Surprisal Plots Research Articles

Dependence of the nascent vibrational distribution of NO(v) on the photolysis wavelength of NO2 in the range λ = 266–327 nm measured by time-resolved Fourier transform infrared emission

Time-resolved FTIR has been used to study the photodissociation of NO2 at photolysis wavelengths of lambda = 266, 282, 295, 308, 320 and 327 nm. Nascent vibrational distributions of the NO(v) fragment have been determined at all wavelengths: 266 nm photolysis populates NO(v = 1-7) and shows a distribution that is inverted at v = 5, whereas 327 nm photolysis populates NO(v = 1-3) and is inverted at v = 2. Surprisal plots were performed on the nascent distributions presented in this work and on all data sets available in the literature in the range 266-370 nm in order to parameterise the wavelength dependence of the nascent distribution of NO(v) from NO2 photolysis. In general, the surprisal parameter was found to be a linear function of wavelength and was used to generate a simple model for the wavelength dependence of the nascent distribution of NO(v) in the region lambda = 265-372.5 nm. The results give a more accurate parameterisation of the formation of NO(v) of use in atmospheric modelling.

Nascent vibrational distributions and relaxation rates of diatomic products of the reactions of O( 1D) with CH 4, C 2H 6, CH 3F, CH 2F 2 and CHF 3 studied by time resolved Fourier transform infrared emission

Time resolved Fourier transform infrared (TRFTIR) emission has been used to study the reactions of CH 4, C 2H 6, CH 3F, CH 2F 2 and CHF 3 with O( 1D). One hundred and ninety-three nanomters photolysis of N 2O was used to prepare O( 1D), and emission analysed from OH( ν = 1–4) for the two hydrocarbons and HF( ν = 1–6) from CH 3F, CH 2F 2 and CHF 3. For the O( 1D) + CH 4 reaction, the nascent OH vibrational distribution showed a population inversion between ν = 1 and 2, and was in excellent agreement with previous laser induced fluorescence and TRFTIR data, as well as with quasi-classical trajectory calculations. Time resolved populations were analysed to yield rate constants for vibrational relaxation of OH( ν) with CH 4, and found to be consistent with stepwise deexcitation rather than chemical removal being dominant. Reaction with C 2H 6 produced a monotonically decreasing population in ν = 1–4 and more rapid relaxation rates than those with methane. For the fluorinated methanes, nascent vibrational populations in HF( ν = 1–6) were measured and shown to be very similar, all monotonically decreasing with ν, and fitting the same vibrational surprisal plot, showing a larger than statistical partitioning of the available energy in vibration. Relaxation rate constants of HF( ν) with the parent fluorinated methane showed values, which increased with increasing H atom content.

The unusual effect of reagent vibrational excitation on the rates of endothermic and exothermic elementary combustion reactions

Surprisal analyses are carried out for the reactions H + O 2( v) → OH + O, O + H 2( v) → OH + H, and OH + H 2( v) → H 2O + H. The rate constants are taken from published quasiclassical trajectory calculations covering the temperature range 300–4000 K. The dichotomy expected when reagent vibrational energy converts an endoergic reaction into an exothermic one is observed. However, contrary to the usual trend observed for the X + HY( v) → Y + HX reaction (X, Y = halogen), here vibrational energy detracts from the rate of the endothermic reaction, and enhances the rate of the exothermic reaction when compared to statistical prior expectations. There are indications that at sufficiently high temperatures there is a role reversal for reagent vibrational energy. Figures are also provided which relate the slopes of surprisal plots for the general reaction A + BC( v) → AB + C to the surprisal parameter, λ, for the state-to-state reaction, A + BC( v) → AB( v′) + C. The procedure as applied to the H + O 2 reaction reveals large discrepancies with experimental measurements of state-to-state rate constants. All published data are reconciled, however, by means of a non-linear surprisal analysis.

Vibrational Distribution of ClO Radicals Produced in the Reaction Cl + O3→ ClO + O2

The nascent vibrational distribution of ClO(X2Π) radicals produced in the ozone destruction reaction Cl + O3 → ClO + O2 has been measured, using vacuum-ultraviolet laser-induced fluorescence of the ClO(C2Σ-−X2Π) transition. The nascent vibrational distribution of the ClO radicals is shown to be strongly inverted, with the relative ratio (v=0):(v=1):(v=2):(v=3):(v=4):(v=5) = 0.8:1:1.3:2.4:2.9:2.7. The slope of the surprisal plots for the vibrational distribution of the product ClO is found to be (−8 ± 2). Vibrational relaxation processes for the ClO radicals in the X2Σ state by collisions are also studied. The upper limit values of the vibrational relaxation rate constants for ClO (v=1→0) by collisions with N2 and Ar molecules are estimated to be both 5 × 10-14 cm3 molecule-1 s-1.

