Relative Integral Cross Sections Research Articles

Steric Effects in the Cl+CHD3(v1=1) Reaction

A recent study has revealed a full 3-dimentional reactive scattering picture of the reaction C1+CHD3(v1=1) as the Cl atoms attack CHD3 from various directions respective to the C—H stretching bond. The reported polarization-dependent differential cross sections provide the most detailed characterization of the influences of reagent alignments on reactivity. To convey the stereo-specific information more accessible to general chemists, we show here, by proper symmetry considerations, how to retrieve from the measurements the relative integral and differential cross sections of two most common collision geometries: the end-on versus side-on attacks. The results, albeit coarse-grained, provide an appealing picture that not only reinforces our intuition about chemical reactivity, but also sheds more light on the conventional (unpolarized) attributes.

Rotational excitation of HDO and D2O by H2: Experimental and theoretical differential cross-sections

We present state-to-state differential cross sections (DCSs) for rotationally inelastic scattering of HDO by normal- and para-H(2) at collision energies of 580 cm(-1) and 440 cm(-1). (2+1) resonance enhanced multiphoton ionization is used to detect rotationally cold HDO molecules before collision and as scattering products, which occupy higher rotational states due to collision with H(2). Relative integral cross sections of HDO are obtained by integrating its DCSs measured at the same experimental conditions. Experimental and theoretical DCSs of HDO scattered by normal- and para-H(2) are in good agreement in 30°-180° range of scattering angles. This partial agreement shows the accuracy of the recently tested potential of H(2)O-H(2), but now by using a completely different set of rotational transitions that are (unlike in H(2)O), not forbidden by nuclear spin restrictions. Similar results are presented for D(2)O scattered by normal-H(2) at collision energy of 584 cm(-1). The agreement between experiment and theory is, however, less good for forward scattering of HDO/D(2)O. A critical analysis of this discrepancy is presented.

State-to-state differential and relative integral cross sections for rotationally inelastic scattering of H2O by hydrogen

State-to-state differential cross sections (DCSs) for rotationally inelastic scattering of H2O by H2 have been measured at 71.2 meV (574 cm−1) and 44.8 meV (361 cm−1) collision energy using crossed molecular beams combined with velocity map imaging. A molecular beam containing variable compositions of the (J = 0, 1, 2) rotational states of hydrogen collides with a molecular beam of argon seeded with water vapor that is cooled by supersonic expansion to its lowest para or ortho rotational levels (JKaKc = 000 and 101, respectively). Angular speed distributions of fully specified rotationally excited final states are obtained using velocity map imaging. Relative integral cross sections are obtained by integrating the DCSs taken with the same experimental conditions. Experimental state-specific DCSs are compared with predictions from fully quantum scattering calculations on the most complete H2O-H2 potential energy surface. Comparison of relative total cross sections and state-specific DCSs show excellent agreement with theory in almost all details.

Kinetics and Dynamics of theS(D21)+H2→SH+HReaction at Very Low Temperatures and Collision Energies

We report combined studies on the prototypical S(1D2) + H2 insertion reaction. Kinetics and crossed-beam experiments are performed in experimental conditions approaching the cold energy regime, yielding absolute rate coefficients down to 5.8 K and relative integral cross sections to collision energies as low as 0.68 meV. They are supported by quantum calculations on a potential energy surface treating long-range interactions accurately. All results are consistent and the excitation function behavior is explained in terms of the cumulative contribution of various partial waves.

An exchange-Coulomb model potential energy surface for the Ne–CO interaction. II. Molecular beam scattering and bulk gas phenomena in Ne–CO mixtures

