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NASA NTRS2005

An Improved Analysis of Forest Carbon Dynamics using Data Assimilation

There are two broad approaches to quantifying landscape C dynamics - by measuring changes in C stocks over time, or by measuring fluxes of C directly. However, these data may be patchy, and have gaps or biases. An alternative approach to generating C budgets has been to use process-based models, constructed to simulate the key processes involved in C exchange. However, the process of model building is arguably subjective, and parameters may be poorly defined. This paper demonstrates why data assimilation (DA) techniques - which combine stock and flux observations with a dynamic model - improve estimates of, and provide insights into, ecosystem carbon (C) exchanges. We use an ensemble Kalman filter (EnKF) to link a series of measurements with a simple box model of C transformations. Measurements were collected at a young ponderosa pine stand in central Oregon over a 3-year period, and include eddy flux and soil C02 efflux data, litterfall collections, stem surveys, root and soil cores, and leaf area index data. The simple C model is a mass balance model with nine unknown parameters, tracking changes in C storage among five pools; foliar, wood and fine root pools in vegetation, and also fresh litter and soil organic matter (SOM) plus coarse woody debris pools. We nested the EnKF within an optimization routine to generate estimates from the data of the unknown parameters and the five initial conditions for the pools. The efficacy of the DA process can be judged by comparing the probability distributions of estimates produced with the EnKF analysis vs. those produced with reduced data or model alone. Using the model alone, estimated net ecosystem exchange of C (NEE)= -251 f 197g Cm-2 over the 3 years, compared with an estimate of -419 f 29gCm-2 when all observations were assimilated into the model. The uncertainty on daily measurements of NEE via eddy fluxes was estimated at 0.5gCm-2 day-1, but the uncertainty on assimilated estimates averaged 0.47 g Cm-2 day-1, and only exceeded 0.5gC m-2 day-1 on days where neither eddy flux nor soil efflux data were available. In generating C budgets, the assimilation process reduced the uncertainties associated with using data or model alone and the forecasts of NEE were statistically unbiased estimates. The results of the analysis emphasize the importance of time series as constraints. Occasional, rare measurements of stocks have limited use in constraining the estimates of other components of the C cycle. Long time series are particularly crucial for improving the analysis of pools with long time constants, such as SOM, woody biomass, and woody debris. Long-running forest stem surveys, and tree ring data, offer a rich resource that could be assimilated to provide an important constraint on C cycling of slow pools. For extending estimates of NEE across regions, DA can play a further important role, by assimilating remote-sensing data into the analysis of C cycles. We show, via sensitivity analysis, how assimilating an estimate of photosynthesis - which might be provided indirectly by remotely sensed data - improves the analysis of NEE.

Williams, Mathew↗

DOE OSTI2024

How spin relaxes and dephases in bulk halide perovskites

Abstract Spintronics in halide perovskites has drawn significant attention in recent years, due to their highly tunable spin-orbit fields and intriguing interplay with lattice symmetry. Here, we perform first-principles calculations to determine the spin relaxation time ( T 1 ) and ensemble spin dephasing time ( $${T}_{2}^{*}$$ T 2 * ) in a prototype halide perovskite, CsPbBr 3 . To accurately capture spin dephasing in external magnetic fields we determine the Landé g -factor from first principles and take it into account in our calculations. These allow us to predict intrinsic spin lifetimes as an upper bound for experiments, identify the dominant spin relaxation pathways, and evaluate the dependence on temperature, external fields, carrier density, and impurities. We find that the Fröhlich interaction that dominates carrier relaxation contributes negligibly to spin relaxation, consistent with the spin-conserving nature of this interaction. Our theoretical approach may lead to new strategies to optimize spin and carrier transport properties.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Structural mechanisms for binding and activation of a contact-quenched fluorophore by RhoBAST