Reaction dynamics in solution: the activated Cl+Cl 2 exchange in fluid Ar

Useful tools are available for the characterization of the dynamics of an isolated binary collision. A renormalization of the exact equations of motion whereby such tools are also applicable to reactions in a solvent is discussed. The well-studied Cl+Cl 2 exchange reaction in fluid Ar at 300 K is used as an illustration. Inter alia, we compute the opacity function, the energy requirements and the energy disposal. Due to the high (≈ 20 kcal mol −1) barrier for the atom exchange and the wide cone of acceptance, the thermal reaction populates quite high vibrational and rotational products' states. The deviation from statistical behavior is well characterized by a linear surprisal plot.

A laser-induced fluorescence determination of the internal state distribution of NO produced in the reaction: H+NO2→OH+NO

Laser-induced fluorescence (LIF) spectra have been recorded of NO produced when H atoms and NO2 react in thermal energy collisions in the region where two uncollimated jets containing the reagents intersect. Spectra of the (0,0), (1,1) and (2,2) bands and the (0,2) and (1,3) bands of the A 2Σ+–X 2Π γ-band system have been observed. Distributions of NO over rovibrational levels have been determined by matching the experimental spectra to simulated spectra. The high J tail of the rotational distributions fit a linear surprisal plot. The analysis leads to average fractional yields of vibration and rotation energy, 〈fvib〉NO=0.056 and 〈frot〉NO=0.10, as well as branching ratios into vibrational (v=0–3), spin–orbit and Λ-doublet states. Preferences are found for the lower 2Π1/2 spin–orbit substate and for the Π(A′) Λ-doublet levels. Combined with results from the preceding paper, the data indicate that ∼31% of the energy released in the reaction should appear as relative translational motion of OH and NO. The reaction appears to proceed via the ground state HONO surface but the complex does not survive sufficiently long for complete energy randomisation: OH is more excited, NO less excited, than would be expected on a purely statistical basis.

The structure and dissociation dynamics of the Ne2Cl2 van der Waals complex

The structure and dynamics of Ne2Cl2 and Ne3Cl2 are studied by laser pump–probe spectroscopy. Analysis of a rotationally resolved B←X excitation band shows that Ne2Cl2 has a distorted tetrahedral structure with a Ne–Ne bond length of 3.23 Å and Ne2 center of mass to Cl2 center of mass distance of 3.12 Å. This structure is very close to that predicted by summing the atom–atom interactions. Excitation spectral shifts suggest a Ne3Cl2 structure with the neon atoms encircling the Cl2 bond axis. The total van der Waals binding energy of Ne2Cl2 is found to be between 145.6 and 148.6 cm−1, which is 20 cm−1 greater than 2*D0(Ne–Cl2)+D0(Ne2). For Cl2 stretching levels below υ′=10, transfer of one Cl2 vibrational quantum to the van der Waals vibrational modes is sufficient to dissociate both neon atoms from the complex. This indicates that the two neon atoms need not dissociate via independent, impulsive ‘‘half-collisions’’ which would require two Cl2 vibrational quanta. Observation of a NeCl2 dissociation fragment, however, indicates that such a sequential mechanism competes with the direct dissociation. Cl2 fragment rotational state population distributions for different initial vibrational levels are characterized using a simple rotational surprisal analysis. Comparison of these surprisal plots to those of the NeCl2 dissociation shows that as the size of the complex increases, so does the degree of statistical redistribution during the reaction. Even for Ne2Cl2, however, the extent of product rotational excitation is only weakly dependent upon the amount of energy available to the products and is always less than predicted by a statistical distribution between the translational and rotational product degrees of freedom.

Determination of NO (v=0–7) product distribution from the N(4S)+O2 reaction using two-photon ionization

The product vibrational state distribution for the reaction N(4S)+O2→NO(2Π,v)+O has been measured using saturated multiphoton ionization spectroscopy to determine NO electronic ground-state distributions. The fraction of the reaction exothermicity appearing in product vibration is 〈 f v〉=0.34; however, the even vibrational levels (v=0,2,4,6) are relatively overpopulated with respect to the odd vibrational levels (v=1,3,5). It is not possible to obtain a good linear-surprisal fit to all the data, but the even and odd subsets fit quite well to individual surprisal plots. The results are compared with previous measurements, including a reanalysis of laser-excited fluorescence data corrected for electronic transition moment and Franck–Condon factor variations. Collisional relaxation is observed at high O2 pressures for NO levels v=4 through 7, and is fit with a phenomenological relaxation model.

