Atomic Size Research Articles

Systematic Study of Hard-Wall Confinement-Induced Effects on Atomic Electronic Structure.

We point out that although a litany of studies have been published on atoms in hard-wall confinement, they have either not been systematic, having only looked at select atoms and/or select electron configurations, or they have not used robust numerical methods. To remedy the situation, we perform in this work a methodical study of atoms in hard-wall confinement with the HelFEM program, which employs the finite element method that trivially implements the hard-wall potential, guarantees variational results, and allows for easily finding the numerically exact solution. Our fully numerical calculations are based on nonrelativistic density functional theory and spherically averaged densities. We consider three levels of density functional approximations: the local density approximation employing the Perdew-Wang (PW92) functional, the generalized-gradient approximation (GGA) employing the Perdew-Burke-Ernzerhof (PBE) functional, and the meta-GGA approximation employing the r2SCAN functional. Importantly, the completely dissimilar density functional approximations are in excellent agreement, suggesting that the observed results are not artifacts of the employed level of theory. We systematically examine low-lying configurations of the H-Xe atoms and their monocations and investigate how the configurations─especially the ground-state configuration─behave as a function of the position of the hard-wall boundary. We perform calculations with both spin-polarized as well as spin-restricted densities and demonstrate that spin-polarization effects are significant in open-shell configurations, even though some previous studies have only considered the spin-restricted model. We demonstrate the importance of considering ground-state changes for confined atoms by computing the ionization radii for the H-Xe atoms and observe significant differences to earlier studies. Confirming previous observations, we identify electron shifts on the outermost shells for a majority of the elements: valence s electrons are highly unfavored under strong confinement, and the high-lying 3d and 4f orbitals become occupied in atoms of periods 2-3 and 3-4, respectively. We also comment on deficiencies of a commonly used density-based estimate for the van der Waals (vdW) radius of atoms and propose a better behaved variant in terms of the number of electrons outside the vdW radius that we expect will prove useful in future studies.

The Lanthanide Contraction: What is an Abnormal and Why?

The lanthanide contraction is a widely known phenomenon in which the ionic radii of the Ln3+ ions decrease across the series from La3+ to Lu3+. As a result, the distance d(Ln-Y), where Y is a ligand donor atom, decreases across the series. As shown previously, the decrease normally has a linear dependence on the number of 4f Ln3+ electrons, n, and the net change, Δ', is between 0.15 and 0.20 Å. However, previous reports have shown that Δ' can be much larger than normal, and it is shown here that Δ' can be much smaller than normal. The present study seeks to determine the source and a possible explanation of these anomalies. A definitive conclusion is that the large Δ' is due to large d(Ln-Y) for the early lanthanides. The small Δ' can result from chelate constraints and intramolecular H-bonding. As an outgrowth of this search, it is shown that consistent radii for donor atoms, r(Y), can be obtained if the system satisfies certain conditions. Finally, the impact of the results on the normal and inverse trans influences is discussed.

Microstructure and Wear and Corrosion Resistance of CoCrFeMoNiSix (x = 0.25, 0.50, 0.75) HEACs Prepared by Plasma Cladding

CoCrFeMoNiSix (x = 0.25, 0.50, 0.75) HEACs were successfully prepared on Q235 steel substrates by the plasma cladding method. The phase structure, microstructure, element distribution, and wear and corrosion resistance of these coatings were investigated by XRD, OM, SEM, EDS, a friction and wear tester, and an electrochemical workstation. The results show that the CoCrFeMoNiSix (x = 0.25, 0.50, 0.75) coatings are composed of a major FCC phase and minor BCC phase. With an increase in Si content, the lattice constant and cell volume of both phases and the BCC phase content in these alloys gradually increase, while the enthalpy of mixing, Gibbs free energy, atomic radius difference, VEC, and phase density decrease. All the three alloys exhibit typical dendritic structures. With an increase in Si content, the enrichment of Mo and Si in the interdendrite region is significantly reduced. The friction coefficients of CoCrFeMoNiSix (x = 0.25, 0.50, 0.75) HEACs show a trend of first increasing, then decreasing, and gradually stabilizing with an increase in time, and are 0.604, 0.526, and 0.534, respectively. The wear resistance of the three alloys is mainly related to the changes in crystallinity and high-strength BCC phase content caused by different Si contents. The polarization curves of CoCrFeMoNiSix (x = 0.25, 0.50, 0.75) high-entropy alloy coatings show an obvious passivation zone, and the corrosion resistance is significantly better than that of Q235 steel substrate. The CoCrFeMoNiSi0.75 coating has the highest self-corrosion potential, smallest self-corrosion current, largest capacitive reactance arc radius, and best corrosion resistance in a 3.5% NaCl solution.