The fluorescent light-up aptamer RhoBAST, which binds and activates the fluorophore–quencher conjugate tetramethylrhodamine-dinitroaniline with high affinity, super high brightness, remarkable photostability, and fast exchange kinetics, exhibits excellent performance in super-resolution RNA imaging. Here we determine the co-crystal structure of RhoBAST in complex with tetramethylrhodamine-dinitroaniline to elucidate the molecular basis for ligand binding and fluorescence activation. The structure exhibits an asymmetric “A”-like architecture for RhoBAST with a semi-open binding pocket harboring the xanthene of tetramethylrhodamine at the tip, while the dinitroaniline quencher stacks over the phenyl of tetramethylrhodamine instead of being fully released. Molecular dynamics simulations show highly heterogeneous conformational ensembles with the contact-but-unstacked fluorophore–quencher conformation for both free and bound tetramethylrhodamine-dinitroaniline being predominant. The simulations also show that, upon RNA binding, the fraction of xanthene-dinitroaniline stacked conformation significantly decreases in free tetramethylrhodamine-dinitroaniline. This highlights the importance of releasing dinitroaniline from xanthene tetramethylrhodamine to unquench the RhoBAST–tetramethylrhodamine-dinitroaniline complex. Using SAXS and ITC, we characterized the magnesium dependency of the folding and binding mode of RhoBAST in solution and indicated its strong structural robustness. The structures and binding modes of relevant fluorescent light-up aptamers are compared, providing mechanistic insights for rational design and optimization of this important fluorescent light-up aptamer-ligand system.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

AL4GAP: Active learning workflow for generating DFT-SCAN accurate machine-learning potentials for combinatorial molten salt mixtures

Machine learning interatomic potentials have emerged as a powerful tool for bypassing the spatiotemporal limitations of ab initio simulations, but major challenges remain in their efficient parameterization. We present AL4GAP, an ensemble active learning software workflow for generating multicomposition Gaussian approximation potentials (GAP) for arbitrary molten salt mixtures. The workflow capabilities include: (1) setting up user-defined combinatorial chemical spaces of charge neutral mixtures of arbitrary molten mixtures spanning 11 cations (Li, Na, K, Rb, Cs, Mg, Ca, Sr, Ba and two heavy species, Nd, and Th) and 4 anions (F, Cl, Br, and I), (2) configurational sampling using low-cost empirical parameterizations, (3) active learning for down-selecting configurational samples for single point density functional theory calculations at the level of Strongly Constrained and Appropriately Normed (SCAN) exchange-correlation functional, and (4) Bayesian optimization for hyperparameter tuning of two-body and many-body GAP models. Here, we apply the AL4GAP workflow to showcase high throughput generation of five independent GAP models for multicomposition binary-mixture melts, each of increasing complexity with respect to charge valency and electronic structure, namely: LiCl–KCl, NaCl–CaCl 2 , KCl–NdCl 3 , CaCl 2 –NdCl 3 , and KCl–ThCl 4 . Our results indicate that GAP models can accurately predict structure for diverse molten salt mixture with density functional theory (DFT)-SCAN accuracy, capturing the intermediate range ordering characteristic of the multivalent cationic melts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

All-optical photoluminescence response of nitrogen-vacancy ensembles in diamond at low magnetic fields

All-optical (AO) microwave-free magnetometry using nitrogen-vacancy (N-𝑉) centers in diamond is attractive due to its broad applicability and reduced experimental complexity. In this work, we investigate room-temperature AO photoluminescence (PL) at low magnetic fields ( <2 mT) using diamonds with N-𝑉 ensembles at parts-per-million (ppm) concentrations. The measured AO-PL contrast features as a function of the applied magnetic field magnitude and direction are correlated with near-degenerate N-𝑉 electronic spin and hyperfine transitions from different N-𝑉 orientations within the diamond host. Reasonable agreement is found between low-field AO-PL measurements and model-based simulations of the effects of resonant dipolar interactions between N-𝑉 centers. The maximum observed AO-PL contrast depends on both the N-𝑉 concentration and the laser-illumination intensity at 532 nm. These results imply different optimal conditions for low-field AO N-𝑉 sensing compared to conventional optically detected magnetic resonance (ODMR) techniques, suggesting new research and application opportunities using AO measurements with lower system complexity, size, weight, and power.

