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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Fully thermal meta-GGA exchange correlation free-energy density functional

The application of density functional theory to materials in the warm dense matter regime has motivated the development of exchange-correlation functionals which incorporate proper, explicit temperature dependence. Previous work has yielded fully-thermal exchange-correlation free energy functionals at the local density approximation (LDA) and generalized gradient approximation (GGA) levels of refinement. Recently an additive thermal correction scheme was utilized to construct a meta-GGA exchange-correlation (XC) functional in which thermal effects are treated at the GGA level. Here, the f TSCAN free-energy XC functional presented here includes thermal effects through the meta-GGA level in the context of the SCAN (strongly constrained and appropriately normed) ground-state functional. The f TSCAN functional provides generality while achieving similar performance to a thermal GGA functional at high temperatures, e.g. pressures within 1% of path integral Monte Carlo simulations of warm dense hydrogen, and a significant improvement over ground-state functionals. At low temperatures, f TSCAN demonstrates improvements in accuracy relative to lower-level and deorbitalized functionals, indicating that calculations using f TSCAN may be expected to perform well across experimentally relevant densities and pressures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Gyrokinetic simulations of momentum flux parasitic to free-energy transfer

Ion Landau damping interacts with a portion of the E × B drift to cause a nondiffusive outward flux of co-current toroidal angular momentum. Quantitative evaluation of this momentum flux requires nonlinear simulations to determine f L , the fraction of fluctuation free energy that passes through ion Landau damping, in fully developed turbulence. Nonlinear gyrokinetic simulations with the GKW code confirm the presence of the systematic symmetry-breaking momentum flux. For simulations with adiabatic electrons, f L scales inversely with the ion temperature gradient, because only the ion curvature drift can transfer free energy to the electrostatic potential. Although kinetic electrons should, in principle, relax this restriction, the ion Landau damping measured in collisionless kinetic-electron simulations remained at low levels comparable with ion-curvature-drift transfer, except when magnetic shear $\hat{s}$ was strong. A set of simulations scanning the electron pitch-angle scattering rate showed only a weak variation of f L with the electron collisionality. Still, collisional-electron simulations with electron temperature greater than ion temperature unambiguously showed electron-curvature-drift transfer supporting ion Landau damping, leading to a corresponding enhancement of the symmetry-breaking momentum flux.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Gyrokinetic simulations of momentum flux parasitic to free-energy transfer

Ion Landau damping interacts with a portion of the E×B drift to cause a non-diffusive outward flux of co-current toroidal angular momentum. Quantitative evaluation of this momentum flux requires nonlinear simulations to determine fL, the fraction of fluctuation free energy that passes through ion Landau damping, in fully developed turbulence. Nonlinear gyrokinetic simulations with the GKW code confirm the presence of the systematic symmetry-breaking momentum flux. For simulations with adiabatic electrons, fL scales inversely with the ion temperature gradient, because only the ion curvature drift can transfer free energy to the electrostatic potential. Although kinetic electrons should in principle relax this restriction, the ion Landau damping measured in collisionless kinetic-electron simulations remained at low levels comparable with ion-curvature-drift transfer, except when magnetic shear was strong. A set of simulations scanning the electron pitch-angle scattering rate showed only a weak variation of fL with the electron collisionality. However, collisional-electron simulations with electron temperature greater than ion temperature unambiguously showed electron-curvature-drift transfer supporting ion Landau damping, leading to a corresponding enhancement of the symmetry-breaking momentum flux.

