Calculated Activation Barriers Research Articles

Unexpected role of electronic coupling between host redox centers in transport kinetics of lithium ions in olivine phosphate materials.

The discrepancy between the trend in the diffusion coefficient of a lithium ion (DLi+) and that in the activation energy of ion hopping signals hidden factors determining ion transport kinetics in layered olivine phosphate materials (LiMPO4). Combining density functional theory (DFT) calculations and the Landau–Zener electron transfer theory, we unravel this hidden factor to be the electronic coupling between redox centers of the host materials. The ion transport process in LiMPO4 is newly described as an ion-coupled electron transfer (ET) reaction, where the electronic coupling effect on DLi+ is considered by incorporating the electronic transmission coefficient into the rate constant of the transfer reaction. The new model and DFT calculation results rationalize experimental values of DLi+ for various LiMPO4 (M = Fe, Mn, Co, Ni) materials, which cannot be understood solely by the calculated activation barrier of ion hopping. Interestingly, the electronic coupling between host redox centers is found to play an essential role. Particularly, the sluggish ion mobility in LiFePO4 is due to a very weak electronic coupling. The obtained insights imply that one can improve the rate performance of intercalation materials for metal-ion batteries through modifying the electronic coupling between redox centers of host materials.

Nonenzymatic Deamidation Mechanism on a Glutamine Residue with a C-Terminal Adjacent Glycine Residue: A Computational Mechanistic Study

The deamidation of glutamine (Gln) residues, which occurs non-enzymatically under physiological conditions, triggers protein denaturation and aggregation. Gln residues are deamidated via the cyclic glutarimide intermediates to l-α-, d-α-, l-β-, and d-β-glutamate residues. The production of these biologically uncommon amino acid residues is implicated in the pathogenesis of autoimmune diseases. The reaction rate of Gln deamidation is influenced by the C-terminal adjacent (N +1) residue and is highest in the Gln-glycine (Gly) sequence. Here, we investigated the effect of the (N + 1) Gly on the mechanism of Gln deamidation and the activation barrier using quantum chemical calculations. Energy-minima and transition-state geometries were optimized by the B3LYP density functional theory, and MP2 calculations were used to obtain the single-point energy. The calculated activation barrier (85.4 kJ mol−1) was sufficiently low for the reactions occurring under physiological conditions. Furthermore, the hydrogen bond formation between the catalytic ion and the main chain of Gly on the C-terminal side was suggested to accelerate Gln deamidation by stabilizing the transition state.

Computational Analysis of the Mechanism of Nonenzymatic Peptide Bond Cleavage at the C-Terminal Side of an Asparagine Residue.

The nonenzymatic peptide bond cleavage at the C-terminal side of Asn residues is a protein post-translational modification that occurs under physiological conditions. This reaction proceeds much slower than the deamidation of the Asn side chain and causes denaturation and hypofunction of proteins. The peptide bond cleavage of Asn is detected primarily in crystallins and aquaporin 0 in the eye lens. Therefore, cleavage is thought to be involved in age-related cataracts. In this study, to clarify the mechanism underlying succinimide formation for the peptide bond cleavage of the Asn residue, we performed quantum chemical calculations on the model compound Ace-Asn-Gly-Nme (Ace = acetyl and Nme = methylamino). The density functional theory with the B3LYP/6-31+G(d,p) level of theory was used to obtain optimized geometries. The results suggested that the reaction proceeds through two steps, cyclization and C-terminal fragment release, and the required proton transfers can be mediated by H2PO4– and HCO3– ions. The conformational change of the main chain on the N-terminal side of Asn was needed for the C-terminal fragmentation step, and a separate conformational change at the C-terminal side was required for the cyclization step. Furthermore, the calculated activation barriers of the reactions catalyzed by the H2PO4– ion (130 kJ mol–1) and the HCO3– ion (123 kJ mol–1) were sufficiently low for the reactions to occur under normal physiological conditions.

