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Results for “Hydrogen bonded clusters”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Surpassing the stiffness-extensibility trade-off of elastomers via mastering the hydrogen-bonding clusters

The current paradigm of elastomer design typically falls into the trade-off between stiffness and extensibility. With a few reports on circumventing this trade-off behavior, e.g., increasing Young's modulus without sacrificing extensibility, the design principles to achieve improvements in both stiffness and extensibility have rarely been demonstrated. Herein, with a model system, i.e., cross-linked polydimethylsiloxane (PDMS) network, we demonstrate two approaches that can surpass the stiffness-extensibility trade-off and provide significant improvement in both parameters. Such an achievement is realized by introducing rationally arranged hydrogen-bonding units, i.e., ureidopyrimidone (UPy), leading to simultaneously improved Young's modulus and extensibility up to 158 and 3 times, respectively. Based on the experimental results, we also propose a microscopic picture of network rearrangement during the stretching process. Moreover, using this picture, we further improved Young's modulus of the elastic network without affecting its extensibility through mastering the distribution/topology of UPy clusters.

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

Determinants for proton location and electron coupled proton transfer in hydrogen bonded pentafluorophenol-anion clusters

This work aims to reveal the determinant factors for proton locations and electron coupled proton transfer (ECPT) in biologically relevant hydrogen bonded systems. Pentafluorophenol-anion clusters [C6F5O-•H+•A-]- are chosen to model active sites of biological functions, with the anion A- being systematically varied to ensure the proton affinities (PAs) of the anions well cover the referenced PA of C6F5O- from being appreciably smaller, similar, and to significantly larger. Negative ion photoelectron spectroscopy of these clusters provides spectroscopic evidence showing that proton location in the anionic state is largely following the PA prediction, while ECPT is observed only for the clusters with the anion possessing the electron binding energy (EBE) significantly larger than that of the referenced C6F5O-. Theoretical calculations suggest these clusters are stabilized by forming single strong hydrogen bond between donor and acceptor, and the associated charge and MO analyses fully support the experimental observations. The current holistic cluster model study indicates that PA is the right determinant that can be used to predict the proton location and describe hydrogen bonding structures, while both PA and EBE of anionic groups play important roles in facilitating ECPT process. This work was supported by U.S. Department of Energy (DOE), Office of Basic Energy Sciences, Division of Chemical Science, Geosciences, and Biosciences (X.-B.W.), and performed using EMSL, a national scientific user facility sponsored by DOE’s Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory, which is operated by Battelle Memorial Institute for the DOE. Part of this work was supported by the National Natural Science Foundation of China (No-11604046 for JZ; No. 11727810 for ZRS), as well as “Chenguang Program” by Shanghai Education Development Foundation, Shanghai Municipal Education Commission (No. 16CG38) and Natural Science Foundation of Shanghai (No. 16ZR1448100) (JZ).

Zhang, Jian↗
DOE OSTI2024

High-Pressure and Temperature Effects on the Clustering Ability of Monohydroxy Alcohols

This study examined the clustering behavior of monohydroxy alcohols, where hydrogen-bonded clusters of up to a hundred molecules on the nanoscale can form. By performing X-ray diffraction experiments at different temperatures and under high pressure, we investigated how these conditions affect the ability of alcohols to form clusters. The pioneering high-pressure experiment performed on liquid alcohols contributes to the emerging knowledge in this field. Implementation of molecular dynamics simulations yielded excellent agreement with the experimental results, enabling the analysis of theoretical models. Here we show that at the same global density achieved either by alteration of pressure or temperature, the local aggregation of molecules at the nanoscale may significantly differ. Surprisingly, high pressure not only promotes the formation of hydrogen-bonded clusters but also induces the serious reorganization of molecules. This research represents a milestone in understanding association under extreme thermodynamic conditions in other hydrogen bonding systems such as water.