intrinsic rotation↗
DOE OSTI2024

Computing equilibrium free energies through a nonequilibrium quench

Many methods to accelerate sampling of molecular configurations are based on the idea that temperature can be used to accelerate rare transitions. These methods typically compute equilibrium properties at a target temperature using reweighting or through Monte Carlo exchanges between replicas at higher temperatures. A recent paper [G. M. Rotskoff and E. Vanden-Eijnden, Phys. Rev. Lett. 122, 150602 (2019)] demonstrated that accurate equilibrium densities of states can also be computed through a nonequilibrium “quench” process, where sampling is performed at a higher temperature to encourage rapid mixing and then quenched to lower energy states with dissipative dynamics. Here, we provide an implementation of the quench dynamics in LAMMPS and evaluate a new formulation of nonequilibrium estimators for the computation of partition functions or free energy surfaces (FESs) of molecular systems. We show that the method is exact for a minimal model of N-independent harmonic springs and use these analytical results to develop heuristics for the amount of quenching required to obtain accurate sampling. We then test the quench approach on alanine dipeptide, where we show that it gives an FES that is accurate near the most stable configurations using the quench approach but disagrees with a reference umbrella sampling calculation in high FE regions. We then show that combining quenching with umbrella sampling allows the efficient calculation of the free energy in all regions. Moreover, by using this combined scheme, we obtain the FES across a range of temperatures at no additional cost, making it much more efficient than standard umbrella sampling if this information is required. Finally, we discuss how this approach can be extended to solute tempering and demonstrate that it is highly accurate for the case of solvated alanine dipeptide without any additional modifications.

Chemistry↗
DOE OSTI2022

Accurate determination of solvation free energies of neutral organic compounds from first principles

The main goal of molecular simulation is to accurately predict experimental observables of molecular systems. Another long-standing goal is to devise models for arbitrary neutral organic molecules with little or no reliance on experimental data. While separately these goals have been met to various degrees, for an arbitrary system of molecules they have not been achieved simultaneously. For biophysical ensembles that exist at room temperature and pressure, and where the entropic contributions are on par with interaction strengths, it is the free energies that are both most important and most difficult to predict. We compute the free energies of solvation for a diverse set of neutral organic compounds using a polarizable force field fitted entirely to ab initio calculations. The mean absolute errors (MAE) of hydration, cyclohexane solvation, and corresponding partition coefficients are 0.2 kcal/mol, 0.3 kcal/mol and 0.22 log units, i.e. within chemical accuracy. The model (ARROW FF) is multipolar, polarizable, and its accompanying simulation stack includes nuclear quantum effects (NQE). The simulation tools’ computational efficiency is on a par with current state-of-the-art packages. The construction of a wide-coverage molecular modelling toolset from first principles, together with its excellent predictive ability in the liquid phase is a major advance in biomolecular simulation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

The Aqueous and Acetonitrile Bond Dissociation Free Energies of N -Hydroxyphthalimide

Widely cited values of 89 and 90.9 kcal/mol for the bond-dissociation free energy of N-hydroxyphthalimide (NHPI) in water and acetonitrile, respectively, are in error. The sources of the errors leading to these values have been explored and corrected. Here, the corrected values are confirmed through new experiments in aqueous and acetonitrile media and are found to be 84.4 ± 0.1 and 80.04 ± 0.06 kcal/mol, respectively.

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

Binding mechanism and binding free energy of amino acids and citrate to hydroxyapatite surfaces as a function of crystallographic facet, pH, and electrolytes

Hydroxyapatite (HAP) is the major mineral phase in bone and teeth. The interaction of individual amino acids and citrate ions with different crystallographic HAP surfaces has remained uncertain for decades, creating a knowledge gap to rationally design interactions with peptides, proteins, and drugs. In this contribution, we quantify the binding mechanisms and binding free energies of the 20 end-capped natural amino acids and citrate ions on the basal (001) and prismatic (010)/(020) planes of hydroxyapatite at pH values of 7 and 5 for the first time at the molecular scale. We utilized over 1500 steered molecular dynamics simulations with highly accurate potentials that reproduce surface and hydration energies of (hkl) hydroxyapatite surfaces at different pH values. Charged residues demonstrate a much higher affinity to HAP than charge-neutral species due to the formation of superficial ion pairs and ease of penetration into layers of water molecules on the mineral surface. Binding free energies range from 0 to -60 kJ/mol and were determined with ~10% uncertainty. The highest affinity was found for citrate, followed by Asp(-) and Glu(-), and followed after a gap by Arg(+), Lys(+), as well as by His(+) at pH 5. The (hkl)-specific area density of calcium ions, the protonation state of phosphate ions, and subsurface directional order of the ions in HAP lead to surface-specific binding patterns. Amino acids without ionic side groups exhibit weak binding, between -3 and 0 kJ/mol, due to difficulties to penetrate the first layer of water molecules on the apatite surfaces. We explain recognition processes that remained elusive in experiments, in prior simulations, discuss agreement with available data, and reconcile conflicting interpretations. In conclusion, the findings can serve as useful input for the design of peptides, proteins, and drug molecules for the modification of bone and teeth-related materials, as well as control of apatite mineralization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Nucleation-mediated reshaping of facetted metallic nanocrystals: Breakdown of the classical free energy picture