Four potential energy surfaces are of current interest for the Ne-CO interaction. Two are high-level fully ab initio surfaces obtained a decade ago using symmetry-adapted perturbation theory and supermolecule coupled-cluster methods. The other two are very recent exchange-Coulomb (XC) model potential energy surfaces constructed by using ab initio Heitler-London interaction energies and literature long range dispersion and induction energies, followed by the determination of a small number of adjustable parameters to reproduce a selected subset of pure rotational transition frequencies for the (20)Ne-(12)C(16)O van der Waals cluster. Testing of the four potential energy surfaces against a wide range of available experimental microwave, millimeter-wave, and mid-infrared Ne-CO transition frequencies indicated that the XC potential energy surfaces gave results that were generally far superior to the earlier fully ab initio surfaces. In this paper, two XC model surfaces and the two fully ab initio surfaces are tested for their abilities to reproduce experiment for a wide range of nonspectroscopic Ne-CO gas mixture properties. The properties considered here are relative integral cross sections and the angle dependence of rotational state-to-state differential cross sections, rotational relaxation rate constants for CO(v=2) in Ne-CO mixtures at T=296 K, pressure broadening of two pure rotational lines and of the rovibrational lines in the CO fundamental and first overtone transitions at 300 K, and the temperature and, where appropriate, mole fraction dependencies of the interaction second virial coefficient, the binary diffusion coefficient, the interaction viscosity, the mixture shear viscosity and thermal conductivity coefficients, and the thermal diffusion factor. The XC model potential energy surfaces give results that lie within or very nearly within the experimental uncertainties for all properties considered, while the coupled-cluster ab initio surface gives results that agree similarly well for all but one of the properties considered. When the present comparisons are combined with the ability to give accurate spectroscopic transition frequencies for the Ne-CO van der Waals complex, only the XC potential energy surfaces give results that agree well with all extant experimental data for the Ne-CO interaction.

Breakdown of the Born-Oppenheimer Approximation in the F+ o -D 2 → DF + D Reaction

The reaction of F with H2 and its isotopomers is the paradigm for an exothermic triatomic abstraction reaction. In a crossed-beam scattering experiment, we determined relative integral and differential cross sections for reaction of the ground F(2P(3/2)) and excited F*(2P(1/2)) spin-orbit states with D2 for collision energies of 0.25 to 1.2 kilocalorie/mole. At the lowest collision energy, F* is approximately 1.6 times more reactive than F, although reaction of F* is forbidden within the Born-Oppenheimer (BO) approximation. As the collision energy increases, the BO-allowed reaction rapidly dominates. We found excellent agreement between multistate, quantum reactive scattering calculations and both the measured energy dependence of the F*/F reactivity ratio and the differential cross sections. This agreement confirms the fundamental understanding of the factors controlling electronic nonadiabaticity in abstraction reactions.

Measurements and Quasi-Quantum Modeling of the Steric Asymmetry and Parity Propensities in State-to-State Rotationally Inelastic Scattering of NO (2Π1/2) with D2

Relative integrated cross sections are measured for spin-orbit-conserving, rotationally inelastic scattering of NO (2Pi1/2), hexapole-selected in the upper Lambda-doublet level of the ground rotational state (j = 0.5), in collisions with D2 at a nominal energy of 551 cm-1. The final state of the NO molecule is detected by laser-induced fluorescence (LIF). The state-selected NO molecule is oriented with either the N end or the O end toward the incoming D2 molecule by application of a static electric field E in the scattering region. This field is directed parallel or antiparallel to the relative velocity vector v. Comparison of signals taken for the different applied field directions gives the experimental steric asymmetry SA, defined by SA = (sigma v upward arrow downward arrow E - sigma v upward arrow upward arrow E)/(sigma v upward arrow downward arrow E + sigma v upward arrow upward arrow E), which is equal to within a factor of -1 to the molecular steric effect, Si-->f identical with (sigmaD2-->NO - sigmaD2-->ON)/(sigmaD2-->NO + sigmaD2-->ON). The dependence of the integral inelastic cross section on the incoming Lambda-doublet component is also measured as a function of the final rotational (jfinal) and Lambda-doublet (epsilonfinal) state. The measured steric asymmetries are similar to those previously observed for NO-He scattering. Spin-orbit manifold-conserving collisions exhibit a larger propensity for parity conservation than their NO-He counterparts. The results are interpreted in the context of the recently developed quasi-quantum treatment (QQT) of rotationally inelastic scattering [Gijsbertsen, A.; Linnartz, H.; Taatjes, C. A.; Stolte, S. J. Am. Chem. Soc. 2006, 128, 8777]. The QQT predictions can be inverted to obtain a fitted hard-shell potential that reproduces the experimental steric asymmetry; this fitted potential gives an empirical estimate of the anisotropy of the repulsive interaction between NO and D2. QQT computation of the differential cross section using this simple model potential shows reasonable agreement with the measured differential cross sections.