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

Characterization of ferredoxins involved in electron transfer pathways for nitrogen fixation implicates differences in electronic structure in tuning 2[4Fe 4S] Fd activity

Ferredoxins (Fds) are small proteins which shuttle electrons to pathways like biological nitrogen fixation. Physical properties tune the reactivity of Fds with different pathways, but knowledge on how these properties can be manipulated to engineer new electron transfer pathways is lacking. Recently, we showed that an evolved strain of Rhodopseudomonas palustris uses a new electron transfer pathway for nitrogen fixation. This pathway involves a variant of the primary Fd of nitrogen fixation in R. palustris, Fer1, in which threonine at position 11 is substituted for isoleucine (Fer1 T11I ). To understand why this substitution in Fer1 enables more efficient electron transfer, we used in vivo and in vitro methods to characterize Fer1 and Fer1 T11I . Electrochemical characterization revealed both Fer1 and Fer1 T11I have similar redox transitions (–480 mV and – 550 mV), indicating the reduction potential was unaffected despite the proximity of T11 to an iron-sulfur (Fe—S) cluster of Fer1. Additionally, disruption of hydrogen bonding around an Fe—S cluster in Fer1 by substituting threonine with alanine (T11A) or valine (T11V) did not increase nitrogenase activity, indicating that disruption of hydrogen bonding does not explain the difference in activity observed for Fer1 T11I . Electron paramagnetic resonance spectroscopy studies revealed key differences in the electronic structure of Fer1 and Fer1 T11I , which indicate changes to the high spin states and/or spin-spin coupling between the Fe—S clusters of Fer1. Finally, our data implicates these electronic structure differences in facilitating electron flow and sets a foundation for further investigations to understand the connection between these properties and intermolecular electron transfer.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Self-interaction correction in water–ion clusters

We study the importance of self-interaction errors in density functional approximations for various water–ion clusters. We have employed the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method in conjunction with LSDA, PBE, and SCAN to describe binding energies of hydrogen-bonded water–ion clusters, i.e., water–hydronium, water– hydroxide, water–halide, as well as non-hydrogen-bonded water–alkali clusters. In the hydrogen-bonded water–ion clusters, the building blocks are linked by hydrogen atoms, although the links are much stronger and longer-ranged than the normal hydrogen bonds between water molecules, because the monopole on the ion interacts with both permanent and induced dipoles on the water molecules. We find that self-interaction errors overbind the hydrogen-bonded water– ion clusters and that FLOSIC reduces the error and brings the binding energies into closer agreement with higher–level calculations. Here, the non-hydrogen-bonded water–alkali clusters are not significantly affected by self-interaction errors. Self-interaction corrected PBE predicts the lowest mean unsigned error in binding energies (≤ 50 meV/H 2 O) for hydrogen-bonded water–ion clusters. Self-interaction errors are also largely dependent on the cluster size, and FLOSIC does not accurately capture the subtle variation in all clusters, indicating the need for further refinement.

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

Competition between Water–Water Hydrogen Bonds and Water–π Bonds in Pyrene–Water Cluster Anions

We present infrared spectra and density functional theory calculations of hydrated pyrene anion clusters with up to four water molecules. The experimental spectra were acquired using infrared Ar messenger photodissociation spectroscopy. Water molecules form clusters on the surface of the pyrene, forming hydrogen bonds with the pi-system. The structures of the water clusters and their interaction with the π-system are encoded in the OH stretching vibrational modes. Here, we find that the interactions between water molecules are stronger than they are between water molecules and the π-system. While all clusters show multiple conformers, three- and four-membered rings are the lowest energy structures in the larger hydrates.