Dipolar interaction↗

DOE OSTI2022

Out of Distribution Detection with Neural Network Anchoring

This is code to reproduce and build on OOD detection from the paper "Out of Distribution Detection with Neural Network Anchoring". Our goal here is to exploit heteroscedastic temperature scaling as a calibration strategy for out of distribution (OOD) detection. Heteroscedasticity here refers to the fact that the optimal temperature parameter for each sample can be different, as opposed to conventional approaches that use the same value for the entire distribution. To enable this, we propose a new training strategy called anchoring that can estimate appropriate temperature values for each sample, leading to state-of-the-art OOD detection performance across several benchmarks. Using NTK theory, we show that this temperature function estimate is closely linked to the epistemic uncertainty of the classifier, which explains its behavior. In contrast to some of the best-performing OOD detection approaches, our method does not require exposure to additional outlier datasets, custom calibration objectives, or model ensembling. Through empirical studies with different OOD detection settings - far OOD, near OOD, and semantically coherent OOD - we establish a highly effective OOD detection approach.

Thiagarajan, Jayaraman↗

DOE OSTI2026

Edge‐Driven Fringe‐Field Effects, Reduced Screening, and Bandgap Widening in Graphene Nanoribbons Enable Single‑Molecule Sensitivity

Graphene nanoribbons (GNRs) offer promising platforms for single‐molecule sensing due to their quasi‐1D channels and discrete electronic states, providing superior sensitivity toward molecular perturbations. While prior studies emphasize smoother edges as essential for optimal performance, the potential benefits of controlled edge roughness remain largely unexplored. Additionally, most investigations focus on GNR arrays, leaving critical edge‐ and width‐dependent factors, including fringe fields, bandgap widening, interactions between adsorbing molecules and GNR atoms, density of states (DOS) suppression, and electrostatic screening lengths, and their collective impact on sensitivity, poorly understood. Here, in this work, we fabricated field‐effect transistors using individual GNRs (widths: 200–20 nm) and characterized their response to molecular adsorption with perfluorooctanoic acid as the model analyte. Narrower ribbons displayed significantly enhanced sensitivity, yielding a coverage‐normalized response of 116 ± 10 mV per molecule in 20 nm‐wide GNRs (from calibrated ensemble Dirac‐point shifts). Experimental and theoretical analyses reveal that this heightened sensitivity arises from stronger fringe fields, width‐dependent quantum confinement effects, reduced DOS, and increased edge roughness that facilitates molecular anchoring, enhanced orbital overlap, and improved charge transfer efficiency. Our findings challenge the conventional assumption that smoother edges inherently enhance sensor performance, demonstrating that controlled edge disorder substantially boosts molecular sensitivity in GNR sensors.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Discovery of Multiple Light-Harvesting States of the Photosynthetic Protein PE545

Cryptophytes are photosynthetic microalga that flourish in a remarkable diversity of natural environments by using pigment-containing proteins with absorption maxima tuned to each ecological niche. While this diversity in the absorption has been well established, the subsequent photophysics is highly sensitive to the local protein environment and so may exhibit similar variation. Thermal fluctuations of the protein conformation are expected to introduce photophysical heterogeneity of the pigments that may have evolved important functional properties in a manner similar to that of the absorption. However, such heterogeneity is averaged out in ensemble measurements and, therefore, has not yet been probed. Here, we report single-molecule measurements of phycoerythrin 545 (PE545), the prototypical cryptophyte antenna protein, in its native dimeric form. A conformational ensemble was resolved consisting of distinct photophysical states with different light-harvesting properties. Proteins that did not quench, partially quenched, or fully quenched absorbed light were observed. Light intensity increased the quenched-state population of the dimer, potentially as a mechanism to deal with the extreme light intensities found in aqueous environments. Cross-linking, which mimics local interactions, introduces this light-dependent functionality while also suppressing other conformational dynamics. The cellular organization can, therefore, actively modulate the protein conformation and dynamics, selecting for distinct levels of light harvesting. Furthermore, the complex conformational equilibrium provides an additional mechanism for cryptophytes and likely other photosynthetic organisms to optimize solar energy capture and conversion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRSDate not supplied

