Modified statistical theory of energy transfer in ion-molecule collisions

The modified statistical theory developed previously for potentials appropriate to interactions in neutral-neutral collisions, is now extended to more strongly attractive potentials involved in ion-neutral collisions. The model system is the collisional deactivation of C₅H₉⁺ by a variety of both polar and non-polar neutral molecules. A 12 - 6 - 4 potential is used for ion interaction with non-polar neutrals, and a 12 - 6 - 4 - 2 potential, as modified by Su and Bowers to take into account the rotational energy of the neutral, for interaction with polar neutrals. Calculated is (ΔE), the average energy lost by the ion in a collision, and compared with experiment. For C₅H₉⁺-CH₄ collisions, the calculated (ΔE) agrees with experiment within 5%. Predictions of the theory, namely that (ΔE) should increase with excitation energy and should decrease with the size of the excited reactant, are found to be in fair agreement with the somewhat ambiguous experimental evidence.     

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.     

The role of correlation in calculations on 1,2-difluoroethylenes. The cis-trans energy difference

Correlation-corrected ab initio calculations predict cis-1,2-difluoroethylene to be more stable than trans. With second-order Rayleigh-Schrödinger Møller-Plesset theory, the cis form is lower by 0.9-1.3 kcal/mol, depending on the basis set, in agreement with the experimental energy difference ΔE = 1.1 kcal/mol. The positive ΔE is primarily due to greater intrapair correlation energy in the cis form.     

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.     

Collisional deactivation of highly vibrationally excited hexafluorobenzene molecules

The collisional deactivation of the internal energy of vibrationally highly excited hexafluorobenzene (HFB) molecules was examined by the analysis of ultraviolet absorption spectra of excited HFB molecules produced by excitation with an ArF(193 nm) laser. The decay time profile of the internal energy was calculated from the observed absorption decay profile of the hot molecule using the conversion relation between the absorbance by hot molecules and the internal energy. Thus the average energy 〈ΔE〉 transferred per collision was estimated by two different models; energy-independent and energy-dependent function for the decay of the internal energy. The obtained values of 〈ΔE〉 indicate that the energy-dependent model may give reasonable values for 〈ΔE〉, but as far as the value of 〈ΔE〉 is concerned, the energy-independent model is likely to be applicable to the analysis in this reaction system. The collisional deactivation mechanism of the hot HFB molecule and the heating-up effect observed at shorter wavelengths are discussed on the basis of the conversion curve.     

Temperature dependence of vibrational energy transfer in the “low” pressure competitive two-channel 1,1-cyclopropane-d2 system

Intermolecular energy transfer has been studied in the two-channel competitive isomerization of 1,1-cyclopropane-d₂, both in the neat system and in the presence of helium bath gas at values of k/k^? centered around 0.02. The competing path ways differ in threshold energy by ≈ 0.6 kcal. The temperature range 773 K to 973 K was covered. Several methods of treating the data, whether by isotopic ratios of rate constants or by temperature dependence of fall off, are each independent of a knowledge of collision cross sections. Used in conjunction, they provide measurements of these quantities. Cyclopropane is an operationally strong collider (β_ω = 1) for itself at 773 K with an average down step size, <ΔE/s> >/ 10 kcal mole ^?1 (>/ 3500 cm^?1). At 973 K the substrate is no longer a strong collider; β_ω declines to ≈ 0.55 with <ΔE/s> ≈ 5.2 kcal mole^?1. For helium the corresponding quantities are β_ω ≈ 0.078 <ΔE/s> ≈ 1.1 kcal mole ^?1 declining to β_ω ≈ 0.010 and <ΔE/s> ≈ 0.53 kcal mole^?1. The several methods of measuring these quantities give excellent independent agreement. Comparison with the earlier theoretical formulation of Tardy and Rabinovitch gives good agreement, the temperature dependence of β_ω for the weak collider, helium, follows the relation β_ω ∝ T^?m, where m /s> 2.     

Reactivity of haloalkanes in their reactions with the chlorine atom

Experimental kinetic data on reactions of the chlorine atom with halogenated derivatives of methane and ethane (37 reactions) have been analyzed by the intersecting-parabolas method. The following five factors have an effect on the activation energy of these reactions: the enthalpy of reaction, triplet repulsion, the electronegativities of the reaction center atoms, the dipole–dipole and multidipole interactions between the reaction center and polar groups, and the effect of π electrons in the vicinity of the reaction center. The increments characterizing the contribution from each factor to the activation energy of the reaction have been calculated. The contribution from the polar interaction, ΔE _μ, to the activation energy depends on the dipole moment of the polar group and obeys the following empirical equation: ln(Δ_{E μ}/Σμ) = ?0.74 + 0.87(ΔE _μ/Σμ) ? 0.084(ΔE _μ/Σμ)².     

