Gas/gas and gas/wall average energy transfer from very low-pressure pyrolysis

It is shown that data obtained using very low-pressure pyrolysis (VLPP) on the pressure and temperature dependence of unimolecular rate coefficients of reactants with several reaction channels yield average energies transferred in gas/gas and gas/wall collisions (the wall being seasoned quartz at 800–1200 K). The downward average energy transferred, «ΔEå, for chlorocyclobutane/ethylene collisions is found to be 1600 cm^?1 at 970 K; «ΔEå for chlorocyclobutane/wall collisions varies from 5000 cm^?1 (wall efficiency β_w = 0.8) at 930 K to 3500 cm^?1 (β_w = 0.4) at 1150 K; similar values are found from published data on cycloheptatriene and cyclopropane-d₂. This indicates that the assumption of unit wall efficiency usually used in fitting VLPP experiments to RRKM theory needs revision.     

A classical trajectory study of the effect of reaction barrier height on the vibrational energy transfer efficiency in the Cl + HCl system

The effects of reaction barrier height and initial rotational excitation of the reactants on the overall rate of H atom exchange between atomic chlorine and HCl (v = 0) and on the 0 → 1 vibrational excitation of HCl via reactive and nonreactive collisions have been investigated using quasiclassical trajectory techniques. Two empirical LEPS potential energy surfaces were employed in the calculations having reaction barrier heights of 9.84 and 7.05 kcal mol^?1. Trajectory studies of planar collisions were carried out on each surface over a range of relative translational energies with the ground-state HCI collision partner given initial rotational excitation corresponding J = 0, 3, and 7. Initial molecular rotation was found to be relatively inefficient in promoting the H atom exchange; the computed rate coefficient for H atom exchange between Cl + HCl (v = 0, J = 7) was only 4 times larger than that for CI + HCI (v = 0, J = 0). The vibrational excitation rate coefficient exhibited a stronger dependence on initial molecular rotational excitation. The observed increase in the vibrational excitation rate coefficient with increasing initial molecular rotational excitation was due primarily to nonreactive intermolecular R → V energy transfer. The vibrational excitation rate coefficients increase with decreasing reaction barrier height.     

Energy transfer in classical collinear and perpendicular central collisions of a structureless atom with a morse oscillator

The energy transfer in classical collinear (C_∞) and perpendicular (C_2v) central collisions of an atom with a Morse oscillator is compared. These collision geometries contribute in classical collisions to experimentally observed inelastic backward scattering of alkali ions from H₂ molecules. For both collision geometries the equations of motion reduce to a set of only two coupled differential equations which can be easily solved numerically. The calculations show that the C_2v collisions are much more effective than C_∞ collisions at all but the very lowest energies. The calculated ΔE/E versus E curves for C_2v collisions using a Born-Mayer potential for the atom atom-in-molecule interaction could be fitted to the experimental results for Na⁺-D₂ yielding reasonable potential values.     

Semiclassical Trajectory Studies of Reactive and Nonreactive Scattering of OH(A 2Σ+) by H2 Based on an Improved Full-Dimensional Ab Initio Diabatic Potential Energy Matrix

We present a new full-dimensional diabatic potential energy matrix (DPEM) for electronically nonadiabatic collisions of OH(A ²Σ⁺) with H₂, and we calculate the probabilities of electronically adiabatic inelastic collisions, nonreactive quenching, and reactive quenching to form H₂O+H. The DPEM was fitted using a many-body expansion with permutationally invariant polynomials in bond-order functions to represent the many-body part. The dynamics calculations were carried out with the fewest-switches with time uncertainty and stochastic decoherence (FSTU/SD) semiclassical trajectory method. We present results both for head-on collisions (impact parameter b equal to zero) and for a full range of impact parameters. The results are compared to experiment and to earlier FSTU/SD and quantum dynamics calculations with a previously published DPEM. The various theoretical results all agree that nonreactive quenching dominates reactive quenching, but there are quantitative differences between the two DPEMs and between the b=0 results and the all-b results, especially for the probability of reactive quenching.     

