Distribution of reaction products (theory). XI. H + F2

The availability for the first time of detailed rate constants k(V′, R′, T′) (where V′, R′ and T′ are product vibrational, rotational and translational excitation) for the highly exothermic reaction H + F₂ → HF(V′, R′) + F has prompted the 3D classical-trajectory study reported here. The potential-energy surface is found to be predominantly repulsive ($\text{A}$_⊥ ≈ 42%, R_⊥ ≈ 58%) corresponding to the rather low fractional conversion of reaction energy into vibration ((f′V) = 0.58 from experiment, and 0.56 from theory). In the homologous series of reactions H + X₂ (X  F, Cl, Br, I) the percentage of repulsive energy-release decreases for X  Cl, Br, I, but increases from X  F to Cl. It is shown that this cannot be due to charge in mass-combination, but can plausibly be explained by the anomolously short range of interaction between the separating X atoms in the case X  F. It is predicted that the more-forward scattered HF will be more rotationally excited. The form of the cross section function S_r(T) (where T is reagent translation) is analysed. In accordance with the expectation for a strongly exothermic reaction, it is found that S_r(T) rises more steeply than S_r(V) (where V is reagent vibrational energy). The effect on the product energy distribution conforms qualitatively to the “adiabatic” behaviour noted in previous work: ΔT → ΔT′ + ΔR′; ΔV → ΔV′. The explanation is to be found in reaction through more-compressed or more-extended intermediate configurations than are characteristic of room temperature reaction. We note the existence of an amplification effect: (ΔT′ + ΔR′)/ΔT ≈ 2, and ΔV′/ΔV ≈ 2.     

Collision-Induced decomposition of peptides. An investigation into the effect of collision gas pressure on translational energy losses

The dependence on the gas pressure of translational energy losses, ΔE, suffered by incident ions in collision with helium target gas atoms was investigated for the [M + Na]⁺ ion of valinomycin. ΔE was measured from the fragment ion peak positions in the mass-analysed ion kinetic energy (MIKE) spectra. The variation of ΔE with target gas pressure was found to be different for different fragment ions. The implications of the results for the number of collisions which may occur under normal collision-induced decomposition conditions (30–40% transmission) are discussed.     

The effect of vibrational bond stretching on rotational inelastic electron-molecule scattering

Differential cross sections for state-to-state rotationally inelastic electron-Na₂ scattering, with the molecule being in the vibrational levelv′'=31, are measured at a collision energy of 150 eV. Angular momentum transfer of up to Δj=26 is observed, which is even more than previously obtained for the vibrational ground statev′'=0. Good agreement is found with theoretical results from a spectator scattering model. This work, in general, elucidates the role of vibrational excitation in collision dynamics under vibrationally sudden conditions.     

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.     

Effects of angular momentum recoupling on depolarization spectra in alkali-rare gas optical half collisions

The depolarization mechanisms of excited alkali atoms interacting with ground state rare gas atoms are investigated using the method of far wing spectroscopy of collision pairs under single collision conditions. From a semiclassical theory explicite expressions for the spectra of alkali multipole components σ _k ^(?) (ω _L ) are derived assuming quasistatic excitation at a localized internuclear separationR _L(ω _L ) related to the laserfrequency ω _L as well as realistic models for the half collision following excitation. The collision models are characterized by different Hund's coupling regions, where excitation takes place and which are traversed on the collision path. Due to selection rules for excitation of populations and coherences and for support of multipoles the σ _k ^(?) (ω _L ) are shown to depend strongly on the collision model. From the spectra thus a labelling of the initial molecular states and mapping of the change in coupling case is possible. Estimations of the contributions of the various angular momentum recoupling effects are given.     

Potential energy curves for ground and excited states of NaLi from ab initio calculations with effective core polarization potentials

Sixteen low-lying electronic states of NaLi are investigated by SCF/valence Cl calculations including core polarization effects by means of an effective potential. Spectroscopic constants are obtained with estimated uncertainties of ΔR_e ? 0.01 Å, Δω_e ? 0.6 cm^?1 and ΔD_e ? 80 cm^?1. From a comparison of experimental and theoretical G(υ) values, we suggest a ground-state dissociation energy of 7093 ± 5 cm^?1. Using our rovibrational energies and recently measured excitation lines, we are able to improve the T_e values and dissociation energies of five excited states to an accuracv of ±8 cm^?1.     

