Zero-point Energy Differences Research Articles

Proton permeation and selective separation of hydrogen isotopes through fullerene nanocages (X12Y12): A DFT insights

To resolve the problem of mobile electrolytes for the permeation of hydrogen isotopes in fuel cells, we have studied herein heteronuclear fullerene nanocages (Al12N12, Al12P12, B12N12, and B12P12) for the separation and permeation of hydrogen isotopes. The separation and permeation of fullerene nanocages for hydrogen isotopes are studied at ωB97XD functional of DFT along with 6–31g (d,p) pople basis set. Zero-point energy (ZPE) is calculated for Protium (H+) and its heavier isotopes including deuterium (D+) and tritium (T+). The Arrhenius equation is employed to calculate the selectivity of protium to deuterium (H+/D+) and deuterium to tritium (H+/T+) isotopes. The selectivity is calculated by using the zero-point energy difference (ZPE) of protium (H+) to its heavier isotopes. The proposed fullerene nanocages estimated better selectivity for proton isotopes. The phosphide-based nanocages (Al12P12, B12P12) provide superior selectivity values of H+/D+ and H+/T+ compared to nitrogen-based nanocages (Al12N12, B12N12). This study provides insights into separation pathways for proton isotopes through nanocages for many industrial applications in the energy sector.

Improving the Accuracy in the Prediction of Transition-Metal Spin-State Energetics Using a Robust Variation-Based Approach: Density Functional Theory, CASPT2 and MC-PDFT Applied to the Case Study of Tris-Diimine Fe(II) Complexes.

Designing ligands for transition metal complexes with a specified low-spin, high-spin or spin-crossover behavior is challenging. A major advance was recently made by Phan et al. [J. Am. Chem. Soc. 2017, 139, 6437-6447] who showed that the spin state of a homoleptic tris-diimine Fe(II) complex can be predicted from the N-N distance in the free diimine. They could thus predict the change in magnetic behavior on passing from the complexes of 2,2'-bipyridine (bpy), 2,2'-biimidazole (bim) and 2,2'-bis-2-imidazoline (bimz) ligands to those obtained with the modified analogs 4,5-diazafluoren-9-one (dafo), 1,1'-(α,α'-o-xylyl)-2,2'-bisimidazole (xbim) and 2,3,5,6,8,9-hexahydrodiimidazo[1,2-a:2', 1'-c]pyrazine (etbimz), respectively. Theoretically, the challenge lies in the accurate determination of the HS-LS zero-point energy difference ΔEHL°. The issue can be circumvented by using a variation-based approach, wherein ΔEHL° is not directly evaluated but obtained from the estimate of its variation Δ(ΔEHL°) in series of related systems, which include one whose ΔEHL° is accurately known [Phys. Chem. Chem. Phys. 2013, 15, 3752-3763; J. Phys. Chem. A 2022, 126, 6221-6235]. In this study, density functional theory (DFT), second-order multireference perturbation theory in its CASPT2 formulation, multiconfigurational pair DFT (MC-PDFT) and its hybrid formulation (HMC-PDFT) have been applied to the determination of Δ(ΔEHL°) in the pairs of complexes , , , and , . In DFT, we used several semilocal functionals and their global hybrids, as well as their D2, D3, D3BJ and D4 dispersion-corrected forms; and in MC-PDFT, different translated and fully translated functionals. The results are consistent with one another and in very good agreement with experiments. They show small to vanishing dependence on key details of the methods used: namely, the exact-exchange contribution to global hybrids; the ionization potential-electron affinity shift and basis sets used in the CASPT2 calculations; and the active spaces employed for the CASSCF wave functions used in the MC-PDFT and HMC-PDFT calculations. Insights into the change in the spin-state energetics accompanying the ligand exchanges were gained through a complexation energy analysis. Using the accurate CCSD(T) estimate of the HS-LS adiabatic energy difference in [J. Chem. Theory Comput. 2012, 8, 4216-4231], the Δ(ΔEHL°)-approach has been applied to the determination of ΔEHL° in the diimine complexes. The CASPT2 and DFT-D2 methods only give results in agreement with experiments. This suggests for the other methods a limitation in their treatment of dispersion which prevents them from accurately describing the spin-state energetics change accompanying the passing from with the tetragonal arrangement of its nitrile ligands to the tris-diimine complexes with the trigonal packing of their bulkier ligands.