Model Calibration for Cancer Risk Projections According to Uncertain Data

This paper presents forward and inverse formulations for the calibration of computational models according to uncertain data. Uncertainty in the data might be caused by a poor metrology system, measurement noise, missing or uncontrollable input variables, or by the inability to directly measure the inputs and/or outputs of interest. The forward approach performs the calibration in the space of the model’s output thereby requiring repeated model simulations. Conversely, the inverse approach leverages an ensemble of solutions to an inverse problem in order to perform the calibration in the space of the model’s parameters. As such, the computational demands of the inverse approach are considerably lower. These strategies are applied to the calibration of a radiation model that in-forms cancer risk projections for future deep space missions.

uncertainty quantification↗

NASA NTRS2022

Artificial Neural Network Modeling for Airline Disruption Management

Since the 1970s, most airlines have incorporated computerized support for managing disruptions during flight schedule execution. However, existing platforms for airline disruption management (ADM) employ monolithic system design methods that rely on the creation of specific rules and requirements through explicit optimization routines, before a system that meets the specifications is designed. Thus, current platforms for ADM are unable to readily accommodate additional system complexities resulting from the introduction of new capabilities, such as the introduction of unmanned aerial systems (UAS), operations and infrastructure, to the system. To this end, we use historical data on airline scheduling and operations recovery to develop a system of artificial neural networks (ANNs), which describe a predictive transfer function model (PTFM) for promptly estimating the recovery impact of disruption resolutions at separate phases of flight schedule execution during ADM. Furthermore, we provide a modular approach for assessing and executing the PTFM by employing a parallel ensemble method to develop generative routines that amalgamate the system of ANNs. Our modular approach ensures that current industry standards for tardiness in flight schedule execution during ADM are satisfied, while accurately estimating appropriate time-based performance metrics for the separate phases of flight schedule execution.

Kolawole Ogunsina↗

DOE OSTI2022

Hybrid quantum-classical algorithms for approximate graph coloring

We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p : the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level- 1 QAOA and level- 1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level- 1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3 -colorable constant-degree graphs. We find that level- 1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2016

Basin-Scale Assessment of the Land Surface Water Budget in the National Centers for Environmental Prediction Operational and Research NLDAS-2 Systems

The purpose of this study is to evaluate the components of the land surface water budget in the four land surface models (Noah, SAC-Sacramento Soil Moisture Accounting Model, (VIC) Variable Infiltration Capacity Model, and Mosaic) applied in the newly implemented National Centers for Environmental Prediction (NCEP) operational and research versions of the North American Land Data Assimilation System version 2 (NLDAS-2). This work focuses on monthly and annual components of the water budget over 12 National Weather Service (NWS) River Forecast Centers (RFCs). Monthly gridded FLUX Network (FLUXNET) evapotranspiration (ET) from the Max-Planck Institute (MPI) of Germany, U.S. Geological Survey (USGS) total runoff (Q), changes in total water storage (dS/dt, derived as a residual by utilizing MPI ET and USGS Q in the water balance equation), and Gravity Recovery and Climate Experiment (GRACE) observed total water storage anomaly (TWSA) and change (TWSC) are used as reference data sets. Compared to these ET and Q benchmarks, Mosaic and SAC (Noah and VIC) in the operational NLDAS-2 overestimate (underestimate) mean annual reference ET and underestimate (overestimate) mean annual reference Q. The multimodel ensemble mean (MME) is closer to the mean annual reference ET and Q. An anomaly correlation (AC) analysis shows good AC values for simulated monthly mean Q and dS/dt but significantly smaller AC values for simulated ET. Upgraded versions of the models utilized in the research side of NLDAS-2 yield largely improved performance in the simulation of these mean annual and monthly water component diagnostics. These results demonstrate that the three intertwined efforts of improving (1) the scientific understanding of parameterization of land surface processes, (2) the spatial and temporal extent of systematic validation of land surface processes, and (3) the engineering-oriented aspects such as parameter calibration and optimization are key to substantially improving product quality in various land data assimilation systems.