Shape stability is key to avoiding degradation of performance for metallic nanocrystals synthesized with facetted non-equilibrium shapes to optimize properties for catalysis, plasmonics, and so on. Reshaping of facetted nanocrystals is controlled by the surface diffusion-mediated nucleation and growth of new outer layers of atoms. Here, Kinetic Monte Carlo (KMC) simulation of a realistic stochastic atomistic-level model is applied to precisely track the reshaping of Pd octahedra and nanocubes. Unexpectedly, separate constrained equilibrium Monte Carlo analysis of the free energy profile during reshaping reveals a fundamental failure of the classical nucleation theory (CNT) prediction for the reshaping barrier and rate. Why? Nucleation barriers can be relatively low for these processes, so the system is not locally equilibrated before crossing the barrier, as assumed in CNT. This claim is supported by an analysis of a first-passage problem for reshaping within a master equation framework for the model that reasonably captures the behavior in KMC simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Development of a multiphase equation of state for gallium with experiments and ab initio free-energy calculations

Here, we present a five-phase equation of state (EOS) for elemental gallium (Ga) that is developed using both experimental data and new theoretical predictions. Four experimentally observed solid phases (Ga-I, Ga-II, Ga-III, and Ga-IV) and one liquid phase are included. To improve our understanding of the thermal behavior of Ga and its phase boundaries under compression, we have performed ab initio density functional theory (DFT) free-energy calculations for the Ga-III and liquid phases, which enables us to determine the melt temperature to be 2214 ± 100 K at 110 GPa, extending significantly beyond the existing experimental melt data, which are limited to 25 GPa. In order to best describe the electron-thermal contribution, which dominates the liquid free energy at high temperatures, we have carried out averaged-atom-in-jellium DFT calculations to cover the entire temperature and density range of the EOS. The resulting multiphase Ga EOS is able to accurately reproduce a diverse variety of data, including known phase boundaries, the principal Hugoniot, low-pressure liquid isobars, and diamond-anvil-cell isotherm measurements at high pressures. It agrees more closely with key experimentally measured properties than other Ga EOS models targeted for high-pressure applications.

Wu, Christine J. [Lawrence Livermore National Labo↗
DOE OSTI2024

Metadynamics investigation of lanthanide solvation free energy landscapes and insights into separations energetics

Lanthanide ion solvation chemistry in nonaqueous phases is key to understanding and developing effective separation processes for these critical materials. Due to the complexity and inherent disorder of the solution phase, a comprehensive picture of the solvated metal ion is often difficult to generate solely from conventional spectroscopic approaches and electronic structure calculations, particularly in the extractant phase. In this work, we use classical molecular dynamics (MD) simulation with an advanced sampling technique, metadynamics, supplemented by experimental spectroscopy and speciation analysis, to measure lanthanide solvation free energy landscapes. We define coordination-based collective variables to probe the entire range of solvation configurations in the organic phase of lanthanum (La), europium (Eu), and lutetium (Lu) nitrate salts bound with a commonly used extractant, N,N′-dimethyl, N,N′-dioctylhexylethoxymalonamide (DMDOHEMA). The known lanthanide extraction trend of La ≈ Eu > Lu is readily explained by the measured free energy surfaces, which show consistent DMDOHEMA coordination from La to Eu, followed by loss of DMDOHEMA coordination from Eu to Lu. These simulations suggest how ligand crowding at the metal center can control selectivity, in this case resulting in the opposite extraction trend as observed with other conventional extractants, where the enthalpic contribution from increasing lanthanide charge density across the series dominates the extraction energetics. We also find that the presence of inner-sphere water, verified by time-resolved fluorescence, diversifies the accessible solvation structures. As a result, understanding solvation requires consideration of an entire thermodynamic ensemble, rather than the single dominant lowest-energy structure, as is often considered out of necessity in interpretation of spectroscopic data or in electronic structure-based ligand design approaches. In general, we demonstrate how metadynamics uniquely enables investigation of complex, multidimensional solvation energetic landscapes, and how it can explain selectivity trends where extraction is controlled by more complex mechanisms than simple charge density-based selectivity.