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

Passivating Nucleobases Bring Charge Transfer Character to Optically Active Transitions in Small Silver Nanoclusters

DNA-wrapped silver nanoclusters (DNA–AgNCs) are known for their efficient luminescence. However, their emission is highly sensitive to the DNA sequence, the cluster size, and its charge state. To get better insights into photophysics of these hybrid systems, simulations based on density functional theory (DFT) are performed. Our calculations elucidate the effect of the structural conformations, charges, solvent polarity, and passivating bases on optical spectra of DNA–AgNCs containing five and six Ag atoms. It is found that inclusion of water in calculations as a polar solvent media results in stabilization of nonplanar conformations of base-passivated clusters, while their planar conformations are more stable in vacuum, similar to the bare Ag5 and Ag6 clusters. Cytosines and guanines interact with the cluster twice stronger than thymines, due to their larger dipole moments. In addition to the base–cluster interactions, hydrogen bonds between bases notably contribute to the structure stabilization. While the relative intensity, line width, and the energy of absorption peaks are slightly changing depending on the cluster charge, conformations, and base types, the overall spectral shape with five well-resolved bands at 2.5–5.5 eV is consistent for all structures. Independent of the passivating bases and the cluster size and charge, the low energy optical transitions at 2.5–3.5 eV exhibit a metal to ligand charge transfer (MLCT) character with the main contribution emerging from Ag-core to the bases. Cytosines facilitate the MLCT character to a larger degree comparing to the other bases. However, the doublet transitions in clusters with the open shell electronic structure (Ag5 and Ag6 + ) result in appearance of additional red-shifted (<2.5 eV) and optically weak band with negligible MLCT character. The passivated clusters with the closed shell electronic structure (Ag5 + and Ag6) exhibit higher optical intensity of their lowest transitions with much higher MLCT contribution, thus having better potential for emission, than their open shell counterparts.

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

The effect of hydrogen-bonding on flavin’s infrared absorption spectrum

Cluster and continuum solvation computational models are employed to model the effect of hydrogen bonding interactions on the vibrational modes of lumiflavin. Calculated spectra were compared to experimental Fourier-transform infrared (FTIR) spectra in the diagnostic 1450–1800 cm –1 range, where intense V C=C , V C=N , V C 2 =O , and V C 4 =O stretching modes of flavin’s isoalloxazine ring are found. Local mode analysis is used to describe the strength of hydrogen-bonding in cluster models. The computations indicate that V C=C and V C=N mode frequencies are relatively insensitive to intermolecular interactions while the V C 2 =O and V C 4 =O modes are sensitive to direct (and also indirect for V C 2 =O ) hydrogen-bonding interactions. Although flavin is neutral, basis sets without the diffuse functions provide incorrect relative frequencies and intensities. The 6-31+G* basis set is found to be adequate for this system, and there is limited benefit to considering larger basis sets. Calculated vibrational mode frequencies agree with experimentally determined frequencies in solution when cluster models with multiple water molecules are used. Accurate simulation of relative FTIR band intensities, on the other hand, requires a continuum (or possibly quantum mechanical/molecular mechanical) model that accounts for long-range electrostatic effects. Lastly, an experimental peak at ca. 1624 cm –1 that is typically assigned to the V C 2 =O vibrational stretching mode has a complicated shape that suggests multiple underlying contributions. Our calculations show that this band has contributions from both the C 6 –C 7 and C 2 = O stretching vibrations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Guanosine Dianions Hydrated by One to Four Water Molecules

Intermolecular interactions as those present in molecule…water complexes may profoundly influence the physico-chemical properties of molecules. Here, we carried out an experimentally-computational study on the doubly-deprotonated guanosine monophosphate…water clusters, [dGMP-2H] 2- •nH 2 O (n=1–4), using a combination of negative anion photoelectron spectroscopy (NIPES) with molecular dynamics (MD) and quantum chemical (QM) calculations. Successive addition of water molecules to [dGMP-2H] 2- increases the experimental adiabatic detachment (ADE) and vertical detachment energy (VDE) by 0.5 to 0.1 eV, depending on the cluster size. In order to choose the representative conformations, we combined MD simulations with a clustering procedure to identify low energy geometries for which ADEs and VDEs were computed at the CAM-B3LYP/6-31++G(d,p) level. Our results demonstrate that the assumed approach lead to the sound geometries and energetics of the studied micro-solvates since the calculated ADEs and VDEs are in pretty good agreement with the experimental characteristics. The evolution of hydrogen bonding with cluster size indicates possibility of the occurrence of proton transfer for clusters comprising a larger number of water molecules.

