Ab initio molecular orbital and RRKM calculations of the thermal decomposition of CH2BrO radical

A theoretical study of the thermal decomposition and isomerization channels of bromomethoxy radical is carried out using ab initio molecular orbital methods and RRKM theory. Three kinds of reaction pathways are examined, bond scission, intramolecular three-center HBr elimination and isomerization. Energy-specific rate coefficients k(E) and thermal rate constants k(T,P) are evaluated using the ab initio data and RRKM theory. Relevance to existing experimental evidence is discussed.     

Structure and stability of thiourea with water, DFT and MP2 calculations

The relative stabilities of thiourea in water are investigated computationally by considering thiourea–water complexes containing up to 1–6 water molecules (CS(NH₂)₂(H₂O)_n=1–6) using density functional theory and MP2 ab initio molecular orbital theory. The results show that the thiourea complex is stable and has an unusually high affinity for incoming water molecules. The clusters are progressively stabilized by the addition of water molecules, as indicated by the increasing of the binding energy. The binding energy of the cluster to each H₂O molecule is about 33 kJ mol⁻¹ for n=1–5.The C–S bond, N–C bond distance, Mulliken populations and binding energy keep approximately constant as the clusters increase in size with an increasing number of H₂O molecules. As the solvation progresses, the C–S distance increases monotonically while the Mulliken populations on the C–S bond reduces monotonically with the addition of each H₂O molecule, indicating that the C–S bond of the thiourea unit in the clusters is de-stabilized with an increasing number of H₂O molecules. Charge transfers for the clusters are mainly found at N, S atoms of the thiourea.     

Molecular structure and conformational stability of allylisocyanate—post-Hartree–Fock and density functional theory studies

The molecular structure and conformational stability of allylisocyanate (CH₂CHCH₂NCO) molecule was studied using the ab initio and DFT methods. The geometries of possible conformers, C-gauche (δ=120°, θ=0°) (δ=C=C–C–N and θ=C–C–N=C) and C-cis N-trans (δ=0° and θ=180°) were optimized employing HF/6-31G^*, MP2/6-31G^* levels of theory of ab initio and BLYP, B3LYP, BPW91 and B3PW91 methods of DFT implementing the atomic basis set 6-311+G(d,p). The structural and physical parameters of the above conformers were discussed with the experimental and theoretical values of the related molecules, methylisocyanate and 3-fluoropropene. It has been found that the N=C=O bond angle is not linear as the experimental result for both the conformers and the theoretical bond angle is 173°. The rotational potential energy surfaces have been performed at the HF/6-31G^*, and MP2/6-31G^* levels of theory. The Fourier decomposition potentials were analysed at the HF/6-31G^*, and MP2/6-31G^* levels of theory. The HF/6-31G^* level of theory predicted that the C-gauche conformer is more stable than the C-cis N-trans conformer by 0.41 kJ/mol, but the MP2 and DFT methods predicted the C-cis N-trans conformer is found to be more stable than the C-gauche conformer. The calculated chemical hardness value at the HF/6-31G^* level of theory predicted the C-cis N-trans form is more stable than C-gauche form, whereas the chemical hardness value at the MP2/6-31G^* level of theory favours the slight preference towards the C-gauge conformer.     

Ab initio study of anomeric effect in 2,2-difluoroglycine

The optimized molecular structures of seven conformations of 2,2-difluoroglycine have been obtained from ab initio calculations. For conformers in which the lone pair of electrons on the nitrogen are antiperiplanar to one of the C–F bonds, that C–F bond is longer than the other C–F bond, which is synperiplanar to the lone pair of electrons. Conformers which have these features are the most stable conformers of those examined. This observation is explained in terms of an anomeric effect of the 1p(N)→σ^*(C–F). At the MP2/6-31G^* level of calculation, conformers IV and V are 21.5 and 18.7 kJ/mol, respectively, more stable than the least stable conformer, VI, which does not exhibit an anomeric effect. Conformer VII was found to be exceptionally stable, in addition to an anomeric effect, this conformer also exhibits features of a FH–O hydrogen bond.     