Direct evidence for ligand-enhanced activity of Cu(i) sites.

Little is known about the strong mediating effect of the ligand sphere and the coordination geometry on the strength and isotopologue selectivity of hydrogen adsorption on the undercoordinated copper(i) site. Here, we explore this effect using gas-phase complexes Cu+(H2O)(H2) n (with n ≤ 3) as model systems. Cu+(H2O) attracts dihydrogen (82 kJ mol -1) more strongly than bare Cu+ (64 kJ mol -1) does. Combining experimental and computational methods, we demonstrate a high isotopologue selectivity in dihydrogen binding to Cu+(H2O), which results from a large difference in the adsorption zero-point energies (2.8 kJ mol-1 between D2 and H2, including an anharmonic contribution of 0.4 kJ mol-1). We investigate its origins and the bond strengthening between Cu+ and H2 upon addition of a single H2O ligand. We discuss the role of the environment and the coordination geometry of the adsorption site in achieving a high selectivity and the ramifications for identifying and designing future materials for adsorptive dihydrogen isotopologue separation.

Deuteration of molecular clumps induced by cosmic rays

The D/H ratio in astrophysical environments has instigated the scientists for at least 50 years. The wide range of values in the interstellar medium (ISM) from 10e to 7 to 10e-1 have usually been claimed to be due to small zero-point energy differences between reactants and products involving D and H (mainly at low temperatures). Here, we present a new source of deuteration processes in the ISM clouds as a result of cosmic ray irradiation. As a study object, we consider a typical molecular clump under the presence of incoming cosmic rays simulated computationally. The calculations were performed employing the Monte Carlo toolkit GEANT4 code (considering hadronic physics) and considering mainly the proton and alpha component of the incoming cosmic rays from the ISM (the dominant ones for the production of secondary protons and deuterons). The results suggest an increasing D/H ratio as function of time in the central part of molecular clumps (<200 AU) with the largest deuteration in the central region of the cloud, and a bump in the D/H ratio around 2–10 AU (which becomes more pronounced for clouds with larger timescales; > 10 Myrs). The results also show that for timescales between 10 and 100 Myrs the central part of the cloud has D/H around 6-16e-3, a value compatible with the observed D/H in some interstellar clouds. This work adds a new piece to the D/H puzzle of the ISM and might also help to explain the D/H ratio measured in different objects inside the Solar system.

The microwave spectrum of the sesamol (1,3-benzodioxol-5-ol) monomer and an analysis of its internal motion

The microwave spectrum of the sesamol (CH2O2C6H3OH) monomer has been collected using CP-FTMW spectroscopy in the 5.5–18.75 GHz region of the electromagnetic spectrum. Density functional theory calculations of the monomer have been performed. B3LYP|cc-pVTZ predicts the global minimum geometry to be s-trans-sesamol where the hydroxyl group is oriented 180° away from the dioxole ring. A second, local minimum, geometry for s-cis-sesamol was calculated to have the hydroxyl group oriented 0° towards the dioxole ring, and the zero-point energy difference between the two geometries is predicted to be 1.4 kJ/mol. Both unique conformers have been identified in the experimental spectrum. In accordance with the predicted dipole moments, only b-type transitions have been observed for s-trans-sesamol, while a- and b-type transitions have been assigned to s-cis-sesamol. The relative intensities in the observed spectrum indicate that the molecular beam contains a higher population of the s-trans-sesamol monomer. Satellite transitions were observed for both sesamol conformers. Treating the parent and satellite transitions as coupled vibrational states, the energy differences and Coriolis coupling constants were determined for each conformer. The magnitude of the coupling constants, the energy difference between the states, and a comparison to a similar state observed in 1,3-benzodioxole indicate that the excited states correspond with CH2 puckering of the dioxiole ring. The second moments of inertia and their contributions from the ring puckering have been analyzed for a series of functionalized molecules including piperonal, 1,3-benzodioxole and sesamol.