STRONG VIBRATIONAL ENHANCEMENT OF SUBSTANTIALLY ENDOTHERMIC REACTION K + HF: A TIME-DEPENDENT QUANTUM WAVE PACKET STUDY

Detailed dynamics of the substantially endothermic reaction K + HF on a new ab initio ground potential energy surface has been studied by means of time-dependent quantum wave packet calculation. The calculations showed that the reaction could be significantly enhanced by vibrational excitation of HF , but not very sensitive to initial rotational excitation. The relative and absolute integral cross sections and the logarithm of the σ(v = 1)/σ(v = 0) ratio have been calculated and compared with available experimental and theoretical results. Relatively good agreement with experiment and other calculations was obtained. Reaction rate constants of this reaction was also calculated and discussed.

Steric asymmetry and lambda-doublet propensities in state-to-state rotationally inelastic scattering of NO(2Π1/2) with He

Relative integrated cross sections are measured for rotationally inelastic scattering of NO(2Pi(1/2)),hexapole selected in the upper lambda-doublet level of the ground rotational state (j = 0.5), in collisions with He at a nominal energy of 514 cm(-1). Application of a static electric field E in the scattering region, directed parallel or antiparallel to the relative velocity vector v, allows the state-selected NO molecule to be oriented with either the N end or the O end towards the incoming He atom. Laser-induced fluorescence detection of the final state of the NO molecule is used to determine the experimental steric asymmetry, [formula: see text], which is equal to within a factor of (- 1) to the molecular steric effect, S(i-->f) is identical with (sigma(He-->NO) - (sigma(He-->ON))/(sigma(He-->NO) + sigma(He-->ON)). The dependence of the integral inelastic cross section on the incoming lambda-doublet component is also observed as a function of the final rotational (j'), spin-orbit (omega'), and lambda-doublet (epsilon') state. The measured steric asymmetries are significantly larger than previously observed for NO-Ar scattering, supporting earlier proposals that the repulsive part of the interaction potential is responsible for the steric asymmetry. In contrast to the case of scattering with Ar, the steric asymmetry of NO-He collisions is not very sensitive to the value of omega'. However, the lambda-doublet propensities are very different for [omega=0.5(F1)-->omega'= 1.5(F2)] and [omega=0.5(F1)-->omega'=0.5(F1)] transitions. Spin-orbit manifold conserving collisions exhibit a propensity for parity conservation at low deltaj, but spin-orbit manifold changing collisions do not show this propensity. In conjunction with the experiments, state-to-state cross sections for scattering of oriented NO(2Pi) molecules with He atoms are predicted from close-coupling calculations on restricted coupled-cluster methods including single, double, and noniterated triple excitations [J. Klos, G. Chalasinski, M. T. Berry, R.Bukowski, and S. M. Cybulski, J. Chem. Phys. 112, 2195 (2000)] and correlated electron-pair approximation [M. Yang and M. H. Alexander, J. Chem. Phys. 103, 6973 (1995)] potential energy surfaces. The calculated steric asymmetry S(i-->f) of the inelastic cross sections at Etr= 514 cm(-1) is in reasonable agreement with that derived from the present experimental measurements for both spin-manifold conserving (F1-->Fl) and spin-manifold changing (F1 --F2) collisions, except that the overall sign of the effect is opposite. Additionally, calculated field-free integral cross sections for collisions at Etr = 508 cm(-1) are compared to the experimental data of Joswig et al. [J. Chem. Phys.85, 1904 (1986)]. Finally, the calculated differential cross section for collision energy Etr= 491 cm(-1) is compared to experimental data of Westley et al. [J. Chem. Phys. 114, 2669 (2001)] for the spin-orbit conserving transition F1 (j = 0.5) -F1f (j' = 3.5).