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

Spin-orbit coupling in molecular complexes beyond van der Waals regime: Key factors for further splitting of 2 P 3/2 ground state

Here, we report a joint spectroscopic and theoretical study probing spin-orbit coupling (SOC) in a variety of molecular complexes between an iodine atom and a ligand (L) with L ranging from Ar, HF to formic/acetic acids, and glycine/N-methylated glycine derivatives. Cryogenic photoelectron spectroscopy of L·I - (L=HCOOH, CH 3 COOH) reveals three distinct peaks, identified as three SOC states, denoted as X(1/2), A(3/2), and B(l/2) for the corresponding neutrals. The X and A separation ΔE XA is measured to be 0.10 eV for both, whereas the X and B gap ΔE XB is 0.98 and 0.97 eV for formic and acetic acid, respectively. These new ΔE XA values are compared with the previously reported values for the molecular complexes L·I· with L=Ar, HF, glycine, and A-methylated glycines. All together these complexes encompass a diversity of intermolecular interactions, from van der Waals to weak and strong hydrogen bonding. While the ΔE XB remains similar, the ΔE XA is shown to be extremely sensitive to the type of ligands and interactions, spanning from 5 meV to 150 meV. High-level relativistic quantum calculations including explicit SOC formulism nicely reproduce all experimental SOC splitting. A direct correlation between the magnitude of ΔE XA with the intermolecular interaction strength or bond distance of the neutral complexes—the stronger interaction (shorter bond length), the greater splitting, is established.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Breaking covalent bonds in the context of the many-body expansion (MBE). I. The purported “first row anomaly” in XH n (X = C, Si, Ge, Sn; n = 1–4)

We present a new, novel implementation of the Many-Body Expansion (MBE) to account for the breaking of covalent bonds, thus extending the range of applications from its previous popular usage in the breaking of hydrogen bonds in clusters to molecules. A central concept of the new implementation is the in situ atomic electronic state of an atom in a molecule that casts the one-body term as the energy required to promote it to that state from its ground state. The rest of the terms correspond to the individual diatomic, triatomic, etc., fragments. Its application to the atomization energies of the XH n series, X = C, Si, Ge, Sn and n = 1–4, suggests that the (negative, stabilizing) 2-B is by far the largest term in the MBE with the higher order terms oscillating between positive and negative values and decreasing dramatically in size with increasing rank of the expansion. The analysis offers an alternative explanation for the purported “first row anomaly” in the incremental H n–1 X–H bond energies seen when these energies are evaluated with respect to the lowest energy among the states of the XH n molecules. Due to the “flipping” of the ground/first excited state between CH 2 ( 3 B 1 ground state, 1 A 1 first excited state) and XH 2 , X = Si, Ge, Sn ( 1 A 1 ground state, 3 B 1 first excited state), the overall picture does not exhibit a “first row anomaly” when the incremental bond energies are evaluated with respect to the molecular states having the same in situ atomic states.

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

Energetics of water expulsion from intervening space between two particles during aggregation

Solvent expulsion away from an intervening region between two approaching particles plays important roles in particle aggregation yet remains poorly understood. Here, in this work, we use metadynamics molecular simulations to study the free energy landscape of removing water molecules from gibbsite and pyrophyllite slit pores representing the confined spaces between two approaching particles. For gibbsite, removing water from the intervening region is both entropically and enthalpically unfavorable. The closer the particles approach each other, the harder it is to expel water molecules. For pyrophyllite, water expulsion is spontaneous, which is different from the gibbsite system. A smaller pore makes the water removal more favorable. When water is being drained from the intervening region, single chains of water molecules are observed in gibbsite pore, while in pyrophyllite pore water cluster is usually observed. Water-gibbsite hydrogen bonds help stabilize water chains, while water forms clusters in pyrophyllite pore to maximize the number of hydrogen bonds among themselves. This work provides the first assessment into the energetics and structure of water being drained from the intervening region between two approaching particles during oriented attachment and aggregation.

