State-resolved Differential Cross Research Articles

Fully state-resolved differential cross sections for the inelastic scattering of the open-shell NO molecule by Ar.

State-resolved differential cross sections (DCSs) for the inelastic scattering of NO(j" = 0.5, Omega" = 1/2) + Ar --> NO(j', Omega' = 1/2, 3/2) + Ar were obtained at a collision energy of 516 cm(-1), both experimentally and theoretically. A crossed molecular beam ion-imaging apparatus was used to measure DCSs for 20 final (j', Omega') states, including spin-orbit conserving (DeltaOmega = 0) and changing (DeltaOmega = 1) transitions. Quantum close-coupling scattering calculations on ab initio coupled-cluster CCSD(T) and CEPA (correlated electron pair approximation) potential energy surfaces were also performed. Although small discrepancies were found for the DeltaOmega = 1 transitions, we find marked agreement between theory and experiment for the collision dynamics of this system, which is the paradigm for the collisional relaxation of a molecular radical.

Crossed-beam studies of neutral reactions: state-specific differential cross sections.

Crossed-molecular-beam and laser techniques have enabled experimentalists to measure the state-resolved differential cross sections of elementary chemical reactions. This article reviews recent progress in this area. Particular emphasis is placed on some intriguing physical phenomena associated with a few benchmark reactions and how these measurements help in answering fundamental questions about reaction dynamics. We examine specifically the geometric phase effects in the reaction H + D2, the dynamical resonance phenomenon in F + HD, the unusually large spin-orbit reactivity in Cl((2)P) + H2, the insertion reaction O((1)D) + H2, and the mode-specific reactivity in Cl + CH4(nu). The give-and-take between experiment and theory in unraveling the physical picture of the dynamics is illustrated throughout this review.

Differential scattering dynamics of F+CH 4→HF( v, J)+CH 3 via high-resolution IR laser dopplerimetry

Product recoil data from F+CH 4→HF( v, J)+CH 3 reactive scattering are obtained using crossed supersonic jets and narrow band ( Δν≈0.0001 cm −1 ) infrared radiation laser direct absorption techniques. The high-resolution infrared radiation profiles of HF( v, J) product exhibit extensive Doppler broadening that directly reflects quantum state-resolved translational distributions in the laboratory frame under single collision conditions. Analyses of Doppler profiles yield information on state-resolved differential cross sections into the HF( v=1) and HF( v=2) vibrational manifolds, which both identify a propensity for forward/backward scattering (|cos( θ)|≈1) over side scattering (|cos( θ)|≈0) in the center-of-mass frame.

Quasi-Classical Trajectory Studies of the Insertion Reactions S(1D) + H2, HD, and D2

In this work, we present the results of a quasi-classical trajectory (QCT) calculation using a newly developed potential energy surface for the title reactions. The integral cross sections, the product state-resolved differential cross sections, the angle-state-specific energy partitions, and other relevant reaction attributes are computed. The QCT integral cross sections, the differential cross sections, and the gross features of the product distributions are consistent with a simple view of the reaction as mediated by capture dynamics in the entrance channel, followed by the statistical decay of a long-lived complex. We present a comparison to the molecular beam experiments of Lee and Liu, which show agreement in the broad pattern of results but also exhibit significant differences in the more finely resolved quantities.

A Quantum State-Resolved Insertion Reaction: O((1)D) + H(2)(J = 0) --> OH((2) product operator product operator product operator, v, N) + H((2)S).

The O((1)D) + H(2) --> OH + H reaction, which proceeds mainly as an insertion reaction at a collisional energy of 1.3 kilocalories per mole, has been investigated with the high-resolution H atom Rydberg "tagging" time-of-flight technique and the quasiclassical trajectory (QCT) method. Quantum state-resolved differential cross sections were measured for this prototype reaction. Different rotationally-vibrationally excited OH products have markedly different angular distributions, whereas the total reaction products are roughly forward and backward symmetric. Theoretical results obtained from QCT calculations indicate that this reaction is dominated by the insertion mechanism, with a small contribution from the collinear abstraction mechanism through quantum tunneling.

Cl+HD (v=1; J=1,2) reaction dynamics: Comparison between theory and experiment

Vibrationally state-resolved differential cross sections (DCS) and product rotational distributions have been measured for the Cl+HD(v=1, J=1)→HCl(DCl)+D(H) reaction at a mean collision energy of 0.065 eV using a photoinitiated reaction (“photoloc”) technique. The effect of HD reagent rotational alignment in the Cl+HD(v=1, J=2) reaction has also been investigated. The experimental results have been compared with exact quantum mechanical and quasiclassical trajectory calculations performed on the G3 potential energy surface of Allison et al. [J. Phys. Chem. 100, 13575 (1996)]. The experimental measurements reveal that the products are predominantly backward and sideways scattered for HCl(v′=0) and HCl(v′=1), with no forward scattering at the collision energies studied, in quantitative agreement with theoretical predictions. The experimental product rotational distribution for HCl(v′=1) also shows excellent agreement with quantum-mechanical calculations, but the measured DCl+H to HCl+D branching ratio is near unity, which is at variance with the theoretical calculations that predict about 3 times larger yield of HCl+D at these collision energies. The reactivity shows a marked dependence on the direction of the HD(v=1, J=2) rotational angular momentum, and experimental measurements of this reagent alignment effect are in good agreement with theoretical predictions.