Selective penetration mechanism of hydrogen isotope through graphene membrane

High selectivity of protons over deuterons transport through one-atom-thick graphene membrane has been demonstrated experimentally, but its fundamental mechanism has been controversially discussed. Proposed hypotheses involve local hydrogenation, but the detailed penetration process has not been rigorously explained. In the present study, based on electron cloud density, transition path selection and corresponding barrier calculations, perfect graphene is quasi-impermeable to protons, yet lateral ring chemically bonded protons adjacent hydrogenated hexa-cyclohydride shows the lowest barrier for the penetration of proton. The bridge-flip as a link provides the site for the penetration of the proton through the graphene. The chemically bonded protons slip into C–C to forms a C–H–C bridge bonds, and then flip over the graphene membrane to complete the penetration process. • Electron cloud distribution is the main factor driving protons to have different penetration paths and barriers. • Protons exhibit lateral ring penetration under the combined action of spatial effects and interatomic forces. • A slight difference in vibrational zero point energies is sufficient to exhibit a higher separation effect.

Porphyrin based channel for separation of proton isotope: A density functional theory study

Porphyrin based 2D materials with single atom thickness and uniform pore size have not been explored for the proton isotopes separation. We computationally designed the porphyrin and its derivatives with the doping of oxygen, sulphur and selenium atoms and computed the kinetic energy barrier for H+, D+, and T+ permeation through porphyrin and core modified porphyrins by using M05-2X along with 6-31G (d,p). Zero-point energy is calculated at transition state for H+ and its other relevant isotopes permeation through porphyrin derivatives. Tunneling ratio of proton isotopes through these 2D structures is calculated by using zero-point energy (ZPE) difference of H+ to its isotopes. Core modification of porphyrin provides better tunneling ratio for proton isotopes. Among these, mono selenium heteroporphyrin provides the most suitable results. Our study provides the molecular level insight of permeation pathway for proton isotopes through these 2D materials.

Gold as an efficient hydrogen isotope separation catalyst in proton exchange membrane water electrolysis

The development of proton exchange membrane water electrolysis (PEMWE) offers an updating potential for electrolytic hydrogen isotope separation. However, it has a significantly lower separation factor than the traditional alkaline water electrolysis. In this study, we propose gold as a promising cathodic catalyst for efficient hydrogen isotope separation in PEMWE. Au/C has a protium-to-deuterium (H/D) separation factor of 7.47 in PEMWE, about twice that of Pt/C. In addition, the full cell's electrochemical performance is comparable to that of its Pt/C counterpart. The separation mechanism in PEMWE is explained by the transitional hydrogen evolution reaction mechanism from Heyrovsky to Tafel for Pt and the unchangeable Volmer mechanism for Au. The high separation factor for Au is also calculated by the H/D zero-point vibrational energy difference between transition state and reaction state through a simple density functional theory calculation. This work offers an effective strategy to improve hydrogen isotope separation efficiency in PEMWE.

Hetero-porphyrin based channel for separation of proton isotope: A density functional theory study

Porphyrin with atomic-level thickness and uniform pore size hasn't yet been studied for the separation of gas molecules, especially for proton isotopes. Herein, we Computationally designed O, S, and Se doped hetero-porphyrin to evaluate its kinetic energy barrier and molecular level insight of the permeation pathway for protium ion and relevant isotopes. Zero-point energy (ZPE) for protium ion isotopes was observed at the transition state while Arrhenius equation has been used to calculate the tunneling ratio of H + /D + and H + /T + . Among all investigated hetero-porphyrins, O–O doped derivative provided the most valuable results with tunneling ratio of 23 and 30 respectively with no energy barrier. • We computationally designed the porphyrin and its derivatives with the doping of oxygen, sulphur and selenium atoms. • Tunneling ratio of proton isotopes through these 2D structures is calculated by using zero-point energy (ZPE) difference of protium ion to its isotopes. • Kinetic energy barrier for H+, D+, and T+ permeation through porphyrin and core modified porphyrins is computed.

