Free Energy Difference Research Articles

Ion Transport at Polymer-Argyrodite Interfaces.

Solid-state electrolytes, particularly polymer/ceramic composite electrolytes, are emerging as promising candidates for lithium-ion batteries due to their high ionic conductivity and mechanical flexibility. The interfaces that arise between the inorganic and organic materials in these composites play a crucial role in ion transport mechanisms. While lithium ions are proposed to diffuse across or parallel to the interface, few studies have directly examined the quantitative impact of these pathways on ion transport and little is known about how they affect the overall conductivity. Here, we present an atomistic study of lithium-ion (Li+) transport across well-defined polymer-argyrodite interfaces. We present a force field for polymer-argyrodite interfacial systems, and we carry out molecular dynamics and enhanced sampling simulations of several composite systems, including poly(ethylene oxide) (PEO)/Li6PS5Cl, hydrogenated nitrile butadiene rubber (HNBR)/Li6PS5Cl, and poly(vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP)/Li6PS5Cl. For the materials considered here, Li-ion exhibits a preference for the ceramic material, as revealed by free energy differences for Li-ion between the inorganic and the organic polymer phase in excess of 13 kBT. The relative free energy profiles of Li-ion for different polymeric materials exhibit similar shapes, but their magnitude depends on the strength of interaction between the polymers and Li-ion: the greater the interaction between the polymer and Li-ions, the smaller the free energy difference between the inorganic and organic materials. The influence of the interface is felt over a range of approximately 1.5 nm, after which the behavior of Li-ion in the polymer is comparable to that in the bulk. Near the interface, Li-ion transport primarily occurs parallel to the interfacial plane, and ion mobility is considerably slower near the interface itself, consistent with the reduced segmental mobility of the polymer in the vicinity of the ceramic material. These findings provide insights into ionic complexation and transport mechanisms in composite systems, and will help improve design of improved solid electrolyte systems.

The electric double layer structure and interface energy of uranium electrode in molten LiCl-KCl-UCl3 mixture: A molecular dynamics simulation study

The electric double layer structure and interface energy of uranium electrode in molten LiCl-KCl-UCl3 mixture, as well as the surface energies of metallic uranium and molten salts, were investigated using molecular dynamics simulations. The surface energies were calculated, respectively, from the pressure tensor and the energy difference for molten salt and uranium, and interface energy was evaluated from the Gibbs free energy difference between systems with and without interface. The surface energies of molten alkali halides are between 76.4 and 201.8 mJ·m−2 and decrease with the increase of radius of the halide anion or the alkali cation for molten salt with the same alkali cation or the same halide anion. The surface energy of uranium depends on the allotrope morphology and crystal facet, and the surface energies of α-U, β-U, and γ-U are 2.36, 1.45, and 1.69 J·m−2 in average for the seven low index crystal facets. The interface energy of uranium and molten LiCl-KCl-UCl3 mixture is about 2.71 J·m−2 and increases with the increase of charge density on the uranium slabs. The molten LiCl-KCl-UCl3 mixture in anodic zone has higher coordination number than that in cathodic zone but similar coordination distance.

Time-asymmetric fluctuation theorem and efficient free-energy estimation.

The free-energy difference ΔF between two high-dimensional systems is notoriously difficult to compute but very important for many applications such as drug discovery. We demonstrate that an unconventional definition of work introduced by Vaikuntanathan and Jarzynski (2008) satisfies a microscopic fluctuation theorem that relates path ensembles that are driven by protocols unequal under time reversal. It has been shown before that counterdiabatic protocols-those having additional forcing that enforces the system to remain in instantaneous equilibrium, also known as escorted dynamics or engineered swift equilibration-yield zero-variance work measurements for this definition. We show that this time-asymmetric microscopic fluctuation theorem can be exploited for efficient free-energy estimation by developing a simple (i.e., neural-network free) and efficient adaptive time-asymmetric protocol optimization algorithm that yields ΔF estimates that are orders of magnitude lower in mean squared error than the generic linear interpolation protocol with which it is initialized.