Studies of a saturated chrome layer on the surface of steel under plasma heating

In this paper, the possibility of saturation of the surface of low-carbon steels with chromium during plasma heating is considered. The analysis of existing methods of surface chrome plating of metals is carried out. The mechanism of diffusion saturation of metal with chromium can be considered as a complex process consisting of separate stages: formation of active chromium atoms near the surface or directly on the metal surface; sorption of atoms by the metal surface; diffusion of chromium atoms into the metal. The results of preliminary experiments on chrome plating of the surface layer using plasma heating are presented. In this experiment, under the action of a plasma arc, the following reactions are possible: the reduction of chromium from chromium oxide with the formation of chromium carbides Cr7C3 and Cr23C6; the formation of complex carbide-cementites (Fe, Cr)3C or (Cr, Fe)23C6. The authors proceeded from the hypothesis that if the amount of chromium in the hardened layer is in the range of 0.3–0.5% (based on X-ray analysis), therefore, in this case all chromium atoms exist in the form of a solid solution. It is known that chromium has an atomic radius r = 0.128 nm, close to the radius of iron r = 0.126 nm, but much larger than the radius of carbon r = 0.07 nm. Thus, the presence of a chromium atom together with a carbon atom in the α-lattice of iron increases the strength of the martensite lattice due to solid-phase hardening, and consequently the microhardness increases (up to 12,000 MPa). Such quantitative values of microhardness are not obtained by other cementation methods. It is proved that saturation of the metal surface with chromium from the paste during plasma heating can lead to the formation of a diffusion chrome-plated layer of steel. New additional studies of the surface layer structure and analysis of the parameters of plasma surface chrome treatment processes will be required in order to achieve the formation of high-quality chrome plating of the surface by creating a coating.

New Algorithms to Generate Permutationally Invariant Polynomials and Fundamental Invariants for Potential Energy Surface Fitting.

Symmetric functions, such as Permutationally Invariant Polynomials (PIPs) and Fundamental Invariants (FIs), are effective and concise descriptors for incorporating permutation symmetry into neural network (NN) potential energy surface (PES) fitting. The traditional algorithm for generating such symmetric polynomials has a factorial time complexity of N!, where N is the number of identical atoms, posing a significant challenge to applying symmetric polynomials as descriptors of NN PESs for larger systems, particularly with more than 10 atoms. Herein, we report a new algorithm which has only linear time complexity for identical atoms. It can tremendously accelerate generation process of symmetric polynomials for molecular systems. The proposed algorithm is based on graph connectivity analysis following the action of the generation set of molecular permutational group. For instance, in the case of calculating the invariant polynomials for a 15-atom molecule, such as tropolone, our algorithm is approximately 2 million times faster than the previous method. The efficiency of the new algorithm can be further enhanced with increasing molecular size and number of identical atoms, making the FI-NN approach feasible for systems with over 10 atoms and high symmetry demands.

Search for high-frequency gravitational waves with Rydberg atoms

We propose high-frequency gravitational wave (GW) detectors with Rydberg atoms. Rydberg atoms are ultra-sensitive detectors of electric fields. By setting up a constant magnetic field, a weak electric field is generated upon the arrival of GWs. The weak electric field signal is then detected by an electromagnetically induced transparency (EIT) in the system of the Rydberg atoms. Recently, the minimum detectable electric field with the Rydberg atoms is further improved by employing superheterodyne detection method. Hence, even the weak signal generated by GWs turns out to be detectable. We calculate the amplitude of Rabi frequency of the Rydberg atoms induced by the GWs and show that the sensitivity of the Rydberg atoms becomes maximum when the size of the Rydberg atoms is close to the wavelength of GWs. We evaluate the minimum detectable amplitude of GWs with Rubidium Rydberg atoms and find that the detector can probe GWs with a frequency f=4.2GHz and an amplitude around 10-20.