Energy transfer as a function of collision energy. I Collision partners: Hydrogen halides + inert gases,hydrogen halides,H2S and propane

Infrared emission has been recorded from a heated seeded supersonic primary beam of HCl or HF (1) prior to collision with a target beam, and (2) subsequent to that collision. Mean collision energy and collision partner were varied systematically. After correction for elastic scattering, the net population change due to inelastic scattering in a translation—rotation (T ? R) energy-transfer encounter was obtained for specific J states ranging from J = 0–16 of vibrational level υ = 1 of the primary-beam molecule. The broad picture is that a net transfer into low-J states out of higher-J states takes place at low collision energies, and the converse at high collision energies. These observations are interpreted in terms of the “exponential model” for the relative cross sections of T ? R inelastic collisions, S^R (J_i → J_f), proposed earlier [J.C. Polanyi and K.B. Woodall, J. Chem. Phys. 56 (1972) 1563], modified here to satisfy microscopic reversibility. The constant C in the model, which governs the exponential decrease in S^R with increasing energy difference ΔE_J between J_f and J_i, can be derived, as a function of collision energy T, from the present experimental data; C decreases as T increases, i.e. larger ΔJ become more probable. In order to check the validity of the model, it was compared with 3D trajectory results; according to this criterion it was found to give a very good representation of S^R(J_i → J_f) with a single value for C, within a limited range of J_i. The collision partners HCl + HF exhibit anomalously efficient rotational deactivation; evidence is presented which indicates that at low collision energies this is due to resonant R → R transfer. Very efficient deactivation of HCl by HCl, at low collision energy, is likely to be due to V — V transfer.     

The influence of the crystal lattice structure on the conduction band energy of oxides of titanium(IV)

The reducing properties of conduction band electrons of anatase, rutile and strontium titanate were correlated with their structures. It was shown by extended Hückel MO calculations on model complexes that the energy levels of the lowest unoccupied molecular orbitals (LUMOs) involving predominantly the 3d_τ orbitals xy, xz and yz of Ti are sensitive to the lattice structure. The calculated LUMO energies are in qualitative agreement with experimental flat-band potentials (E_1b) and band-gap energies (E_g). The presently unknown E_g and E_1b of brookite are estimated as 3.14 eV and = −0.03 V versus NHE, respectively. These values are intermediate between anatase and rutile.     

Quantum chemical calculations of intracell potential profile in superionic transition range in LaF3

The results of quantum chemical calculations of the potential profile in the LaF₃ crystal lattice in the range of superionic phase transition are presented for clusters containing 24 to 1200 ions. It is found that the values of formation energy E _a of vacancy-interstitial fluoride ion defects and potential barriers E _d hindering the movement of fluoride ions and determining the efficiency of charge transport in the lattice grow monotonously from the minimum values E _a = 0.12 eV and E _d = 0.22 eV for a 24-ion cluster to the maximum E _a = 0.16 eV and E _d = 0.26 eV for clusters of 576 and 1200 ions. It is shown that the values of E _a and E _d obtained for the dielectric phase (T < T _c) are several times the values of E _a and E _d for the superionic state (T ≥ T _c) of LaF₃. The values of E _a and E _d obtained by quantum chemical calculations from clusters of 576 and 1200 ions agree well with energies E _a and E _d obtained from the analysis of the data of the Raman and quasielastic light scattering.     