The molecular structure and the puckering potential function of silacyclobutane as determined by gas electron diffraction and relaxation constraints from ab initio calculations

Gas electron diffraction is applied to determine the geometric parameters of the silacyclobutane molecule using a dynamic model where the ring puckering was treated as a large amplitude motion. The structural parameters and the parameters of the potential function were refined taking into account the relaxation of the molecular geometry estimated from ab initio calculations at the MP2/6-311+G(d, p) level of theory. The potential function has been described as V() = V₀[(/_e)² − 1]² with the following parameters V₀ = 0.82 ± 0.60 kcal/mol and _e = 33.5 ± 2.7°, where is a puckering angle of the ring.

The geometric parameters at the minimum V() (r_a in Å, in degrees and uncertainties given as three times the standard deviations including a scale error) are: r(Si–H_ax) = 1.467(96), r(Si–H_eq) = 1.468(96), r(Si–C) = 1.885(2), r(C–C) = 1.571(3), r(C–H) = 1.100(3), CSiC = 77.2(9), HSiH = 108.3, SiCH_eq = 123.5(16), SiCH_ax = 111.9(16), CC₅H_eq = 118.4(24), CC₅H_ax = 112.3(24), HC₃H = 107.7, δ(HSiH) = 6.6, δ(HC₃H) = 7.0, where the tilts δ, HSiH, and HC₃H are estimated from ab initio constraints. The structural parameters are compared with those obtained for related compounds.     

Far infrared spectra, conformational equilibria, vibrational assignments, ab initio calculations and structural parameters for 2-bromoethanol

The far infrared spectrum from 370 to 50 cm⁻¹ of gaseous 2-bromoethanol, BrCH₂CH₂OH, was recorded at a resolution of 0.10 cm⁻¹. The fundamental O–H torsion of the more stable gauche (Gg′) conformer, where the capital G refers to internal rotation around the C–C bond and the lower case g to the internal rotation around the C–O bond, was observed as a series of Q-branch transitions beginning at 340 cm⁻¹. The corresponding O–H torsional modes were observed for two of the other high energy conformers, Tg (285 cm⁻¹) and Tt (234 cm⁻¹). The heavy atom asymmetric torsion (rotation around C–C bond) for the Gg′ conformer has been observed at 140 cm⁻¹. Variable temperature (−63 to −100°C) studies of the infrared spectra (4000–400 cm⁻¹) of the sample dissolved in liquid xenon have been recorded. From these data the enthalpy differences have been determined to be 411±40 cm⁻¹ (4.92±0.48 kJ/mol) for the Gg′/Tt and 315±40 cm⁻¹ (3.76±0.48 kJ/mol) for the Gg′/Tg, with the Gg′ conformer the most stable form. Additionally, the infrared spectrum of the gas, and Raman spectrum of the liquid phase are reported. The structural parameters, conformational stabilities, barriers to internal rotation and fundamental frequencies have been obtained from ab initio calculations utilizing different basis sets at the restricted Hartree–Fock or with full electron correlation by the perturbation method to second order. The theoretical results are compared to the experimental results when appropriate. Combining the ab initio calculations with the microwave rotational constants, r₀ adjusted parameters have been obtained for the three 2-haloethanols (F, Cl and Br) for the Gg′ conformers.     

Ab initio CI study of the reaction between NH2 and NO

Using ab initio CI calculations we have evaluated the structural, energetic and kinetic parameters of the reaction between NH₂ and NO. In light of the results obtained, it appears that while the formation of molecular nitrogen is highly probable, the reaction pathway leading to N₂H+OH cannot be thermodynamically excluded. The kinetic model based on the RRKM and TST methods leads to a calculated rate constant at 298 K (k = 1.64×10⁻¹¹ cm³ molecule⁻¹ s⁻¹) which is comparable to that determined experimentally and which decreases with temperature in the range 200–700 K.     

Theoretical study of the elimination kinetics of several 2-substituted ethyl N,N-dimethylcarbamates in the gas phase, [(CH3)2NCOOCH2CH2Z, Z=CH2Cl, C≡CH, C≡N]

The theoretical studies of the gas-phase elimination of 2-substituted ethyl N,N-dimethylcarbamates (Z=CH₂Cl, C≡CH, C≡N) were performed using ab initio MP2/6-31G and MP2/6-31G(d) levels of theory. The gas phase elimination reaction of these carbamates yields N,N-dimethylcarbamic acid and the corresponding substituted olefin in a rate-determining step. The intermediate N,N-dimethylcarbamic acid is unstable and rapidly decomposes through a four-membered cyclic transition state to dimethylamine and CO₂ gas. The results of these calculations suggest a mechanism to be concerted, asynchronous, and a six-membered cyclic transition state structure. Plotting the relative theoretical rate coefficients against Taft's σ* values gave an approximate straight line (ρ*=0.4057, r=0.9894 at 360 °C). The correlation between experimental log k_rel vs. theoretical log k_rel. for these 2-substituted ethyl N,N-dimethylcarbamates gave an approximate straight line (r=0.9715 at 360 °C), suggesting the same type of mechanism.     

