Ab Initio Model Research Articles

Vacuum-thermal alteration of lunar soil: Evidence from iron whiskers on troilite in Chang’e-5 samples

The formation of a unique microstructure of minerals on the surface of airless bodies is attributed to space weathering. However, it is difficult to distinguish the contributions of meteorite impacts and solar wind to the modification of lunar soil, resulting in limited research on the space weathering mechanism of airless bodies. The thermochemical reactivity of troilite can be used to distinguish the contributions of impact events and solar wind to the modification of lunar soil and provide evidence for space weathering of lunar soil. We examined the structure of a single particle of troilite in the Chang’e-5 lunar soil and determined whether an impact caused the thermal reaction. Microanalysis showed that troilite underwent substantial mass loss during thermal desulfurization, forming a crystallographically aligned porous structure with iron whiskers, an oxygen-rich layer, and other crystallographic and thermochemical evidence. We used an ab initio deep neural network model and thermodynamic calculations to conduct experiments and determine the anisotropy and crystal growth of troilite. The surface microstructure of troilite was transformed by the thermal reaction in the vacuum on the lunar surface. Similar structures have been found in near-Earth objects (NEOs), indicating that small bodies underwent the same impact-induced thermal events. Thus, thermal reactions in a vacuum are likely ubiquitous in the solar system and critical for space weathering alterations of the soil of airless bodies.

Comprehensive theoretical study of the effects of facet, oxygen vacancies, and surface strain on iron and cobalt impurities in different surfaces of anatase TiO2.

We report the results of systematic ab initio modelling of various configurations of iron and cobalt impurities embedded in the (110), (101), and (100) surfaces of anatase TiO2, with and without oxygen vacancies. The simulation results demonstrate that incorporation into interstitial voids at the surface level is significantly more favourable than other configurations for both iron and cobalt. The calculations also demonstrate the crucial effect of the facet as well as the lesser effects of other factors, such as vacancies and strain on the energetics of defect incorporation, magnetic moment, bandgap, and catalytic performance. It is further shown that there is no tendency towards the segregation or clustering of impurities on the surface. The calculated free energies of the hydrogen evolution reaction in acidic media predict that iron impurities embedded in the (101) surface of anatase TiO2 can be a competitive catalyst for this reaction.

LUMINI PACKAGE FOR AB INITIO MODELING OF DOSIMETRIC EXPERIMENTS

The paper presents the capabilities of the new Lumini code for ab initio modeling of dosimeter efficiency parameters. It is based on a scaling method that allows unifying the parameters of the kinetic model of the dosimeter without the numerous approximations used to interpret experimental results of thermal-, phosphorescence, and partial illumination of irradiated semiconductors. For the first time, the Monte Carlo method was used to consider the influence of statistical fluctuations in the energy and kinetic parameters of the model on the dosimetric parameters of typical dosimeters. As a first step, the data of Lumini's interpretation of the experimental TLD spectra of 500K dosimeters irradiated on the M-30 microtron was discussed.

Uncertainty quantification of collective nuclear observables from the chiral potential parametrization

Abstract We perform an uncertainty estimate of quadrupole moments and B(E2) transition rates that inform nuclear collectivity. In particular, we study the low-lying states of 6Li and 12C using the ab initio symmetry-adapted no-core shell model. For a narrow standard deviation of approximately 1% on the low-energy constants which parametrize high-precision chiral potentials, we find output standard deviations in the collective observables ranging from approximately 3-6%. The results mark the first step towards a rigorous uncertainty quantification of collectivity in nuclei that aims to account for all sources of uncertainty in ab initio descriptions of challenging collective and clustering observables.