The role of structural symmetry on proton tautomerization: A DFTB/Meta-Dynamics computational study

Porphyrins, phthalocayanines and their derivatives have found interesting applications in various fields such as molecular electronics, optoelectronics, and sensorics. Common to this class of molecules with a metal-free core is the existence of hydrogen tautomerization reactions. Since the reaction only involves the motion of a pair of hydrogen atoms, it provides a rather simple, yet non-trivial test bed for advanced simulation tools. In this investigation, we exploit state-of-the-art quantum Metadynamics simulations complemented with Nudged Elastic Band (NEB) calculations, to study the effect of structural symmetry on the proton transfer tautomerism of functionalized porphyrins and porphyrazines. Calculated activation barriers using Metadynamics and NEB show a rather good quantitative agreement. We also demonstrate that the set of chosen collective variables in the Metadynamics simulations plays an important role for the appropriate description of the reaction path and dynamics of the system.

Study of the Rate-Determining Step of Rh Catalyzed CO2 Reduction: Insight on the Hydrogen Assisted Molecular Dissociation

In the context of climate change mitigation, CO2 methanation is an important option for the production of synthetic carbon-neutral fuels and for atmospheric CO2 recycling. While being highly exothermic, this reaction is kinetically unfavorable, requiring a catalyst to be efficiently activated. Recently Rh nanoparticles gained attention as effective photocatalyst, but the rate-determining step of this reaction on Rh surface has not been characterized yet. In this work, Density Functional Theory and Nudged Elastic Band calculations were performed to study the Rh-catalyzed rate-determining step of the CO2 methanation, which concerns the hydrogen assisted cleavage of the CO* molecule and subsequent formation of CH* and O* (* marks adsorbed species), passing through the CHO* key intermediate. The configurations of the various adsorbates on the Rh (100) surface were investigated and the reaction mechanism was studied exploiting different exchange-correlation functionals (PBE, RPBE) and the PBE+U technique. The methanation rate-determining step consists of two subprocesses which subsequently generate and dissociate the CHO* species. The energetics and the dynamics of such processes are extensively studied and described. Interestingly, PBE and PBE+U calculated activation barriers are in good agreement with the available experimental data, while RPBE largely overestimate the CHO* dissociation barrier.

Effect of Pd Coordination and Isolation on the Catalytic Reduction of O2 to H2O2 over PdAu Bimetallic Nanoparticles.

The direct synthesis of hydrogen peroxide (H2 + O2 → H2O2) may enable low-cost H2O2 production and reduce environmental impacts of chemical oxidations. Here, we synthesize a series of Pd1Aux nanoparticles (where 0 ≤ x ≤ 220, ∼10 nm) and show that, in pure water solvent, H2O2 selectivity increases with the Au to Pd ratio and approaches 100% for Pd1Au220. Analysis of in situ XAS and ex situ FTIR of adsorbed 12CO and 13CO show that materials with Au to Pd ratios of ∼40 and greater expose only monomeric Pd species during catalysis and that the average distance between Pd monomers increases with further dilution. Ab initio quantum chemical simulations and experimental rate measurements indicate that both H2O2 and H2O form by reduction of a common OOH* intermediate by proton-electron transfer steps mediated by water molecules over Pd and Pd1Aux nanoparticles. Measured apparent activation enthalpies and calculated activation barriers for H2O2 and H2O formation both increase as Pd is diluted by Au, even beyond the complete loss of Pd-Pd coordination. These effects impact H2O formation more significantly, indicating preferential destabilization of transition states that cleave O-O bonds reflected by increasing H2O2 selectivities (19% on Pd; 95% on PdAu220) but with only a 3-fold reduction in H2O2 formation rates. The data imply that the transition states for H2O2 and H2O formation pathways differ in their coordination to the metal surface, and such differences in site requirements require that we consider second coordination shells during the design of bimetallic catalysts.

Thermal decomposition of N-butyl-N-methyl pyrrolidinium tetrafluoroborate and N-butyl-N-methyl pyrrolidinium hexafluorophosphate: Py-GC–MS and DFT study

The thermal stability and decomposition mechanisms of pyrrolidinium based ionic liquids (ILs) N-butyl-N-methyl pyrrolidinium tetrafluoroborate (Pyr14 BF4) and N-butyl -N- methyl pyrrolidinium hexafluorophosphate (Pyr14 PF6) have been investigated using pyrolysis-GC–MS (Py-GC–MS) and B3LYP/6-311++G(d,p) level of density functional theory (DFT). Pyr14 PF6 decomposes through E2 elimination and a bimolecular nucleophilic substitution (SN2) while Pyr14BF4 exhibit SN2 along with a competitive E2 elimination and ring opening pathway. Kissinger method and Ozawa-Flynn-Wall (FWO) methods were used for calculating the activation energy parameters for the thermal decomposition of ILs, and are comparable with the computationally calculated activation barriers.