Ab initio quantum chemical studies of reaction mechanism for CH2CO with NCO

An extensive quantum chemical study of the potential energy surface (PES) for all possible isomerization and dissociation reactions of CH₂CO with NCO is reported at the DFT (B3LYP/6-311++G(d,p)) and CCSD(T)/cc-pVDZ//B3LYP/6-311++G(d,p) levels of theory. For the CH₂CO+NCO reaction, the formation of CO+CH₂NCO via an addition–elimination mechanism is the dominant channel on the doublet surface. While the formation of CO+CH₂OCN via bimolecular substitution reaction is in the secondary. Meanwhile, the isomerization and dissociation reactions of the products, CH₂NCO and CH₂OCN, also have been investigated using the same theoretical approach. It can be concluded that these reaction channels are not feasible kinetically at low or fairly high temperatures. On the basis of the ab initio data, the total rate constants for the CH₂CO+NCO reaction in the T=296–560 K range have been computed using conventional transition state theory with Wigner tunneling correction and fitted by a rate expression as k=2.14×10⁻¹² (cm³ molecule⁻¹ s⁻¹) exp(654.29/T). The calculated total rate constants with Wigner tunneling correction for the CH₂CO+NCO reaction are in good agreement with the available experimental values.     

Ab initio structural trends and torsional sensitivity in n-hexane and comparisons with crystallographic structural results

The molecular structures of n-hexane were determined by RHF/4-21G ab initio geometry optimization at 30° grid points in its three-dimensional τ₁(C11–C8–C5–C1), τ₂(C14–C11–C8–C5), τ₃(C17–C14–C11–C8) conformational space. Of the resulting 12×12×12=1728 grid structures, 468 are symmetrically non-equivalent and were optimized constraining the torsions τ₁, τ₂, and τ₃ to the respective grid points, while all other structural parameters were relaxed without any constraints. From the results, complete parameter surfaces were constructed using natural cubic spline functions, which make it possible to calculate parameter gradients, |P|=[(∂P/∂τ_i)²+(∂P/∂τ_j)²]^1/2, where P is a C–C bond length or C–C–C angle. The parameter gradients provide an effective measure of the torsional sensitivity of the system and indicate that dynamic activities in one part of the molecule can significantly affect the density of states, and thus the contributions to vibrational entropy, in another part. This opens the possibility of dynamic entropic conformational steering in complex molecules; i.e. the generation of free energy contributions from dynamic effects of one part of a molecule on another. When the conformational trends in the calculated C–C bond lengths and C–C–C angles are compared with average parameters taken from some 900 crystallographic structures containing n-hexyl fragments or longer C–C bond sequences, some correlation between calculated and experimental trends in angles is found, in contrast to the bond lengths for which the two sets of data are in complete disagreement. The results confirm experiences often made in crystallography. That is, effects of temperature, crystal structure and packing, and molecular volume effects are manifested more clearly in bond lengths than bond angles which depend mainly on intramolecular properties. Frequency analyses of the τ₁, τ₂ and τ₃ torsional angles in the crystal structures show conformational steering in the sense that, if τ₁ is trans peri-planar (170°≤τ₁≤180°; −180°≤τ₁≤−170°), the values of τ₂ and τ₃ are clustered closely around the ideal gauche (±60°) and trans (±180°) positions. In contrast, when τ₁ is in the region (50°≤τ₁≤70°), there is a definite increase in the populations of τ₂ and τ₃ at −90 and −150°.     