A roadmap from the bond strength to the grain-boundary energies and macro strength of metals

Correlating the bond strength with the macro strength of metals is crucial for understanding mechanical properties and designing multi-principal-element alloys (MPEAs). Motivated by the role of grain boundaries in the strength of metals, we introduce a predictive model to determine the grain-boundary energies and strength of metals from the cohesive energy and atomic radius. This scheme originates from the d-band characteristics and broken-bond spirit of tight-binding models, and demonstrates that the repulsive/attractive effects play different roles in the variation of bond strength for different metals. Importantly, our framework not only applies to both pure metals and MPEAs, but also unravels the distinction of the bond strength caused by elemental compositions, lattice structures, high-entropy, and amorphous effects. These findings build a physical picture across bond strength, grain-boundary energies and strength of metals by using easily accessible material properties and provide a robust method for the design of high-strength alloys.

Construction of Mn-Defective S/Mn0.4Cd0.6S for Promoting Photocatalytic N2 Reduction.

Improving catalytic performance by controlling the microstructure of materials has become a hot topic in the field of photocatalysis, such as the surface defect site, multistage layered morphology, and exposed crystal surface. Due to the differences in the metal atomic radius (Mn and Cd) and solubility product constant (MnS and CdS), Mn defect easily occurred in the S/Mn0.4Cd0.6S (S/0.4MCS) composite. To optimize the photocatalytic performance in N2 fixation, the effects of the synthesis conditions and reaction conditions for S/0.4MCS were explored and systematically studied. Combined with the experimental characterization and theoretical calculation, not only the photocatalytic reaction pathway but also the key steps of N2 reduction were explored. Moreover, the transfer mechanism of photogenerated charge carriers (PCCs) formed between S and 0.4MCS was studied, which enhanced the utilization rate of photogenerated electrons (e-) and holes (h+). This work detailedly discusses the relationship between microstructure and photocatalytic performance, which is beneficial for the design of efficient photocatalyst.

Синтез самоармованого порошкового матеріалу на основі високоентропійного сплаву

In this work, the formation of a self-reinforced HEA–WC powder material during the mechanical alloying (MA) of a mixture of elemental powders of the W-Fe-Co-Ni system in a planetary ball mill in a gasoline environment was investigated. X-ray diffraction (XRD), microstructural, and energy dispersive spectral (EDS) analysis revealed that after 20 hours of MA of the powders in a carbon-containing medium, a powder material based on a high-entropy alloy was formed. HEA based powder material contains two solid solutions with BCC and FCC crystal structure, as well as a carbide WC phase formed "in-situ" owing to the large negative value of the mixing enthalpy between carbon and tungsten. The “in-situ” formation of WC particles contributes to the enhancement of interfacial bonding with the metal matrix of the HEA. All phase components of the HEA–WC powder material are in the nanostructured state. The particles of the powder material have a close to spherical shape and a bimodal particle size distribution. The powder material consists of fine particles with a size of 1–10 μm and their agglomerates with a size up to 100 μm. The microstructure of the particles consists of the main gray phase of the BCC solid solution, dark spaces of the FCC solid solution and fine WC particles with a size of 0.1 μm to 1 μm evenly distributed in the HEA matrix. High-entropy alloys with the addition of carbon are promising in terms of practical application, because carbon, having a small atomic radius, dissolves as an interstitial element in the crystal lattice of the substitutional solid solutions of the HEA principal elements and, as a result, significantly affects their structure and phase composition, and, therefore, will contribute to the improvement of the mechanical properties of the self-reinforced powder material due to the effects of both solid-solution strengthening by interstitial atoms and the precipitation strengthening by the carbide phase particles.

Effects of Doping on Elastic Strain in Crystalline Ge-Sb-Te.

Phase-change random access memory (PcRAM) faces significant challenges due to the inherent instability of amorphous Ge2Sb2Te5 (GST). While doping has emerged as an effective method for amorphous stabilization, understanding the precise mechanisms of structural modification and their impact on material stability remains a critical challenge. This study provides a comprehensive investigation of elastic strain and stress in crystalline lattices induced by various dopants (C, N, and Al) through systematic measurements of film thickness changes during crystallization. Through detailed analysis of cross-sectional electron microscopy data and theoretical calculations, we reveal distinct behavior patterns between interstitial and substitutional dopants. Interstitial dopants (C and N) generate substantial elastic strain energy (~9 J/g) due to their smaller atomic radii (0.07-0.08 nm) and ability to occupy spaces between lattice sites. In contrast, substitutional dopants (Al) produce lower strain energy (~5 J/g) due to their similar atomic radius (0.14 nm) to host atoms. We demonstrate that N doping achieves higher elastic strain energy compared to C doping, attributed to its preferential formation of Ge-N bonds and resulting lattice distortions. The correlation between dopant properties, structural features, and induced strain energy provides quantitative insights for optimizing dopant selection. These findings establish a fundamental framework for understanding dopant-induced thermodynamic stabilization in GST materials, offering practical guidelines for enhancing the reliability and performance of next-generation PcRAM devices.

