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DOE OSTI2026

Rational design of heterogeneous single-site catalysts via surface organometallic chemistry

Single-site heterogeneous catalysts offer an attractive route to unite the molecular precision of homogeneous catalysis with the durability and practical advantages of solids. Surface organometallic chemistry (SOMC) provides a particularly powerful strategy for this purpose by grafting molecular precursors onto tailored surfaces and converting support functionalities into ligand environments for isolated metal centers. As a result, SOMC brings the language and logic of coordination chemistry to heterogeneous catalysis, where the support becomes an integral part of the active site coordination sphere. This Review surveys recent progress in the rational design of SOMC-derived single-site catalysts, with emphasis on synthetic routes, post synthetic transformations, and the deliberate tuning of catalytic behavior through metal-support interactions. Discussions are made on how support identity, hydroxyl topology, acidity, and redox activity shape the geometry, electronic structure, and oxidation state of supported metal sites, as well as how these factors determine activity, selectivity, and stability. We also examine a central limitation of these systems: despite their molecularly informed design, supported single sites often exist as structurally distributed ensembles rather than uniform species, particularly on amorphous supports. This site heterogeneity, along with catalyst dynamics under operating conditions, remains a major barrier to definitive structure-activity relationships. Therefore, emerging approaches that combine advanced characterization, first-principles modeling, ensemble kinetics, and machine learning to resolve active-site structure and guide catalyst development are highlighted. Together, these advances position SOMC as a versatile coordination chemistry framework for the predictive design of heterogeneous catalysts with well-defined molecularly tailored active sites.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Sculpting Non-Machinable Porous Materials

The goal of this project was to establish the scientific basis for subtractive manufacturing (sculpting) of porous materials using ion beams. Using the catcher foil technique, complemented with molecular dynamics simulations, we studied the dependence of the sputtering yield of Ag and Au nanofoams as a function of foam monolith density, ion mass, and the beam incidence angle, and compared these dependencies to those measured for full-density solids. We found that the foam sputtering yield was considerably lower than for the full-density solid. The sputtering yield increased with beam incidence angle, and the open structure of the foam suppressed the development of collision cascades. We also found that the sputtering yield decreased with increasing foam density. The simulation revealed a significant redeposition of sputtered atoms in the foam.

36 MATERIALS SCIENCE↗

DOE OSTI2021

PYSEQM

PYSEQM is a package for performing semi-empirical quantum mechanical (SEQM) simulations on molecular systems utilizing PyTorch. SEQM simulations determine molecular properties (energy, electron density, dipole moment, ect.) by solving an approximate Schrödinger equation for the motions of electrons in a molecule. The use of PyTorch provides three specific advantages. First, it allows the calculations to be offloaded to GPU accelerators, giving an order of magnitude increase in speed. Second, back propagation is used to get atomic forces (derivative of the total energy with respect to atomic position) at the same computational cost as the energy calculation itself. Finally, the use of PyTorch makes for a natural interface to modern machine learning methods, which can be used to adjust the semi-empirical parameters build into SEQM methods. Additionally, PYSEQM implements various other optimizations for performing quantum mechanics based molecular dynamics, including SP2 for rapid GPU based solution of the self-consistent field algorithm, and the extended Lagrangian method for rapid QM-MD.

