Temperature Dependence Of Free Energy Research Articles

Solid-liquid phase boundary of oxide solid solutions using neural network potentials

We propose a cost-effective computational approach for predicting the phase boundary of oxide solid solutions, i.e., melting point, by identifying the point where the free energies of the solid and liquid phases are equivalent. To evaluate the melting point, we computed the temperature-dependent free energies of both phases using the thermodynamic integration (TI) method. This was combined with the reverse-scaling technique, employing the Einstein model for the solid and the scaled Uhlenbeck–Ford model for the liquid as the reference systems. The change in free energy between the real and reference states in the present TI method was calculated as the ensemble average of the configurations sampled from molecular dynamics (MD) simulations using neural network potentials (NNPs) trained on first-principles density functional theory (DFT) data. Initially, we benchmarked copper (Cu) as a typical metal. Tungsten (W) and magnesium oxide (MgO) were then tested as typical high melting-point metals and oxides, respectively, achieving good agreement with both ab initio MD (AIMD) results and experimental data. We then applied our established approach to a BaO–CaO oxide solid solution, observing that the computed phase boundary aligns well with Calphad predictions from previous studies. The integration of NNPs into phase boundary prediction is essential for reducing computational costs while ensuring accuracy, compared with AIMD-based approaches.

Energy landscapes of homopolymeric RNAs revealed by deep unsupervised learning

Conformational dynamics of RNA plays important roles in a variety of cellular functions such as transcriptional regulation, catalysis, scaffolding, and sensing. Recently, RNAs with low-complexity sequences have been shown to phase separate and form condensate phases similar to lowcomplexity protein domains. The affinity for phase separation and the material characteristics of RNA condensates are strongly dependent on sequence composition and patterning. We hypothesize that differences in the affinities for RNA phase separation can be uncovered by studying sequence-dependent conformational dynamics of single RNA chains. To this end, we have employed atomistic simulations and deep dimensionality reduction techniques to map temperature-dependent conformational free energy landscapes for 20 base-long homopolymeric RNA sequences: poly(U), poly(G), poly(C), and poly(A). The energy landscapes of homopolymeric RNAs reveal a plethora of metastable states with qualitatively different populations stemming from differences in base chemistry. Through detailed analysis of base, phosphate, and sugar interactions, we show that experimentally observed temperature-driven shifts in metastable state populations align with experiments on RNA phase transitions. Specifically, we find that the thermodynamics of unfolding of homopolymeric RNA follows the poly(G) > poly(A) > poly(C) > poly(U) order of stability, mirroring the propensity of RNA to form condensates. To conclude, this work shows that at least for homopolymeric RNA sequences the single-chain conformational dynamics contains sufficient information for predicting and quantifying condensate forming affinities of RNAs. Thus, we anticipate that atomically detailed studies of temeprature -dependent energy landscapes of RNAs will be a useful guide for understanding the propensity of various RNA molecules to form condensates.

Electronic Moment Tensor Potentials include both electronic and vibrational degrees of freedom

We present the electronic moment tensor potentials (eMTPs), a class of machine-learning interatomic models and a generalization of the classical MTPs, reproducing both the electronic and vibrational degrees of freedom, up to the accuracy of ab initio calculations. Following the original polynomial interpolation idea of the MTPs, the eMTPs are defined as polynomials of vibrational and electronic degrees of freedom, corrected to have a finite interatomic cutoff. Practically, an eMTP is constructed from the classical MTPs fitted to a training set, whose energies and forces are calculated with electronic temperatures corresponding to the Chebyshev nodes on a given temperature interval. The eMTP energy is hence a Chebyshev interpolation of the classical MTPs. Using the eMTP, one can obtain the temperature-dependent vibrational free energy including anharmonicity coming from phonon interactions, the electronic free energy coming from electron interactions, and the coupling of atomic vibrations and electronic excitations. Each of the contributions can be accessed individually using the proposed formalism. The performance of eMTPs is demonstrated for two refractory systems which have a significant electronic, vibrational and coupling contribution up to the melting point—unary Nb, and a disordered TaVCrW high-entropy alloy. Highly accurate thermodynamic and kinetic quantities can now be obtained just by using eMTPs, without any further ab initio calculations. The proposed construction to include the electronic degree of freedom can also be applied to other machine-learning models.