Mechanism for the appearance of H + by electroionization of CH 4. A surprisal analysis

Previous experimental results on the threshold energy and on the range of the first wide translational energy distribution of H +, resulting from electron impact on CH 4, are interpreted. The translational energy surprisal of this distribution has been evaluated with respect to a statistically calculated one. The surprisal plot shows a fourth power dependence on f T with a negative mean slope associated with a large Δ S exc value of ≈≈ 4 eu. An “a priori” calculated P 0( E T| E) distribution, including four constraints, fits fairly well the observed translational energy distribution.

Vibrational enhancement of the reaction rate and steric requirements in the H + D 2(ν) and D + H 2(χ) reactions

The cone of acceptance for H + H 2 reactive collisions is shown to open up upon stretching of the H 2 bond. At a given translational energy, the steric factor is thus much larger for vibrationally excited reagents as demonstrated by classical trajectory computations for H + D 2(ν) and D + H 2(ν). At a given total energy, the efficacy of reagent vibrational excitation is conveniently represented by a surprisal plot. The surprisal parameter is essentially isotopically invariant.

State-resolved quantum yields of the reactions of metastable Ca(3P, 1D) with NO2 and N2O

Absolute chemiluminescence and quenching (beam attenuation) cross sections were measured for the title reactions in a beam/gas experiment. In the Ca* + NO2 system, both quantities are about twice as large as in the N2O reaction. The chemiluminescence quantum yields, corrected for infrared emission from the A1Σ+ and A′ 1Π states, are of similar magnitude YCL(Ca* + N2O) = 7.2 ± 1.1% and YCL(Ca* + N2O) = 8.0 ± 0.9%. The quenching cross sections are στ(Ca* + N2O) = 153 ± 32 Å2 and στ(Ca* + N2O) = 73.2 ± 5.7 Å2, consistent with a long-range harpooning process in the former and an electron transfer at closer range for the latter system. The partial resolution of CL spectra was aided by lifetime-separated spectroscopy. The principal emitter in both systems is the long-lived CaO(A′ 1Π), next to minor yields of CaO in the short-lived A1Σ+, B1Π, and "orange and green arc band" states. The results are discussed in light of adiabatic correlations. The arc states are argued to arise in nearly coplanar collisions from the rearrangement of an excited intermediate. An information theoretical analysis reveals considerable dynamical bias in the form of non-linear surprisal plots.

Vibrational distributions of AlF(a 3Π) produced by crossed-beam collisions of Al and F2 at two kinetic energies

Chemiluminescent spectra of AlF(a 3Π) produced in the reaction of Al with an F2 nozzle beam are reported at two different nozzle temperatures. From spectral simulations treating AlF(a 3Π) in the intermediate case between Hund’s cases (a) and (b), it is found that the peak position of the derived vibrational distribution is shifted to a higher vibrational state for the higher temperature case. Both vibrational distributions give linear surprisal plots with nearly the same highly negative slope. In order to explain the shift of the vibrational distribution, a collinear model calculation for multiple nonadiabatic processes is proposed.

Infrared chemiluminescence from the reactions F + HBr, F + H 2Se, and Cl + H 2Se

Infrared chemiluminescence from HF and HCl has been observed and yielded vibrational and rotational population distributions for the reactions F + HBr, F + H 2Se, and Cl + H 2Se. Evaluation of the spectra recorded by a commercial Fourier-transform spectrometer under low-flow conditions gave the following relative vibrational populations: for F − HBr. N υ = 1 : N υ = 2 : N υ = 3 : N υ = 4 = 0.45 : 0.31 : 0.13 : 0.11: for F + H 2Se, N υ = 1 : N υ = 2 : N υ = 3 : N υ = 4 : N υ = 5 = 0.29 : 0.35 : 0.24 : 0.09 : 0.03: for Cl + H 2Se, N υ = 1 : N υ = 2 : N υ = 3 = 0.40 : 0.51 : 0.09. All three vibrational surprisal plots show a significant deviation from linearity. Neglecting the contributions from N υ = 0, the total energy is partitioned into vibration and rotation as follows: 〈 f V〉 = 0.49 and 〈 f R〉 = 0.09 for F + HBr, 〈 f V〉 = 0.41 and 〈 f R〉 = 0.07 for F + H 2Se, 〈 f V〉 = 0.53 and 〈 f R〉 = 0.10 for Cl + H 2Se. Inclusion of estimates for N υ = 0 gives the more realistic values 〈 f V〉 = 0.24, 0.34, and 0.49 respectively. Whereas 9 ± 3% of the collisions between F + HBr yield Br in the excited 2P 1 2 state, no rovibrationally excited HSe fragments were detected in the two other systems. Consistent values for the bond dissociation energy D 0 0(HSeH) = 329 ± 5 kJ/mol and the enthalpy of formation Δ H 10 0 (HSe) = 137 ± 5 kJ/mol are derived from the highest observed HCl and HF levels.