Combined crossed-beam studies of C(3PJ)+C2H4→C3H3+H reaction dynamics between 0.49 and 30.8 kJ mol−1

The reaction C(3PJ)+C2H4(X 1A1)→C3H3+H(2S1/2) has been studied using complementary crossed molecular beam techniques. Integral cross sections have been obtained in the range of relative translational energies ET=0.49–24.9 kJ mol−1 in experiments conducted with pulsed supersonic beams coupled with laser-induced fluorescence detection of H(2S1/2) atoms. The major reaction pathway leading to HCCCH2 (propargyl)+H has been found without any barrier, with relative integral cross sections that are proportional to (ET)−0.60±0.03 below 8 kJ mol−1. Threshold for a minor pathway, leading also to H formation, occurs around 6 kJ mol−1; the relative importance of this second pathway increases with relative translational energy. Differential cross sections have been obtained at three relative translational energies: ET=9.1, 17.2, and 30.8 kJ mol−1 in experiments conducted with continuous supersonic molecular beams coupled with universal mass spectrometric detection and time-of-flight analysis. At the lowest ET of 9.1 kJ mol−1 formation of HCCCH2 (propargyl)+H is observed to be the dominant channel with a nearly forward–backward symmetric angular distribution in the center-of-mass (cm) frame; about 35% of the total available energy is channeled into translation indicating that the propargyl radical is highly internally excited; formation of less stable C3H3 isomer(s) is minor (2%). As ET increases, formation of appreciable, increasingly larger fractions of less stable propyn-l-yl and/or cyclopropenyl isomers is also observed. These findings are consistent with the integral cross-section measurements. While formation of propargyl is thought to proceed via an osculating complex mechanism following addition of C(3PJ) to the double bond of ethylene, the dynamics of formation of the less stable isomers is going through a long-lived complex, as witnessed by an isotropic cm angular distribution. The H2 elimination channel leading to C3H2 formation has not been found to occur, which suggests that inter-system-crossing to the ground singlet C3H4 potential energy surface manifold has low probability and/or the H2-elimination process on the triplet surface is characterized by a very large exit potential barrier.

Low energy differential and integral electron-impact cross sections for the2s22p4 3P →2p33s 3So excitation in atomic oxygen

Differential and integral cross sections (ICSs) for excitation in atomic oxygen have been measured at electron-impact energies of15, 17.5, 20, 22.5 and 27.5 eV. Differential measurements were conducted with aconventional electron energy-loss spectrometer and a microwave discharge sourceof atomic oxygen. Relative differential cross sections (DCSs) were determinedbetween 15 and 30 eV impact energy. With the help of theoretical predictionsof the shape of the DCS at large angles, measured results were extrapolated to180° scattering angle and relative ICSs were deduced. The relative excitation function was normalizedto the 30 eV impact energy ICS given by Kanik et al (2001 J. Phys. B: At. Mol. Opt. Phys. 342647). Normalization of the ICS values allowed the measured DCSs to be put on theabsolute scale. Theoretical calculations of the DCSs were carried out using theR-matrixwith the pseudostates approach. A total of 22 spectroscopic bound and autoionizing states,together with 19 pseudostates, were included in the close-coupling expansion. Thepseudostates were chosen to simulate continuum target states. Theoretical results, alongwith other available experimental data, have been compared with the current experimentalresults.

Integral cross-section of the [formula omitted] reaction between 0.41 and 12.0 kJ/mol

The reaction C( 3 P J)+ O 2( X 3Σ g −)→ CO( X 1Σ +)+ O( 1 D 2) has been studied with pulsed, crossed, supersonic molecular beams in the range of relative translational energies E T =0.41–12.0 kJ/ mol . C( 3 P J) reactant and O( 1 D 2) product have been detected by laser-induced fluorescence in the vacuum ultra-violet. Relative integral cross-sections have been found proportional to ( E T) −1.00±0.03 below E T=6 kJ/mol, indicating that the reaction proceeds without any threshold energy.