WO<Subscript>3</Subscript> films prepared by thermal oxidation of magnetron-sputtered tungsten: Synthesis and properties

X-ray powder diffraction shows that a monoclinic WO_2.90 film is formed during the thermal oxidation of 200-nm-thick magnetron-sputtered metallic tungsten on quartz substrates at T = 793 K. Temperature elevation to T = 840 K yields orthorhombic WO₃ with preferred (001) orientation. Adsorption spectroscopy shows that these films have high transparency (～90%) in the wavelength range 450–900 nm, and interference is observed in the transparency range. Two types of transitions are discovered: indirect transitions with the energies E _gi = 2.77 and 2.41 eV and direct transitions with the energies E _gd = 5.49 and 4.82 eV for the oxide films formed at 793 and 840 K, respectively. The tendency toward the increase in the transition energy with increasing annealing temperature proves that the crystallinity and order of the film improve.     

Recurrence calculations of organic compound boiling temperatures from data on preceding homologues

A new approach to calculating the temperatures of boiling at atmospheric pressure (T _b) of organic compounds from arbitrary homologous series is suggested. The approach is based on the linear dependence of these values on T _b for the preceding homologues, T _b(n) = aT_b(n ? 1) + b. This dependence, revealed for the first time, was used to obtain a recurrence relation for calculating T _b of organic compounds within any series from the data on three simpler homologues of the same series. The mean a and b values can be used to estimate T _b of an arbitrary organic compound from T _b for one preceding homologue with an accuracy not inferior to that provided by the modern ACD software. Correlations of the general form P(n) = aP(n ? 1) + b are observed not only for the boiling points of organic compounds but also for their other properties P (refractive indexes, relative densities, and ionization energies). This opens up the possibility of creating unified algorithms for calculating various physicochemical constants of organic compounds instead of particular algorithms for every particular property known earlier.     

The kinetic and internal energies of OH(A2Σ+) produced by electron stimulated desorption from TiO2, NaCl and SrF2 surfaces

The kinetic and internal energies of OH(A ²Σ⁺) radicals produced by electron-stimulated desorption from H₂O-exposed TiO₂, NaCl and SrF₂ surfaces are reported. The kinetic energies were determined by measuring the spatial extent of the fluorescence above each substrate surface, while the vibrational and rotational energies were determined by analyzing the intensity distribution of the rovibrational spectra. We find that OH* from NaCl and SrF₂ has low kinetic energy, 80 and 150 meV, respectively, and low rotational excitation, T_rot ≈ 340–450 K. OH* from TiO₂ is more energetic, E_kin = 250 meV and T_rot ≈ 1000 K. The OH* vibrational excitation is high. T_vib ≈ 2000 K, and independent of the nature of the substrate.     

Ion pair formation in alkali-SF6 collisions: Dependence on collisional and vibrational energy

The dependence of ion pair formation in collisions of fast alkali atoms (K, Na and Li) with SF₆ on the initial relative kinetic energy and the internal energy of the target molecule has been studied by the crossed molecular beam method. Using a mass spectrometer we have measured total cross sections for negative ion formation as a function of translational and internal energy. Collision energies ranged from threshold up to 35 eV and SF₆ source temperatures were varied from 300 K to 850 K.By means of an inverse Laplace transform of the measured cross sections, we have determined total specific cross sections for each negative ion depending on the SF₆ vibrational energy and at fixed relative kinetic energy.The relative importance of both collisional and internal energy in promoting the electron transfer process is discussed for the various reaction channels in terms of a collision model. An essential feature of this model is the stretching of the S-F molecular ion bond during the collision. The product show complete relaxation in the threshold region, i.e., vibrational and collisional energy are equivalent: This holds for the SF⁻₆ formation only near threshold and for the SF⁻₅ and F⁻ formation up to about 2 eV above threshold. In the post-threshold region the effect of the internal energy on the cross section dominates over that of the translational energy.From these measurements the adiabatic electron affinity of SF₆ is inferred to be 0.32 ± 0.15 eV, T = 0 K. Some other thermodynamic data are deduced: EA(SF₅) > 2.9 ± 0.1 eV (T = 300 K) and D₀(SF⁻₅-F) = 1.0 ± 0.1 eV.     