Electronic energy partitioning in reactions occurring on more than one potential energy surface: Metastable Mg(3P) atoms with halogen molecules

For the reactions metastable Mg(3P) atoms and dihalogen molecules F2, Cl2, and Br2 we have measured by a beam-gas experiment the absolute cross sections for all three electronic reaction channels: formation of MgX(X 2Σ+) ground state, MgX(A 2Π) chemiluminescent products and MgX+(1Σ+) chemi-ions. The chemiluminescence and chemi-ion yields both turn out to be of the order of 1% in all three systems. By qualitative MO theory, it is shown that the dynamical bottleneck in the adiabatic chemiluminescence channel is an early barrier and in the diabatic chemi-ionization process a spin flip occurring during the approach phase, following a long-range electron transfer. An information theoretic analysis reveals considerable dynamic bias associated with most of the CL and CI products [except for MgCl (A 2Π)], and the surprisal plots are nonlinear for all three reactions.

Classical trajectory studies of the reaction F + I2

The reaction F + I2→ IF + I has been studied using classical trajectory methods. A procedure is presented for selecting an appropriate extended L.E.P.S. surface for the reaction, in which the well depth is fixed at the value corresponding to the known stability of I2F. When this is done, the Sato parameters are uniquely related and a systematic variation of one of them in a series of trajectory calculations allows a surface to be selected by matching the calculated reaction properties with the corresponding experimental values. It is found that, for this exothermic reaction with a well located in the exit valley of the surface, as the minimum of the well is moved into the exit valley, the vibrational excitation of the products is increased. An extended trajectory analysis was performed to calculate the form of the product recoil angular and energy scattering distributions, the IF vibrational state distribution, and the values of the reaction cross-section and thermal rate coefficient. Good agreement is found between the calculated and experimental molecular-beam angular and translational energy distributions. At a collisional energy of 8.4 kJ mol–1, the I2F intermediate is apparently not sufficiently long-lived to give statistical energy partitioning. The IF vibrational distribution is strongly inverted and yields a better linear surprisal plot when FV2 is used as a variable rather than FV. The calculations do not reproduce the experimentally observed second peak in the IF vibrational distribution at v= 0. This may arise from a second reaction pathway on another surface, possibly involving the production of I*(2P1/2), which has a cross-section which may be up to twice as large as that for the pathway populating the high vibrational states of IF.

Energy distribution among reaction products. XIV. F + CH 4, F + CH 3X(X  Cl, Br, I), F + CH nCl 4− n( n = 1−3)

The infrared chemiluminescence technique has been used to obtain relative rate constants k(ν′) for HF(ν′) formed in the following reaction: ▪ For reaction (1) the detailed rate constants [ k(ν′ = 1) = 0.30; k(ν′ = 2) = 1.00; k(ν′ = 3) = 0.15; mean fraction of the available energy entering vibration <⨍ ′ ν> = 0.56] confirmed, at much lower reagent pressures, results obtained by previous workers. In series I there was a slight increase in fraction of the energy entering vibration as the molecular reagent altered from CH 3Cl to CH 3Br to CH 3I, viz <⨍ ′ ν> = 0.50 (1a), <⨍ ′ ν> = 0.58 (1b), <⨍ ′ ν> = 0.60 (1c). In series 2, by contrast, there was a marked decrease in fractional conversion of the available energy into vibration with increasing chlorination of the molecular reagent; <⨍ ′ ν> = 0.50 (1a), <⨍ ′ ν> = 0.23 (2a), <⨍ ′ ν> = 0.13 (2b). The rate constants into ν′ = 0, k(ν′ = 0), were obtained by extrapolation of surprisal plots; the trends for both series were, however, also evident from k(ν′ > 0). No separate initial rotational distribution was observed for any of these reactions, indicating that the peak of the initial distribution is not far removed from a 300 K thermal distribution. The decrease in <⨍ ′ ν> for the HF products along series 2 was tentatively ascribed to increasing internal excitation in the ejected radicals CH 2Cl, CHCl 2, CCl 3, due to increase in the number of secondary encounters between HF and the departing radical.