Conformational and structural studies of ethyl fluorosilane from temperature dependent FT-IR spectra of krypton solutions and ab initio calculations

The infrared spectra (3200–30 cm⁻¹) of gaseous and solid ethyl fluorosilane, CH₃CH₂SiH₂F, have been recorded. Additionally, the Raman spectra (3200–30 cm⁻¹) of the liquid and solid have been recorded and quantitative depolarization values obtained. Both the gauche and trans conformers have been identified in the fluid phases but only the gauche conformer remains in the solid. Variable temperature (−105 to −150°C) studies of the infrared spectra of the sample dissolved in liquid krypton have been carried out. From these data, the enthalpy difference has been determined to be 54±16 cm⁻¹ (646±191 J/mol) with the gauche conformer the more stable form. This is consistent with the predictions from ab initio, MP2/6-311+G(2d,2p), calculation as well as those with smaller basis sets with full electron correlations. A complete vibrational assignment is proposed for both the trans and gauche conformers based on infrared band contours, relative intensities, depolarization values, and group frequencies, which are supported by normal-coordinate calculations utilizing the force constants from MP2/6-31G(d) ab initio calculations. Complete equilibrium geometries have been determined for both rotamers by ab initio calculations employing a variety of basis sets up to 6-311+G(2d,2p) at levels of restricted Hartree–Fock (RHF) and/or Moller Plesset to the second order (MP2) with full electron correlation. The adjusted r₀ parameters have been obtained for both conformers from a combination of the previously reported rotational constants with ab initio predicted values. All results are compared to similar quantities of some corresponding molecules.     

Spectroscopy of C–H stretching vibrations of gas-phase cyclohexene

The fundamental and overtone spectra of the C–H stretching of cyclohexene in the gas phase have been measured using FTIR spectroscopy in the range 2800–11 500 cm⁻¹ (Δv=1–4) and intracavity dye laser spectrometry in the range 12 900–17 500 cm⁻¹ (Δv=4–7). Up to Δv=6, the spectra show disturbed structure. The transitions observed are mainly interpreted on the basis of a comparative study with the previous experimental and theoretical work relative to 3,3,6,6-d₄-cyclohexene. Ab initio calculations of molecular geometries and fundamental vibrational frequencies have also been performed in a molecule-fixed cartesian coordinates to calculate the first derivative of the dipole moment function and of the polarisability tensor in order to reproduce the fundamental infrared and Raman spectra. In the overtone spectra, possibility of Fermi resonances between the methylenic C–H bond stretchings and combination states involving other low-frequency modes is qualitatively discussed.     

Infrared and Raman spectra, conformational stability, ab initio calculations of structure, and vibrational assignment of 2-hexyne

The infrared spectra (3500–50 cm⁻¹) of the gas and solid and the Raman spectra (3500–50 cm⁻¹) of the liquid and solid have been recorded for 2-hexyne, CH₃–CC–CH₂CH₂CH₃. Variable temperature studies of the infrared spectrum (3500–400 cm⁻¹) of 2-hexyne dissolved in liquid krypton have also been recorded. Utilizing four anti/gauche conformer pairs, the anti(trans) conformer is found to be the lower energy form with an enthalpy difference of 74±8 cm⁻¹ (0.88±0.10 kJ/mol) determined from krypton solutions over the temperature range −105 to −150 °C. At room temperature it is estimated that there is 42% of the anti conformer present. Equilibrium geometries and energies of the two conformers have been determined by ab initio (HF and MP2) and hybrid DFT (B3LYP) methods using a number of basis sets. Only the HF and DFT methods predict the anti conformer as the more stable form as found experimentally. A vibrational assignment is proposed based on the force constants, relative intensities, depolarization ratios from the ab initio and DFT calculations and on rotational band contours obtained using the calculated equilibrium geometries. From calculated energies it is shown that the CH₃ group exhibits almost completely free rotation which is in agreement with the observation of sub-band structure for the degenerate methyl vibrations from which values of the Coriolis coupling constants, ζ, have been determined. The results are compared to similar properties of some corresponding molecules.     