The born approximation as a simple diagnostic method for direct molecular collisions with applications to Cl + HI and F + H2 reactions

Born approximation computations are presented and discussed for the Cl + HI → I + HCl and F + H₂ → H + HF reactions and their isotopic analogues. Most aspects of the role of reagent energy or the energy disposal in the products previously deduced from experiment or trajectory computations can be accounted for the Born approximation. The procedure used here neglects the interaction between non-bonded atoms. It does thereby provide a very simple computational scheme which requires as input only the spectroscopic constants of the reactants and products. In addition it offers simple qualitative interpretations of the trends in the results. The overall satisfactory agreement between the present results and past studies lends credibility to the basic propensity rule provided by the Born approximation: The most probable transitions are those that minimize the momentum transfer to the nuclei. The principle is discussed with special reference to exothermic (E′_T ? E_T) and endothermic transitions.The computations for Cl + HI indicate a decline of the reaction cross section with increasing kinetic energy and a strong enhancement by HI rotational energy. The surprisal analysis confirms the absence of vibrational population inversion for endothermic transitions. For the F + H₂ (and isotopic variants) reactions, the product-rotational state distribution extends nearly to the energy cut-off. The vibrational state distribution is somewhat different for para- and normal H₂ and, in general, the collision outcome is very sensitive to the initial rotational state of H₂ particularly at low translational energies. The HF/DF branching ratio is F + HD collisions is increasing with increase of the HD rotational state. The vibrational surprisal is essentially isotopically invariant.     

Production and decomposition of highly excited 2-butyl radicals by the addition of hot hydrogen atoms to but-2-ene. Cross section for the addition reaction

Highly excited 2-butyl radicals have been generated by addition of hot hydrogen atoms to but-2-ene. Atoms of initial energy 130 kJ mol^?1 and 161 kJ mol^?1 were produced by photolysis of H₂S. Rates of decomposition of the highly excited 2-butyl radicals were monitored by analysis of stabilization and decomposition products, and the extent of energy-loss of the hydrogen atoms in nonreactive collisions assessed by measuring the effect of added xenon on product yields. A model involving the cross-section for the addition reaction, energy transfer in nonreactive collisions between hydrogen atoms and but-2-ene, RRKM rate constants for decomposition of excited 2-butyl radicals, and collisional energy transfer from the radicals, has been used to calculate product yields for comparison with experimental values. It is concluded that the cross-section for addition of hydrogen atoms of energy about 130 kJ mol^?1 to but-2-ene is 0.055 ± 0.028 nm². This value is compatible with the A factor for the thermal addition reaction.     

Electronic spectra parameters as a tool for studying the structure of the catalytic center and the mechanism of activation of d 0-transition metal complexes in olefin polymerization

The quantum-chemical model formerly designed is described, which explains the high reactivity of the d ⁰-transition metal-carbon σ-bond in concerted reactions including polymerization of olefins. In this model, the energy of transition from the ground singlet state to the excited singlet or triplet state corresponding to the transfer of electron density from the metal-carbon bond to vacant d-atomic orbitals correlates with its relative elongation after which a change in the valence state of a metal begins. This change is caused by the difference in the geometries of valence s-, p-, and d-atomic orbitals having close energies; as a result, at a certain bond elongation, partial uncoupling of electrons involved in bonding takes place so that one of them becomes localized on d-atomic orbital. This process facilitates formation of the reactive state of the bond of the biradical type and leads to a reduction in the energy barrier of the insertion of an olefin molecule into this bond. Lower energies of this barrier correspond to lower values of ΔE(S ₀ → S _j ) and ΔE(S ₀ → T _j ). As shown at the example of zirconocenes Cp₂ZrMe₂ and Me₂CCp₂ZrMe₂, alongside with a reduction in the energy barrier of olefin insertion into the Zr-Me bond of the cationic complex being formed, the characteristic absorption band in the spectrum of the corresponding neutral derivative shifts to the long-wave region. This band is attributed to the transfer of the electron density from the Zr-Me bond to the Zr atom. Analysis is performed of the causes for bathochromic shifts of the long-wave absorption band for adduct formation in the systems including metallocene and Al-containing cocatalyst.     