Phosphor-doping modulates the d-band center of Fe atoms in Fe-N4 catalytic sites to boost the activity of oxygen reduction

Regulating the electronic structure by phosphor-doping is a preferred strategy to boost the performance of carbon-based catalysts for oxygen reduction reaction (ORR). Here, a porous Fe, P, N-codoped carbon catalyst (PCF-FeTz-900) is designed by a phytic acid-assisted thermal etching strategy, in which P atoms are first doped into the carbon matrix to form a stable PC bond, and then FeN4 sites are produced from Fe-2,4,6-Tris(2-pyridyl)-s-triazine complex (Fe-TPTz). Theoretical calculations suggest that the electrons are transferred from the doped P atom to the neighboring FeN4 sites, which facilitates the ORR at the Fe sites by reducing the energy barrier and the adsorption energy of intermediates. Additionally, the P-doped FeN4 (FeN4P) structure manifests a lower free energy difference than that of FeN4 and the d-band center of Fe is also lowered, which further ensures its higher ORR catalytic ability. As a result, the PCF-FeTz-900 catalyst exhibits superior ORR activity and stability in alkaline electrolyte, and the assembled primary zinc-air battery shows greater performances compared to the commercial Pt/C catalyst. This work can provide an effective pathway for modulating the performance of doped-carbon materials in energy conversion devices.

Effects of Nd-doping on crystal phase, structure and photocatalytic performance of TiO2 powders prepared by sol-gel method

Abstract In this work, 0.3–2 mol% neodymium (Nd) doped titanium dioxide (TiO2) powder was prepared by sol–gel method. The XRD showed that the anatase phase occur for the Nd doped TiO2 powders, and the Nd doping suppressed the original rutile phase for the pure TiO2 powder. SEM and TEM revealed that Nd doping reduced the tendency of severe aggregation and increased the specific surface area compare with pure TiO2 powder, and the Gibbs free energy difference did not reach the critical value of the phase transition driving force, while the adjustment of the Ti-O bond length caused by the addition of Nd3+ impeded the transformation of TiO2 to rutile phase. The photocatalytic activity test results for Methylene blue show that the 0.5 mol% Nd doped TiO2 had the best photocatalytic activity with the degradation efficiency of 96.2%.

Equations of state and hysteresis loops in isothermal cavitation

This paper investigates the influence of the use of the cubic equation of state (EOS) in the isothermal cavitation of compressible fluids. To do so, a thermodynamic consistent cavitation model that was recently proposed has been used. This model is derived under the Thermodynamics of Irreversible Processes and considers the irreversible dissipative character of the phase change transformation. Numerical simulations carried out using linear and cubic EOS are presented and compared. Neglecting surface tension effects, the results obtained demonstrate that there is no significant difference between the responses of these two types of EOS for water up to saturation pressures up to about 200 kPa. Hysteresis loops observed in the simulations with both types of EOS are virtually the same. It suggests that linear EOSs can provide good approximations for metastable behaviors (intrinsically present in cubic EOS) as well as for the Gibbs free energy difference (the thermodynamic force associated with irreversible phase change transformation), rendering a great simplification in the analysis.

Study of photosensitizer dyes for high-performance dye-sensitized solar cells application: A computational investigation

Dye-sensitized solar cells (DSSCs) offer a promising, cost-effective alternative to conventional photovoltaic systems. Organic sensitizers, capable of capturing a broad spectrum of sunlight, are key components in DSSCs, but their development and testing are often time-consuming and expensive. Quantum chemical calculations, specifically Density Functional Theory (DFT), have emerged as valuable tools to evaluate potential dye candidates, streamlining the design process and reducing costs. This study investigated the molecular structures and photophysical properties of three common dye classes used in high-performance DSSCs: natural pigments, anthocyanidin pigments, and squaraine dyes. Employing DFT and time-dependent DFT (TD-DFT) at the B3LYP/6–31G level, key parameters such as the HOMO-LUMO energy gap, free energy differences for electron injection and dye regeneration, short-circuit current density, total reorganization energy, and open-circuit voltage were analyzed. Additionally, maximum absorption wavelengths and oscillator strength values were calculated. Our findings provide valuable insights into the optical and electrical properties of these natural dyes, aiding DSSC manufacturers in selecting optimal sensitizers. This research highlights the potential of computational methods in accelerating dye development and improving the overall efficiency of DSSC technology.

Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories.

The accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH3) molecule and the nucleophilic substitution (SN2) reaction F- + CH3F → FCH3 + F-. We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Simulating Crystallization in a Colloidal System Using State Predictive Information Bottleneck Based Enhanced Sampling.

We investigate crystal nucleation in supersaturated colloid suspensions using enhanced molecular dynamics simulations augmented with machine learning techniques. The simulations reveal that crystallization in the model colloidal system studied here, with particles interacting through a repulsive screened Coulomb Yukawa potential, proceeds from vapor to dense liquid droplet to crystalline phases across multiple high barriers. Employing a one-dimensional reaction coordinate derived from the State Predictive Information Bottleneck framework, our simulations capture back-and-forth phase transitions across multiple barriers effectively in biased metadynamics simulations. We obtain relative free energy differences between different phases and also quantify the roles of different molecular level features in driving the phase changes.

Hydrogen Spillover Mechanism at the Metal–Metal Interface in Electrocatalytic Hydrogenation

AbstractHydrogen spillover in metal‐supported catalysts can largely enhance electrocatalytic hydrogenation performance and reduce energy consumption. However, its fundamental mechanism, especially at the metal–metal interface, remains further explored, impeding relevant catalyst design. Here, we theoretically profile that a large free energy difference in hydrogen adsorption on two different metals (|ΔGH‐metal(i)−ΔGH‐metal(ii)|) induces a high kinetic barrier to hydrogen spillover between the metals. Minimizing the difference in their d‐band centers (Δϵd) should reduce |ΔGH‐metal(i)−ΔGH‐metal(ii)|, lowering the kinetic barrier to hydrogen spillover for improved electrocatalytic hydrogenation. We demonstrated this concept using copper‐supported ruthenium–platinum alloys with the smallest Δϵd, which delivered record high electrocatalytic nitrate hydrogenation performance, with ammonia production rate of 3.45±0.12 mmol h−1 cm−2 and Faraday efficiency of 99.8±0.2 %, at low energy consumption of 21.4 kWh kgamm−1. Using these catalysts, we further achieve continuous ammonia and formic acid production with a record high‐profit space.

Revisiting Aspirin Polymorphic Stability Using a Machine Learning Potential.

In this study, we present a systematic computational investigation to analyze the long-debated free energy stability of two well-known aspirin polymorphs, denoted as Form I and Form II. Specifically, we developed a strategy to collect training configurations covering diverse interatomic interactions between representative functional groups in aspirin crystals. Utilizing a state-of-the-art neural network interatomic potential (NNIP) model, we trained an accurate machine learning potential to simulate aspirin crystal dynamics under finite temperature conditions with ∼0.46 kJ/mol/molecule accuracy. Employing the trained NNIP model, we performed thermodynamic integration to assess the free energy difference between aspirins I and II, accounting for the anharmonic effects in a large supercell consisting of 512 molecules. For the first time, our results convincingly demonstrated that Form I is more stable than Form II at 300 K, ranging from 0.74 to 1.83 kJ/mol/molecule, aligning with experimental observations. Unlike the majority of previous simulations based on (quasi)harmonic approximations in a small super cell, which often found degenerate energies between aspirins I and II, our findings underscore the importance of anharmonic effects in determining polymorphic stability ranking. Furthermore, we proposed the use of the rotational degrees of freedom of methyl and ester/phenyl groups in aspirin crystals as characteristic motions to highlight rotational entropic contribution that favors the stability of Form I. From the structural perspective, we also found that the subtle free energy difference can be used to explain the distinct thermal expansion responses as observed in both experimental and simulation data. Beyond the aspirin polymorphism, we anticipate that such entropy-driven stabilization can be broadly applicable to many other organic systems, suggesting that our approach holds great promise for stability studies in small-molecule drug design.