Dynamics of the C+C2H2 reaction from differential and integral cross-section measurements in crossed-beam experiments

The reaction between atomic carbon and acetylene has been investigated using complementary crossed molecular beam techniques. Differential cross sections have been obtained for the reactions of both ground and excited carbon atoms, C(3PJ, 1D2)+C2H2(X 1Σg+), in experiments conducted with continuous supersonic beams, mass spectrometric detection, and time-of-flight analysis at a relative translational energy of 29.3 kJ mol−1. The reaction C(3PJ)+C2H2(X 1Σg+) has been found to lead to C3H+H and C3+H2 products in comparable amounts. Both H and H2 elimination pathways are found to proceed through the formation of a C3H2 long-lived intermediate complex whose lifetime may be comparable to its rotational period. The spin-forbidden H2 elimination channel is attributed to the occurrence of intersystem-crossing between the triplet and singlet manifolds of the C3H2 potential-energy surfaces. The reaction C(1D2)+C2H2(X 1Σg+) has been found to lead to formation of C3H+H, with a C3H center-of-mass angular distribution strongly forward peaked, indicating a short-lived intermediate complex. Integral cross sections have been obtained for the C(3PJ)+C2H2(X 1Σg+)→C3H+H(2S1/2) reaction in experiments conducted with pulsed, supersonic molecular beams in the range of relative translational energies ET=0.38−25.5 kJ mol−1, the H(2S1/2) product being detected by laser-induced fluorescence. The reaction has been found to be without a barrier, relative integral cross sections being proportional to (ET)−0.80±0.03 below ET=10 kJ mol−1. These findings provide direct evidence that the C(3PJ)+C2H2 reaction can occur under the physical conditions prevailing in dense interstellar clouds and, in particular, that it may be the source of both C3H and C3 species in these extreme environments.

Crossed-beam study of the [formula omitted] reaction between 4 and 240 meV relative translational energy

The reaction C( 3 P J)+ C 2 D 2( X 1Σ g +) → C 3 D+ D( 2 S 1/2) has been studied with pulsed, crossed, supersonic molecular beams, in the range of relative translational energies ε tr=4–240 meV. The D( 2 S 1/2) product has been detected by laser-induced fluorescence. The reaction is found to be slightly exoergic, with no barrier. Relative integral cross-sections are proportional to ( ε tr) −0.72±0.03 below ε tr=50 meV. These findings, along with energetics considerations, suggest that the analogous C( 3 P J)+ C 2 H 2( X 1Σ g +) → C 3 H+ H( 2 S 1/2) reaction is also a barrierless process.

State to state He–CO rotationally inelastic scattering

Relative integral cross sections for rotational excitation of CO in collisions with He were measured at energies of 72 and 89 meV. The cross sections are sensitive to anisotropy in the repulsive wall of the He–CO interaction. The experiments were done in crossed molecular beams with resonance enhanced multiphoton ionization detection. The observed cross sections display interference structure at low Δj, despite the average over the initial CO rotational distribution. At higher Δj, the cross sections decrease smoothly. The results are compared with cross sections calculated from two high quality potential energy surfaces for the He–CO interaction. The ab initio SAPT surface of Heijmen et al. [J. Chem. Phys. 107, 9921 (1997)] agrees with the data better than the XC(fit) surface of Le Roy et al. [Farad. Disc. 97, 81 (1994)].

Vibrational and Translational Energy Effects in the Reaction of Ammonia Ions with Water Molecules

