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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Towards accurate orbital-free simulations: A generalized gradient approximation for the noninteracting free energy density functional

For orbital-free ab initio molecular dynamics, especially on systems in extreme thermodynamic conditions, we provide the first pseudo-potential-adapted generalized gradient approximation (GGA) functional for the non-interacting free energy. This is achieved by systematic finite-temperature extension of our recent LKT ground state non-interacting kinetic energy GGA functional (Phys. Rev. B 98, 041111(R) (2018)). We test the performance of the new functional first via static lattice calculations on crystalline aluminum and silicon. Then we compare deuterium equation of state results against both path-integral Monte Carlo and conventional (orbital-dependent) Kohn-Sham results. The new functional, denoted LKTF, outperforms the previous best semi-local free energy functional, VT84F (Phys. Rev. B 88, 161108(R) (2013)), and provides modestly faster simulations. Finally, we discuss subtleties of identification of kinetic and entropic contributions to non-interacting free-energy functionals obtained by extension from ground state orbital-free kinetic energy functionals.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Comparison of Equilibrium and Nonequilibrium Approaches for Relative Binding Free Energy Predictions

Alchemical relative binding free energy calculations have recently found important applications in drug optimization. A series of congeneric compounds are generated from a preidentified lead compound, and their relative binding affinities to a protein are assessed in order to optimize candidate drugs. While methods based on equilibrium thermodynamics have been extensively studied, an approach based on nonequilibrium methods has recently been reported together with claims of its superiority. However, these claims pay insufficient attention to the basis and reliability of both methods. Here we report a comparative study of the two approaches across a large data set, comprising more than 500 ligand transformations spanning in excess of 300 ligands binding to a set of 14 diverse protein targets. Ensemble methods are essential to quantify the uncertainty in these calculations, not only for the reasons already established in the equilibrium approach but also to ensure that the nonequilibrium calculations reside within their domain of validity. If and only if ensemble methods are applied, we find that the nonequilibrium method can achieve accuracy and precision comparable to those of the equilibrium approach. Compared to the equilibrium method, the nonequilibrium approach can reduce computational costs but introduces higher computational complexity and longer wall clock times. There are, however, cases where the standard length of a nonequilibrium transition is not sufficient, necessitating a complete rerun of the entire set of transitions. This significantly increases the computational cost and proves to be highly inconvenient during large-scale applications. Our findings provide a key set of recommendations that should be adopted for the reliable implementation of nonequilibrium approaches to relative binding free energy calculations in ligand-protein systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Alchemical Free Energy Estimators and Molecular Dynamics Engines: Accuracy, Precision, and Reproducibility

The binding free energy between a ligand and its target protein is an essential quantity to know at all stages of the drug discovery pipeline. Assessing this value computationally can offer insight into where efforts should be focused in the pursuit of effective therapeutics to treat a myriad of diseases. In this work, we examine the computation of alchemical relative binding free energies with an eye for assessing reproducibility across popular molecular dynamics packages and free energy estimators. The focus of this work is on 54 ligand transformations from a diverse set of protein targets: MCL1, PTP1B, TYK2, CDK2, and thrombin. These targets are studied with three popular molecular dynamics packages: OpenMM, NAMD2, and NAMD3 alpha. Trajectories collected with these packages are used to compare relative binding free energies calculated with thermodynamic integration and free energy perturbation methods. The resulting binding free energies show good agreement between molecular dynamics packages with an average mean unsigned error between them of 0.50 kcal/mol. The correlation between packages is very good, with the lowest Spearman’s, Pearson’s and Kendall’s tau correlation coefficients being 0.92, 0.91, and 0.76, respectively. Agreement between thermodynamic integration and free energy perturbation is shown to be very good when using ensemble averaging.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1977

Variational energy principle for compressible, baroclinic flow. 2: Free-energy form of Hamilton's principle

The first and second variations are calculated for the irreducible form of Hamilton's Principle that involves the minimum number of dependent variables necessary to describe the kinetmatics and thermodynamics of inviscid, compressible, baroclinic flow in a specified gravitational field. The form of the second variation shows that, in the neighborhood of a stationary point that corresponds to physically stable flow, the action integral is a complex saddle surface in parameter space. There exists a form of Hamilton's Principle for which a direct solution of a flow problem is possible. This second form is related to the first by a Friedrichs transformation of the thermodynamic variables. This introduces an extra dependent variable, but the first and second variations are shown to have direct physical significance, namely they are equal to the free energy of fluctuations about the equilibrium flow that satisfies the equations of motion. If this equilibrium flow is physically stable, and if a very weak second order integral constraint on the correlation between the fluctuations of otherwise independent variables is satisfied, then the second variation of the action integral for this free energy form of Hamilton's Principle is positive-definite, so the action integral is a minimum, and can serve as the basis for a direct trail and error solution. The second order integral constraint states that the unavailable energy must be maximum at equilibrium, i.e. the fluctuations must be so correlated as to produce a second order decrease in the total unavailable energy.