Synchronous Regulation of Ferroelectric and Spin Polarization for High‐Efficiency Photocatalytic Water Splitting

AbstractEnhancing the ferroelectric polarization field and tuning the electron spin polarization as novel approaches to improve photocatalytic performance have sparked considerable research interest. Obviously, a straightforward strategy to simultaneously regulate ferroelectric and spin polarization will have a very attractive application prospect. In this study, a series of Bi4NbO8Cl‐Ni photocatalysts are synthesized by doping different concentrations of magnetic element Ni into ferroelectric semiconductor Bi4NbO8Cl. Due to the significant difference in atomic radius, Ni doping induces greater structural distortion and enhances the deviation of positive and negative charge centers in the crystal, thereby resulting in a stronger ferroelectric polarization field. Moreover, spin polarization is induced in the electrons, and photogenerated carriers exhibit higher spatial separation efficiency under magnetic field. Thanks to the synchronous regulation of ferroelectric and spin polarization by Ni doping, the average rates of H2 and O2 production from photocatalytic water splitting over Bi4NbO8Cl‐Ni under visible light are 342.6 and 207.1 µmol g−1 h−1, respectively, which are 10.6 and 2.7 times those of pure Bi4NbO8Cl. Notably, under an applied magnetic field of 300 mT, the average production rates are further promoted up to 616.7 and 331.4 µmol g−1 h−1. This study offers a novel strategy to significantly improve photocatalytic performance.

Machine Learning Boosted Entropy-Engineered Synthesis of CuCo Nanometric Solid Solution Alloys for Near-100% Nitrate-to-Ammonia Selectivity.

Nanometric solid solution alloys are utilized in a broad range of fields, including catalysis, energy storage, medical application, and sensor technology. Unfortunately, the synthesis of these alloys becomes increasingly challenging as the disparity between the metal elements grows, due to differences in atomic sizes, melting points, and chemical affinities. This study utilized a data-driven approach incorporating sample balancing enhancement techniques and multilayer perceptron (MLP) algorithms to improve the model's ability to handle imbalanced data, significantly boosting the efficiency of experimental parameter optimization. Building on this enhanced data processing framework, we developed an entropy-engineered synthesis approach specifically designed to produce stable, nanometric copper and cobalt (CuCo) solid solution alloys. Under conditions of -0.425 V (vs RHE), the CuCo alloy exhibited nearly 100% Faraday efficiency (FE) and a high ammonia production rate of 232.17 mg h-1 mg-1. Stability tests in a simulated industrial environment showed that the catalyst maintained over 80% FE and an ammonia production rate exceeding 170 mg h-1 mg-1 over a testing period of 120 h, outperforming most reported catalysts. To delve deeper into the synergistic interaction mechanisms between Cu and Co, in situ Raman spectroscopy was utilized for real-time monitoring, and density functional theory (DFT) calculations further substantiated our findings. These results not only highlight the exceptional catalytic performance of the CuCo alloy but also reflect the effective electronic and energy interactions between the two metals.

An Investigation into Empirical Equations for Predicting Density and Packing Density Parameters Across Diverse Chemical Compositions: A Theoretical Approach

This work investigates an empirical equation for predicting the density and packing density parameter for different chemical combinations. The empirical equation suggested by Makishima and Mackenzie (1973) was employed to calculate the values of Vi, which indicates the packing density parameter and the equation proposed by Inaba and Fujino (2010) was utilized to calculate the density values. To determine the density values accurately, Vi is essential. This research focuses on revisiting the density model established by Inaba and Fujino (2010) to increase its accuracy. It is found that the ionic packing ratio is approximately constant and independent of the chemical composition. For different categories of glasses, including silicate, tellurite, and phosphate. The density has been meticulously calculated. These calculations rely on compositional parameters such as molecular weight, molecular fractions, and notably, the ionic radius of various metals. Density values are fundamental to the theoretical examination of radiation properties in the Phy-x/PSD software. Utilizing advanced tools and software allows for the prediction of glass physical parameters, which are indispensable in the fields of optical devices and electronic materials. This research establishes a connection between the composition of oxide glasses and their density. Consequently, it enhances our understanding of the properties and behaviour of these materials.