Nebgen, Benjamin↗

DOE OSTI2023

NbTaV_BCC_SolidSolution_128atoms_VASP6

We performed density functional theory (DFT) calculations for body-centered-cubic (BCC) structures with 128 lattices sites of solid solution ternary alloys niobium-tantalum-vanadium (Nb-Ta-V). The first-principle code that has been used to run the calculations is the closed-source Vienna Ab-Initio Simulation Package (VASP). The calculations have been collected by sampling chemical compositions across the entire compositional range. The chemical compositions have been sampled by progressively changing the number of atoms per constituent by 8. For each chemical composition of binaries and ternaries, the first-principle calculations have been run for 100 randomized arrangements of the constituents on the BCC lattice sites. We collected data for a total of 10,500 randomized atomic structures over 105 chemical compositions. The calculations have been collected on NERSC-Perlmutter using the VASP 6.3.2. The VASP calculations for every atomic structure have been performed in 2 main steps: 1. Starting from an ideal body-centered-cubic (BCC) structure, geometry optimization with low precision has been executed to perform a preliminary optimization of the atomic structure. The output for this calculations is available in the files 0.CONTCAR, 0.OUTCAR, rlx1.out. 2. Using the atomic structure resulting from the preliminary geometry optimization, a second geometry optimization has been performed using normal precision. The output for this calculations is available in the files CONTCAR, OUTCAR, rlx2.out, vaspout.h5, and vasprun.xml. Every chemical composition sampled across the composition range in the dataset has its own directory. The convention used to name the directories for ternary alloys is AXBYCZ, where A, B, and C refer to the constituents, and X, Y, and Z are positive integers that represent the number of atoms for each constituent and their values still sum up to 128. Each atomic structure associated with a specific chemical composition has its own sub-directory within the directory of the corresponding chemical composition. The sub-directories for each atomic structure for each chemical composition are named 'case-*', where * is a positive integer that spans all the values from 1 through 100, extremes included. The files contained in each sub-directory 'case-*' for each atomic structure are as follows: 1. INCAR: input file that contains various parameters and settings for controlling the behavior of the electronic structure calculations 2. 0.POSCAR: input file that defines the atomic structure of a system 3. 0.CONTCAR: output file that provides the atomic positions and cell parameters after the first geometry optimization has been run with the precision variable set to PREC=Low in the INCAR file 4. 0.OUTCAR: output file that contains detailed information about the progress of a calculation after the first geometry optimization has been run with the precision variable set to PREC=Low in the INCAR file 5. rlx1.out: file with diagnostic information about the execution of the first geometry optimization with precision variable set to PREC=Low in the INCAR file 6. POSCAR: input file that defines the atomic structure of a system after the first geometry optimization has been run at low precision. This represents the input for the second geometry optimization run with the precision variable set to PREC=Normal in the INCAR file 7. CONTCAR: output file that provides the atomic positions and cell parameters after the second geometry optimization has been run with the precision variable set to PREC=Normal in the INCAR file 8. OUTCARL: output file that contains detailed information about the progress of a calculation after the second geometry optimization has been run with the precision variable set to PREC=Normal in the INCAR file 9. rlx2.out: file with diagnostic information about the execution of the second geometry optimization with precision variable set to PREC=Normal in the INCAR file 10. vaspout.h5: hierarchical HDF5 file containing the inputs and outputs of a VASP calculation. To analyze the data in this file we recommend using py4vasp. This file is only produced if the VASP version used is compiled with HDF5 support 11. vasprun.xml: contains similar information to OUTCAR, but in an xml format. This research is sponsored by the Artificial Intelligence Initiative as part of the Laboratory Directed Research and Development (LDRD) Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the US Department of Energy under contract DE-AC05-00OR22725. This work used resources of the Oak Ridge Leadership Computing Facility, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725, under Directorate Discretionary awards MAT025 (Materials Science) and LRN026 (Machine Learning), and INCITE award MAT201. This work also used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, under award ERCAP0025216.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Modeling Nanoconfinement Effects Using Active Learning