Vibrational emission by HCl from the ClF–H2 chemical laser

The zero-gain and equal-gain temperature methods have been used to measure vibrational rate-constant ratios for the reaction: H+ClF→HCl+F: N1/N0=3.5±0.8, N2/N1=2.3±0.3 and N3/N2=0.9±.2. These data are in accord with relative rate constant measurements obtained through chemiluminescence studies. Furthermore, they provide the first information about k0 and they narrow considerably the uncertainty range for k1. Combining all of the available data, a ’’best’’ value of the fraction of available energy into vibration, fv=0.40, is obtained. With the complete set of vibrational rate constants, a linear surprisal plot can be obtained by assuming that only a portion of the energy released is ’’available’’ for vibrational excitation. It is suggested that this portion measures the energy released in the reaction entry channel, Polanyi’s ’’attractive energy release.’’ This interpretation is consistent with the results of similar treatments of the rate constant data for the H+X2 reactions (X=F, Cl, Br).

Theoretical investigations of rotationally inelastic collisions in the CO2+He system using a b i n i t i o, electron-gas, and ‘‘experimental’’ potential-energy surfaces

The inelastic collision dynamics of the rigid rotor (CO2,He) system have been examined on three different potential-energy surfaces, an ab initio SCF surface, an electron-gas surface, and a potential obtained by deconvolution of molecular-beam scattering data. Thermally averaged cross sections, state-to-state integral cross sections, and differential cross sections have been computed on each surface as a function of collision energy and initial CO2 rotation state from the results of about 28 500 quasiclassical trajectories. At energies less than the depth of the van der Waals well, the SCF surface is found to be inadequate in that it underestimates the state-to-state cross sections by as much as a factor of 5. However, at collision energies in excess of the well depth, all surfaces are found to yield results whose maximum difference is about 20%. Of the surfaces investigated, the electron-gas model predicts the largest degree of rotational inelasticity. Previously reported computations by Preston and Pack indicate this inelasticity to be too large. The present calculations suggest that this is not directly connected to the magnitude or location of the attractive well but rather to the steepness of the repulsive potential which is largest for the electron-gas surface. Nearly linear surprisal plots are obtained for the SCF and electron-gas surfaces. The surprisal for the ’’experimental’’ surface is significantly more sigmoid in shape. The shapes of the state-to-state differential cross sections are very similar, and they may be correlated with the magnitude of the integral state-to-state cross sections. In general, it is concluded that except at very low collision energies on the SCF surface, each of the potentials permits reasonably accurate calculations of the properties associated with thermal scattering.

Energy distribution of the fragments produced by photodissociation of CS2 at 193 nm

Gaseous CS2 was dissociated at 193 nm into CS and S. The translational and internal energy distributions of the CS fragments were measured. There is now overwhelming evidence that the upper electronic state S3 is predissociative. In fact there are three upper states of importance, the initially excited S3, a state which dissociates to CS(X 1Σ) and S(1D) and a triplet state which dissociates to CS(X 1Σ) and S(3P). The CS fragments were rotationally excited with an average rotational energy ∼3.5 kcal/mole. The vibrational populations were also strongly inverted for both the 1D and the 3P dissociations and their surprisal plots were linear. CS fragments were found with v?7. Of the dissociations resulting in CS fragments with v?6, 80±10% of the S atoms are produced in the 1D state and 20±10% in the 3P state.

Quantum collinear reaction probabilities for vibrationally excited reactants : F+H2(v≤2)→FH(v′≤5)+H

Quantum mechanical reaction probabilities are reported for the collinear reaction F+H2(v)→FH(v′)+H in an energy range where two or three vibrational H2 states v are open. Rotated Morse-cubic spline representations of the extended LEPS surfaces Muckerman I and V, and an adaptation of the BOPS SCFCI surface have been used. The scattering is dominated by resonances. A detailed investigation of the different kinds of resonance behaviour is presented. For the two LEPS surfaces, overall features of the reaction probability curves can be correlated qualitatively in a one-to-one manner. Differences between the BOPS and LEPS reaction probabilities are more pronounced for v=1 than for v=0. For all surfaces, effects of vibrational excitation show a much more systematic behaviour in terms of the reverse reaction than for the forward reaction. A multi-step mechanism is deduced for the reaction, and an attempt is made to give an interpretation in terms of physical concepts including centrifugal effects, Franck-Condon transitions and quasibound states. No obvious simple trends emerge from a surprisal analysis. Most surprisal plots are markedly non-linear in the energy range considered.