Role of site–specific doping in stabilizing high–nickel cathodes for high-performance lithium- ion -batteries

The growing demand for high-capacity and energy-dense lithium-ion batteries has driven the increase of nickel content in commercially available cathodes. However, during deep charging (delithiation), these Ni-rich cathodes experience a detrimental phase transformation and a sudden, significant decrease in lattice volume. This lattice collapse is considered the primary culprit behind the limitations in the cathode's electrochemical performance. Notably, the exact cause-and-effect relationship between the phase change and the collapse remains unclear. In the present study, the effect of the site of substitution on the performance of the LiNiO2 cathode has been investigated by adopting tungsten as a dopant. To gain deeper insights into this connection within Ni-rich LiNiO2, the contraction of the c-axis and the change in the a-axis during the delithiation have been investigated using ab initio density functional theory. Findings reveal that the free energy difference between the suspected phases in Ni-rich LiNiO2 is minimal at room temperature, facilitating the transition from the H2 to the H3 phase. This transition appears to be driven by the movement (gliding) of the NiO2 layer towards the adjacent Li layer. The findings of the present study indicate that among two different configurations due to different sites of substitution, the WLNO-2 configuration suppresses H2 –H3 phase conversion to a greater extent by hindering the gliding of the NiO2 layer toward the Li layer. Furthermore, a reduction in the collapse of the c-axis lattice during deep de-lithiation for the WLNO-2 configuration has been observed. This reduced collapse is primarily attributed to the altered charge distribution within oxygen atoms and the weakened screening effect from lithium ions.

Free Energy Differences in Nonequilibrium Thermodynamic Processes.

Systems which may be allowed to go out of equilibrium have been of interest recently. A quantity is formulated whose average over an ensemble of microscopic realizations of the process depends only on the initial and final states. This is so even though the system may not be in equilibrium during the process. A generalization to the case where the initial and final states are not equilibrium states is developed here. Quantum analogues of these relations are derived, and an indication of how this might be applied to study entropy increase in thermodynamics is presented.

Size-Dependent Ab Initio Atomistic Thermodynamics from Cluster to Bulk: Application to Hydration of Titania Nanoparticles.

Ab initio atomistic thermodynamics (AIAT) has become an indispensable tool to estimate Gibbs free energy changes for solid surfaces interacting with gaseous species relative to pressure (p) and temperature (T). For such systems, AIAT assumes that solid vibrational contributions to Gibbs free energy differences cancel out. However, the validity of this assumption is unclear for nanoscale systems. Using hydrated titania nanoparticles (NPs) as an example, we estimate the vibrational contributions to the Gibbs free energy of hydration (ΔGhyd(T,p)) for arbitrary NP size and degree of hydration. Comparing ΔGhyd(T,p) phase diagrams for NPs when considering these contributions (AIATnano) relative to a standard AIAT approach reveals significant qualitative and quantitative differences, which only become negligible for large systems. By constructing a size-dependent ΔGhyd(T,p) phase diagram, we illustrate how our approach can provide deeper insights into how nanosytems interact with their environments, with many potential applications (e.g., catalytic nanoparticles, biological colloids, nanoparticulate pollutants).