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

Remotely Bonded Bridging Dioxygen Ligands Enhance Hydrogen Transfer in a Silica-Supported Tetrairidium Cluster Catalyst

A longstanding challenge in catalysis by noble metals has been to understand the origin of enhancements of rates of hydrogen transfer that result from bonding of oxygen near metal sites. We investigated structurally well-defined catalysts consisting of supported tetrairidium carbonyl clusters with single-atom (apical iridium) catalytic sites for ethylene hydrogenation. Reaction of the clusters with ethylene and H 2 followed by O 2 led to the onset of catalytic activity as a terminal CO ligand at each apical Ir atom was removed and bridging dioxygen ligands replaced CO ligands at neighboring (basal-plane) sites. The presence of the dioxygen ligands caused a 6-fold increase in the catalytic reaction rate, which is explained by the electron-withdrawing capability induced by the bridging dioxygen ligands, consistent with the inference that reductive elimination is rate determining. Electronic structure calculations demonstrate an additional role of the dioxygen ligands, changing the mechanism of hydrogen transfer from that involving equatorial hydride ligands to that involving bridging hydride ligands. This mechanism is made evident by an inverse kinetic isotope effect observed in ethylene hydrogenation reactions with H 2 and, alternatively, with D 2 on the cluster incorporating the dioxygen ligands, and is a consequence of quasi-equilibrated hydrogen transfer in this catalyst. The same mechanism accounts for rate enhancements induced by the bridging dioxygen ligands for the catalytic reaction of H 2 with D 2 to give HD. Here, we posit that the mechanism involving bridging hydride ligands facilitated by oxygen ligands remote from the catalytic site may have some generality in catalysis by oxide-supported noble metals.

02 PETROLEUM↗
DOE OSTI2026

Hydrophobic Metal–Organic Frameworks Enable Superior High-Pressure Ammonia Storage through Geometric Design

Hydrophobic metal–organic frameworks (MOFs) are typically overlooked for ammonia storage due to weak host–guest interactions. Here, we demonstrate that four structurally analogous aluminum-based MOFs exhibit a counterintuitive behavior whereby framework geometry, rather than ligand hydrophilicity, determines high-pressure NH 3 adsorption performance. The hydrophobic CAU-23 achieved an exceptional capacity matching hydrophilic analogs despite its poor low-pressure uptake. This pressure-dependent enhancement stems from the unique 4-cis-4-trans geometry of CAU-23 compared to the purely cis arrangement of MIL-160 and KMF-1 and the alternating cis-trans configuration of MOF-303. Critically, CAU-23 retained 95% capacity over three high-pressure cycles, whereas hydrophilic MOFs suffered 39–46% irreversible losses due to strong NH 3 -framework interactions that compromise structural integrity. Grand canonical Monte Carlo simulations reveal that high pressure enables NH 3 clustering through intermolecular hydrogen bonding, bypassing the need for strong host–guest interactions. High-pressure powder X-ray diffraction measurements confirm the exceptional mechanical resilience of CAU-23, showing complete structural recovery upon decompression despite exhibiting the highest pressure sensitivity among the studied MOFs. An extended analog, HE-CAU-23, validates this design principle with further enhanced capacity. Furthermore, these findings reveal a paradigm shift toward hydrophobic MOFs with optimized geometry for high-performance and regenerable gas storage applications.