Transfer learning for molecular property predictions from small datasets

Machine learning has emerged as a new tool in chemistry to bypass expensive experiments or quantum-chemical calculations, for example, in high-throughput screening applications. However, many machine learning studies rely on small datasets, making it difficult to efficiently implement powerful deep learning architectures such as message passing neural networks. In this study, we benchmark common machine learning models for the prediction of molecular properties on two small datasets, for which the best results are obtained with the message passing neural network PaiNN as well as SOAP molecular descriptors concatenated to a set of simple molecular descriptors tailored to gradient boosting with regression trees. To further improve the predictive capabilities of PaiNN, we present a transfer learning strategy that uses large datasets to pre-train the respective models and allows us to obtain more accurate models after fine-tuning on the original datasets. The pre-training labels are obtained from computationally cheap ab initio or semi-empirical models, and both datasets are normalized to mean zero and standard deviation one to align the labels’ distributions. This study covers two small chemistry datasets, the Harvard Organic Photovoltaics dataset (HOPV, HOMO–LUMO-gaps), for which excellent results are obtained, and the FreeSolv dataset (solvation energies), where this method is less successful, probably due to a complex underlying learning task and the dissimilar methods used to obtain pre-training and fine-tuning labels. Finally, we find that for the HOPV dataset, the final training results do not improve monotonically with the size of the pre-training dataset, but pre-training with fewer data points can lead to more biased pre-trained models and higher accuracy after fine-tuning.

New experimental measurements of the Collision Induced Absorptions of H2-H2 and H2-He in the 3600-5500 cm−1 spectral range from 120 to 500 K

The Collision-Induced Absorption (CIA) fundamental band of H2 has been studied in the 3600-5500 cm−1 spectral range for temperatures ranging from 120 to 500 K for both a pure H2 gas and a H2-He mixture. We used a simulation chamber called PASSxS (Planetary Atmosphere System Simulation x Spectroscopy) developed at INAF/ISAC which contains a Multi-Pass cell interfaced with a Fourier Spectrometer, aligned to reach an optical path of 3.28 m. The H2-H2 and H2-He binary absorption coefficients (BACs) have been derived for seven temperatures in the chosen range and provided in tabular form, including the unexplored high-temperature range above 300 K. We also calculated the integral of the H2-H2 and H2-He experimental BACs in the reduced 4000-5000 cm−1 spectral range, finding a linear trend with temperature in both cases. The integrals have also been computed with larger uncertainties for the whole band, in the total 3600-5500 cm−1 spectral range including the band's wings, partially affected by the water vapor absorption. The integrals calculated over the whole and reduced spectral ranges are collected in tables. In addition, we performed measurements with a H2-He mix for different mixing ratios to explore possible deviations from the linear combination of the BACs. The experimental BACs have been shown in comparison with Abel and Borysow's ab initio models for a temperature of about 400 K, resulting in a good agreement over almost the whole spectral range, with a maximum deviation around the main peak of the band. Data and models also show a good agreement in the linear trend of the integrated BACs with temperature, apart from the H2-H2 Borysow's BACs, which follow a quadratic trend. Finally, we resolved all the interference dips, which were not taken into account by the existing theoretical models.

Ab Initio Molecular Dynamics Simulations of Phosphocholine Interactions with a Calcium Oxalate Dihydrate (110) Surface.

We use ab initio modeling (CASTEP) to help elucidate the crystallization phenomena and chemistry behind kidney stone composition and formation. To explore the stone formation process, we have constructed a surface model of calcium oxalate dihydrate-the mineral most commonly found in patients with hypercalciuria and modeled stone growth, by simulating further calcium oxalate adsorption onto the surface (-7.446 eV, -0.065 eV/atom). Furthermore, urine analysis of kidney stone patients has previously revealed that their urine contains higher concentrations of phospholipids compared to healthy individuals. Therefore, to investigate the interactions between urinary macromolecules and the growing crystal surfaces at an atomic level, we have performed ab initio molecular dynamics simulations of phosphocholine adsorption on calcium oxalate surfaces. We have shown that the phosphocholine headgroups become entrapped within the growing crystal and the lowest energy structures (-18.008 eV, -0.0396 eV/atom) are those where the calcium oxalate dihydrate surfaces have become disrupted, with reorganization of their crystallographic structure. Urinary calculi (kidney stones) are a common ailment affecting around 10% of the world's population and resulting in nearly 90,000 finished consultant episodes (FCE) each year in the United Kingdom [Hospital Episode Statistics, Admitted Patient Care-England, 2011-12 NHS Digital, 2021-2022. https://digital.nhs.uk/data-and-information/publications/statistical/hospital-admitted-patient-care-activity/hospital-episode-statistics-admitted-patient-care-england-2011-12].