Wang, Xiaoyu↗
DOE OSTI2023

Enhanced Configurational Sampling Approaches to Alchemical Ligand Binding Free Energy Simulations: Current Status and Challenges

In this study, ligand binding free energy simulations (LB-FES) have been routine tasks in modern drug discovery campaign. A long-standing challenge for LB-FES is the difficulty in adequately sampling nontrivial environmental reorganizations in response to ligand binding. Therefore, various enhanced configurational sampling (ECS) approaches were devised to speed up fluctuations of relevant slow degrees of freedom (SDOF) and ensure simulation convergence. However, in contrast to the achievements in parametrization, software performance, and workflow automation, efficient ECS methodology suitable for high throughput screening remains in an early stage of development. Here, a review of ECS developments with LB-FES is presented, revisiting current approaches and underlining the major technical pitfalls and challenges. This Perspective focuses on alchemical LB-FES on account of their predominant role in high throughput drug screening as well as the established partnership with ECS. The critical aspects of designing ECS approaches, from both theoretical and applied perspectives, are described. This work is intended to provide a contemporary review of the scientific, technical, and practical issues associated with the accelerating convergence of alchemical LBFES.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Consequences of the failure of equipartition for the p – V behavior of liquid water and the hydration free energy components of a small protein

Earlier we showed that in the molecular dynamics simulation of a rigid model of water it is necessary to use an integration time-step δ t ≤ 0.5 fs to ensure equipartition between translational and rotational modes. Here we extend that study in the NVT ensemble to NpT conditions and to an aqueous protein. We study neat liquid water with the rigid, SPC/E model and the protein BBA (PDB ID: 1FME) solvated in the rigid, TIP3P model. We examine integration time-steps ranging from 0.5 fs to 4.0 fs for various thermostat plus barostat combinations. We find that a small δ t is necessary to ensure consistent prediction of the simulation volume. Hydrogen mass repartitioning alleviates the problem somewhat, but is ineffective for the typical time-step used with this approach. The compressibility, a measure of volume fluctuations, and the dielectric constant, a measure of dipole moment fluctuations, are also seen to be sensitive to δ t . Using the mean volume estimated from the NpT simulation, we examine the electrostatic and van der Waals contribution to the hydration free energy of the protein in the NVT ensemble. These contributions are also sensitive to δ t . In going from δ t = 2 fs to δ t = 0.5 fs, the change in the net electrostatic plus van der Waals contribution to the hydration of BBA is already in excess of the folding free energy reported for this protein.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Dataset for manuscript "Consequences of the failure of equipartition for the p-V behavior of liquid water and the hydration free energy components of a small protein"

Previously, we showed that in the molecular dynamics simulation of a rigid model of water it is necessary to use an integration time-step dt that is less than or equal to 0.5 fs to ensure equipartition between translational and rotational modes. We extended that study in the NVT ensemble to NpT conditions and to an aqueous protein. We study neat liquid water with the rigid, SPC/E model and the protein BBA (PDB ID: 1FME) solvated in the rigid, TIP3P model. We examined integration time-steps ranging from 0.5 fs to 4.0 fs for various thermostat plus barostat combinations. We find that a small time-step, dt, is necessary to ensure consistent prediction of the simulation volume. Hydrogen mass repartitioning alleviates the problem somewhat, but is ineffective for the typical time-step used with this approach. The compressibility, a measure of volume fluctuations, is seen to be sensitive to dt. Using the mean volume estimated from the NpT simulation, we examined the electrostatic and van der Waals contribution to the hydration free energy of the protein in the NVT ensemble. These contributions are also sensitive to dt. In going from a time-step of 2 fs to a time-step of 0.5 fs, the change in the net electrostatic plus van der Waals contribution to the hydration of BBA is already in excess of the folding free energy reported for this protein. The data-set contains the simulation metadata and log files that support the claims noted above.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Superconductivity out of a non-Fermi liquid: Free energy analysis