Schmid, L. A.↗
NASA NTRS1985

Statistical mechanics of light elements at high pressure. VII - A perturbative free energy for arbitrary mixtures of H and He

A model free energy is presented which accurately represents results from 45 high-precision Monte Carlo calculations of the thermodynamics of hydrogen-helium mixtures at pressures of astrophysical and planetophysical interest. The free energy is calculated using free-electron perturbation theory (dielectric function theory), and is an extension of the expression given in an earlier paper in this series. However, it fits the Monte Carlo results more accurately, and is valid for the full range of compositions from pure hydrogen to pure helium. Using the new free energy, the phase diagram of mixtures of liquid metallic hydrogen and helium is calculated and compared with earlier results. Sample results for mixing volumes are also presented, and the new free energy expression is used to compute a theoretical Jovian adiabat and compare the adiabat with results from three-dimensional Thomas-Fermi-Dirac theory. The present theory gives slightly higher densities at pressures of about 10 megabars.

Hubbard, W. B.↗
DOE OSTI2022

Computing Free Energies with Fluctuation Relations on Quantum Computers

As a central thermodynamic property, free energy enables the calculation of virtually any equilibrium property of a physical system, allowing for the construction of phase diagrams and predictions about transport, chemical reactions, and biological processes. Thus, methods for efficiently computing free energies, which in general is a difficult problem, are of great interest to broad areas of physics and the natural sciences. The majority of techniques for computing free energies target classical systems, leaving the computation of free energies in quantum systems less explored. Recently developed fluctuation relations enable the computation of free energy differences in quantum systems from an ensemble of dynamic simulations. While performing such simulations is exponentially hard on classical computers, quantum computers can efficiently simulate the dynamics of quantum systems. Here, we present an algorithm utilizing a fluctuation relation known as the Jarzynski equality to approximate free energy differences of quantum systems on a quantum computer. In this work we discuss under which conditions our approximation becomes exact, and under which conditions it serves as a strict upper bound. Furthermore, we successfully demonstrate a proof of concept of our algorithm using the transverse field Ising model on a real quantum processor. As quantum hardware continues to improve, we anticipate that our algorithm will enable computation of free energy differences for a wide range of quantum systems useful across the natural sciences.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2013

Good Practices in Free-energy Calculations

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.

Pohorille, Andrew↗
DOE OSTI2025

Nonadiabatic Force Matching for Alchemical Free-Energy Estimation

We propose a method to compute free-energy differences from nonadiabatic alchemical transformations by using flow-based generative models. The method, nonadiabatic force matching, hinges on estimating the dissipation along an alchemical switching process in terms of a nonadiabatic force field that can be learned through stochastic flow matching. The learned field can be used in conjunction with short-time trajectory data to evaluate upper and lower bounds on the alchemical free energy that variationally converge to the exact value if the field is optimal. Applying the method to evaluate the alchemical free energy of atomistic models shows that it can substantially reduce the simulation cost of a free-energy estimate at a negligible loss of accuracy when compared with thermodynamic integration.

Computational chemistry↗
DOE OSTI2021

Subleading corrections to the S 3 free energy of necklace quiver theories dual to massive IIA

We investigate the S 3 free energy of N = 3 Chern-Simons-matter quiver gauge theories with gauge group U(N) r (r ≥ 2) where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-N limit. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the ’t Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy F = – log Z are then compared in the overlapping parameter regime. The Fermi-gas approach also hints at a universal 1/6 log N correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect the sub-leading correction of the planar free energy in the large ’t Hooft parameter limit to match higher-derivative corrections to the tree-level holographic dual free energy, which have not yet been fully investigated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Predicting the viability of beta-lactamase: How folding and binding free energies correlate with beta-lactamase fitness