Evolutionary sequence and structural basis for the distinct conformational landscapes of Tyr and Ser/Thr kinases

Protein kinases are molecular machines with rich sequence variation that distinguishes the two main evolutionary branches – tyrosine kinases (TKs) from serine/threonine kinases (STKs). Using a sequence co-variation Potts statistical energy model we previously concluded that TK catalytic domains are more likely than STKs to adopt an inactive conformation with the activation loop in an autoinhibitory folded conformation, due to intrinsic sequence effects. Here we investigate the structural basis for this phenomenon by integrating the sequence-based model with structure-based molecular dynamics (MD) to determine the effects of mutations on the free energy difference between active and inactive conformations, using a thermodynamic cycle involving many (n = 108) protein-mutation free energy perturbation (FEP) simulations in the active and inactive conformations. The sequence and structure-based results are consistent and support the hypothesis that the inactive conformation DFG-out Activation Loop Folded, is a functional regulatory state that has been stabilized in TKs relative to STKs over the course of their evolution via the accumulation of residue substitutions in the activation loop and catalytic loop that facilitate distinct substrate binding modes in trans and additional modes of regulation in cis for TKs.

Probabilistic Work Extraction on a Classical Oscillator Beyond the Second Law.

We demonstrate experimentally that, applying optimal protocols that drive the system between two equilibrium states characterized by a free energy difference ΔF, we can maximize the probability of performing the transition between the two states with a work W smaller than ΔF. The second law holds only on average, resulting in the inequality ⟨W⟩≥ΔF. The experiment is performed using an underdamped oscillator evolving in a double-well potential. We show that with a suitable choice of parameters the probability of obtaining trajectories with W≤ΔF can be larger than 95%. Very fast protocols are a key feature to obtain these results, which are explained in terms of the Jarzynski equality.

Experimental constraints on Mg isotope fractionation during the aragonite–calcite transition and implications for seawater δ26Mg reconstruction

The linkage between the variation of the seawater Mg budget and the long-term carbon cycle can be elucidated by seawater Mg isotope composition (δ26Mg). However, obtaining primary seawater δ26Mg signatures from marine archives is challenging due to the widespread alteration of diagenesis. Aragonite, a common primary marine carbonate, can effectively record seawater δ26Mg but is prone to alteration and transformation into calcite during early diagenesis. Therefore, a comprehensive understanding of Mg isotope behavior during the aragonite–calcite transition is essential to enhance the applicability of aragonite δ26Mg. In this study, we investigate the variation of aragonite δ26Mg during diagenesis with a limited supply of Mg by conducting a series of well-controlled aragonite–calcite transition experiments in a closed system. The experimental conditions encompass temperatures of 60 and 90 °C, the presence of Ca and Na in the solution, varying Na concentrations, as well as the presence of calcite seed. Results demonstrate that the significant decrease of bulk carbonate δ26Mg is accompanied by a substantial amount of Mg released into the solution during the aragonite–calcite transition, and the amount of released Mg is controlled by fluid chemistry via altering Mg partitioning in calcite. Furthermore, Mg isotope fractionation during calcite precipitation is influenced by temperature, ionic strength, and the presence of calcite seed, while kinetics played a negligible role in our experiments. Combined with previous experiments, the temperature-dependent Mg isotope fractionation during calcite precipitation in unseeded experiments is Δ26Mgcal-sol = (−0.13 ± 0.06) × 106/T2 – (0.47 ± 0.68). This fractionation is systematically higher than that of seeded experiments by 0.3–0.6 ‰ from 15 to 90 °C and can mainly be attributed to differences in surface free energy between homogeneous and heterogeneous calcite nucleation. These findings offer fundamental understandings of the Mg isotope behavior during the aragonite–calcite transformation, providing useful insights for interpreting the variation of δ26Mg in experimental and natural carbonates and facilitating ancient seawater δ26Mg reconstruction.

Microwave Spectroscopy of Chiral Astrochemical Candidate Vinyloxirane: The Missing Gauche Conformer.