Ab initio computations from 78Ni towards 70Ca along neutron number N = 50

We present coupled-cluster computations of nuclei with neutron number N=50 “south” of 78Ni using nucleon-nucleon and three-nucleon forces from chiral effective field theory. We find an erosion of the magic number N=50 toward 70Ca manifesting itself by an onset of deformation and increased complexity in the ground states. For 78Ni, we predict a low-lying rotational band consistent with recent data, which up until now has been a challenge for ab initio nuclear models. Ground states are deformed in 76Fe, 74Cr, and 72Ti, although the spherical states are too close in energy to unambiguously identify the shape of the ground state within the uncertainty estimates. In 70Ca, the potential energy landscape from quadrupole-constrained Hartree-Fock computations flattens, and the deformation becomes less rigid. We also compute the low-lying spectra and B(E2) values for these neutron-rich N=50 nuclei.

Linking excess entropy and acentric factor in spherical fluids.

Introduced by Pitzer in 1955, the acentric factor (ω) has been used to evaluate a molecule's deviation from the corresponding state principle. Pitzer devised ω based on a concept called perfect liquid (or centric fluid), a hypothetical species perfectly adhering to this principle. However, its physical significance remains unclear. This work attempts to clarify the centric fluid from an excess entropy perspective. We observe that the excess entropy per particle of centric fluids approximates -kB at their critical points, akin to the communal entropy of an ideal gas in classical cell theory. We devise an excess entropy dissection and apply it to model fluids (square-well, Lennard-Jones, Mie n-6, and the two-body abinitio models) to interpret this similarity. The dissection method identifies both centricity-independent and centricity-dependent entropic features. Regardless of the acentric factor, the attractive interaction contribution to the excess entropy peaks at the density where local density is most enhanced due to the competition between the local attraction and critical fluctuations. However, only in centric fluids does the entropic contribution from the local attractive potential become comparable to that of the hard sphere exclusion, making the centric fluid more structured than acentric ones. These findings elucidate the physical significance of the centric fluid as a system of particles where the repulsive and attractive contributions to the excess entropy become equal at its gas-liquid criticality. We expect these findings to offer a way to find suitable intermolecular potentials and assess the physical adequacy of equations of state.

Simulation and modelling of the detergent corona around the membrane protein MhsT based on SAXS data

For membrane proteins, ab initio modelling based on a single curve of small-angle X-ray scattering (SAXS) is precluded by the presence of detergent molecules bound to the hydrophobic region of the protein. MEMPROT was developed for the modelling of protein–detergent complexes based on the SAXS curve of the complex, and on an a priori representation of the detergent corona by an elliptical semi-torus surrounding the protein. In previous studies, MEMPROT has succeeded in modelling several membrane proteins solubilized in n-dodecyl-β-maltopyranoside (DDM). However, it has never been tested on proteins solubilized in other detergents. To understand whether the geometrical shape currently parametrized in MEMPROT could be applied to a broader catalogue of protein–detergent complexes, here, MEMPROT was used to model the detergent corona around the multi-hydrophobic substrate transporter from Bacillus halodurans solubilized in four different detergents, namely DDM, n-decyl-β-maltopyranoside (DM), 4-cyclohexyl-1-butyl-β-D-maltoside (Cymal4) and decyl-maltose-neopentyl-glycol (DMNG). The study indicates a significant variation in detergent shapes, depending on the type of detergent. The modelling results suggest that the elliptical semi-torus with a circular closure is an excellent approximation for long-tailed detergents (DDM and DM) but leads to a slightly poorer agreement with the data for DMNG and Cymal4, which have a shorter hydrophobic tail, smaller than the half-width of the protein hydrophobic region. Here, for the latter, it is hypothesized that a corona with a flatter closure would be a better shape descriptor.

Ab initio study of Z(N) = 6 magicity* *This work is partially supported by the National Natural Science Foundation of China (Grant Nos. 12175280, 12250610193, 12375143, 11975282, 11705240, 11435014), the Natural Science Foundation of Gansu Province, China (Grant Nos. 20JR10RA067, 23JRRA675), the Chinese Academy of Sciences "Light of West China" Program, the Key Research Program of the Chinese Academy of

The existence of magic numbers of protons and neutrons in nuclei is essential for understanding the nuclear structure and fundamental nuclear forces. Over decades, researchers have conducted theoretical and experimental studies on a new magic number, Z(N)=6, focusing on observables such as radii, binding energy, electromagnetic transition, and nucleon separation energies. We performed ab initio no-core shell model calculations for the occupation numbers of the lowest single particle states in the ground states of Z(N)=6 and Z(N)=8 isotopes (isotones). The results of our calculations do not support Z(N)=6 as a magic number over a range of atomic numbers. However, 14C and 14O exhibit the characteristics of double-magic nuclei.