Temperature dependence of the rate constant for reactions of hydrated electrons with H, OH and H2O2

The temperature dependence of the rate constants, for the reactions of hydrated electrons with H atoms, OH radicals and H₂O₂ has been determined. The reaction with H atoms, studied in the temperature range 20–250°C gives k(20°C) = 2.4 × 10¹⁰M^-1s¹ and the activation energy E_A = 14.0 kJ mol^-1 (3.3 kcal mol^-1). For reaction with OH radicals the corresponding values are, k(20°C) = 3.1 × 10¹⁰M^-1s^-1 and E_A = 14.7 kJ mol^-1 (3.5 kcal mol^-1) determined in the temperature range 5–175°C. For reaction with H₂O₂ the values are, k(20°C) = 1.2 × 10¹⁰M^-1s^-1 and E_A = 15.6 kJ mol^-1 (3.7 kcal mol^-1) measured from 5–150°C. Thus, the activation energy for all three fast reactions is close to that expected for diffusion controlled reactions. As phosphates were used as buffer system, the rate constant and activation energy for the reaction of hydrated electron with H₂PO₄^- was determined to k(20°C) = 1.5 × 10⁷M^-1s^-1 and E_A = 7.4 kJ mol^-1 (1.8 kcal mol^-1) in the temperature range 20–200°C.     

Structure and conformational properties of carbonylbisimidosulfuryl fluoride, O=C(N=S(O)F2)2

The molecular structure and conformational properties of O=C(N=S(O)F₂)₂ (carbonylbisimidosulfuryl fluoride) were determined by gas electron diffraction (GED) and quantumchemical calculations (HF/3-21G* and B3LYP/6-31G*). The analysis of the GED intensities resulted in a mixture of 76(12)% syn–syn and 24(12)% syn–anti conformer (ΔH⁰=H⁰(syn–anti)−H⁰(syn–syn)=1.11(32) kcal mol⁻¹) which is in agreement with the interpretation of the IR spectra (68(5)% syn–syn and 32(5)% syn–anti, ΔH⁰=0.87(11) kcal mol⁻¹). syn and anti describe the orientation of the S=N bonds relative to the C=O bond. In both conformers the S=O bonds of the two N=S(O)F₂ groups are trans to the C–N bonds. According to the theoretical calculations, structures with cis orientation of an S=O bond with respect to a C–N bond do not correspond to minima on the energy hyperface. The HF/3-21G* approximation predicts preference of the syn–anti structure (ΔE=−0.11 kcal mol⁻¹) and the B3LYP/6-31G* method results in an energy difference (ΔE=1.85 kcal mol⁻¹) which is slightly larger than the experimental values. The following geometric parameters for the O=C(N=S)₂ skeleton were derived (r_a values with 3σ uncertainties): C=O 1.193 (9) Å, C–N 1.365 (9) Å, S=N 1.466 (5) Å, O=C–N 125.1 (6)° and C–N=S 125.3 (10)°. The geometric parameters are reproduced satisfactorily by the HF/3-21G* approximation, except for the C–N=S angle which is too large by ca. 6°. The B3LYP method predicts all bonds to be too long by 0.02–0.05 Å and the C–N=S angle to be too small by ca. 4°.     

Rates of the reactions CN + H2CO and NCO + H2CO in the temperature range 294–769 K

The rate coefficients of the reactions: (1) CN + H₂CO → products and (2) NCO + H₂CO → products in the temperature range 294–769 K have been determined by means of the laser photolysis-laser induced fluorescence technique. Our measurements show that reaction (1) is rapid: k₁(294 K) = (1.64 ± 0.25) x 10⁻¹¹ cm³ molecule⁻¹ s⁻¹; the Arrhenius relation was determined as k₁ = (6.7 ± 1.0) x 10⁻¹¹ exp[(−412 ± 20)/T] cm³ molecule⁻¹ s⁻¹. Reaction (2) is approximately a tenth as rapid as reaction (1) and the temperature dependence of k₂ does not conform to the Arrhenius form: k₂ = 4.62 x 10⁻¹⁷T^1.71 exp(198/T) cm³ molecule⁻¹ s⁻¹. Our values are in reasonable agreement with the only reported measurement of k₁; the rate coefficients for reaction (2) have not been previously reported.     

Kinetics study of the gas-phase reactions of C2F5OC(O)H and n-C3F7OC(O)H with OH radicals at 253–328 K

The rate constants, k₁ and k₂ for the reactions of C₂F₅OC(O)H and n-C₃F₇OC(O)H with OH radicals were measured using an FT-IR technique at 253–328 K. k₁ and k₂ were determined as (9.24 ± 1.33) × 10⁻¹³ exp[−(1230 ± 40)/T] and (1.41 ± 0.26) × 10⁻¹² exp[−(1260 ± 50)/T] cm³ molecule⁻¹ s⁻¹. The random errors reported are ±2 σ, and potential systematic errors of 10% could add to the k₁ and k₂. The atmospheric lifetimes of C₂F₅OC(O)H and n-C₃F₇OC(O)H with respect to reaction with OH radicals were estimated at 3.6 and 2.6 years, respectively.     