The reaction of vibrationally state-selected ammonia ions with deuterated water is investigated with a quadrupole−octopole−quadrupole apparatus. Relative integral reaction cross sections for all ionic products are measured for collisional energies from 0.5 to 10.0 eV (center of mass) and ammonia ion vibrational states 1020-10 and 1122. The predominant charged products have masses of 18 and 21 amu and are shown to be NH2D+ (formal isotope exchange) and D2OH+ (proton transfer), respectively. Small amounts of product are also observed at masses 19, 20, and 22 amu. The cross section for proton transfer decreases with increasing collisional energy, but it increases with increasing internal energy at all collisional energies studied. The cross section for formal isotope exchange increases with increasing collisional energy and increases with increasing internal energy only at low collisional energies. Comparing the reactivity of NH3+(1025) to that of NH3+(1122) (internal energies of 0.60 and 0.63 eV, respectively) shows whether the system is sensitive to the specific vibrational motion, or only to the total amount of internal energy. The present system is shown not to be vibrational-mode selectivethe two internal preparations having comparable reactive cross sections at all collisional energies studied. The projection of the product velocity onto the ion-beam axis is obtained by transforming the experimentally measured product time-of-flight profiles. These velocity profiles contain information regarding energy released into product recoil. The isotope exchange products scatter tightly (0.6 eV, hwhm) about the center of mass and display forward−backward symmetry. The proton-transfer products yield a bimodal velocity distribution with one peak in the backward direction and another on the center of mass. The data observed for the isotope-exchange product indicate a reaction mechanism in which the first step is collision-induced dissociation of the ammonia ion (or water molecule), resulting in a hydrogen (deuterium) atom and an [NH2D2O]+ ([NH3OD]+) complex. This complex may decay to form the products NH2D+ and OD (OH). The majority of the D2OH+ product is formed via direct proton transfer.

Observation of an anomalous increase in total cross sections with high vibrational excitation in the Li2 (v=0–21)+Na reactive system

The effect of initial vibrational excitation on Li2(v,J)+Na collisions was studied experimentally and theoretically. The relative integral cross sections σ(v,J) were measured in a crossed beam experiment for vibrational states v populated thermally or by optical pumping, and for final states detected by laser induced fluorescence. It is found that σ(v,J) increases by 35±7% between v=0 and v=20, while the dependence on the initial rotational state J is insignificant, within ±5%. The effect of vibrational enhancement is about twice as large as that found for the Li2–rare gas systems for the same amount of vibrational excitation. The effect is about an order of magnitude larger than predicted by our quasiclassical trajectory calculations on a LEPS potential energy surface, thus suggesting that additional long-range potential terms ought to be included. We also attempted to measure state-selectively the LiNa (v′,J′) products from the thermal reaction and found an upper limit of the reactive cross section of 1 Å2. This contrasts with the trajectory calculations that predict a 20 times larger cross section; we thus conclude that the reactive part of the potential also needs to be re-evaluated.

Steric effects in total integral reaction cross sections for Sr+HF(v=1,j=1,m=0)→SrF+H

In a crossed beam study we have investigated the reactive scattering of Sr atoms from state prepared HF molecules. All measurements have been performed for two different directional distributions (alignments) of the molecular axis of HF favoring either end-on or side-on attacks. Using a surface ionization detector we have measured angular distributions of the total SrF flux at various collision energies ranging from Etr=230 to 626 meV. We found that the total product flux as well as the relative total integral reaction cross sections deduced from these data are markedly influenced by the prepared alignments (steric effect). The energy dependence of the steric effect has been quantitatively rationalized using the angle-dependent line-of-centers model. The resulting anisotropic height of the potential energy barrier features a minimum at a bent transition state. Ab initio potential energy surfaces calculated for the homologous systems Mg+HF and Ca+HF substantiate this result.

Long-range features of the F-HBr and F-HI potential energy surfaces from crossed molecular-beam experiments: a model analysis

Relative differential and integral cross sections for scattering of fluorine atoms by hydrogen bromide and hydrogen iodide have been measured at collision energies from 5 to 175 meV. Treating the experimental data in terms of a single potential of the Lennard-Jones type, we have evaluated the well depths and equilibrium distances of the long-range interaction potentials.

Beam scattering study of the charge transfer prcess N 2+ (He, He +)N + at low collision energies

The single-electron charge transfer process between N 2+ and He was investigated in low energy scattering experiments over the collision energy range 3.8–12.0 eV (c.m.). Relative differential and integral cross sections were obtained from scattering diagrams for the state-to-state processes of formation of N + ( 1 D) and N + ( 3 P) products in collisions of N 2+ ( 2 P) + He( 1 S). The ratio of integral cross sections of the two states formation, σ int( 1 D)/σ int( 3 P), decreases from 1.0 to 0.7 between 3.8 and 12.0 eV.