Phosphorus Doping Effects on the Optoelectronic Properties of K₂AgAsBr₆ Double Perovskites for Photovoltaic Applications

This work explores the modifications of optoelectronic properties in K₂AgAsBr₆ double perovskites induced by phosphorus doping. First-principles calculations using the CASTEP code with the PBE functional were carried out based on density functional theory (DFT). Our research investigates the electronic structure and optical behavior of the cubic Fm-3m phase of K₂AgAsBr₆, K₂AgAs₀.₈P₀.₂Br₆, and K₂AgAs₀.₆P₀.₄Br₆ to elucidate the impact of progressive phosphorus (P) substitution. P was chosen for its potential to modify the electronic structure due to its smaller atomic radius and different valence orbital energies compared to As. Our results reveal a systematic narrowing of the band gap with increasing P content, from 0.749 eV for the undoped compound to 0.587 eV for K₂AgAs₀.₈P₀.₂Br₆ and 0.424 eV for K₂AgAs₀.₆P₀.₄Br₆. This trend is attributed to the upward shift of the valence band maximum due to the higher energy of P 3p orbitals compared to As 4p orbitals. Analysis of the density of states confirms increased hybridization between P-p and As-p states at the valence band edge. Optical properties, including absorption coefficient, dielectric function, refractive index, and extinction coefficient, demonstrate a consistent red-shift and broadening of spectral features with P doping. Notably, P-substituted compounds exhibit enhanced absorption in the visible light region, with up to a 20% increase in the absorption coefficient at 550 nm for K₂AgAs₀.₆P₀.₄Br₆ compared to the undoped compound. This study reveals that elemental substitution offers a viable route to tailor optical and electronic properties of double perovskites, paving the way for the design of novel materials for next-generation photovoltaic and photoelectric devices.

Identifying determinants of γ’ phase coarsening behavior in Co/CoNi-based superalloys with explainable artificial intelligence (XAI)

The coarsening of γ’ phases in superalloys is influenced by multiple factors and significantly impacts mechanical properties, such as strength and creep resistance. While classical kinetic theory delineates the coarsening mechanisms of γ’ phases, it has limitations when excessive coarsening occurs. The challenge of identifying the pivotal factors that markedly affect the kinetic behavior of γ’ phase coarsening remains largely unresolved. This study utilized eXtreme Gradient Boosting (XGBoost) models to identify the CP and CPAE features that characterize the coarsening behavior of γ’ phases in Co/CoNi-based superalloys. Through meticulous analysis of CP features [aging temperature (T ), the atomic fraction of the Ti element (c Ti), the atomic fraction of the V element (c V), and the atomic fraction of the Ta element (c Ta)] and CPAE features [T , Young’s modulus (E ), electronegativity (EN ), atomic radius (r ), c Ti, the differences of atomic radius (σr ), and the differences of electronegativity (σEN )], we derived explicit mathematical expressions using symbolic classification approach, which offers improved interpretability compared to traditional black-box models. Our findings indicate that T , c Ti, c Ta, E and σr are dominant factors influencing γ’ coarsening behavior across different Co/CoNi-based superalloys. Notably, T , c Ti, c Ta and σr exhibit an inverse correlation with the γ’ coarsening behavior, whereas E shows a positive correlation. These insights provide valuable guidance for determining whether coarsening occurs in newly designed alloys. Furthermore, they facilitate the design of innovative anti-coarsening Co/CoNi-based superalloys. This knowledge is instrumental in enhancing alloy formulations, ensuring their performance and longevity in demanding environments where thermal stability is paramount.

Planar tetracoordinate beryllium in σ-aromatic Li4Be and Na4Be clusters: A missing member in first-octal row planar tetracoordinate family.

While planar tetracoordinate (pt) centers have been extensively explored from carbon to other octal-row elements or their heavier analogs, their counterparts involving alkali (A) and alkaline-earth metals (Ae) remain elusive due to the large atomic radius and absence of p orbitals. In this work, we found six hitherto unknown anionic ptA (A4A-) and neutral ptAe (A4Ae) centers through an extensive exploration of potential energy surfaces. The D4h-symmetry ptBe structures in Li4Be and Na4Be emerge as the lowest-energy configurations, and all the other ptA/ptAe structures are higher in energy or saddle points. The global-minimum ptBe structure can be described as Be- with a 2s12px12py1 electronic configuration, forming three σ electron sharing interactions with quartet Li4+/Na4+ motifs. The delocalized σ orbitals contribute to σ aromaticity, thereby enhancing the overall stability of these intriguing title ptBe species. Furthermore, these ptBe systems can be encapsulated within the [n]cycloparaphenylene nanoloop (n = 7, 8) thermochemically spontaneously, without any disturbance in planarity in the ptBe moiety, where the systems get stabilized by a predominant electrostatic interaction between Li4/Na4 and the nanoloop.