Distance dependence analysis of the electron transfer reactivity for the metastable FeOH2/FeOH2 system: an ab initio investigation

A novel theoretical scheme and ab initio application in discussing the electron transfer (ET) reactivity are presented in this paper, and are also calibrated in terms of the mono-hydrated iron ion system, Fe²⁺–OH₂/Fe³⁺–OH₂. The detailed geometry optimizations have been made at UMP2(full)/6-311+G^* level, and the activation geometrical configuration and the energy have been obtained at this level of theory using the activation model and the ab initio potential energy surface fitted from MP2(full)/6-311+G^* single point energies. The corresponding energy quantities (such as the activation energy, and dissociation energy) have also been obtained at different levels of theory (HF, MP2, MP3, MP4, QCISD and PUHF, PMP2 and PMP3 with the spin-projection) and a same basis set (6-311+G^*). The electron correlation calculations include the all electron correlation and the valence electron correlation. The electronic transmission coefficient is calculated using the ab initio potential energy surface slopes and the coupling matrix element determined from the two-state model and the Slater-type d-electron wave functions. The pair distribution function is calculated using two different schemes. Taking the pair distribution function and the local ET rate into account, a statistically averaged overall observed ET rate scheme and a spherically averaged local ET rate scheme are proposed. The relevant kinetic parameters are obtained in terms of these new schemes at different ab initio calculational levels. The contact distance dependence of these parameters and the applicability of the presented models and ab initio calculational method are also discussed.     

Exocyclic push–pull conjugated compounds. Part 3. An experimental NMR and theoretical MO ab initio study of the structure, the electronic properties and barriers to rotation about the exocyclic partial double bond in 2-exo-methylene- and 2-cyanoimino-quinazolines and -benzodiazepines

The structure of a number of 2-exo-methylene substituted quinazolines and benzodiazepines, respectively, 1, 3a,b, 4 (X=–CN,–COOEt) and their 2-cyanoimino substituted analogues 2, 3c,d (X=–CN,–SO₂C₆H₄–Me(p) was completely assigned by the whole arsenal of 1D and 2D NMR spectroscopic methods. The E/Z isomerism at the exo-cyclic double bond was determined by both NMR spectroscopy and confirmed by ab initio quantum chemical calculations; the Z isomer is the preferred one, its amount proved dependent on steric hindrance. Due to the push–pull effect in this part of the molecules the restricted rotation about the partial C²,C¹¹ and C²,N¹¹ double bonds, could also be studied and the barrier to rotation measured by dynamic NMR spectroscopy. The free energies of activation of this dynamic process proved very similar along the compounds studied but being dependent on the polarity of the solvent. Quantum chemical calculations at the ab initio level were employed to prove the stereochemistry at the exo-cyclic partial double bonds of 1–4, to calculate the barriers to rotation but also to discuss in detail both the ground and the transition state of the latter dynamic process in order to better understand electronic, inter- and intramolecular effects on the barrier to rotation which could be determined experimentally. In the cyanoimino substituted compounds 2, 3c,d, the MO ab initio calculations evidence the isomer interconversion to be better described by the internal rotation process than by the lateral shift mechanism.     

Thermogravimetric study on perovskite-like oxygen permeation ceramic membranes

The oxygen permeation properties of mixed-conducting ceramics SrFeCo_0.5O_3−δ (SFCO), Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ (BSCFO), La_0.2Sr_0.8Co_0.8Fe_0.2O_3−δ (LSCFO) and Ba_0.95Ca_0.05Co_0.8Fe_0.2O_3−δ (BCCFO) were studied by thermogravimetric method in the temperature range 600–900 °C. The results show that the oxygen adsorption rate constants k_a of all material are larger than oxygen desorption rate constants k_d and both k_a and k_d are not strongly dependent on temperature in the studied temperature range. The oxygen vacancy contents δ(N₂) and δ(O₂) in nitrogen and oxygen and their difference Δδ = δ(N₂) − δ(O₂) play an important role in determining the temperature behavior of oxygen permeation flux J_O2.