Potential energy barrier for proton transfer in compressed benzoic acid.

Benzoic acid (BA) is a model system for studying proton transfer (PT) reactions. The properties of solid BA subject to high pressure (exceeding 1 kbar = 0.1 GPa) are of particular interest due to the possibility of compression-tuning of the PT barrier. Here we present simulations aimed at evaluating the value of this barrier in solid BA in the 1 atm – 15 GPa pressure range. We find that pressure-induced shortening of O⋯O contacts within the BA dimers leads to a decrease in the PT barrier, and subsequent symmetrization of the hydrogen bond. However, this effect is obtained only after taking into account zero-point energy (ZPE) differences between BA tautomers and the transition state. The obtained results shed light on previous experiments on compressed benzoic acid, and indicate that a common scaling behavior with respect to the O⋯O distance might be applicable for hydrogen-bond symmetrization in both organic and inorganic systems.

Deuterium Isotope Effects on Acid-Base Equilibrium of Organic Compounds.

Deuterium isotope effects on acid–base equilibrium have been investigated using a combined path integral and free-energy perturbation simulation method. To understand the origin of the linear free-energy relationship of versus , we examined two theoretical models for computing the deuterium isotope effects. In Model 1, only the intrinsic isotope exchange effect of the acid itself in water was included by replacing the titratable protons with deuterons. Here, the dominant contribution is due to the difference in zero-point energy between the two isotopologues. In Model 2, the medium isotope effects are considered, in which the free energy change as a result of replacing H2O by D2O in solute–solvent hydrogen-bonding complexes is determined. Although the average change from Model 1 was found to be in reasonable agreement with the experimental average result, the dependence of the solvent isotope effects is absent. A linear free-energy relationship is obtained by including the medium effect in Model 2, and the main factor is due to solvent isotope effects in the anion–water complexes. The present study highlights the significant roles of both the intrinsic isotope exchange effect and the medium solvent isotope effect.

Rotational spectra and conformational analysis of 2-bromobutane

The rotational spectra of 2-bromobutane were obtained by using a chirped-pulse Fourier-transform microwave (CP-FTMW) spectrometer in the frequency range 8–18 GHz. Hyperfine structures of both bromine isotopologues (I = 3/2) for the three conformers (G+, A, and G−) have been investigated to determine the rotational constants, centrifugal distortion constants, and nuclear quadrupole coupling constants of bromine (Br). The conformational compositions for G+, A, and G− in the supersonic jet, estimated by relative intensity measurements, are 55%, 28%, 17%, respectively, for the 79Br species, and 52%, 33%, 15%, respectively, for the 81Br species. However, the small zero-point energy differences of isotopomers can be negligible and can be considered as an average value instead of individual values, which is 54%, 30%, 16% for G+, A, and G− species. The nuclear quadrupole coupling tensors (χxx, χyy, and χzz) of Br and the quadrupolar angles were obtained, and the χzz value of 2-bromobutane is compared with those of other alkyl bromides. The spectroscopic constants, rs coordinates of Br and the dipole moments of the most stable G+ conformer are predicted well from the ab initio calculations at the MP2/6–311++G(2d,2p) level.

Isotope effect of methane adsorbed on fcc metal (1 1 1) surfaces

By means of the van der Waals density functional and quasi-harmonic approximation, we predict that the adsorption potential energies of CD4 on various fcc metal (111) surfaces are shallower than those of CH4, whereas the equilibrium distances from the surface are larger. This isotope effect originates from the softening of the CH bond pointing toward the surface, leading to the significant lowering of its vibrational frequency and hence the large zero-point energy difference between CH4 and CD4. The CH bond softening is attributed to the hybridization of the lowest unoccupied molecular orbital with the substrate state.