Factors determining the reactivity of the bromine atom toward haloalkanes

Experimental data concerning reactions of the bromine atoms with haloalkanes and carbonyl compounds (25 reactions) have been analyzed within the intersecting parabolas model. The following factors have an effect on the activation energy of these reactions: enthalpy of reaction, triplet repulsion, electronegativity of reaction center atoms, dipole–dipole and multidipole interactions of the reaction center with polar groups, and the interaction of π electrons with electrons of the reaction center. The increments characterizing the contribution from each factor to the activation energy of the reaction have been calculated. The increment ΔEμ, which characterizes the dipole–dipole interaction in the transition state, and the dipole moment of the polar group (μ) are correlated by the following empirical equation: ln(ΔE _μ/Σμ) = ?0.14 + 0.47(ΔE _μ/Σμ) ? 0.024(ΔE _μ/Σμ)².     

Quantum chemical study of aromatic diamine and dianhydride reactivities in acylation reactions

Semi-empirical calculations of isolated diamines and model anhydrides and of their interaction energy, ΔE, have been made. Reactivity indices of diamines and dianhydrides (atom charges, characteristics of frontier orbitals) have been found. Analysis of the ΔE components has shown that chemical structure of diamines affects mainly electrostatic and charge transfer contributions to ΔE. Chemical structure of diahnydrides influences most significantly charge transfer component. Results of the ΔE calculation have substantiated the choice of reactivity indices.     

Laser fluorescence studies of HF rotational relaxation

Rotation relaxation of HF in HF-Ar mixtures was observed using a laser infrared fluorescence technique. A specific vibrational-rotational state of HF was excited, and the fluorescence from HF was monitored. Total rotational energy-transfer rates, and individual state-to-state transition probabilities were obtained for υ = 1, J = 3 (ΔJ = ± 1, ±2) and υ = 1, J = 5; (ΔJ= ±1, ?2, ?3). The transition probabilities decreased with increasing ΔE_J,J, the energy transferred from R → T (rotation to translation). The data were fitted to a simple exponential model k_JJ, α exp(-ClΔE_J,J'l). C was estimated to be 1.55 ± 0.25 kcal^?1 mole.     

Polarization energy of a localized charge in a molecular crystal. VI. Effect of excitons

The polarization energy of a localized charge carrier in a molecular crystal changes by ΔP near an exciton, viewed as a localized excited molecule of changed polarizability. Experimental polarizability changes in the first excited singlet state are used to calculate ΔP for various carrier and exciton positions in benzene, naphthalene, anthracene and tetracene. As the excited-state polarizability is larger, ΔP is normally negative, with minima ranging from ?12 meV in benzene to ?83 meV in tetracene. The change in charge-quadrupole energy ΔW_Q is estimated for naphthalene using a theoretical quadrupole moment for the first triplet state. At most sites |ΔW_Q| > |ΔP|, but the sign of ΔW_Q varies. The net exciton interaction with electrons in naphthalene varies from ?49 to +45 meV and with holes from ?106 to +29 meV. This behaviour is broadly complementary to that previously calculated for vacancies.     

A measurement of the average kinetic energy released during the unimolecular decomposition of CO2 ion clusters

A combined molecular beam—mass spectrometer apparatus has been used to measure the average kinetic energy E_t released during the unimolecular decomposition of CO₂ ion clusters in the field-free region of the mass spectrometer. For the reaction (CO₂), _n→ (CO_2n?1+CO₂, the measured value for E_t is found to increase as n increases from 3 to 13.     

The X<Superscript>−</Superscript>···benzohydrazide complexes: the interplay between anion-π and H-bond interactions

The compounds containing the benzohydrazide (BH) nucleus have a variety of biological activities because of various noncovalent intermolecular interactions. The interplay between anion-π and H-bond interactions, which can affect the activity of compounds, has been investigated in ten substituted BH exposed to the chloride ion using the quantum mechanical calculations. The total interaction energy is separated into the anion-π (ΔE _Aπ) and H-bond (ΔE _HB) contributions where both interactions are presented in the complexes. The electron-withdrawing substituents (EWSs) increase |ΔE _Aπ| and decrease |ΔE _HB|, while reversed changes are observed with the electron-donating substituents (EDSs). In addition, the total binding energy (ΔE) becomes more/less negative in the presence of EWSs/EDSs. The synergetic effects of mentioned interactions and substituent effects have also been investigated using the atoms in molecules (AIM), natural bond orbital (NBO) and molecular electrostatic potential (MEP) analyses. A good correlation is found between the energy data and the Hammett constants, the minimum of electrostatic potential (V _min) and the results of population analyses.     