Substrate-Assisted Atomic Dispersion of Cobalt for Alkaline Water Electrolysis.

Atomically dispersed single-atom catalysts have recently attracted broad research interest due to their high atom efficiency and unique catalytic performance. In this study, atomic dispersion of cobalt is achieved using a chemical bath deposition method on a highly stable alkali titanate film (Ti/KTiO). These films were characterized using a variety of techniques, with atomic dispersion confirmed via grazing incidence X-ray absorption spectroscopy and ab initio modeling of single-atom systems. This modeling indicated that the alkali ion incorporated into the film facilitates atomic dispersion. Experimentally, the Ti/KTiO-supported Co(OH)2 catalysts exhibited remarkable electrochemical performance, with an overpotential of 163 mV to achieve a current density of 10 mA cm-2 with a catalyst loading of ∼0.1 mg cm-2 and high stability. These results show the potential of Ti/KTiO/Co(OH)2 catalysts for atomically efficient hydrogen production.

Enhanced particle acceleration in a pulsar wind interacting with a companion

Context. Pulsar winds have been shown to be preferred sites of particle acceleration and high-energy radiation. Numerous studies have been conducted to better characterize the general structure of such relativistic plasmas in isolated systems. However, many pulsars are found in binary systems and there are currently no ab initio models available that would include both the pulsar magnetosphere and the wind of the pulsar in interaction with a spherical companion. Aims. We investigate the interaction between a pulsar wind and a companion to probe the rearrangement of the pulsar wind, assess whether it leads to an enhancement of particle acceleration, and predict the high-energy radiative signature that stems from this interaction. We consider the regime where the companion is small enough to hold between two successive stripes of the wind. Methods. We performed two-dimensional (2D) equatorial particle-in-cell simulations of an inclined pulsar surrounded by a spherical, unmagnetized, perfectly conducting companion settled in its wind. Different runs correspond to different distances and sizes of the companion. Results. We find that the presence of the companion significantly alters the structure of the wind. When the companion lies beyond the fast magnetosonic point, a shock is established and the perturbations are advected in a cone behind the companion. We observe an enhancement of particle acceleration due to forced reconnection as the current sheet reaches the companion surface. Hence, high-energy synchrotron radiation is also amplified. The orbital light curves display two broad peaks reaching up to 14 times the high-energy pulsed flux emitted by an isolated pulsar magnetosphere. These effects increase with the growth of the companion size and with the decrease of the pulsar-companion separation. Conclusions. The present study suggests that a pulsar wind interacting with a companion induces a significant enhancement of high-energy radiation that takes the form of an orbital-modulated hollow cone of emission, which should be detectable by galactic-plane surveys, possibly with long-period radio transient counterparts.

Selective Synthesis and Crystal Chemistry of Candidate Rare-Earth Kitaev Materials: Honeycomb and Hyperhoneycomb Na2PrO3.

Rare-earth oxides have attracted interest as a platform for studying frustrated magnetism arising from bond-dependent anisotropic interactions. Ordered rock salt compounds Na2PrO3 crystallize in two polymorphs (α and β) comprising honeycomb and hyperhoneycomb lattices of octahedrally coordinated Pr4+ (4f1). Although possible realization of antiferromagnetic Kitaev interactions is anticipated for these phases on the basis of ab initio models, the air sensitivity of the two polymorphs has hampered reliable crystal growth and physical property measurements. Here, we have succeeded in preparing powder and single crystals of both α- and β-Na2PrO3 using modified synthetic procedures. Revised crystal structures for both polymorphs are obtained from refinement of untwinned single-crystal X-ray diffraction data.

AlphaFold2 Reveals Structural Patterns of Seasonal Haplotype Diversification in SARS-CoV-2 Nucleocapsid Protein Variants.