Secondary kinetic deuterium isotope effects on unimolecular cleavage reactions: Zero-point vibrational energy and qualitative RRKM theory.

Secondary kinetic isotope effects arise as the result of transition-state zero-point vibrational energy differences. Unimolecular simple cleavage reactions of gas-phase ions in mass spectrometers allow detailed studies of isotope effects on competing reactions, particularly when examined in intramolecular competition experiments where interpretation requires very few simplifying assumptions. The zero-point energy differences reflect changes of isotope sensitive vibrational properties, and both α- and β-secondary deuterium isotope effects are related to the sp 3 → sp 2 hybridization changes that accompany bond cleavage. Deuterium substitution three bonds or more removed from the bond broken also gives rise to isotope effects, but their origin is less easily interpreted. The magnitude and variation of the observed effects depend not only on zero-point energy differences; a number of additional factors play a role. The influence of the critical energy, the excess energy, the size of the reactant, and the presence of competing reactions can be rationalized within a simple, qualitative RRKM framework. The distinction between kinetic and thermodynamic isotope effects is not always obvious.

Ultrathin Metal–Organic Framework Nanosheets-Derived Yolk–Shell Ni 0.85 Se@NC with Rich Se-Vacancies for Enhanced Water Electrolysis

We present a controlled fabrication of selective ultrathin metal–organic framework (MOF) nanosheets as preassembling platforms, yolk–shell structured with a few-layered N-doped carbon (NC) shell-en...

Isotope enrichment in neon clusters grown in helium nanodroplets.

Neon cluster ions Nes + grown in pre-ionized, mass-to-charge selected helium nanodroplets (HNDs) reveal a strong enrichment of the heavy isotope 22Ne that depends on cluster size s and the experimental conditions. For small sizes, the enrichment is much larger than previously reported for bare neon clusters grown in nozzle expansions and subsequently ionized. The enrichment is traced to the massive evaporation of neon atoms in a collision cell that is used to strip helium from the HNDs. We derive a relation between the enrichment of 22Ne in the cluster ion and its corresponding depletion factor F in the vapor phase. The value thus found for F is in excellent agreement with a theoretical expression that relates isotopic fractionation in two-phase equilibria of atomic gases to the Debye temperature. Furthermore, the difference in zero-point energies between the two isotopes computed from F agrees reasonably well with theoretical studies of neon cluster ions that include nuclear quantum effects in the harmonic approximation. Another fitting parameter provides an estimate for the size si of the precursor of the observed Nes +. The value is in satisfactory agreement with the size estimated by modeling the growth of Nes + and with lower and upper limits deduced from other experimental data. On the other hand, neon clusters grown in neutral HNDs that are subsequently ionized by electron bombardment exhibit no statistically significant isotope enrichment at all. The finding suggests that the extent of ionization-induced dissociation of clusters embedded in HNDs is considerably smaller than that for bare clusters.

Instanton theory of tunneling in molecules with asymmetric isotopic substitutions.

We consider quantum tunneling in asymmetric double-well systems for which the local minima in the two wells have the same energy, but the frequencies differ slightly. In a molecular context, this situation can arise if the symmetry is broken by isotopic substitutions. We derive a generalization of instanton theory for these asymmetric systems, leading to a semiclassical expression for the tunneling matrix element and hence the energy-level splitting. We benchmark the method using a set of one- and two-dimensional models, for which the results compare favorably with numerically exact quantum calculations. Using the ring-polymer instanton approach, we apply the method to compute the level splittings in various isotopomers of malonaldehyde in full dimensionality and analyze the relative contributions from the zero-point energy difference and tunneling effects.

Isotope Effects Induced by Molecular Compression.