One of the long-standing holy grails of molecular evolution has been the ability to predict an organism’s fitness directly from its genotype. With such predictive abilities in hand, researchers would be able to more accurately forecast how organisms will evolve and how proteins with novel functions could be engineered, leading to revolutionary advances in medicine and biotechnology. In this work, we assemble the largest reported set of experimental TEM-1 β-lactamase folding free energies and use this data in conjunction with previously acquired fitness data and computational free energy predictions to determine how much of the fitness of β-lactamase can be directly predicted by thermodynamic folding and binding free energies. We focus upon β-lactamase because of its long history as a model enzyme and its central role in antibiotic resistance. Based upon a set of 21 β-lactamase single and double mutants expressly designed to influence protein folding, we first demonstrate that modeling software designed to compute folding free energies such as FoldX and PyRosetta can meaningfully, although not perfectly, predict the experimental folding free energies of single mutants. Interestingly, while these techniques also yield sensible double mutant free energies, we show that they do so for the wrong physical reasons. We then go on to assess how well both experimental and computational folding free energies explain single mutant fitness. We find that folding free energies account for, at most, 24% of the variance in β-lactamase fitness values according to linear models and, somewhat surprisingly, complementing folding free energies with computationally-predicted binding free energies of residues near the active site only increases the folding-only figure by a few percent. This strongly suggests that the majority of β-lactamase’s fitness is controlled by factors other than free energies. Overall, our results shed a bright light on to what extent the community is justified in using thermodynamic measures to infer protein fitness as well as how applicable modern computational techniques for predicting free energies will be to the large data sets of multiply-mutated proteins forthcoming.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1994

Direct measurement of free-energy barrier to nucleation of crystallites in amorphous silicon thin films

A method is introduced to measure the free-energy barrier W(sup *), the activation energy, and activation entropy to nucleation of crystallites in amorphous solids, independent of the energy barrier to growth. The method allows one to determine the temperature dependence of W(sup *), and the effect of the preparation conditions of the initial amorphous phase, the dopants, and the crystallization methds on W(sup *). The method is applied to determine the free-energy barrier to nucleation of crystallites in amorphous silicon (a-Si) thin films. For thermally induced nucleation in a-Si thin films with annealing temperatures in the range of from 824 to 983 K, the free-energy barrier W(sup *) to nucleation of silicon crystals is about 2.0 - 2.1 eV regardless of the preparation conditions of the films. The observation supports the idea that a-Si transforms into an intermediate amorphous state through the structural relaxation prior to the onset of nucleation of crystallites in a-Si. The observation also indicates that the activation entropy may be an insignificant part of the free-energy barrier for the nucleation of crystallites in a-Si. Compared with the free-energy barrier to nucleation of crystallites in undoped a-Si films, a significant reduction is observed in the free-energy barrier to nucleation in Cu-doped a-Si films. For a-Si under irradiation of Xe(2+) at 10(exp 5) eV, the free-energy barrier to ion-induced nucleation of crystallites is shown to be about half of the value associated with thermal-induced nucleation of crystallites in a-Si under the otherwise same conditions, which is much more significant than previously expected. The present method has a general kinetic basis; it thus should be equally applicable to nucleation of crystallites in any amorphous elemental semiconductors and semiconductor alloys, metallic and polymeric glasses, and to nucleation of crystallites in melts and solutions.

Shi, Frank G.↗
NASA NTRS2019

Determining the Transport of Magnetic Helicity and Free Energy in the Sun's Atmosphere

The most important factors determining solar coronal activity are believed to be the availability of magnetic free energy and the constraint of magnetic helicity conservation. Direct measurements of the helicity and magnetic free energy in the coronal volume are difficult, but their values may be estimated from measurements of the helicity and free energy transport rates through the photosphere. We examine these transport rates for a topologically open system such as the corona, in which the magnetic fields have a nonzero normal component at the boundaries, and derive a new formula for the helicity transport rate at the boundaries. In addition, we derive new expressions for helicity transport due to flux emergence/submergence versus photospheric horizontal motions. The key feature o four formulas is that they are manifestly gauge invariant. Our results are somewhat counterintuitive in that only the lamellar electric field produced by the surface potential transports helicity across boundaries, and the solenoidal electric field produced by a surface stream function does not contribute to the helicity transport. We discuss the physical interpretation of this result. Furthermore, we derive an expression for the free energy transport rate and show that a necessary condition for free energy transport across a boundary is the presence of a closed magnetic field at the surface, indicating that there are current systems within the volume. We discuss the implications of these results for using photospheric vector magnetic and velocity field measurements to derive the solar coronal helicity and magnetic free energy, which can then be used to constrain and drive models for coronal activity.