Predicting Thermochemical Equilibria with Interacting Defects: Sr1−xCexMnO3−δ Alloys for Water Splitting

Solar thermochemical hydrogen is one of the few potential routes towards direct fuel production from renewable energy sources, but the thermodynamic boundary conditions for efficient and economic energy conversion are challenging. Success or failure of a given oxide working material depends on the subtle balance between enthalpy and entropy contributions in the redox processes. Developing a mechanistic understanding of the behavior of materials on the basis of atomistic models and first-principles calculations is an important part of advancing the technology. One challenge is to quantitatively predict thermochemical equilibria at high concentrations when the redox-active defects start to interact with each other, thereby impeding the formation of additional defects. This problem is of more general importance to applications that rely on high levels of off-stoichiometry or doping, including, for example, batteries, thermoelectrics, and ceramic fuel cells. To account for such repulsive defect interactions, we introduce a statistical mechanics approach, defining an expression for the free energy of defect interaction based on limited sampling of defect configurations in density functional theory supercell calculations. The parameterization of this energy contribution as a function of defect concentration and temperature allows on-the-fly simulation of thermochemical equilibria. The approach consistently incorporates finite temperature effects by including the leading contributions to the temperature-dependent free energy for the case at hand, i.e., the ideal gas and configurational enthalpies and entropies. We demonstrate the capability and utility of the approach by simulating the water splitting redox processes for Sr1−xCexMnO3−δ alloys. Published by the American Physical Society 2024

Elemental partitioning and corrosion resistance of Ni–Cr alloys revealed by accurate ab-initio thermodynamic and electrochemical calculations

Elemental partitioning during thermal processing can significantly affect the corrosion resistance of bulk alloys operating in aggressive electrochemical environments, for which, despite decades of experimental and theoretical studies, the thermodynamic and electrochemical mechanisms still lack accurate quantitative descriptions. Here, we formulate an ab initio thermodynamic model to obtain the composition- and temperature-dependent free energies of formation (ΔfG) for Ni–Cr alloys, a prototypical group of corrosion-resistant metals, and discover two equilibrium states that produce the driving forces for the elemental partitioning in Ni–Cr. The results are in quantitative agreement with the experimental studies on the thermodynamic stability of Ni–Cr. We further construct electrochemical (potential–pH) diagrams by obtaining the required ΔfG values of native oxides and (oxy)hydroxides using high-fidelity ab-initio calculations that include exact electronic exchange and phononic contributions. We then analyze the passivation and electrochemical trends of Ni–Cr alloys, which closely explain various oxide-film growth and corrosion behaviors observed on alloy surfaces. We finally determine the optimal Cr content range of 14–34 at%, which provides the Ni–Cr alloys with both the preferred heat-treatment stability and superior corrosion resistance. We conclude by discussing the consequences of these findings on other Ni–Cr alloys with more complex additives, which can guide the further optimization of industrial Ni–Cr-based alloys.

Temperature-dependent solvent reorganization entropies, free energies, and transition dipole strengths for the photoexcitation of Reichardt's dye B30.

Absorption spectra of the solvatochromic dye 2,6-diphenyl-4-2,4,6-triphenyl-1-pyridinophenolate (B30) were measured in seven solvents of varying polarity over temperature ranging from each solvent's freezing point to 300K. The excitation energies and their variances allowed calculations of the solvent reorganization energies, reorganization free energies and reorganization entropies as functions of temperature. The entropies of solvent packing around the chromophore are found to make major contributions to the reorganization free energies. The variances of the excitation energies depend only weakly on temperature, in disagreement with an expression that is often used for solvent reorganization free energies. Polar solvents reduce the transition dipole strength of B30's long-wavelength absorption band, probably because interactions with the solvent enhance the charge-transfer character of the transition. The dipole strength drops further at low temperatures.

Effects of temperature and microwave on the stability of the blast effector complex APikL2A/sHMA25 as determined by molecular dynamics analyses.