MOFs↗
DOE OSTI2020

Microsolvation in V + (H 2 O) n Clusters Studied with Selected-Ion Infrared Spectroscopy

Gas phase ion-molecule clusters of the form V + (H 2 O) n (n = 1-30) are produced by laser vaporization in a supersonic expansion. These ions are analyzed and mass-selected with a time-of-flight mass spectrometer and investigated with infrared laser photodissociation spectroscopy. The small clusters (n ≤ 7) are studied with argon tagging, while the larger clusters are studied via the elimination of water molecules. The vibrational spectra for the small clusters include only free O-H stretching vibrations, while larger clusters exhibit red-shifted hydrogen bonding vibrations. The spectral patterns reveal that the coordination around V + ions is completed with four water molecules. A symmetric square-planar structure forms for the n = 4 ion, and this becomes the core ion in larger structures. Clusters up to n = 8 have mostly two-dimensional structures, but hydrogen bonding networks evolve to three-dimensional structures in larger clusters. The free O-H vibration of AAD (acceptor-acceptor-donor) coordinated surface molecules converges to a frequency near that of bulk water by the cluster size of n = 30. However, the splitting of this vibration for AAD- versus AD-coordinated molecules is still different compared to other singly-charged or doubly-charged cation-water clusters. Finally, this indicates that cation identity and charge-site location in the cluster can produce discernible spectral differences for clusters in this size range.

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

An extensive assessment of the performance of pairwise and many-body interaction potentials in reproducing ab initio benchmark binding energies for water clusters n = 2–25

We assess the performance of 7 pairwise additive (TIP3P, TIP4P, TIP4P-ice, TIP5P, OPC, SPC, SPC/E) and 8 families of many-body potentials (q-AQUA, HIPPO, AMOEBA, EFP, TTM, WHBB, MB-pol, MB-UCB) in reproducing high-level ab initio benchmark values, CCSD(T) or MP2 at the complete basis set (CBS) limit for the binding energy and the many-body expansion (MBE) of water clusters n = 2–11, 16–17, 20, 25. By including a large range of cluster sizes having dissimilar hydrogen bonding networks, we obtain an understanding of how these potentials perform for different hydrogen bonding arrangements that are mostly outside of their parameterization range. While it is appropriate to compare the results of ab initio based many-body potentials directly to the electronic binding energies (D e 's), the pairwise additive ones are compared to the enthalpies at T = 298 K, ΔH(298 K), as the latter class of force fields are parametrized to reproduce enthalpies (implicitly accounting for zero-point energy corrections) rather than binding energies. We find that all pairwise additive potentials considered overestimate the reference ΔH values for the n = 2–25 clusters by >13%. For the water dimer (n = 2) in particular, the errors are in the range 83–119% for the pairwise additive potentials studied since these are based on an effective rather than the true 2-body interaction specifically designed as a means of partially accounting for the missing many-body terms. This stronger 2-body interaction is achieved by an enhanced monomer dipole moment that mimics its increase from the gas phase monomer to the condensed phase value. Indeed, for cluster sizes n ≥ 4 the percent deviations become slightly smaller (albeit all exceeding 13%). In contrast, we find that the many-body potentials perform more accurately in reproducing the electronic binding energies (D e 's) throughout the entire cluster range (n = 2–25), all reproducing the ab initio benchmark binding energies within ±7% of the respective CBS values. We further assess the ability of a subset of the many-body potentials (MB-UCB, q-AQUA, MB-pol, and TTM2.1-F) to also reproduce the magnitude of the ab initio many-body energy terms for water cluster sizes n = 7, 10, 16 and 17. The potentials show an overall good agreement with the available benchmark values. However, we identify characteristic differences upon comparing the many-body terms at both the ab initio-optimized geometries and the respective potential-optimized geometries to the reference ab initio values. Additionally, by applying this analysis to a wide range of cluster sizes, trends in the MBE of the potentials with increasing cluster size can be identified. Finally, in an attempt to draw a parallel between the pairwise additive and many-body potentials, we report the analysis of the individual molecular dipole moments for water clusters with 1 to ~4 solvation shells with the TTM2.1-F potential. We find that the internally solvated water molecules have in general a larger molecular dipole moment ranging from 2.6–3.0 D. This justifies the use of an enhanced, with respect to the gas-phase value, molecular dipole moment for the pairwise additive potentials, which is intended to fold in the many body terms into an effective (enhanced) pairwise interaction through the choice of the charges. These results have important implications for the development of future generations of efficient, transferable, and highly accurate classical interaction potentials in both the pairwise additive and many-body categories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