Zero-point energies (ZPEs) of hydroxyl ion and hydrogen and water molecules, free and compressed in C60 cages, are computed; the excess energy acquired by molecules under compression is in the range 2-3 kcal/mol and depends on the isotopes. The differences in ZPE of compressed isotopic molecules strongly exceed those of the free molecules, resulting in the large deuterium and tritium isotope effects. These effects induced by compression are suggested as a probe for testing molecular compression of enzymatic sites; they may be important for understanding enormously large isotope effects observed in some enzymatic reactions, where they are attributed to the tunneling.

Photolysis-induced scrambling of PAHs as a mechanism for deuterium storage

Aims. We investigate the possible role of polycyclic aromatic hydrocarbons (PAHs) as a sink for deuterium in the interstellar medium (ISM) and study UV photolysis as a potential underlying chemical process in the variations of the deuterium fractionation in the ISM. Methods. The UV photo-induced fragmentation of various isotopologs of deuterium-enriched, protonated anthracene and phenanthrene ions (both C14H10 isomers) was recorded in a Fourier Transform Ion Cyclotron Resonance Mass Spectrometer. Infrared multiple photon dissociation spectroscopy using the Free-Electron Laser for Infrared eXperiments was applied to provide IR spectra. Infrared spectra calculated using density functional theory were compared to the experimental data to identify the isomers present in the experiment. Transition-state energies and reaction rates were also calculated and related to the experimentally observed fragmentation product abundances. Results. The photofragmentation mass spectra for both UV and IRMPD photolysis only show the loss of atomic hydrogen from [D − C14H10]+, whereas [H − C14D10]+ shows a strong preference for the elimination of deuterium. Transition state calculations reveal facile 1,2-H and -D shift reactions, with associated energy barriers lower than the energy supplied by the photo-excitation process. Together with confirmation of the ground-state structures via the IR spectra, we determined that the photolytic processes of the two different PAHs are largely governed by scrambling where the H and the D atoms relocate between different peripheral C atoms. The ∼0.1 eV difference in zero-point energy between C–H and C–D bonds ultimately leads to faster H scrambling than D scrambling, and increased H atom loss compared to D atom loss. Conclusions. We conclude that scrambling is common in PAH cations under UV radiation. Upon photoexcitation of deuterium-enriched PAHs, the scrambling results in a higher probability for the aliphatic D atom to migrate to a strongly bound aromatic site, protecting it from elimination. We speculate that this could lead to increased deuteration as a PAH moves towards more exposed interstellar environments. Also, large, compact PAHs with an aliphatic C–HD group on solo sites might be responsible for the majority of aliphatic C–D stretching bands seen in astronomical spectra. An accurate photochemical model of PAHs that considers deuterium scrambling is needed to study this further.

Hypothesis about electron quantum tunneling during sonochemical splitting of water molecule.

Quantum tunneling in chemistry is often attributed to the processes at low or near room temperatures when the rate of thermal reactions becomes far less than the rate of quantum tunneling. However, in some rapid processes, quantum tunneling can be observed even at high temperatures. Herein, we report the experimental evidence for anomalous H/D kinetic isotope effect (KIE) during sonochemical dissociation of water molecule driven by 20 kHz power ultrasound measured in H2O/D2O mixtures saturated with Ar or Xe. Hydrogen released during ultrasonic treatment is enriched by light isotope. The observed H/D KIE (α = 2.15-1.50) is much larger than what is calculated assuming a classical KIE for Tg = 5000 K (α = 1.15) obtained from the sonoluminescence spectra in H2O and D2O. Furthermore, the α values sharply decrease with increasing of H2O content in H2O/D2O mixtures reaching a steady-state value close to α = 1.50, which also cannot be explained by O-H/O-D zero-point energy difference. We suggest that these results can be understood in terms of quantum electron tunneling occurring in nonequilibrium picosecond plasma produced at the last stage of cavitation bubble collapse. Thermal homolytic splitting of water molecule is inhibited by extremely short lifetime of such plasma. On the contrary, immensely short traversal time for electron tunneling in water allows H2O dissociation by quantum tunneling mechanism.