and then using the symmetry of the stellar energy distribution, tentatively to get the centroid position: assume that the current pixel is the star centroid position, and then calculates and gets the difference of the sum of the energy which in the symmetric direction(in this paper we take the two directions of transverse and longitudinal) and the equal step length(which can be decided through different conditions, the paper takes 9 as the step length) of the current pixel, and obtain the centroid position in this direction when the minimum difference appears, and so do the other directions, then the validation comparison of simulated star images, and compare with several traditional methods, experiments shows that the positioning accuracy of the method up to 0.001 pixel, has good effect to calculate the centroid of low SNR conditions; at the same time, uses this method on a star map which got at the fixed observation site during daytime in near-infrared band, compare the results of the paper's method with the position messages which were known of the star, it shows that :the multi-step minimum energy difference method achieves a better

Semi-empirical anzatz for Helmholtz free energy calculation: Thermal properties of silver along shock Hugoniot

NASA Astrophysics Data System (ADS)

Joshi, R. H.; Thakore, B. Y.; Bhatt, N. K.; Vyas, P. R.; Jani, A. R.

2018-02-01

A density functional theory along with electronic contribution is used to compute quasiharmonic total energy for silver, whereas explicit phonon anharmonic contribution is added through perturbative term in temperature. Within the Mie-Grüneisen approach, we propose a consistent computational scheme for calculating various thermophysical properties of a substance, in which the required Grüneisen parameter γth is calculated from the knowledge of binding energy. The present study demonstrates that no separate relation for volume dependence for γth is needed, and complete thermodynamics under simultaneous high-temperature and high-pressure condition can be derived in a consistent manner. We have calculated static and dynamic equation of states and some important thermodynamic properties along the shock Hugoniot. A careful examination of temperature dependence of Grüneisen parameter reveals the importance of temperature-effect on various thermal properties.

Crystallization of glass-forming liquids: Specific surface energy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schmelzer, Jürn W. P., E-mail: juern-w.schmelzer@uni-rostock.de; Abyzov, Alexander S.

2016-08-14

A generalization of the Stefan-Skapski-Turnbull relation for the melt-crystal specific interfacial energy is developed in terms of the generalized Gibbs approach extending its standard formulation to thermodynamic non-equilibrium states. With respect to crystal nucleation, this relation is required in order to determine the parameters of the critical crystal clusters being a prerequisite for the computation of the work of critical cluster formation. As one of its consequences, a relation for the dependence of the specific surface energy of critical clusters on temperature and pressure is derived applicable for small and moderate deviations from liquid-crystal macroscopic equilibrium states. Employing the Stefan-Skapski-Turnbullmore » relation, general expressions for the size and the work of formation of critical crystal clusters are formulated. The resulting expressions are much more complex as compared to the respective relations obtained via the classical Gibbs theory. Latter relations are retained as limiting cases of these more general expressions for moderate undercoolings. By this reason, the formulated, here, general relations for the specification of the critical cluster size and the work of critical cluster formation give a key for an appropriate interpretation of a variety of crystallization phenomena occurring at large undercoolings which cannot be understood in terms of the Gibbs’ classical treatment.« less

Doppler Temperature Coefficient Calculations Using Adjoint-Weighted Tallies and Continuous Energy Cross Sections in MCNP6

NASA Astrophysics Data System (ADS)

Gonzales, Matthew Alejandro

The calculation of the thermal neutron Doppler temperature reactivity feedback co-efficient, a key parameter in the design and safe operation of advanced reactors, using first order perturbation theory in continuous energy Monte Carlo codes is challenging as the continuous energy adjoint flux is not readily available. Traditional approaches of obtaining the adjoint flux attempt to invert the random walk process as well as require data corresponding to all temperatures and their respective temperature derivatives within the system in order to accurately calculate the Doppler temperature feedback. A new method has been developed using adjoint-weighted tallies and On-The-Fly (OTF) generated continuous energy cross sections within the Monte Carlo N-Particle (MCNP6) transport code. The adjoint-weighted tallies are generated during the continuous energy k-eigenvalue Monte Carlo calculation. The weighting is based upon the iterated fission probability interpretation of the adjoint flux, which is the steady state population in a critical nuclear reactor caused by a neutron introduced at that point in phase space. The adjoint-weighted tallies are produced in a forward calculation and do not require an inversion of the random walk. The OTF cross section database uses a high order functional expansion between points on a user-defined energy-temperature mesh in which the coefficients with respect to a polynomial fitting in temperature are stored. The coefficients of the fits are generated before run- time and called upon during the simulation to produce cross sections at any given energy and temperature. The polynomial form of the OTF cross sections allows the possibility of obtaining temperature derivatives of the cross sections on-the-fly. The use of Monte Carlo sampling of adjoint-weighted tallies and the capability of computing derivatives of continuous energy cross sections with respect to temperature are used to calculate the Doppler temperature coefficient in a research

Correlations after quantum quenches in the XXZ spin chain: failure of the generalized Gibbs ensemble.