Magnaporthe oryzae is the causal agent of rice blast, and understanding how abiotic stress affects the resistance of plants to this disease is useful for designing disease control strategies. In this paper, the effects of temperature and microwave irradiation on the effector complex comprising APikL2A from M. oryzae and sHMA25 from foxtail millet were investigated by molecular dynamics simulations using the GROMACS software package. While the structure of APikL2A/sHMA25 remained relatively stable in a temperature range of 290K (16.85°C) to 320K (46.85°C), the concave shape of the temperature-dependent binding free energy curve indicated that there was maximum binding affinity between APikL2A and sHMA25 at 300K-310K. This coincided with the optimum infectivity temperature, thus suggesting that coupling of the two polypeptides may play a role in the infection process. A strong oscillating electric field destroyed the structure of APikL2A/sHMA25, although it was stable and not susceptible to weak electric fields.

Ab initio prediction of temperature-dependent stability of heterogeneous B19′ phase in TiNi alloy using atomistically informed Eshelby’s ellipsoidal inclusion

In this study, we energetically predicted the temperature-dependent stability of the heterogeneous B19′ phase in the B2 matrix of TiNi alloys using density functional theory (DFT) and phonon analysis informed Eshelby’s ellipsoidal inclusion. The temperature-dependent eigenstrains and elastic constants for Eshelby’s ellipsoidal inclusion were calculated using DFT and phonon analysis under a quasi-harmonic approximation. The stable orientation of the disk-shaped B19′ phase in the B2 matrix and its total strains were evaluated with respect to temperature using Eshelby’s ellipsoidal inclusion analysis. Using the total strains, the elastically deformed atomic structure of the heterogeneous B19′ phase in the B2 matrix was determined, and its temperature-dependent free energy was calculated using DFT calculations and phonon analysis. Comparing the temperature-dependent free energies of the B2 and elastically deformed B19′ structures, we successfully predicted that the transformation between the two phases occurs at 300 K, which agrees with experimental observations. Moreover, it is shown that the temperature-dependent difference in the elastic constants between the B19′ phase and B2 matrix influences the phase transformation, which is the origin of the shape-memory effect of TiNi alloy.

Insights on the interaction of SARS-CoV-2 variant B.1.617.2 with antibody CR3022 and analysis of antibody resistance

BackgroundThe existence of mutated Delta (B.1.617.2) variants of SARS-CoV-2 causes rapid transmissibility, increase in virulence, and decrease in the effectiveness of public health. Majority of mutations are seen in the surface spike, and they are considered as antigenicity and immunogenicity of the virus. Hence, finding suitable cross antibody or natural antibody and understanding its biomolecular recognition for neutralizing surface spike are crucial for developing many clinically approved COVID-19 vaccines. Here, we aim to design SARS-CoV-2 variant and hence, to understand its mechanism, binding affinity and neutralization potential with several antibodies. ResultsIn this study, we modelled six feasible spike protein (S1) configurations for Delta SARS-CoV-2 (B.1.617.2) and identified the best structure to interact with human antibodies. Initially, the impact of mutations at the receptor-binding domain (RBD) of B.1.617.2 was tested, and it is found that all mutations increase the stability of proteins (ΔΔG) and decrease the entropies. An exceptional case is noted for the mutation of G614D variant for which the vibration entropy change is found to be within the range of 0.133–0.004 kcal/mol/K. Temperature-dependent free energy change values (ΔG) for wild type is found to be − 0.1 kcal/mol, whereas all other cases exhibit values within the range of − 5.1 to − 5.5 kcal/mol. Mutation on spike increases the interaction with the glycoprotein antibody CR3022 and the binding affinity (CLUSpro energy = − 99.7 kcal/mol). The docked Delta variant with the following antibodies, etesevimab, bebtelovimab, BD-368–2, imdevimab, bamlanivimab, and casirivimab, exhibit a substantially decreased docking score (− 61.7 to − 112.0 kcal/mol) and the disappearance of several hydrogen bond interactions. ConclusionCharacterization of antibody resistance for Delta variant with respect to the wild type gives understanding regarding why Delta variant endures the resistance boosted through several trademark vaccines. Several interactions with CR3022 have appeared compared to Wild for Delta variant, and hence, it is suggested that modification on the CR3022 antibody could further improve for the prevention of viral spread. Antibody resistance decreased significantly due to numerous hydrogen bond interactions which clearly indicate that these marketed/launched vaccines (etesevimab) will be effective for Delta variants. Graphical Abstract▪

Computing the Gromov-Wasserstein Distance between Two Surface Meshes Using Optimal Transport