Acetylene vs ketones on the route to base-promoted assembly of furans or 6,8-dioxabicyclo[3.2.1]octanes and cyclopentenols: a quantum-chemical study

The electronic characteristics of substrates (α,β-unsaturated ketones) and reagents (carbanions of ketones and ethynide ions), as well as thermodynamic and kinetic characteristics both their interaction and the formation of final products have been evaluated using the B2PLYP/6-311+G**//B3LYP/6-31+G* and B3LYP/6-311++G**//B3LYP/6-31+G* quantum-chemical approaches. Reactivity indices that adequately describe the electrophilic and nucleophilic properties of the substrates and reagents are proposed. It has been shown that, regardless of the nature of substrates and reagents, the formation of cyclopentenols and furans is thermodynamically favorable, while the presence of bulky substituents leads to an increase in energy during the formation of 6,8-dioxabicyclo[3.2.1]octanes and explains in this case their absence in products. The calculated activation barriers of the competing reactions of the nucleophilic addition of ethynide ions and ketone carbanions to the double C=C bond of α,β-unsaturated ketones are correlated with the observed reaction direction and the proposed reactivity indices.

Mechanistic study of the biosynthesis of R-phenylcarbinol by acetohydroxyacid synthase enzyme using hybrid quantum mechanics/molecular mechanics simulations

The biosynthesis of R-phenylacetylcarbinol (R-PAC) by the acetohydroxy acid synthase, (AHAS) is addressed by molecular dynamics simulations (MD), hybrid quantum mechanics/molecular mechanics (QM/MM), and QM/MM free energy calculations. The results show the reaction starts with the nucleophilic attack of the C2α atom of the HEThDP intermediate on the Cβ atom of the carbonyl group of benzaldehyde substrate via the formation of a transition state (TS1) with the HEThDP intermediate under 4′-aminopyrimidium (APH+) form. The calculated activation free energy for this step is 17.4kcal mol−1 at 27 °C. From this point, the reaction continues with the abstraction of Hβ atom of the HEThDP intermediate by the Oβ atom of benzaldehyde to form the intermediate I. The reaction is completed with the cleavage of the bond C2α-C2 to form the product R-PAC and to regenerate the ylide intermediate under the APH+ form, allowing in this way to reinitiate to the catalytic cycle once more. The calculated activation barrier for this last step is 15.9kcal mol−1 at 27 °C.

Phase transition and trigger mechanism of initial reaction under pressure for benzofuroxan energetic materials: Raman spectroscopy and first‐principle calculations

AbstractLow‐pressure (below 2 GPa) Raman spectra of benzofuroxan are investigated using a gasketed Mao–Bell‐type sapphire anvil cell and Raman spectrometer to clarify the pressure‐induced structural change and molecular vibration behavior. The first‐principle calculations are performed to compare with the experimental data and to analyze the phase transition and trigger mechanism of initial reaction. Variations of pressure‐induced Raman band width, shift, and intensity are examined. The results show that the benzofuroxan molecule will become nonplanar with increasing pressure. A phase transition occurs because of an abrupt redshift in shift–pressure relationship and reduction of the cell volume, appearing of a new vibration band above 0.13 GPa. Several active vibration modes are found, and the effects of the active mode vibrations on the initial decomposition of benzofuroxan are analyzed using the relaxed scan method for the main change in bond length, bond angle, or dihedral angle to obtain the optimal reaction channel leading to initial decomposition. The results demonstrate that the initial decomposition is the open‐loop reaction in N(O)–O position, which is originated from the increase of dihedral angle O‐C‐N(O)‐O from the out‐of‐plane torsional vibration of furoxan ring (518 cm−1). The scanning energy barrier related to dihedral angle O‐C‐N(O)‐O is about 22.6 kcal/mol, which is consistent with the calculated activation barrier (18.1 kcal/mol) of open‐loop reaction. This proves the reliability of our conclusions.