PubMed

Pozsgay, B; Mestyán, M; Werner, M A; Kormos, M; Zaránd, G; Takács, G

2014-09-12

We study the nonequilibrium time evolution of the spin-1/2 anisotropic Heisenberg (XXZ) spin chain, with a choice of dimer product and Néel states as initial states. We investigate numerically various short-ranged spin correlators in the long-time limit and find that they deviate significantly from predictions based on the generalized Gibbs ensemble (GGE) hypotheses. By computing the asymptotic spin correlators within the recently proposed quench-action formalism [Phys. Rev. Lett. 110, 257203 (2013)], however, we find excellent agreement with the numerical data. We, therefore, conclude that the GGE cannot give a complete description even of local observables, while the quench-action formalism correctly captures the steady state in this case.

Pourbaix ("E"-pH-M) Diagrams in Three Dimensions

ERIC Educational Resources Information Center

Pesterfield, Lester L.; Maddox, Jeremy B.; Crocker, Michael S.; Schweitzer, George K.

2012-01-01

"E"-pH (Pourbaix) diagrams provide an important graphical link between the thermodynamic calculations of potential, pH, equilibrium constant, concentration, and changes in Gibbs energy and the experimentally observed behavior of species in aqueous solutions. The utility of "E"-pH diagrams is extended with the introduction of an additional…

Geochemical Sources of Energy for Chemolithoautotrophic Metabolisms in Global Hydrothermal Ecosystems

NASA Astrophysics Data System (ADS)

Lu, G. S.; Amend, J.; LaRowe, D.

2017-12-01

Chemolithoautotrophic microorganisms are important primary producers in hydrothermal environments. The potential catabolic energy sources that thermophilic chemolithoautotrophs can take advantage of can be quantified by combining analytical geochemical data and thermodynamic calculations. This approach explicitly considers how microbial communities are shaped by environmental conditions such as temperature, pressure, pH and the concentrations of electron donors and acceptors. In this study, we have calculated the Gibbs free energy available from 730 redox reactions in 30 terrestrial, shallow-sea, and deep-sea hydrothermal venting systems around the world (326 geochemical data sets) to better determine the relationship between microbial physiology and environment. The reactions with NO2-, O2, MnO2 and NO3- as terminal electron acceptors yield 5-20 kJ/mol e- more energy in terrestrial and shallow-sea hydrothermal systems than in deep-sea hydrothermal settings. However, reactions in which As5+, S0, FeS2 and SO42- as electron acceptors are more favorable by 5-30 kJ/mol e- in deep-sea hydrothermal systems than in the other two types of hydrothermal systems. The most exergonic reactions were predominantly NO2-, O2, MnO2 and NO3- reduction or Fe2+, pyrite, CO and CH4 oxidation. In contrast, reduction of N2, CO, and CO2 or oxidation of N2, Mn2+, and NO2-, though still often exergonic, yielded significantly less energy. Our results provide a comprehensive view of the distribution of energy supplies from redox reactions in high-temperature ecosystems on a global scale. Furthermore, the bioenergetic modeling carried out in this study can be used to test physiological predictions made from metagenomic and proteomic data sets, explore in situ biogeochemical interactions, predict possible but yet-to-be observed metabolisms and guide cultivation efforts.

Calculating Time-Integral Quantities in Depletion Calculations

DOE PAGES

Isotalo, Aarno

2016-06-02

A method referred to as tally nuclides is presented for accurately and efficiently calculating the time-step averages and integrals of any quantities that are weighted sums of atomic densities with constant weights during the step. The method allows all such quantities to be calculated simultaneously as a part of a single depletion solution with existing depletion algorithms. Some examples of the results that can be extracted include step-average atomic densities and macroscopic reaction rates, the total number of fissions during the step, and the amount of energy released during the step. Furthermore, the method should be applicable with several depletionmore » algorithms, and the integrals or averages should be calculated with an accuracy comparable to that reached by the selected algorithm for end-of-step atomic densities. The accuracy of the method is demonstrated in depletion calculations using the Chebyshev rational approximation method. Here, we demonstrate how the ability to calculate energy release in depletion calculations can be used to determine the accuracy of the normalization in a constant-power burnup calculation during the calculation without a need for a reference solution.« less

Free Energy Perturbation Calculations of the Thermodynamics of Protein Side-Chain Mutations.

PubMed