The COVID-19 pandemic saw the emergence of various Variants of Concern (VOCs) that took the world by storm, often replacing the ones that preceded them. The characteristic mutant constellations of these VOCs increased viral transmissibility and infectivity. Their origin and evolution remain puzzling. With the help of data mining efforts and the GISAID database, a chronology of 22 haplotypes described viral evolution up until 23 July 2023. Since the three-dimensional atomic structures of proteins corresponding to the identified haplotypes are not available, ab initio methods were here utilized. Regions of intrinsic disorder proved to be important for viral evolution, as evidenced by the targeted change to the nucleocapsid (N) protein at the sequence, structure, and biochemical levels. The linker region of the N-protein, which binds to the RNA genome and self-oligomerizes for efficient genome packaging, was greatly impacted by mutations throughout the pandemic, followed by changes in structure and intrinsic disorder. Remarkably, VOC constellations acted co-operatively to balance the more extreme effects of individual haplotypes. Our strategy of mapping the dynamic evolutionary landscape of genetically linked mutations to the N-protein structure demonstrates the utility of ab initio modeling and deep learning tools for therapeutic intervention.

Direct Observation of Competing M1 and M3 Transitions in ^{10}B.

Excited states in ^{10}B were populated with the ^{10}B(p,p^{'}γ)^{10}B^{*} reaction at 8.5MeV and their γ decay was investigated via coincidence γ-ray spectroscopy. The emitted γ rays were measured using large-volume LaBr_{3}:Ce and CeBr_{3} detectors placed in anti-Compton shields. This allowed the observation of weak γ-ray transitions, such as the M3 transition between the J^{π},T=0^{+},1 isobaric analog state (IAS) and the J^{π},T=3^{+},0 ground state and the E2 transition between the J^{π},T=2_{1}^{+},0 state and the IAS, i.e., performing measurements of branching ratios at the level of λ≥10^{-4}. For the first time in ^{10}B, the competing M1 and M3 transitions from the decay of the IAS have been observed in a γ spectroscopy experiment. The experimental results are compared with abinitio no-core shell model calculation using the newest version of the local position-space chiral N^{3}LO nucleon-nucleon interaction. The calculations reproduce correctly the ordering of the bound states in ^{10}B, and are in reasonable agreement with the observed branching ratios and reduced transition probabilities.

Making Peace with Random Phases: Ab Initio Conical Intersection Quantum Dynamics in Random Gauges.

Ab initio modeling of conical intersection wave packet dynamics is crucial for various photochemical, photophysical, and biological processes. However, adiabatic electronic states obtained from electronic structure computations involve random phases, or more generally, random gauge fixings, which cannot be directly used in the modeling of nonadiabatic wave packet simulations. Here we develop a random-gauge local diabatic representation that allows an exact modeling of conical intersection dynamics directly using the adiabatic electronic states with phases randomly assigned during the electronic structure computations. Its utility is demonstrated by an exact ab initio modeling of the two-dimensional Shin-Metiu model with and without an external magnetic field. Our results provide a simple approach to integrating the electronic structure computations into nonadiabatic quantum dynamics, thus paving the way for ab initio modeling of conical intersection dynamics.

Probing the Structure of the Electrochemical Interface Using in-Situ Surface X-Ray Scattering Techniques

Surface X-ray Scattering (SXS) or Surface X-ray Diffraction (SXRD) using synchrotron radiation is a powerful tool for the study of single crystal metal electrodes in the electrochemical environment. The single crystal surfaces have well defined adsorption sites and this enables fundamental links to be made between the surface atomic structure and the electrochemical response as has been illustrated, for example, in electrocatalysis [1]. As the development of electrochemical surface science progresses, there is a growing need for a comprehensive understanding of the atomic sturcture of electrochemical interface, both of the solid electrode and in the liquid electrolyte. This is because changes in the atomic structure across the interface induced by changes in the electric field can affect the system’s reactivity and stability [2]. These processes can be subtle and do not always involve the direct transfer of charge between electrode and electrolyte. Examples include metal surface relaxation and surface reconstruction, as well as charging of the double layer, which leads to rearrangement of the electrolyte side of the interface [3]. To further extend the fundamental understanding of the electrochemical interface structure, we have been developing resonant surface x-ray diffraction (RSXRD), a technique which combines diffraction with spectroscopy, to investigate the charge distribution in the double layer region. Combining experimental data and first-principles calculations, in-situ RSXRD was used to establish the charge distribution both at the Pt(111) electrode surface and at the Cu(001)-c(2x2)-Br electrode surface [5,6].In this talk results of recent studies of single crystal metal electrodes to probe the liquid side of the interface, particularly the role of cations in the electrochemical double layer, will be presented. The results include a systematic study of the low index Ag(hkl) surfaces to explore the role of the surface atomic geometry in determining the electrolyte layering and an exploration of the role that Cs+ cations play in forming the double layer structures on single crystal Au and Pt electrodes.[1] Y. Gründer and C. A. Lucas, Surface X-ray Diffraction Studies of Single Crystal Electrocatalysts, Nano Energy, 29, 378 (2016)[1] O. M. Magnussen and A. Groß, Toward an Atomic-Scale Understanding of Electrochemical Interface Structure and Dynamics. Journal of the American Chemical Society, 141, 4777 (2019)[2] Y. Gründer and C.A. Lucas, Potential-induced structural deformation at electrode surfaces. Current Opinion in Electrochemistry, 19, 168 (2020)[3] Y. Soldo-Olivier et al., Unraveling the Charge Distribution at the Metal-Electrolyte Interface Coupling in Situ Surface Resonant X-ray Diffraction with Ab Initio Calculations, ACS Catalysis, 12, 2375 (2022)[4] Y. Gründer et al., Charge Reorganization at the Adsorbate covered Electrode Surface probed through in-situ resonant X-ray Diffraction Combined with Ab-initio Modelling, Journal of Physical Chemistry C, 126, 4612 (2022)