Predicting the spatial configuration of gas in nanopores of is relevant in applications such as fluid flow forecasting and hydrocarbon reserves estimation. For example, shale reservoirs have suffered from computationally intractable multiscale problems, since fluid properties such as viscosity, density, and adsorption must be calculated by using expensive molecular dynamics (MD) simulations within each nanopore, whereas flow through these connected nanopores must be simulated at the micrometer scale. We utilize machine learning techniques to quickly and accurately model nanoscale confinement effects as an important step toward bridging the nano and micro scales. Our workflow is based on building and training physics-based deep-neural-networks models by learning from a database of MD calculations. The model accounts for the adsorption phenomenon by predicting the statistical distribution of gas inside nanopores. Because large databases of MD calculations are expensive to create, we investigate active learning (AL) as a data set construction strategy. In this workflow, new data are selected based on the model uncertainty via the query-by-committee approach. We show that our workflow obtains accurate models that generalize to real scanning electron microscopy geometries with 1/10th of the number of MD calculations required vs random data set generation. Our method enables the possibility of modeling nanoconfinement effects at the mesoscale, where complex connected sets of nanopores affect flow.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Advancing Multiscale Simulation of Plasma-Surface Interfaces

We report the development of an atomistic-informed, surface-state-dependent predictive model for particle exchange in a carbon-tungsten plasma-surface interface. The predictive model uses machine learning (ML) techniques to learn the energy and angular distributions for particle exchange and rate functions for surface state evolution from molecular dynamics simulations of cumulative bombardment of tungsten by energetic carbon ions. Each predictive component is sensitive to the energy and trajectory of incident plasma species and the surface state. The surface state is represented by a set of surface state descriptors, which were derived from the atomistic surface state for each independent carbon bombardment event. These descriptors are representative of the composition and degree of amorphization of the outermost angstrom of surface material and were chosen to optimize predictive performance for particle exchange at the interface. The distributions for particle exchange (reflection/sputtering) are demonstrated to vary with each surface state descriptor, motivating the development of surface-state-dependent particle exchange models for plasma simulations. The performance of various ML methods was compared, including polynomial quantile regression, artificial neural networks, k-nearest neighbors, and random forest algorithms, with polynomial regression performing the best for interpolation and extrapolation of learned relationships. In addition to the particle exchange model, a neutral network was developed and used to identify data sufficiency throughout surface descriptor space, which will enable real-time feedback during future data production to ensure data is produced where it is most needed, and we provide commentary on improvements to the data production workflow for future endeavors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1994

Program Computes Thermodynamic Functions

PAC91 is latest in PAC (Properties and Coefficients) series. Two principal features are to provide means of (1) generating theoretical thermodynamic functions from molecular constants and (2) least-squares fitting of these functions to empirical equations. PAC91 written in FORTRAN 77 to be machine-independent.

Mcbride, Bonnie J.↗

DOE OSTI2025

Treyson Ricks - Intern Showcase Poster

Quinone-based sorbents offer a tunable, energy-efficient route to electrochemical CO2 capture, but systematic guidance for molecular design is lacking. Here, we report a high-throughput computational workflow that combines density functional theory (DFT) screening with machine-learning (ML) modeling to evaluate CO2 binding thermodynamics across several quinone derivatives, spanning benzoquinones, naphthoquinones, and anthraquinones. In addition to using solvents to stabilize the quinone anion and dianion, we studied the effect of ion-pairing on the reduction potentials and the CO2 binding energy. Automated Python scripts handled geometry optimizations and adduct-formation energies on an HPC cluster, reducing manual effort significantly. This integrated platform can uncover structure–property relationships and enables rapid in silico evaluation of untested candidates. We present one example from our workflow to showcase the capability of using quinones with ion-pairing to effectively capture CO2. Our approach paves the way for the rational selection of optimal quinone sorbents and can be extended with experimental thermochemical and kinetic data, alternative redox cycles, and stability assessments to accelerate development of next-generation electrochemical CO2 capture materials.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗

DOE OSTI2020

Raman spectrum and polarizability of liquid water from deep neural networks

We introduce a scheme based on machine learning and deep neural networks to model the environmental dependence of the electronic polarizability in insulating materials. Application to liquid water shows that training the network with a relatively small number of molecular configurations is sufficient to predict the polarizability of arbitrary liquid configurations in close agreement with ab initio density functional theory calculations. In combination with a neural network representation of the interatomic potential energy surface, the scheme allows us to calculate the Raman spectra along 2-nanosecond classical trajectories at different temperatures for H 2 O and D 2 O. The vast gains in efficiency provided by the machine learning approach enable longer trajectories and larger system sizes relative to ab initio methods, reducing the statistical error and improving the resolution of the low-frequency Raman spectra. Decomposing the spectra into intramolecular and intermolecular contributions elucidates the mechanisms behind the temperature dependence of the low-frequency and stretch modes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Editorial: Artificial Intelligence and Machine Learning Applications in Plant Genomics and Genetics

In plants, as in other species, genotypic variation in combination with environmental variation leads to differences in the biochemical makeup of cells, measurable as molecular phenotypes. These in turn influence physiological and developmental traits such as organ formation and plant growth, and eventually traits relevant in agriculture, such as yield and stress tolerance. Thus, relating genotypes to phenotypes yields fundamental insights into the regulation of important processes in plant development and physiology, but also provides the ability to predict yield and quality traits in specific environments, which is essential in basic plant science and molecular breeding of resilient plants in changing environments.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2025

Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTi⁢O3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Multi-Omics Reveals Temporal Scales of Carbon Metabolism in Synechococcus Elongatus PCC 7942 Under Light Disturbance

Central carbon metabolism in model cyanobacteria involves multiple pathways to adapt to energy-light limitations across diel cycles. However, the success in mechanistic modeling for phenotypic prediction of the protein regulators in the metabolic state depends on capturing the vast possibilities emerging from multiple regulatory pathways in complex biological processes. Here, we developed a physics-informed machine learning approach based on energy-landscape concepts to predict regulatory proteins responding to cyclic circadian and unforeseen light perturbations in cyanobacterial metabolic networks. Our approach provides interpretable de novo models for inferring gene expression dynamics from Synechococcus elongatus over diel cycles and using redox proteome analysis to distinguish immediate light-responsive elements from circadian-regulated processes in carbon metabolism pathways. We identified distinct temporal signatures with the analysis of the redox proteome: there was an immediate shift in cysteine redox states accompanied by a limited change in protein abundance under constant illumination and after 2 hours of darkness. This discovery indicates that the generation of reductants coordinates photoinduced electron transport with redox metabolic pathways in two discernable molecular mechanisms: fast redox-based protein modifications occur immediately after the light disturbance, followed by slow transcriptional regulations across networks. This temporal regulation reveals how metabolic networks integrate rapid light responses with programmed circadian rhythms to maintain cellular homeostasis under the light-energy limitations over the diel cycle.

Biomolecular & subcellular processes↗

DOE OSTI2025

The design space of E(3)-equivariant atom-centred interatomic potentials

Abstract Molecular dynamics simulation is an important tool in computational materials science and chemistry, and in the past decade it has been revolutionized by machine learning. This rapid progress in machine learning interatomic potentials has produced a number of new architectures in just the past few years. Particularly notable among these are the atomic cluster expansion, which unified many of the earlier ideas around atom-density-based descriptors, and Neural Equivariant Interatomic Potentials (NequIP), a message-passing neural network with equivariant features that exhibited state-of-the-art accuracy at the time. Here we construct a mathematical framework that unifies these models: atomic cluster expansion is extended and recast as one layer of a multi-layer architecture, while the linearized version of NequIP is understood as a particular sparsification of a much larger polynomial model. Our framework also provides a practical tool for systematically probing different choices in this unified design space. An ablation study of NequIP, via a set of experiments looking at in- and out-of-domain accuracy and smooth extrapolation very far from the training data, sheds some light on which design choices are critical to achieving high accuracy. A much-simplified version of NequIP, which we call BOTnet (for body-ordered tensor network), has an interpretable architecture and maintains its accuracy on benchmark datasets.