Roles of Enhancement of C−H Activation and Diminution of C−O Formation Within M1‐Phase Pores in Propane Selective Oxidation

AbstractPropane and propene oxidations on M1 phase MoVTeNb mixed oxide catalysts exhibit relatively high selectivity to acrolein and acrylic acid. We probe the ability of the reactant molecules to access the catalytic sites inside the heptagonal pores of these oxides and analyze elementary steps that limit selectivity. Measured propane/cyclohexane activation rate ratios on MoVTeNbO are nearly an order of magnitude higher than non‐microporous VOx/SiO2, which suggests significant contribution of M1 phase pores to propane activation because both molecules react via homologous rate‐limiting C−H activation. Density functional theory suggests that desired C3H8 dehydrogenation and C3H6 allylic oxidation to acrolein and acrylic acid are limited by C−H activation steps, while less valuable oxygenates form via steps limited by C−O bond formation. Calculated activation barriers for C−O formation are invariably higher than C−H activation when these activations occur inside the pores, suggesting that reactions restricted within the pores are highly selective to desired products. These results demonstrate the role of pore confinement and a framework to assess selectivity limitation in hydrocarbon oxidations involving a complex network of sequential and parallel steps.

Quantum mechanical investigations of base-catalyzed cycloaddition reaction between phenylacetylene and azidobenzene

In this study, the mechanism for both the Huisgen 1,3-dipolar cycloaddition and the base-catalyzed cycloaddition reactions between phenylacetylene and azidobenzene has been investigated with density functional theory, namely at the M06-2X/6-31G(d) computational level. Later, the reaction has been modeled with a representative simple alkyne and a simple azide to concentrate solely on how the difference bases affect the mechanism of the reaction between phenylacetylene and azidobenzene as charged components. In this study, another mechanism of this reaction with uncharged components has been proposed to compare the calculated thermodynamic and kinetic properties for charged and uncharged systems. The calculated activation barrier differences between the catalyzed and the uncatalyzed reactions are consistent with the faster and the regioselective synthesis of the triazole product in the presence of solvents. The calculated barrier of the rate-determining step in the base-catalyzed mechanism with the uncharged system is lower than that with charged systems. Finally, the reaction leading to final product formation in uncharged system is more spontaneous than that in the charged system, and the same applies to the total reaction in the presence of solvents.

Multiscale Simulation for Effects of the Li+ Addition at the Initial Stage of Zn Electrodeposition Processes

A Zn negative electrode is a promising material for large-scale energy storage devices because of its safety and high energy density. The problem for its application is the irregular deposition such as dendritic and mossy structural growths on the electrode during charge-discharge cycles. Application of additives is an effective and practical solution to control the surface morphology. Recently, it is reported that cationic surfactants lead to the smooth surface morphology of the Zn deposits [1]. Our past study also proposed that the Li+ addition particularly could control the morphology effectively [2]. To consider the effect of Li+, which has not been well understood, it is important to systematically analyze the cationic additive effects. Besides, it should be understood at the atomic scale. In this study, a multiscale simulation that combined a kinetic Monte Carlo (KMC) simulation and a first-principle calculation based on density functional theory (DFT) was performed to investigate the Li+ additive effects for the Zn electrodeposition from the molecular viewpoint.Among several parameters, the surface diffusion of electrodeposited adatoms is known to be one of the most critical factors to determine the morphology of deposits. This indicates that profound understanding of the connection between the surface diffusion behavior and the morphology in the presence of additives leads us to elucidate its effect at the atomic scale. So we examined the surface diffusion of the Zn adatom by DFT as a significant step for deposition. The calculated activation barriers of the surface diffusions were implemented in the KMC simulations. All DFT calculations were performed by Quantum-ESPRESSO code with the effective screening medium + the reference interaction site model (ESM-RISM) [3]. The surface diffusion and deposition were taken into account as possible events in the KMC simulation code. There are three types of the surface diffusion included in the simulations: (a) surface diffusion on (0001), (b) on (0-110), and (c) interlayer diffusion on (0001) called Ehrlich-Schwoebel barrier.The surface diffusion of the Zn adatom on (0001) in the presence of Li+ or K+, as common cationic additives, were simulated by DFT. The activation energy in the presence of Li+ was 13.7 kJ/mol, while that in the presence of K+ was 14.5 kJ/mol; the surface diffusion in the presence of Li+ is faster. The detailed analysis of the solvation structure at the solid-liquid interface showed that the interaction between the Zn adatom and the water molecule was weakened in the presence of Li+. This is because Li+ forms strong solvation structures and water molecules are more likely to interact with Li+ than the Zn adatom. On the other hand, the water molecules near the surface were relatively relaxed in the presence of K+. In this case, the Zn adatom is solvated strongly. The difference in such solvation structures causes the difference in diffusion tendencies (Fig. 1). The KMC simulations revealed that the fast surface diffusion on (0001) by the effect of Li+ enhanced the growth of (0001) on the surface. This effect is critical to determine the surface morphology of the deposits.[1] M. Shimizu, K. Hirahara, S. Arai, PCCP, 21, 7045-7052 (2019).[2] T. Otani, T. Yasuda, M. Kunimoto, M. Yanagisawa, Y. Fukunaka, T. Homma, Electrochim. Acta, 305, 90-100 (2019).[3] S. Nishihara, M. Otani, Phys. Rev. B, 96, 115429-115433 (2017). Figure 1