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.     

Quantum mechanical calculations of vibrational transition probabilities in collinear atom–triatom collisions

Quantum mechanical calculations have been made of vibrational transition probabilities in the collinear collision of an inert gas atom with either CO₂ or OCS. The dependence of the transition probability on the relative translational energy and the reduced mass is similar to that found for atom–diatom collisions. The transition P_{00 → 10} (excitation of the first stretching mode) is much greater than P_{00 → 01} (the second stretching mode). This is largely due to the difference in frequencies but it has been shown that there is an independent mass factor responsible for this difference.     

Molecular dynamics study of orientational order and rotational melting in clusters of TeF6

Molecular dynamics simulations of the behavior of molecules in crystalline clusters of TeF₆ were carried out on systems of 100, 150, 250, and 350 molecules. Several diagnostic functions were applied to investigate whether rotational melting occurred before translational melting. These functions included the coefficient of rotational diffusionD _θ(T), the “orientational Lindemann index” δ_θ(T), the “orientational angular distribution function”Q(θ,T), and the “orientational pair-correlation function”g _θ(r, T). All indicators implied that rotational melting occurred before translational melting, that it began with the outermost molecules, and that its onset for smaller clusters was at lower temperatures than for larger clusters. Results also showed that the rotational transition coincided with the transition from a lower symmetry phase (monoclinic) to cubic, a phenomenon that had been noted by others to occur with some regularity for systems of globular molecules.     

Dynamics of the reaction H2+(He,H)HeH+. Influence of various forms of reactant energy on the total and differential cross section

Results of quasiclassical trajectory calculations of reactive processes between He atoms and H₂⁺ (υ, J) molecular ions in the collision energy interval 0.5–5.0 eV (c.m.) for a large number of selected υ, J combinations are analyzed with respect to the influence of the initial translational, vibrational, and rotational energy on the total and differential reaction cross sections. Vibrational energy is more effective in promoting the reaction than translational energy. Small rotational excitation has a negligible effect, whereas high rotational excitation has a similar influence on the reaction cross sections as the vibrational excitation of the same magnitude.     

Location of energy barriers. VI. The dynamics of endothermic reactions,ab + c

A systematic 3D classical-trajectory study has been made of the effect of reagent energy distribution and mass combination on the dynamics of endothermic reaction. The potential-energy hypersurface was endothermic by 35.7 kcal mole^?1. Reagent translation, T′, and vibration, V′, was varied in the range up to T′ + V′ = 90 kcal mole^?. Among the principal findings for the equal-mass case were the following. (i) There is an orders-of-magnitude increase in reaction cross section when energy is transferred from T′ to V′, until an optimal distribution over T′ and V′ is achieved at V′ ?, T′. There is a qualitative difference between the forms of the reactive cross section dependences S(T′) V′ and S(V′)_T′. (ii) The greater efficacy of V′ than T′ in promoting endothermic reaction is marked even at total reagent energies ≈ 3 x the endothermic barrier height. (iii) The total reactive cross section for endothermic reaction increases to large values (≈ gas kinetic) as V′ increased to several times the barrier height. (iv) Reagent energy in excess of that required to cross the endothermic barrier is subject to the same “adiabatic” transformation into product energy as was previously observed for exothermic reactions: ΔT′ → ΔT + ΔR (where R is enhanced product rotational energy), and ΔV′ → ΔV. This is explained in terms of induced repulsive energy release in the former case, and induced attractive energy release in the latter. (v) The molecular product is backwards or sideways scattered. Enhanced V′ at constant T′ diminishes product repulsion, giving rise to more-forward scattering. (vi) These findings remain qualitatively unchanged when extreme mass combinations H H + L and L H + H (L = 1 amu, H = 80 amu) are substituted for the equal-mass combination, L L + L. Effects ascribable to a “late” barrier are accentuated for HH + L. and diminished for L H + H. (vii) The total reactive cross section at a given reagent energy increases in the sequence H H + L, L L + L, L H + H, for simple kinematic reasons. (viii) The dynamics on this endothermic potential-energy surface resemble, in all the points listed above, the dynamics on a thermoneutral surface which has its barrier crest in the coordinate of separation (surface II of part I of this series).     