Computer Science↗

DOE OSTI2024

A graph neural network-state predictive information bottleneck (GNN-SPIB) approach for learning molecular thermodynamics and kinetics

Molecular dynamics simulations offer detailed insights into atomic motions but face timescale limitations. Enhanced sampling methods have addressed these challenges but even with machine learning, they often rely on pre-selected expert-based features. Here, in this work, we present a Graph Neural Network-State Predictive Information Bottleneck (GNN-SPIB) framework, which combines graph neural networks and the state predictive information bottleneck to automatically learn low-dimensional representations directly from atomic coordinates. Tested on three benchmark systems, our approach predicts essential structural, thermodynamic and kinetic information for slow processes, demonstrating robustness across diverse systems. The method shows promise for complex systems, enabling effective enhanced sampling without requiring pre-defined reaction coordinates or input features.

Zou, Ziyue↗

DOE OSTI2023

Dimensionally reduced machine learning model for predicting single component octanol–water partition coefficients

Abstract MF-LOGP, a new method for determining a single component octanol–water partition coefficients ( $$LogP$$ LogP ) is presented which uses molecular formula as the only input. Octanol–water partition coefficients are useful in many applications, ranging from environmental fate and drug delivery. Currently, partition coefficients are either experimentally measured or predicted as a function of structural fragments, topological descriptors, or thermodynamic properties known or calculated from precise molecular structures. The MF-LOGP method presented here differs from classical methods as it does not require any structural information and uses molecular formula as the sole model input. MF-LOGP is therefore useful for situations in which the structure is unknown or where the use of a low dimensional, easily automatable, and computationally inexpensive calculations is required. MF-LOGP is a random forest algorithm that is trained and tested on 15,377 data points, using 10 features derived from the molecular formula to make $$LogP$$ LogP predictions. Using an independent validation set of 2713 data points, MF-LOGP was found to have an average $$RMSE$$ RMSE = 0.77 ± 0.007, $$MAE$$ MAE = 0.52 ± 0.003, and $${R}^{2}$$ R 2 = 0.83 ± 0.003. This performance fell within the spectrum of performances reported in the published literature for conventional higher dimensional models ( $$RMSE$$ RMSE = 0.42–1.54, $$MAE$$ MAE = 0.09–1.07, and $${R}^{2}$$ R 2 = 0.32–0.95). Compared with existing models, MF-LOGP requires a maximum of ten features and no structural information, thereby providing a practical and yet predictive tool. The development of MF-LOGP provides the groundwork for development of more physical prediction models leveraging big data analytical methods or complex multicomponent mixtures. Graphical Abstract

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Machine learning-enabled discovery of ionic liquid–solvent electrolytes exhibiting high ionic conductivity

Ionic liquids (ILs), which are a class of materials with versatile nature and growing popularity, are facing impediments toward widespread usage as electrolytes due to various factors such as low ionic conductivity, high viscosity, high market price etc. One of the ways these limitations can be addressed is by mixing ILs with a molecular solvent. In a combinatorial sense, there exists an immense number of specific IL–solvent combinations. An exhaustive experimental or even simulation-based investigation of the chemical space spanned by such combinations can be extremely time-consuming, expensive, and nearly impossible. An alternative approach is to employ machine learning-based models developed from available databases. Although there exists prior literature that integrates machine learning to investigate mixtures of specific solvents with ILs, these models lack generalization necessitating development of a large number of ML models to handle various solvents. To remedy this shortcoming, as a part of designing green electrolytes with high ionic conductivity that can have potential applications in next-generation batteries and solar cells, this work aims to develop a unified machine learning model to predict ionic conductivity of any IL–solvent mixture system. In this regard, three models, namely, Random Forest, extreme gradient boosting (XGBoost), and artificial neural network (ANN) were formulated using the NIST ILThermo database. The dataset contained 549 unique ionic liquids from 16 cation families and 81 unique solvents, representing a total of 23 712 datapoints. SHAPLEY additive explanation (SHAP) method was used to assess the impact of various features on model prediction and their significance was compared with literature to gain physical insight about the model behavior. Finally, using the developed models, approximately 2.5 million IL–solvent mixtures at five different compositions were screened at room temperature. The high-throughput screening yielded nearly 19 000 IL–solvent mixtures for which ionic conductivity was found to exceed the ionic conductivity of conventional Li-ion battery electrolyte.