In this paper, we present an in-depth analysis of the condensation energy E c for a superconductor in a situation when superconductivity emerges out of a non-Fermi liquid due to pairing mediated by a massless boson. This is the case for electronic-mediated pairing near a quantum-critical point in metal, for pairing in SYK-type models, and for phonon-mediated pairing in the properly defined limit, when the dressed Debye frequency vanishes. We consider a subset of these quantum-critical models, in which the pairing in a channel with a proper spatial symmetry is described by an effective 0 + 1 dimensional model with the effective dynamical interaction V(Ω m ) = g¯ γ /|Ω m | γ , where γ is model-specific (the γ model). In previous papers, we argued that the pairing in the γ model is qualitatively different from that in a Fermi liquid, and the gap equation at T = 0 has an infinite number of topologically distinct solutions, Δ n (ω m ), where an integer n, running between 0 and infinity, is the number of zeros of Δ n (ω m ) on the positive Matsubara axis. This gives rise to the set of extrema of E c at E c,n , of which E c,0 is the global minimum. Here, the spectrum E c,n is discrete for a generic γ < 2 but becomes continuous at γ = 2–0. Here, we discuss in more detail the profile of the condensation energy near each E c,n and the transformation from a discrete to a continuous spectrum at γ → 2. We also discuss the free energy and the specific heat of the γ model in the normal state.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Correlated particle transport enables biological free energy transduction

Studies of biological transport frequently neglect the explicit statistical correlations among particle site occupancies (i.e., they use a mean-field approximation). Neglecting correlations sometimes captures biological function, even for out-of-equilibrium and interacting systems. Here, we show that neglecting correlations fails to describe free energy transduction, mistakenly predicting an abundance of slippage and energy dissipation, even for networks that are near reversible and lack interactions among particle sites. Interestingly, linear charge transport chains are well described without including correlations, even for networks that are driven and include site-site interactions typical of biological electron transfer chains. We examine three specific bioenergetic networks: a linear electron transfer chain (as found in bacterial nanowires), a near-reversible electron bifurcation network (as in complex III of respiration and other recently discovered structures), and a redox-coupled proton pump (as in complex IV of respiration).

bacterial nanowires↗
DOE OSTI2021

Nanoparticle O–H Bond Dissociation Free Energies from Equilibrium Measurements of Cerium Oxide Colloids

A novel equilibrium strategy for measuring the hydrogen atom affinity of colloidal metal oxide nanoparticles is presented. Reactions between oleate-capped cerium oxide nanoparticle colloids (nanoceria) and organic proton-coupled electron transfer (PCET) reagents are used as a model system. Nanoceria redox changes, or hydrogen loadings, and overall reaction stoichiometries were followed by both 1 H NMR and X-ray absorption near-edge spectroscopies. Furthermore, these investigations revealed that, in many cases, reactions between nanoceria and PCET reagents reach equilibrium states with good mass balance. Each equilibrium state is a direct measure of the bond strength, or bond dissociation free energy (BDFE), between nanoceria and hydrogen. Further studies, including those with larger nanoceria, indicated that the relevant bond is a surface O–H. Thus, we have measured surface O–H BDFEs for nanoceria—the first experimental BDFEs for any nanoscale metal oxide. Remarkably, the measured CeO–H BDFEs span 13 kcal mol –1 (0.56 eV) with changes in the average redox state of the nanoceria colloid. Possible chemical models for this strong dependence are discussed. We propose that the tunability of ceria BDFEs may be important in explaining its effectiveness in catalysis. More generally, metal oxide BDFEs have been used as predictors of catalyst efficacy that, traditionally, have only been accessible by computational methods. These results provide important experimental benchmarks for metal oxide BDFEs and demonstrate that the concepts of molecular bond strength thermochemistry can be applied to nanoscale materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Determination of the N–H Bond Dissociation Free Energy in a Pyridine(diimine)molybdenum Complex Prepared by Proton-Coupled Electron Transfer