NLDAS-2↗

DOE OSTI2020

Finite-Temperature Structures of Supported Subnanometer Catalysts Inferred via Statistical Learning and Genetic Algorithm-Based Optimization

Single-atom catalysts (SACs) minimize noble metal utilization and can alter the activity and selectivity of supported metal nanoparticles. However, the morphology of active centers, including single atoms and subnanometer clusters of a few atoms, remains elusive due to experimental challenges. The computational cost to describe numerous cluster shapes and sizes makes direct first-principles calculations impractical. We present a computational framework to enable structure determination for single-atom and subnanometer cluster catalysts. As a case study, we obtained the low energy structures of Pd n (n = 1-21) clusters supported on CeO 2 (111), which are critical components of automobile three-way catalysts. Trained on density functional theory data, a three-dimensional cluster expansion is established using statistical learning to describe the Hamiltonian and predict energies of supported Pdn clusters of any structure. Low energy stable and metastable structures are identified using a Metropolis Monte Carlo-based genetic algorithm in the canonical ensemble at 300 K. We observe that supported single atoms sinter to form bilayer clusters and large cluster isomers share similarities in both shape and energy, and elucidate the significance of the support and microstructure on cluster stability. We discovered a simple surrogate structure-energy model, where the energy per atom scales with the square root of the average first coordination number, which can be used to estimate energies and compare the stability of clusters. Our framework, applicable to any metal/support system, fills an important methodological gap to predict the stability of supported metal catalysts in the subnanometer regime.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Deep Learning Image Segmentation for Atmospheric Rivers

Abstract The identification of atmospheric rivers (ARs) is crucial for weather and climate predictions as they are often associated with severe storm systems and extreme precipitation, which can cause large impacts on society. This study presents a deep learning model, termed ARDetect, for image segmentation of ARs using ERA5 data from 1960 to 2020 with labels obtained from the TempestExtremes tracking algorithm. ARDetect is a convolutional neural network (CNN)-based U-Net model, with its structure having been optimized using automatic hyperparameter tuning. Inputs to ARDetect were selected to be the integrated water vapor transport (IVT) and total column water (TCW) fields, as well as the AR mask from TempestExtremes from the previous time step to the one being considered. ARDetect achieved a mean intersection-over-union (mIoU) rate of 89.04% for ARs, indicating its high accuracy in identifying these weather patterns and a superior performance than most deep learning–based models for AR detection. In addition, ARDetect can be executed faster than the TempestExtremes method (seconds vs minutes) for the same period. This provides a significant benefit for online AR detection, especially for high-resolution global models. An ensemble of 10 models, each trained on the same dataset but having different starting weights, was used to further improve on the performance produced by ARDetect, thus demonstrating the importance of model diversity in improving performance. ARDetect provides an effective and fast deep learning–based model for researchers and weather forecasters to better detect and understand ARs, which have significant impacts on weather-related events such as floods and droughts.

Galea, Daniel↗

NASA NTRS1992

Optimization of armored spherical tanks for storage on the lunar surface

A redundancy strategy for reducing micrometeroid armoring mass is investigated, with application to cryogenic reactant storage for a regenerative fuel cell (RFC) on the lunar surface. In that micrometeoroid environment, the cryogenic fuel must be protected from loss due to tank puncture. The tankage must have a sufficiently high probability of survival over the length of the mission so that the probability of system failure due to tank puncture is low compared to the other mission risk factors. Assuming that a single meteoroid penetration can cause a storage tank to lose its contents, two means are available to raise the probability of surviving micrometeoroid attack to the desired level. One can armor the tanks to a thickness sufficient to reduce probability of penetration of any tank to the desired level or add extra capacity in the form of spare tanks that results in survival of a given number out of the ensemble at the desired level. A combination of these strategies (armoring and redundancy) is investigated. The objective is to find the optimum combination which yields the lowest shielding mass per cubic meter of surviving fuel out of the original ensemble. The investigation found that, for the volumes of fuel associated with multikilowatt class cryo storage RFC's, and the armoring methodology and meteoroid models used, storage should be fragmented into small individual tanks. Larger installations (more fuel) pay less of a shielding penalty than small installations. For the same survival probability over the same time period, larger volumes will require less armoring mass per unit volume protected.