The Gromov-Wasserstein (GW) formalism can be seen as a generalization of the optimal transport (OT) formalism for comparing two distributions associated with different metric spaces. It is a quadratic optimization problem and solving it usually has computational costs that can rise sharply if the problem size exceeds a few hundred points. Recently fast techniques based on entropy regularization have being developed to solve an approximation of the GW problem quickly. There are issues, however, with the numerical convergence of those regularized approximations to the true GW solution. To circumvent those issues, we introduce a novel strategy to solve the discrete GW problem using methods taken from statistical physics. We build a temperature-dependent free energy function that reflects the GW problem’s constraints. To account for possible differences of scales between the two metric spaces, we introduce a scaling factor s in the definition of the energy. From the extremum of the free energy, we derive a mapping between the two probability measures that are being compared, as well as a distance between those measures. This distance is equal to the GW distance when the temperature goes to zero. The optimal scaling factor itself is obtained by minimizing the free energy with respect to s. We illustrate our approach on the problem of comparing shapes defined by unstructured triangulations of their surfaces. We use several synthetic and “real life” datasets. We demonstrate the accuracy and automaticity of our approach in non-rigid registration of shapes. We provide numerical evidence that there is a strong correlation between the GW distances computed from low-resolution, surface-based representations of proteins and the analogous distances computed from atomistic models of the same proteins.

Thermodynamic stability of human lipocalin-type prostaglandin D synthase under various pH conditions.

Lipocalin-type prostaglandin D synthase (L-PGDS) binds various hydrophobic small molecules. Since we aim to use human L-PGDS as a carrier in a drug delivery system (DDS) for poorly water-soluble drugs, quality control of the protein is indispensable. In this study, we investigated the thermodynamic stability of human L-PGDS under various pH conditions. Differential scanning calorimetry revealed that the thermal unfolding of L-PGDS was an almost-reversible two-state transition between the native and unfolded states over the pH range from 2.5 to 7.4. The linear relationship of ΔH(Tm) to Tm in this pH range gave a heat capacity change (ΔCp) of 4.76kJ/(K·mol), which was small compared to those commonly found in globular proteins. The temperature-dependent free energy of unfolding, ΔG(T), specified by Tm, ΔH(Tm) and ΔCp, showed a pH dependence with the highest value at pH7.4 closest to the isoelectric point of 8.3. The small value of Cp resulted in a large value of ΔG(T), which contributed to the stability of the protein. Taken together, these results demonstrated that human L-PGDS is sufficiently thermostable for storage and practical use and can be useful as a delivery vehicle of protein-based DDS.

Predicting hot-electron free energies from ground-state data

Machine-learning potentials are usually trained on the ground-state, Born-Oppenheimer energy surface, which depends exclusively on the atomic positions and not on the simulation temperature. This disregards the effect of thermally-excited electrons, that is important in metals, and essential to the description of warm dense matter. An accurate physical description of these effects requires that the nuclei move on a temperature-dependent electronic free energy. We propose a method to obtain machine-learning predictions of this free energy at an arbitrary electron temperature using exclusively training data from ground-state calculations, avoiding the need to train temperature-dependent potentials, and benchmark it on metallic liquid hydrogen at the conditions of the core of gas giants and brown dwarfs. This work demonstrates the advantages of hybrid schemes that use physical consideration to combine machine-learning predictions, providing a blueprint for the development of similar approaches that extend the reach of atomistic modelling by removing the barrier between physics and data-driven methodologies.

High accuracy neural network interatomic potential for NiTi shape memory alloy

Nickel-titanium (NiTi) shape memory alloys (SMA) are widely used, however simulating the martensitic transformation of NiTi from first principles remains challenging. In this work, we developed a neural network interatomic potential (NNIP) for near-equiatomic Ni-Ti system through active-learning based acquisitions of density functional theory (DFT) training data, which achieves state-of-the-art accuracy. Phonon dispersion and potential-of-mean-force calculations of the temperature-dependent free energy have been carried out. This NNIP predicts temperature-induced, stress-induced, and defect-induced martensitic transformations from atomic simulations, in significant agreement with experiments. The NNIP can directly simulate the superelasticity of NiTi nanowires, providing a tool to guide their design.