Hydration heat capacities of hydrophobic solutes at 248–373 K

A new equation is suggested to define the temperature dependence of the Gibbs energy of hydration of hydrophobic substances: ΔG ⁰ = b ₀ + b ₁ T + b ₂lnT. According to this equation, the hydration heat capacity is in inverse proportion to temperature. Consistent values of hydration heat capacity of nonpolar solutes have been obtained for different temperatures using data on solubility and dissolution enthalpy. The contributions of the hydrocarbon radicals and OH group to the heat capacity of hydration of the compounds were found for the temperature range 248–373 K. The hydration heat capacity of the hydroxyl group has a weak dependence on temperature and increases by only 12 J/(mol·K) in the specified temperature interval. Changes in the hydration entropy of hydrophobic and OH groups are calculated for the temperature increasing from 248 K to 373 K.     

Vibrational energy exchange of the DF (ν=2) state with DF (ν=0)

The energy transfer rate for the reaction DF (ν=1) + DF (ν=1)^k_νν→ DF (ν=0) + DF (ν=2) + ΔE=91.6 cm^?1 has been studied in a combined shock-tube laser-induced fluorescence experiment at temperatures from 295 to 720°K. The rate coefficient k_νν for the exothermic reaction was found to vary as T^?1 when expressed in units of cm³/mole sec. At T=295°K, the probability of the reaction is approximately 0.2 per collision.     

Energy dependence of the cross section for alkali—methyl iodide reactions

The dependence of the reaction cross section for all the alkali—methyl iodide reactions on the translational energy in the range E_T = 0–40 kcal/mole has been discussed in an idealized collision model of hard-sphere interaction between colliding particles. In all reaction of the family, the cross section increases sharply with E_T showing an Arrhenius-like positive energy dependence for E_T just past threshold and then takes a maximum value. The maximum value is largest for the Cs reaction and decreases with the alkali mass except that it slightly increases from Rb to K, and the peak becomes broader as the mass decreases. In the post-maximum region the cross section decreases slowly with E_T.     

Vibrational energy transfer in the two-channel 1,1-cyclopropane-d2 isomerization system. Krypton bath gas

The study of intermolecular energy transfer in the 1,1-cyclopropane-d₂ system has been repeated for the neat gas at 973 K and has been extended to krypton bath gas at 823 K and 973 K. The method of study is by the competitive collisional activation “spectroscopy” technique for this two-channel competitive isomerization system. Results at 823 K give the relative collisional efficiency of krypton as β ≈ 0.46, at k/k_∞ ≈ 0.02 and yield the average down-jump energy step as 〈ΔE〉 ≈ 1200 cm^?1 on the basis of a stepladder model for the distribution of down-step sizes. At 973 K and k/k_∞ = 0.02, β ≈ 0.07 and 〈ΔE〉 ≈ 500 cm^?8, for both an exponential and stepladder distribution of down-step sizes. Agreement with related earlier data for other bath gases and for neat cyclopropane is good and verifies again a decrease in energy transfer collisional efficiency, and a decrease in 〈ΔE〉, with rise of temperature, as previously reported for this system.     

Observed translational energy dependence of the K + C2H5I → KI + C2H5 reaction cross section from 0.17 to 0.55 eV (c.m.)

Relative values of the total reaction cross section σ_R for the crossed molecular beam reaction K + C₂H₅I → KI + C₂H₅ have been measured over the translational energy (E_T) range 0 17–0.55 eV. It is found that σ_R decreases monotonically with E_T over this range, any maximum in σ_R(E_T) is presumed to lie below 0.17 eV.