Bents, D. J.↗

NASA NTRS1992

Optimization of armored spherical tanks for storage on the lunar surface

Bents, D. J.↗

DOE OSTI2023

Uncertainty quantification of a deep learning fuel property prediction model

Deep learning models are being widely used in the field of combustion. Given the black-box nature of typical neural network based models, uncertainty quantification (UQ) is critical to ensure the reliability of predictions as well as the training datasets, and for a principled quantification of noise and its various sources. Deep learning surrogate models for predicting properties of chemical compounds and mixtures have been recently shown to be promising for enabling data-driven fuel design and optimization, with the ultimate goal of improving efficiency and lowering emissions from combustion engines. In this study, UQ is performed for a multi-task deep learning model that simultaneously predicts the research octane number (RON), Motor Octane Number (MON), and Yield Sooting Index (YSI) of pure components and multicomponent blends. The deep learning model is comprised of three smaller networks: Extractor 1, Extractor 2, and Predictor, and a mixing operator. The molecular fingerprints of individual components are encoded via Extractor 1 and Extractor 2, the mixing operator generates fingerprints for mixtures/blends based on linear mixing operation, and the predictor maps the fingerprint to the target properties. Two different classes of UQ methods, Monte Carlo ensemble methods and Bayesian neural networks (BNNs), are employed for quantifying the epistemic uncertainty. Combinations of Bernoulli and Gaussian distributions with DropConnect and DropOut techniques are explored as ensemble methods. All the DropConnect, DropOut and Bayesian layers are applied to the predictor network. Aleatoric uncertainty is modeled by assuming that each data point has an independent uncertainty associated with it. The results of the UQ study are further analyzed to compare the performance of BNN and ensemble methods. Although this study is confined to UQ of fuel property prediction, the methodologies are applicable to other deep learning frameworks that are being widely used in the combustion community.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2022

Large Scale Study of Ligand–Protein Relative Binding Free Energy Calculations: Actionable Predictions from Statistically Robust Protocols

The accurate and reliable prediction of protein–ligand binding affinities can play a central role in the drug discovery process as well as in personalized medicine. Of considerable importance during lead optimization are the alchemical free energy methods that furnish an estimation of relative binding free energies (RBFE) of similar molecules. Recent advances in these methods have increased their speed, accuracy, and precision. This is evident from the increasing number of retrospective as well as prospective studies employing them. However, such methods still have limited applicability in real-world scenarios due to a number of important yet unresolved issues. Here, we report the findings from a large data set comprising over 500 ligand transformations spanning over 300 ligands binding to a diverse set of 14 different protein targets which furnish statistically robust results on the accuracy, precision, and reproducibility of RBFE calculations. We use ensemble-based methods which are the only way to provide reliable uncertainty quantification given that the underlying molecular dynamics is chaotic. These are implemented using TIES (Thermodynamic Integration with Enhanced Sampling). Results achieve chemical accuracy in all cases. Ensemble simulations also furnish information on the statistical distributions of the free energy calculations which exhibit non-normal behavior. We find that the “enhanced sampling” method known as replica exchange with solute tempering degrades RBFE predictions. We also report definitively on numerous associated alchemical factors including the choice of ligand charge method, flexibility in ligand structure, and the size of the alchemical region including the number of atoms involved in transforming one ligand into another. Our findings provide a key set of recommendations that should be adopted for the reliable application of RBFE methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