Replica symmetry breaking in random non-Hermitian systems

Recent studies have revealed intriguing similarities between the contribution of wormholes to the gravitational path integral and the phenomenon of replica symmetry breaking observed in spin glasses and other disordered systems. Interestingly, these configurations may also be important for the explanation of the information paradox of quantum black holes. Motivated by these developments, we investigate the thermodynamic properties of a $PT$-symmetric system composed of two random non-Hermitian Hamiltonians with no explicit coupling between them. After performing ensemble averaging, we identify numerically and analytically a robust first-order phase transition in the free energy of two models with quantum chaotic dynamics: the elliptic Ginibre ensemble of random matrices and a non-Hermitian Sachdev-Ye-Kitaev (SYK) model. The free energy of the Ginibre model is temperature independent in the low-temperature phase. The SYK model has similar behavior for sufficiently low temperature, and then it experiences a possible continuous phase transition to a phase with a temperature-dependent free energy before the first-order transition takes place at a higher temperature. We identify the order parameter of the first-order phase transition and obtain analytical expressions for the critical temperature. The mechanism behind the transition is the existence of replica symmetry breaking configurations coupling left and right replicas that control the low-temperature limit of the partition function. We speculate that quantum chaos may be necessary for the observed dominance of off-diagonal replica symmetry breaking configurations in the low-temperature limit.

Atomistic simulation framework for molten salt vapor-liquid equilibrium prediction and its application to NaCl.

Knowledge of the vapor-liquid equilibrium (VLE) properties of molten salts is important in the design of thermal energy storage systems for solar power and nuclear energy production applications. The high temperatures involved make their experimental determination problematic, and the development of both macroscopic thermodynamic correlations and predictive molecular-based methodologies are complicated by the requirement to appropriately incorporate the chemically reacting vapor-phase species. We derive a general thermodynamic-based atomistic simulation framework for molten salt VLE prediction and show its application to NaCl. Its input quantities are temperature-dependent ideal-gas free energy data for the vapor phase reactions and density and residual chemical potential data for the liquid. If these are not available experimentally, the former may be predicted using standard electronic structure software, and the latter may be predicted by means of classical atomistic simulation methodology. The framework predicts the temperature dependence of vapor pressure, coexisting phase densities, vapor phase composition, and vaporization enthalpy. It also predicts the concentrations of vapor phase species present in minor amounts (such as the free ions), quantities that are extremely difficult to measure experimentally. We furthermore use the results to obtain an approximation to the complete VLE binodal dome and the critical properties. We verify the framework for molten NaCl, for which experimentally based density and chemical potential data are available in the literature. We then apply it to the analysis of NaCl simulation data for two commonly used atomistic force fields. The framework can be readily extended to molten salt mixtures and to ionic liquids.

Phase decomposition and strengthening in HfNbTaTiZr high entropy alloy from first-principles calculations

Phase decomposition influences significantly the mechanical properties of high entropy alloys (HEAs). Prediction of the phase decomposition of HEA is greatly hindered by the hyper-dimensional composition space of the alloys. In the present work, we propose to represent the HEAs as various pseudo-binary alloys of which the temperature dependent free energies as functions of compositions may be readily calculated by using first-principles methods in combination with thermodynamic models. With the calculated free energies, the phase diagrams of the pseudo-binary alloys may be constructed and the phase decomposition can be predicted. This procedure is applied to Hf-Nb-Ta-Ti-Zr alloy with body-centered cubic (BCC) structure. We predict that the equiatomic HfNbTaTiZr HEA suffers from phase decomposition below critical temperature of 1298 K. The HEA decomposes most favorably to BCC NbTa-rich and HfZr-rich phases. The BCC HfZr-rich phase transfers to a hexagonal close-packed structure (HCP) phase at low temperature. The predicted compositions of the decomposed phases are in good agreement with experiment and Thermal-Calc modeling. Furthermore, the effect of the phase decomposition on the strength of the HEA is evaluated by considering the solid-solution and precipitation strengthening mechanisms. The precipitation strengthening effect is stronger than the solid-solution strengthening at the low annealing temperature but becomes weaker at high annealing temperature.