Comparison of helium and argon as collision gases in the high energy collision-induced decomposition of MH+ ions of peptides

Collision-induced decompositions (CID) of protonated peptides were studied using a four-sector mass spectrometer. The collision gases employed were helium and argon. The CID spectra of several peptides covering the molecular mass region of 905–2465 u were recorded. These investigations established several previously unrecognized differences between the CID spectra obtained with helium and argon as collision gases. These can be summarized as follows: (1) Structurally significant and specific side chain fragmentations (d_n ^f, w_n ^f and v_n, ion types) are greatly reduced or completely missing in the CID spectra obtained with helium as a collision gas compared to those obtained with argon. (2) As the peptide molecular mass increases, argon, which is heavier than helium, is increasingly more efficient than helium for generating fragment ions.     

Location of energy barriers. VIII. Reagent → product energy conversion on surfaces with sudden or gradual late-barriers

At energies well above the threshold for reaction, the effect of additional reagent vibration (ΔV′) and relative translation (ΔT′) on the product energy distribution (V,R,T,) has been examined on four different substantially endothermic potential-energy surfaces for two extreme mass combinations (LH + H $\text{endo}$ L + HH and HH + L $\text{endo}$ H + HL). As noted previously, additional reagent vibration tends to be retained as product vibration, ΔV′ → ΔV, and a similar approximate adiabaticity applies to translation, ΔT′ → ΔT + ΔR. The present work is concerned with the effect of potential-energy surface and extreme mass-combination on these generalizations. The surfaces examined had late barrier-crests, but surfaces designated S exhibited a sudden rise to the barrier-crest and G a gradual rise. The extent of adiabaticity was found to be significantly greater on the gradual (G-type) surfaces than on the sudden (S-type) ones. The mass-combination LH + H $\text{endo}$ L + HH (in which enhanced reagent orbital angular momentum correlates with enhanced product rotation) was anomalous in giving ΔT′ → ΔR.     

Activation parameters of supercritical and gas-phase β-pinene thermal isomerization

New data on enthalpy and entropy contributions to the energy barrier of β-pinene thermal isomerization were obtained. The rate of β-pinene conversion is higher in supercritical EtOH (P = 120 atm) than in the gas phase (P ≤ 1 atm, without solvent, or for inert carrier gas N₂) at equal temperatures. The highest activation energy E _Σ of total β-pinene conversion is also observed in reactions in the supercritical (sc) condition. Activation parameters ΔH _Σ ^# , ΔS _Σ ^# , and ΔG _Σ ^# depend strongly on the reaction pressure. Thus, at P ≤ 1 atm (gas-phase reaction) the values of ΔS _Σ ^# are negative, while at sc conditions at P = 120 atm is positive. The linear dependences lnk _Σ0 ? E _Σ and ΔS _Σ ^# ? ΔS _Σ ^# indicate an isokinetic relation (IKR) and enthalpy-entropy compensation effect (EEC). The isokinetic temperature was calculated (T _iso = 605.5 ± 22.7 K). It was shown that elevation of temperature reduces the value of ΔG _Σ ^# (T) upon sc thermolysis only, whereas in all gas-phase reactions ΔG _Σ ^# (T) increases. At equal reaction temperatures, the greatest values of K _eq ^# (T) proved to be typical for thermolysis in sc-EtOH. We hypothesize that the rate of total β-pinene conversion increases dramatically due to a considerable shift in equilibrium toward higher concentrations of activated complex y _TS ^# . A detailed analysis of activation parameters shows that the IKR and EEC coincide, evidence of a common mechanism of β-pinene conversion observed under different reaction conditions, including thermolysis in sc-EtOH.     