Dual‐Active Centers Linked by Oxygen Transfer for Enhancing Proximity‐Orientation Effect of Nanozyme

AbstractProximity‐orientation effects (POE) are essential for enzymes, as the spatial arrangement and orientation of catalytic sites strongly influence substrate binding and enhance catalysis. However, nanozymes often face limitations due to weak POE arising from uniform catalytic interfaces. Herein, Co atoms are incorporated into the lattice of Pt‐based nanozymes, exploiting differences in electron configuration and atomic radius between transition metals and noble metals. This integration induced lattice distortion formed new catalytic sites, and restricted the transport path, thereby enhancing the POE. Such transition metal‐doped alloy nanozyme (TANzyme) can be functioned as a self‐cascading nanozyme with artificial catalase‐oxidase activity. Density functional theory calculations demonstrated that the Pt site selectively decomposed H2O2 into H2O and O2, while the Co site specifically adsorbed O2 and conversed into superoxide anions, so an oxygen transfer path to connect dual‐active centers not only increased the POE but also improved catalytic specificity. Additionally, by leveraging the efficient catalytic property of TANzyme, a visual origami‐based sensing strategy is developed for the cascade detection of H2O2, nucleic acids, and marine toxins. This strategy highlighted the pivotal role of POE in enhancing the catalytic specificity of nanozymes, mimicking natural POE in enzymes, and providing a solution to design next‐generation nanozymes.

Ground state manipulation of atomic waveguide by a giant atom

Abstract In this paper, we study the ground state of a Rydberg atomic waveguide, which is coupled to a giant atom nonlocally via two or multiple sites. This many body system undergoes the degeneracy broken or energy level anti-crossing, depending on the parity of the size of the giant atom and the detuning between the atomic transition frequency and that of the driving field. Together with manipulation of the energy gap, we further show the interesting alternative atomic magnetization in the waveguide and the simultaneous suppression of the atomic magnetization and enhancement of atomic correlation.

Bayesian Analysis Reveals the Key to Extracting Pair Potentials from Neutron Scattering Data.

Learning interaction potentials from the structure factor is frequently seen as impractical due to accuracy constraints of neutron and X-ray scattering experiments. This study reexamines this historic inverse problem using Bayesian inference and probabilistic machine learning on a Mie fluid to elucidate how measurement noise impacts the accuracy of recovered potentials. To perform reliable potential reconstruction, we recommend that scattering data must have noise smaller than 0.005 up to ∼30 Å-1 at a standard bin width 0.05 Å-1. At uncertainties below this threshold, Mie potentials can be determined within approximately ±1.3 for the repulsive exponent, ±0.068 Å for atomic size, and ±0.024 kcal/mol in well-depth with 95% confidence. These findings highlight the potential of uniting scattering and machine learning to overcome a century-old physics problem, infer local atomic forces to serve as a vital benchmark for model validation, and enhance the accuracy of molecular simulations.

Optimal Dielectric Boundary for Binding Free Energy Estimates in the Implicit Solvent.

Accuracy of binding free energy calculations utilizing implicit solvent models is critically affected by parameters of the underlying dielectric boundary, specifically, the atomic and water probe radii. Here, a multidimensional optimization pipeline is used to find optimal atomic radii, specifically for binding calculations in the implicit solvent. To reduce overfitting, the optimization target includes separate, weighted contributions from both binding and hydration free energies. The resulting five-parameter radii set, OPT_BIND5D, is evaluated against experiment for binding free energies of 20 host-guest (H-G) systems, unrelated to the types of structures used in the training. The resulting accuracy for this H-G test set (root mean square error of 2.03 kcal/mol, mean signed error of -0.13 kcal/mol, mean absolute error of 1.68 kcal/mol, and Pearson's correlation of r = 0.79 with the experimental values) is on par with what can be expected from the fixed charge explicit solvent models. Best agreement with the experiment is achieved when the implicit salt concentration is set equal or close to the experimental conditions.