Augmenting zero-Kelvin quantum mechanics with machine learning for the prediction of chemical reactions at high temperatures

The prediction of temperature effects from first principles is computationally demanding and typically too approximate for the engineering of high-temperature processes. Here, we introduce a hybrid approach combining zero-Kelvin first-principles calculations with a Gaussian process regression model trained on temperature-dependent reaction free energies. We apply this physics-based machine-learning model to the prediction of metal oxide reduction temperatures in high-temperature smelting processes that are commonly used for the extraction of metals from their ores and from electronics waste and have a significant impact on the global energy economy and greenhouse gas emissions. The hybrid model predicts accurate reduction temperatures of unseen oxides, is computationally efficient, and surpasses in accuracy computationally much more demanding first-principles simulations that explicitly include temperature effects. The approach provides a general paradigm for capturing the temperature dependence of reaction free energies and derived thermodynamic properties when limited experimental reference data is available.

Significant phonon anharmonicity drives phase transitions in CsPbI3

Due to its high chemical stability and high power conversion efficiency as a solar cell absorber, the inorganic halide perovskite, CsPbI3, is considered one of the most promising competitors to its hybrid organic-inorganic counterpart, CH3NH3PbI3. However, the phase transition from the photoactive black phase to the inactive yellow phase is a remarkable limitation that harms long-term phase stability. In particular, the phase transitions follow different pathways as the temperature increases and/or decreases, a phenomenon that is anomalous and remains poorly understood. In this study, we systematically calculated the temperature-dependent free energy of CsPbI3 in different crystal phases (α, β, γ, δ) by considering the phonon contribution to the Gibbs free energy. It is found that the free energy results from calculations that include harmonic phonons cannot reproduce experimental observations. Alternatively, we utilized the renormalized phonon quasiparticle approach to derive the free energies of different CsPbI3 phases at finite temperatures. Based on these calculated free energies, whose derivations included the anharmonic effect, we observed phase-transition processes consistent with experimental results. The analysis of the temperature effect on the phonon frequencies further demonstrated that anharmonic effects in the CsPbI3 had a significant influence on its phase transitions.

Phase Decomposition and Strengthening in Hfnbtatizr High Entropy Alloy from First-Principles Calculations

Phase decomposition influences significantly the mechanical properties of high entropy alloys (HEAs). Prediction of the phase decomposition of HEA is greatly hindered by the hyper-dimensional composition space of the alloys. In the present work, we propose to represent the HEAs as various pseudo-binary alloys of which the temperature dependent free energies as functions of compositions may be readily calculated by using first-principles methods in combination with thermodynamic models. With the calculated free energies, the phase diagrams of the pseudo-binary alloys may be constructed and the phase decomposition can be predicted. This procedure is applied to Hf-Nb-Ta-Ti-Zr alloy with body-centered cubic (BCC) structure. We predict that the equiatomic HfNbTaTiZr HEA suffers from phase decomposition below critical temperature of 1298 K. The HEA decomposes most favorably to BCC NbTa-rich and HfZr-rich phases. The BCC HfZr-rich phase transfers to a hexagonal close-packed structure (HCP) phase at low temperature. The predicted compositions of the decomposed phases are in good agreement with experiment and Thermal-Calc modeling. Furthermore, the effect of the phase decomposition on the strength of the HEA is evaluated by considering the solid-solution and precipitation strengthening mechanisms. The precipitation strengthening effect is stronger than the solid-solution strengthening at the low annealing temperature but becomes weaker at high annealing temperature.

Hypercooling limit and physical properties of liquid MoNbReTaW refractory high-entropy alloy

ABSTRACT The thermophysical properties of refractory MoNbReTaW high-entropy alloy in both supercooled liquid and high-temperature solid states were explored by an electrostatic levitation technique. The maximum supercooling attains 504 K, and the hypercooling limit is derived as 571 K. The liquid density at liquidus temperature is measured to be 13.3 g cm−3, which increases linearly with decreasing temperature at a slope of 6.83 × 10−4 g cm−3 K−1. The liquid alloy exhibits 5.3% relative volume shrinkage during crystallization. The thermal expansion coefficient of liquid and solid alloy at liquidus temperature are determined as 5.0 × 10−5 K−1 and 3.6 ×10−5 K−1, respectively. The liquid specific heat at liquidus temperature is found to be 38.2 J mol−1 K−1, and basically displays a linear decreasing tendency with temperature. According to the calculated enthalpy of fusion 24.7 kJ mol−1 and measured specific heats, the temperature-dependent entropy and Gibbs free energy difference between supercooled liquid and crystalline solid are obtained.