The pyridine(diimine) molybdenum bis(imido) complex, ( iPr PDI)Mo(=NTol) 2 (Tol = 4-methylphenyl) was synthesized by addition of two equivalents of 4-methylphenylazide to a corresponding molybdenum benzene derivative, ( iPr PDI)Mo(η 6 -C 6 H 6 ) ( iPr PDI = 2,6-(2,6-iPr 2 C 6 H 3 N=CMe) 2 C 5 H 3 N). Protonation of ( iPr PDI)Mo(=NTol) 2 with 2,6-lutinidum triflate yielded a cationic molybdenum amido complex, [( iPr PDI)Mo(NHTol)(=NTol)][OTf], which was further transformed into the neutral molybdenum amido complex, ( iPr PDI)Mo(NHTol)(=NTol) by reduction with zinc powder. A series of spectroscopic, synthetic and pK a determination studies along with electrochemical measurements by the protonation-reduction pathway were used to establish an N–H bond dissociation free energy (BDFE) between 65-69 kcal/mol for the molybdenum imido-amido compound, ( iPr PDI)Mo(NHTol)(=NTol). Full molecule DFT studies provided a computed value of 61 kcal/mol. By contrast, reduction of ( iPr PDI)Mo(=NTol) 2 with KC 8 afforded the corresponding anionic molybdenum complex, K[( iPr PDI)Mo(=NTol) 2 ] that has a potassium cation intercalated with the pyridine and the tolyl groups. Protonation of K[( iPr PDI)Mo(=NTol) 2 ] with the weak amidinium acids [TBD(H)][BArF 24 ] (TBD = triazabicyclodecene, BArF 24 = B[3,5-(CF 3 ) 2 C 6 H 3 ] 4 ) also produced the neutral molybdenum amido complex, ( iPr PDI)Mo(NHTol)(=NTol). Measurement of the pKa and oxidation potential of K[( iPr PDI)Mo(=NTol) 2 ] provided a range of 69-73 kcal/mol for the N–H BDFE of ( iPr PDI)Mo(NHTol)(=NTol), in good agreement with the protonation-reduction route and completing the square scheme. The similar pK a and redox potentials obtained from each pathway demonstrate that both sequences are energetically feasible for PCET events. This study on the determination of N–H BDFE of the molybdenum amido complex renders fundamental insight into the N 2 reduction cycle by proton-coupled electron transfer.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Actinium–DOTA coordination in water from hybrid ML/MM: Structure, free energies, and water-exchange pathways

Quantitative simulation of trivalent ƒ-block chelates in water remains challenging because bonded and non-bonded force-field models make different approximations for coordination structure, exchange dynamics, and ion–ligand interactions in highly charged systems. Here, we develop a hybrid machine-learning/molecular-mechanics (ML/MM) framework for Ac 3+ –DOTA in explicit solvent by training an E(3)-equivariant neural network potential (MACELES) on mechanically embedded QM/MM data for Ac aquo and Ac–DOTA species and coupling it to NAMD 2.14 with particle-mesh Ewald electrostatics. Nanosecond ML/MM trajectories remain numerically stable and preserve chelate integrity, yielding a compact DOTA inner shell with an inner-sphere water coordination number of CN Ac,O w ≈ 1.7 arising from a dynamic equilibrium between one- and two-water states (37.5% and 59.9% of frames; three waters 2.5%). A 5 ns potential of mean force shows two low-lying basins at CN Ac,O w ≈ 1 and CN Ac,O w ≈ 2. DFT end-state free energies are consistent with the ML/MM profile, and DFT minimum-energy paths provide a qualitative electronic-structure reference for the observed basin connectivity. State-resolved kinetics reveal picosecond water-exchange pathways that couple hydration changes to transient DOTA arm fluctuations, and training-set comparisons show that temperature-matched Ac–DOTA data optimize energy/force accuracy while more diverse solvated data improve charge prediction. Overall, the present hybrid ML/MM model provides a practical description of Ac 3+ –DOTA hydration thermodynamics and short-time exchange behavior in explicit water at MD-like cost.

Actinium↗