25 ENERGY STORAGE↗

DOE OSTI2021

A comparative study of machine learning models for predicting the state of reactive mixing

Mixing phenomena are important mechanisms controlling flow, species transport, and reaction processes in fluids and porous media. Accurate predictions of reactive mixing are critical for many Earth and environmental science problems such as contaminant fate and remediation, macroalgae growth, and plankton biomass evolution. Here, to investigate the evolution of mixing dynamics under different scenarios (e.g., anisotropy, fluctuating velocity fields), a finite-element-based numerical model was built to solve the fast, irreversible bimolecular reaction-diffusion equations to simulate a range of reactive-mixing scenarios. A total of 2,315 simulations were performed using different sets of model input parameters comprising various spatial scales of vortex structures in the velocity field, time-scales associated with velocity oscillations, the perturbation parameter for the vortex-based velocity, anisotropic dispersion contrast (i.e., ratio of longitudinal-to-transverse dispersion), and molecular diffusion. The outputs comprised concentration profiles of reactants and products. The inputs to and outputs from these simulations were concatenated into feature and label matrices, respectively, to train 20 different machine learning (ML) models intended to emulate system behavior. These 20 ML emulators, based on linear methods, Bayesian methods, ensemble learning methods, and multilayer perceptrons (MLPs), were trained to classify the state of mixing and predict three quantities of interest (QoIs) characterizing species production, decay (i.e., average concentration, square of average concentration), and degree of mixing (i.e., variances of species concentration). Unsurprisingly, linear classifiers and regressors failed to reproduce the QoIs; however, ensemble methods (classifiers and regressors) and the MLP model accurately classified the state of reactive mixing and the QoIs. Among ensemble methods, random forest and decision-tree-based AdaBoost faithfully predicted the QoIs. At run time, trained ML emulators produced results times faster than the finite-element simulations. Due to their low computational expense and high accuracy, ensemble and MLP models are excellent emulators for these numerical simulations and great utilities in uncertainty quantification exercises, which can require 1,000s of forward model runs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Predicting Small Molecule Transfer Free Energies by Combining Molecular Dynamics Simulations and Deep Learning

Accurately predicting small molecule partitioning and hydrophobicity is critical in the drug discovery process. There are many heterogeneous chemical environments within a cell and entire human body. For example, drugs must be able to cross the hydrophobic cellular membrane to reach their intracellular targets, and hydrophobicity is an important driving force for drug–protein binding. Atomistic molecular dynamics (MD) simulations are routinely used to calculate free energies of small molecules binding to proteins, crossing lipid membranes, and solvation but are computationally expensive. Machine learning (ML) and empirical methods are also used throughout drug discovery but rely on experimental data, limiting the domain of applicability. We present atomistic MD simulations calculating 15,000 small molecule free energies of transfer from water to cyclohexane. This large data set is used to train ML models that predict the free energies of transfer. We show that a spatial graph neural network model achieves the highest accuracy, followed closely by a 3D-convolutional neural network, and shallow learning based on the chemical fingerprint is significantly less accurate. A mean absolute error of ~4 kJ/mol compared to the MD calculations was achieved for our best ML model. We also show that including data from the MD simulation improves the predictions, tests the transferability of each model to a diverse set of molecules, and show multitask learning improves the predictions. This work provides insight into the hydrophobicity of small molecules and ML cheminformatics modeling, and our data set will be useful for designing and testing future ML cheminformatics methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