First-principles investigation of methanol synthesis from CO2 hydrogenation on Cu@Pd core–shell surface

In this paper, the density functional theory calculation is used to investigate the reaction mechanisms of CO2 hydrogenation to CH3OH on the Cu@Pd core–shell surface. In particular, the possible adsorption sites, structural parameters, and adsorption energies of all intermediates are determined. All the reaction energies and the activation barriers of elementary steps involved in the possible hydrogenation mechanisms, including the HCOO pathway, the COOH pathway, and the RWGS + CO-Hydro pathway, are studied in detail. The calculated activation barrier of the rate-determining step is 1.84 eV for the HCOO pathway, 1.45 eV for the COOH pathway, and 1.17 eV for the RWGS + CO-Hydro pathway. Therefore, the most favorable hydrogenation mechanism on the Cu@Pd core–shell surface is following the reverse water–gas shift reaction followed by CO hydrogenation and will be completed via the route of CO2* → trans-COOH* → cis-COOH* → CO* → HCO* → HCOH* → H2COH* → CH3OH*. Compared with Cu-based catalysts such as Cu(111), Cu29 cluster, Cu19 cluster, and Cu(211), the Cu@Pd core–shell catalyst is demonstrated to have higher catalytic activity toward CO2 hydrogenation to CH3OH.

Solid-State 17O NMR Studies of Sulfonate Jump Dynamics in Crystalline Sulfonic Acids: Insights into the Hydrogen Bonding Effect.

We report variable-temperature (VT) 17O solid-state nuclear magnetic resonance (NMR) spectra for three crystalline sulfonic acids: l-cysteic acid monohydrate (CA), 3-pyridinesulfonic acid (PSA), and p-toluenesulfonic acid monohydrate (TSA). We were able to analyze the experimental VT 17O NMR spectra to obtain the activation barriers for SO3- jumps in these systems. Using the density functional-based tight-binding (DFTB) method, we performed potential energy surface scans for SO3- jumps in the crystal lattice of CA, PSA, and TSA, as well as for three related crystalline sulfonic acids (taurine, homotaurine, and 4-aminobutane-1-sulfonic acid) for which relevant 17O solid-state NMR data are available in the literature. The calculated activation barriers are in reasonable agreement with the experimental values. On the basis of the DFTB results, we hypothesized that activation barriers for SO3- jumps in the crystal lattice depend largely on the hydrogen bonding energy difference between the ground state and the transition state.

Observation of Molecular Hydrogen Produced from Bridging Hydroxyls on Anatase TiO2(101).

Anatase TiO2 is used extensively in a wide range of catalytic and photocatalytic processes and is a promising catalyst for hydrogen production. Here, we show that molecular hydrogen was produced from bridging hydroxyls (HOb) on the (101) surface of single-crystal anatase (TiO2(101)). This stands in contrast to rutile TiO2(110), where HOb pairs react to form H2O. Electron bombardment at 30 K produced bridging oxygen vacancies in the surface. Deuterated bridging hydroxyls (DOb) were subsequently formed via dissociation of adsorbed D2O and confirmed by infrared reflection-absorption spectroscopy. During temperature-programmed desorption (TPD) spectroscopy, D2 desorption was observed at 520 K. Density functional theory calculations show that both H2 and H2O production from HOb are endothermic at 0 K on TiO2(101), but H2 (H2O) desorption is entropically driven above 230 K (800 K). The calculated activation barrier for H2 desorption is 1.40 eV, which is similar to the desorption energy obtained from analysis of the D2 TPD spectra. The H2 desorption likely proceeds in two steps: H atom diffusion on the surface and then recombination.