Parameterization of 241Am and 230Th alpha particle energy in dependence on distance traveled in air

A new method is introduced in this paper for calculating alpha particle energy versus traveled distance (APETD) in air as emitted from ²⁴¹Am and ²³⁰Th sources as well as the alpha range versus its energy and its energy versus distance. This method is to derive the stated relevant equations and in particular to speed up the calculation of E(x) by a Monte-Carlo simulation. By a fitting procedure, an analytical formula E(x) was determined in terms of a series of powers of distance x. Then a randomly sampled x can be quickly transformed into a corresponding energy E. The APETD calculations were run on a Microsoft Windows 7 32?bit operating system with a maximum usable memory of 3?GB. The results of calculations for alphas of the above two radionuclides in air compared to those of others using a different method are in good agreement. The above stated equations as derived in this paper are presented and the process time for applying the new method has been greatly improved.     

The position of the VO3−4 charge-transfer transition as a function of the VO distance

The lowest singlet excited states of the VO^3?₄ complex are calculated as a function of the VO bond distance using the Hartree-Fock-Slater discrete variational method. The calculated average singlet transition energies ¹ΔE(?₁ → 2e) support assignments made before.     

Vibrational analysis of the electronic spectrum of ethylene based onab initio SCF-CI calculations

Ab initio calculations for CH₂ twisting and CC stretching vibrational wavefunctions and energy levels are reported for various electronic states of ethylene C₂H₄. Electronic transition moments between these states are also obtained to allow a calculation of the oscillator strengths for vibrational transitions involved in various electronic band systems; from this study it is concluded that thevertical electronic energy differenceΔE _e may differ significantly from the energy of the absorption maximumΔE _max with which it is often equated. In particular it is found in the case of theπ→π ^* singlet-singlet excitation of ethylene that theΔE _e value overestimates the most probable vibrational transition energy (7.89 eV) by some 0.4 eV, thereby offering an explanation for the fact that previous attempts to predict the location of theV-N Franck-Condon absorption maximum have consistently obtained substantially higher results than the 7.66 eV value actually observed. Similar calculations for various Rydberg species and for theN-T transition are also found to obtain a quite consistent representation of the electronic spectrum of this system.     

Simultaneous determination of the activation energy and the reaction kinetic model from the analysis of a single curve obtained by a novel method

It has been demonstrated that a single plot of the values of Δlnα^1/2/Δln(1-α) (taken from a single α?T curve obtained under a controlled linear increase of the reaction rate) as a function of the corresponding values of Δ(1/T)/Δln(1?α) permits the simultaneous determination of both the activation energy and the kinetic model in accordance with a solid state reaction.     

Spontaneity of reactions of triazine dendric molecules in aqueous medium illustrated with excess viscosities,volumes and free energies

The far-reaching applications of the dendric units?–?2,4,6 trichloro-triazine (2,4,6 TCT), triaceto-triazine (2,4,6 TAT), trihydroxy-triazine (2,4,6 THT) and tridiethylmalonate-triazine (2,4,6 TDEMTA) for reactions in an aqueous medium have been assessed in the present study. Some of their fundamental properties, such as density and viscosity, have been measured to calculate the excess volume (V ^E), viscosity (η ^E) and molar free activation energy (Δ G ^E) at 298.15?K for 6.25–10.0?×?10^?4?mol?kg^?1. The positive values of Δ G ^E for such units suggest their weaker response with water. THT around 3.0?×?10^?7 mole fraction shows maximum Δ G ^E values. The lowest values of Δ G ^E are recorded for TCT.     

Level-to-level vibrational energy transfer studies: energy dependence and observation of product species for azulenes(S0, Evib) + CO2

V—V energy transfer from a large molecule excited to vibrational energies of chemical interest has been demonstrated by detection of ≈ 1.5% yield of CO₂(001) due to energy transfer from azulene (E_vib ≈ 30600 cm^?1. Also, the average enery lost per collision by azulene was measured as a function of E_vib, and the rate constant for CO₂(001) deactivation by azulene was determined.     

A double rainbow interpretation of rotational energy transfer in energetic NO/Ag(111) collisions

The mechanism of rotational energy transfer in energetic (E ? eV) NO/Ag(111) collisions is investigated in quantal rigid-rotor/static-surface calculations. Reasonable agreement with recent experimental results is obtained for the case of a strongly asymmetric interaction potential which leads to two well-separated rotational rainbows at low and at high E_rot, respectively.