Schuck, Peter W.↗
DOE OSTI2021

Graphical Gaussian Process Regression Model for Aqueous Solvation Free Energy Prediction of Organic Molecules in Redox Flow Battery

The solvation free energy of organic molecules is a critical parameter in determining emergent properties such as solubility, liquid-phase equilibrium constants, and pKa and redox potentials in an organic redox flow battery. In this work, we present a machine learning (ML) model that can learn and predict the aqueous solvation free energy of an organic molecule using Gaussian process regression method based on a new molecular graph kernel. To investigate the performance of the ML model on electrostatic interaction, the nonpolar interaction contribution of solvent and the conformational entropy of solute in solvation free energy, three data sets with implicit or explicit water solvent models, and contribution of conformational entropy of solute are tested. We demonstrate that our ML model can predict the solvation free energy of molecules at chemical accuracy with a mean absolute error of less than 1 kcal/mol for subsets of the QM9 dataset and the Freesolv database. To solve the general data scarcity problem for a graph-based ML model, we propose a dimension reduction algorithm based on the distance between molecular graphs, which can be used to examine the diversity of the molecular data set. It provides a promising way to build a minimum training set to improve prediction for certain test sets where the space of molecular structures is predetermined.

25 ENERGY STORAGE↗
DOE OSTI2024

Acceleration of Solvation Free Energy Calculation via Thermodynamic Integration Coupled with Gaussian Process Regression and Improved Gelman–Rubin Convergence Diagnostics

The determination of the solvation free energy of ions and molecules holds profound importance across a spectrum of applications spanning chemistry, biology, energy storage, and the environment. Molecular dynamics simulations are powerful tools for computing this critical parameter. Nevertheless, the accurate and efficient calculation of the solvation free energy becomes a formidable endeavor when dealing with complex systems characterized by potent Coulombic interactions and sluggish ion dynamics and, consequently, slow transition across various metastable states. Here, in the present study, we expose limitations stemming from the conventional calculation of the statistical inefficiency g in the thermodynamic integration method, a factor that can hinder the determination of convergence of the solvation free energy and its associated uncertainty. Instead, we propose a robust scheme based on Gelman–Rubin convergence diagnostics. We leverage this improved estimation of uncertainties to introduce an innovative accelerated thermodynamic integration method based on the Gaussian Process regression. This methodology is applied to the calculation of the solvation free energy of trivalent rare-earth elements immersed in ionic liquids, a scenario in which the aforementioned challenges render standard approaches ineffective. The proposed method proves to be effective in computing solvation free energy in situations where traditional thermodynamic integration methods fall short.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Membrane hydrophobicity determines the activation free energy of passive lipid transport

The collective behavior of lipids with diverse chemical and physical features determines a membrane's thermodynamic properties. Yet, the influence of lipid physicochemical properties on lipid dynamics, in particular interbilayer transport, remains underexplored. Here, we systematically investigate how the activation free energy of passive lipid transport depends on lipid chemistry and membrane phase. Through all-atom molecular dynamics simulations of 11 chemically distinct glycerophospholipids, we determine how lipid acyl chain length, unsaturation, and headgroup influence the free energy barriers for two elementary steps of lipid transport: lipid desorption, which is rate limiting, and lipid insertion into a membrane. Consistent with previous experimental measurements, we find that lipids with longer, saturated acyl chains have increased activation free energies compared to lipids with shorter, unsaturated chains. Lipids with different headgroups exhibit a range of activation free energies; however, no clear trend based solely on chemical structure can be identified, mirroring difficulties in the interpretation of previous experimental results. Compared to liquid-crystalline phase membranes, gel phase membranes exhibit substantially increased free energy barriers. Overall, we find that the activation free energy depends on a lipid's local hydrophobic environment in a membrane and that the free energy barrier for lipid insertion depends on a membrane's interfacial hydrophobicity. Both of these properties can be altered through changes in lipid acyl chain length, lipid headgroup, and membrane phase. Thus, the rate of lipid transport can be tuned through subtle changes in local membrane composition and order, suggesting an unappreciated role for nanoscale membrane domains in regulating cellular lipid dynamics.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

In heterogeneous catalysis, free energy profiles of reactions govern the mechanisms, rates, and equilibria. Energetics are conventionally computed using the harmonic approximation (HA), which requires determination of critical states a priori. Here, we use neural networks to efficiently sample and directly calculate the free energy surface (FES) of a prototypical heterogeneous catalysis reaction—the dissociation of molecular nitrogen on ruthenium—at density-functional-theory-level accuracy. We find that the vibrational entropy of surface atoms, often neglected in HA for transition metal catalysts, contributes significantly to the reaction barrier. The minimum free energy path for dissociation reveals an “on-top” adsorbed molecular state prior to the transition state. While a previously reported flat-lying molecular metastable state can be identified in the potential energy surface, it is absent in the FES at relevant reaction temperatures. Finally, these findings demonstrate the importance of identifying critical points self-consistently on the FES for reactions that involve considerable entropic effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS2001

Calculating Free Energies Using Average Force

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.

Darve, Eric↗