Mechanism of CO Oxidation on Pd/CeO2(100): The Unique Surface‐Structure of CeO2(100) and the Role of Peroxide

AbstractUnderstanding the atomic mechanism of low‐temperature CO oxidation on a heterogeneous catalyst is challenging. We performed density functional theory (DFT) calculations to identify the surface structure and reaction mechanism responsible for low‐temperature CO oxidation on Pd/CeO2 (100) surfaces. DFT calculations reveal the formation of a unique zigzag chain structure by the oxygen and Ce atoms of the topmost surface of CeO2(100) with Pd atoms located between the zigzag chains. O2 adsorbed on such Pd atoms is stable in the presence of CO but plays a very important role in lowering the activation barrier for low‐temperature CO oxidation by forming a square‐planar PdO4 structure and facilitating further O2 adsorption. In‐situ Raman spectroscopy studies confirm the adsorbed oxygen species to be peroxides. The calculated activation barrier for CO oxidation, based on the mechanism suggested by these unique structures and peroxides, is 31.2 kJ/mol, in excellent agreement with our experimental results.

Mechanisms of Degradation of Toxic Nerve Agents: Quantum-chemical Insight into Interactions of Sarin and Soman with Molybdenum Dioxide

With the urgent need to provide an efficient and reliable protection for people from fatal chemical and biological weapons, our fundamental understanding of how toxins interact with filters is far from complete. The situation is further complicated by natural difficulties of performing experimental measurements with lethal toxins. Unlike experiments, computational modeling offers an attractive and safe yet reliable way of studying behavior of toxic agents on a variety of substrates at a great level of detail. Here, we report DFT-based quantum-chemical calculations of adsorption and decomposition of DMMP, sarin and soman on MoO2 (011) surface. Our calculations show that MoO2 strongly adsorbs toxic nerve agents and quickly decomposes them.Decomposition of DMMP on the MoO2 (011) surface proceeds via the PO-CH3 bond breaking and a formation of a surface methoxy group. The calculated activation barrier for this reaction is 131.5 kJ mol−1. Unlike DMMP, decomposition of sarin and soman proceeds via the dealkylation reaction yielding propene and 3,3-dimethyl-1-butene, respectively. Decomposition of sarin requires a remarkably low energy (53.7 kJ mol−1), whereas the similar reaction in soman requires 50 kJ mol−1 more energy. We also make specific predictions to guide Ambient-Pressure X-ray Photoelectron Spectroscopy (APXPS) experiments on sarin interaction with MoO2 samples. We conclude that MoO2 serves as an efficient substrate able of degrading toxins.

Alkaline Stability of Novel Aminated Polyphenylene-Based Polymers in Bipolar Membranes

This research investigated stability of two novel aminated polyphenylene polymers as anion exchange layers in bipolar membranes. Bipolar membrane stability was tested under operating conditions of 50 mA/cm2, and under conditions of soaking in room temperature 1 M NaOH. The stability of the custom made bipolar membranes was compared with those for two commercial membranes. For the polyphenylene-based membranes, there was no measurable increase in operating voltage when run continuously at a current density of 50 mA/cm2. For the two commercial membranes, the operating voltages increased by 3.2 to 4.4 mV per day when operated continuously over an 85 day testing period. Commercial membrane degradation in 1 M NaOH was similar to that under real operating conditions, with average rates of voltage increase of 3.2 to 3.5 mV/d. The custom made membrane containing a quaternary ammonium-tethered poly(biphenylalkylene) (PBPA) anion exchange layer did not show any loss in performance in either stability test. Density functional theory (DFT) simulations were used to calculate activation barriers and reaction energies for nucleophilic attack on the polymer backbones and cation functional groups on each of the four anion exchange polymers. Cation loss from all four polymers was thermodynamically favorable, with activation barriers ranging from 64 to 138 kJ/mol. The two commercial polysulfone-based anion exchange membranes were susceptible to cleavage of the ether bonds. However, the polyphenylene-based anion exchange polymers were considerably more stable with respect to backbone cleavage. The DFT calculations showing that the PBPA polymer was the most stable confirmed the results of the stability tests.

Stabilization of small nitrogen clusters via spatial constraint

We apply density functional theory to calculate activation barriers for dissociations of small all-nitrogen clusters N4 and N6. The effect of external spatial constraint was also considered. We found that spatial constraint results in significant stabilization of both regarded clusters. So, the spatial constraint can be considered as an efficient method for stabilization of high-energy nitrogen structures.