AI-Driven Deep Learning Techniques in Protein Structure Prediction.

Protein structure prediction is important for understanding their function and behavior. This review study presents a comprehensive review of the computational models used in predicting protein structure. It covers the progression from established protein modeling to state-of-the-art artificial intelligence (AI) frameworks. The paper will start with a brief introduction to protein structures, protein modeling, and AI. The section on established protein modeling will discuss homology modeling, ab initio modeling, and threading. The next section is deep learning-based models. It introduces some state-of-the-art AI models, such as AlphaFold (AlphaFold, AlphaFold2, AlphaFold3), RoseTTAFold, ProteinBERT, etc. This section also discusses how AI techniques have been integrated into established frameworks like Swiss-Model, Rosetta, and I-TASSER. The model performance is compared using the rankings of CASP14 (Critical Assessment of Structure Prediction) and CASP15. CASP16 is ongoing, and its results are not included in this review. Continuous Automated Model EvaluatiOn (CAMEO) complements the biennial CASP experiment. Template modeling score (TM-score), global distance test total score (GDT_TS), and Local Distance Difference Test (lDDT) score are discussed too. This paper then acknowledges the ongoing difficulties in predicting protein structure and emphasizes the necessity of additional searches like dynamic protein behavior, conformational changes, and protein-protein interactions. In the application section, this paper introduces some applications in various fields like drug design, industry, education, and novel protein development. In summary, this paper provides a comprehensive overview of the latest advancements in established protein modeling and deep learning-based models for protein structure predictions. It emphasizes the significant advancements achieved by AI and identifies potential areas for further investigation.

High-temperature boron partitioning and isotope fractionation between basaltic melt and fluid

In the last two decades, boron has gained significance as a geochemical tracer in mantle studies, particularly related to fluid-mediated processes. In our investigation, we explore how boron and its stable isotopes distribute between basaltic melt and hydrous fluid under conditions relevant to magmatic degassing in the shallow crust (1000–1250 °C, 150–250 MPa). We utilized a synthetic MORB-like composition with added boric-acid isotope standard (NIST-SRM951a) and additional trace elements, subjecting it to varying pressure, temperature, and melt-fluid ratios using an internally heated pressure vessel. The B isotope composition in the quenched glasses were determined through femtosecond laser ablation coupled to a multi-collector inductively-coupled-plasma mass spectrometer. Our experiments revealed that, even at the highest temperatures, boron strongly partitions into the fluid phase, accompanied by significant B isotope fractionation. This leads to an enrichment of the heavy B isotope in the fluid, with a constrained Δ11Bmelt-fluid range of -1.7 ± 0.9‰, consistent with ab-initio modeling results. These findings highlight the potential of B isotopes to trace geochemical processes at elevated temperatures with \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\Delta}^{11}{{B}}_{melt-fluid}=2.913-9.693\\frac{{10}^{6}}{{{T}}^{2}}$$\\end{document}. Our results have implications for predicting the δ11B of degassed, water-bearing basaltic magmas and estimating the B isotope composition of their mantle source.