Vibrational deactivation of HF(υ = 1) in the H2O + HF dimer: HF(υ = 1) + H2O(000) → HF(υ = 0) + H2O(001) + ΔE

The vibration-vibration energy transfer in the near-resonant collision HF(υ = 1) + H₂O(000) → HF(υ = 0) + H₂O(001) + ΔE = 205 cm^?1 has been investigated on the basis of the model of the nonrigid H₂O-HF dimer formation for temperatures not greatly higher than room temperature. The energy mismatch ΔE is considered to be removed by the slow translational motion of two molecules in the complex about their equilibrium separation. A strong negative temperature dependence of the energy exchange rate is shown between 300 and 500 K.     

The Franck—Condon principle for radiationless transitions in molecules and a selection rule for morse oscillators

The Franck—Condon (FC) principle for the tunnel radiationless transition (RT) is formulated. It reads that the RT occurs at constant values of the nuclear coordinates q* and of the classical momenta p*. However, unlike the optical transitions, q* and p* take non-physical values since the tunnel RT is a classically forbidden process. As a result of energy conservation, the potential surfaces of two given electronic states cross with one another at the nuclear configuration q*. It is concluded that the electronic-orbital selection rules and the numerical values of the purely electronic matrix elements are governed by the configuration q* rather than by the equilibrium nuclear configuration as was supposed previously. The configuration q* for the T₁ → S₀ intersystem crossing in aromatic hydrocarbons is described in terms of a large displacement of only one H atom from its equilibrium position along the CH bond (perhaps, there is also some out-of-plane displacement). Using the FC principle, it is found that the anharmonicity of the local CH bond vibrations results in a strong dependence of the T₁ → S₀ intersystem crossing rates upon the sign of the CH bond-length change between two given electronic states, Δq = R_T1 - R_S0. Namely, the following “selection rule” holds: these RTs are allowed at Δq < 0 and they are forbidden at Δq > 0, the prohibition factor being of the order of 10²–10⁴. Finally, an oscillatory dependence of the FC factors upon Δq is explained, using the FC principle, in terms of quantum interference in the total transition probability, of which the amplitude is a sum of the transition amplitudes due to different crossing points q*. The interference effects are believed to be insignificant for RTs in molecules with large energy gaps and so they are eliminated in the usual manner by adding up the partial probabilities rather than the partial amplitudes. The classical FC factor thus obtained smoothly depends upon Δq (and upon other parameters as well). This procedure also provides an analytical continuation of the FC factor to non-integral quantum numbers.     

Internal excitation effects in the photodissociation of size selected ethylene and methanol dimers

The infrared photodissociation spectra of C₂H₄ and CH₃OH dimers are measured for different internal excitation energies ΔE. The dimers are size-selected in a scattering process with He and the internal energy is varied by using (1) different collision energies, (2) different scattering angles and (3) by measuring the complete energy loss spectra with and without laser radiation by time-of-flight analysis of the scattered clusters. For (CH₃OH)₂ the width Γ of the spectrum increases strongly with ΔE, while the cross section at the maximum is constant, a normal behaviour for an inhomogeneously broadened system. For (C₂H₄)₂ Γ is nearly constant after a sort of threshold and the cross section increases with increasing ΔE. These results are explained by hot band excitation and the coupling to the darkv ₁₀-mode.     

Rotational relaxation in S1 glyoxal: Cross sections and a search for propensity rules

Details of rotational energy transfer from a few selected K′J′ levels in the zero point vibrational level of ¹Au(S₁) glyoxal vapor have been studied. The cross section for destruction of an initial K′J′ level by rotational relaxation in collision with ground electronic state glyoxal is about 240 A² or 4.5 times gas kinetic. Much of the rotational transfer within the S₁ state occurs with large ΔK′ and ΔJ′. No strong propensities for △K′ = 0, ± 1, ± 2, or ± 3 with small ΔJ′ changes occur in collisions with ground electronic state glyoxal. The study was made by examination of the rotational structure in the 5₁⁰ emission band at various pressures after excitation in the 0,0 band of the S₁—S₀ system with the 454.5 nm argon ion line.     

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.     

Third virial coefficient and nonadditivity of the first-order repulsive interactions of rare-gas atoms

Corrections to the third virial coefficient derived from the first-order three-body exchange forces, ΔC₁(T), in helium, neon and argon have been calculated. Inclusion of ΔC₁ and the corrections due to the non-exchange three-body forces leads to a satisfactory agreement with experimental data.