The recent detection of a chiral molecule, propylene oxide, in the interstellar medium provides impetus for investigation of related analogues as candidates for discovery of a second chiral species. Vinyloxirane (VO) shares many of the characteristics of propylene oxide that favored its remote detection such as modest size, appreciable dipole moment and modest adsorption to water ice. The microwave spectrum of vinyloxirane at room temperature has been studied in the 18 - 26 GHz region. Rotational transitions of the previously undetected gauche-1 conformer have been assigned and fitted. The quantum number range of anti conformer transitions has been greatly expanded, providing improved molecular constants. Vibrational satellite transitions were assigned and fitted for the lowest frequency ν27 torsion mode, for 2ν27, and for the ν26 C=CC bend of anti VO, along with ν27 satellites of gauche-1. The rovibrational analyses were assisted by anharmonic vibrational calculations at B3LYP-D3/aug-cc-PVTZ, B2PLYPD3/cc-pVTZ, and DSDPBEP86/cc-pVTZ levels. Experimental peak intensities provide a population ratio Ngauche-1/Nanti of 0.36 ± 0.06, corresponding to a Gibbs free energy difference of 2.5 ± 0.4 kJ mol-1 in favor of the anti conformer, in agreement with the density functional theory results. In the gauche-1 conformer, the torsional angle between vinyl group and oxirane ring, τC=CCM, is optimized at -35° to favor an intramolecular CvinylH11...O interaction. The gauche-2 conformer with τC=CCM of + 74° suffers from CvinylH11...HCcyclopropyl repulsion so that it is calculated to be 8-9 kJ mol-1 higher than gauche-1. Reinterpretation of earlier Raman spectra suggests that the gauche-2 conformer had not been observed as reported.

Assessing the Accuracy and Efficiency of Free Energy Differences Obtained from Reweighted Flow-Based Probabilistic Generative Models.

Computing free energy differences between metastable states characterized by nonoverlapping Boltzmann distributions is often a computationally intensive endeavor, usually requiring chains of intermediate states to connect them. Targeted free energy perturbation (TFEP) can significantly lower the computational cost of FEP calculations by choosing a set of invertible maps used to directly connect the distributions of interest, achieving the necessary statistically significant overlaps without sampling any intermediate states. Probabilistic generative models (PGMs) based on normalizing flow architectures can make it much easier via machine learning to train invertible maps needed for TFEP. However, the accuracy and applicability of approaches based on empirically learned maps depend crucially on the choice of reweighting method adopted to estimate the free energy differences. In this work, we assess the accuracy, rate of convergence, and data efficiency of different free energy estimators, including exponential averaging, Bennett acceptance ratio (BAR), and multistate Bennett acceptance ratio (MBAR), in reweighting PGMs trained by maximum likelihood on limited amounts of molecular dynamics data sampled only from end-states of interest. We carry out the comparisons on a set of simple but representative case studies, including conformational ensembles of alanine dipeptide and ibuprofen. Our results indicate that BAR and MBAR are both data efficient and robust, even in the presence of significant model overfitting in the generation of invertible maps. This analysis can serve as a stepping stone for the deployment of efficient and quantitatively accurate ML-based free energy calculation methods in complex systems.

How to Sample Dozens of Substitutions per Site with λ Dynamics.

Alchemical free energy methods are useful in computer-aided drug design and computational protein design because they provide rigorous statistical mechanics-based estimates of free energy differences from molecular dynamics simulations. λ dynamics is a free energy method with the ability to characterize combinatorial chemical spaces spanning thousands of related systems within a single simulation, which gives it a distinct advantage over other alchemical free energy methods that are mostly limited to pairwise comparisons. Recently developed methods have improved the scalability of λ dynamics to perturbations at many sites; however, the size of chemical space that can be explored at each individual site has previously been limited to fewer than ten substituents. As the number of substituents increases, the volume of alchemical space corresponding to nonphysical alchemical intermediates grows exponentially relative to the size corresponding to the physical states of interest. Beyond nine substituents, λ dynamics simulations become lost in an alchemical morass of intermediate states. In this work, we introduce new biasing potentials that circumvent excessive sampling of intermediate states by favoring sampling of physical end points relative to alchemical intermediates. Additionally, we present a more scalable adaptive landscape flattening algorithm for these larger alchemical spaces. Finally, we show that this potential enables more efficient sampling in both protein and drug design test systems with up to 24 substituents per site, enabling, for the first time, simultaneous simulation of all 20 amino acids.