Dynamics of the Reaction O(3P) + H2S → OH + SH. 2. State-Resolved Differential Cross Sections and Angular Momentum Correlations

Measurements are reported of Doppler resolved polarized laser-induced fluorescence of the OH product of the O(3P) + H2S reaction, leading to estimates of the differential cross sections and angular momentum correlations in the system. O(3P) was produced with translational energy above the barrier to reaction by the polarized 355 nm photolysis of NO2. Three quantum states were studied in detail. For the most populated OH level, v‘ ‘ = 1, N‘ ‘ = 6, the scattering for the A‘ ‘ Λ doublet was found to be largely sideways/backward, with the remaining energy appearing as product translation, and measurements of average Λ doublet scattering showed similar behavior for the A‘ Λ doublet. The same scattering dynamics were observed for the v‘ ‘ = 0, N‘ ‘ = 13 state. For the rotationless v‘ ‘ = 1, N‘ ‘ = 1 state the results were more ambiguous, but if the same distribution of available energy appeared in the SH fragment as deduced for the measurements on rotationally excited OH, then the scattering was seen to be clea...

The dynamics of the hydrogen exchange reaction at 2.20 eV collision energy: Comparison of experimental and theoretical differential cross sections

The H+D2(v=0,j=0)→HD(v′,j′)+D isotopic variant of the hydrogen atom exchange reaction has been studied in a crossed molecular beam experiment at a collision energy of 2.20 eV. Kinetic energy spectra of the nascent D atoms were obtained by using the Rydberg atom time-of-flight technique. The extensive set of spectra collected has permitted the derivation of rovibrationally state-resolved differential cross sections in the center-of-mass frame for most of the internal states of the HD product molecules, allowing a direct comparison with theoretical predictions. Accurate 3D quantum mechanical calculations have been carried out on the refined version of the latest Boothroyd–Keogh–Martin–Peterson potential energy surface, yielding an excellent agreement with the experimentally determined differential cross sections. The comparison of the results from quasi-classical trajectory calculations on the same potential surface reveals some discrepancies with the measured data, but shows a good global accordance. The theoretical calculations demonstrate that, at this energy, reactive encounters are predominantly noncollinear and that collinear collisions lead mostly to nonreactive recrossing. The experimental results are satisfactorily accounted for by theoretical calculations without consideration of Geometric Phase effects.

Quantum mechanical and quasiclassical trajectory study of state-to-state differential cross sections for the F+D2→DF+D reaction in the center-of-mass and laboratory frames

Quantum mechanical (QM) and quasiclassical (QCT) state-resolved integral and differential cross sections for the DF(v′,j′) products of the F+D2(v=0, j=0, 1, 2) reaction have been calculated on the abinitio potential energy surface of Stark and Werner at five collision energies in the range 34.5–240 meV with the twofold purpose of comparing extensively the QM and QCT dynamics of this reaction and of rationalizing the results of high resolution crossed molecular beam experiments performed by Toennies and co-workers (Gottingen) and by Lee and co-workers (Berkeley). The comparison with experiment is carried out not only in the center-of-mass but also in the laboratory frame, involving the simulation of experimental laboratory angular distributions and time-of-flight spectra. An overall agreement is found between theory and experiment for the rovibrationally state-resolved integral and differential cross sections. In particular, both theoretical calculations confirm the experimental observation of a significant increase of product rotational excitation for all DF vibrational states on going from backward to sideways and forward scattering regions, with the only exception of the forward scattered DF products in v′=4, which are rotationally cooler than those scattered at intermediate scattering angles. However, significant discrepancies remain between the theoretical results and those of the crossed beam experiments, suggesting that the full understanding of the dynamics of this prototypic reaction is still a challenge.

Quantum mechanical and quasiclassical simulations of molecular beam experiments for the F+H2→HF+H reaction on two ab initio potential energy surfaces

Laboratory (LAB) angular distributions (AD) measured in molecular beam experiments by Lee and co-workers in 1985 and very recently by Keil and co-workers for the prototypic F+H2 reaction have been simulated using new quantum mechanical (QM) and quasiclassical trajectory (QCT) state-resolved differential cross sections (DCS) calculated on the ab initio potential energy surfaces (PES) by Stark and Werner (SW) and by Hartke, Stark and Werner (HSW); the latter PES includes spin-orbit coupling corrections added to the entrance channel of the former. The simulations of the 1985 LAB ADs performed using the new QM calculations on the SW PES show a very good agreement with the experimental results for all final vibrational states of the HF product. The inclusion of spin-orbit coupling corrections in the ab initio HSW PES does not seem to improve the agreement between theoretical and experimental results. As for the simulation of the recent experiments of Keil and co-workers, the LAB ADs are very well reproduced by the QM and QCT results on both the SW and HSW PESs with the exception of the negative signal measured at LAB scattering angles of about −8°, arising from HF scattering into the forward hemisphere for the v′=1, j′=5,6,7 states. This peak cannot be accounted for by either of the QM and QCT calculations on any of the two PESs.

Rotational State Resolved Differential Cross Sections for the Reaction F + D2 → DF + D at Collision Energies 140−240 meV

Product rotationally state-resolved differential cross sections (DCS) have been determined for the DF(vf, jf) products of the F + D2 (vi = 0, ji = 0, 1, 2) reaction from the detailed analysis of high resolution crossed molecular beam experiments at the collision energies of 140, 180, and 240 meV. An increasing rotational excitation when going from the backward to the sideways and forward scattering regions is observed for all vibrational DF states, except for vf = 4. The DF products in vf = 4 scattered in the forward region (θcm = 0°−20°) are rotationally cooler than those scattered at intermediate scattering angles (θcm = 30°−100°). The experimental results are compared with quasiclassical trajectory (QCT) calculations on the ab initio potential energy surface (PES) of Stark and Werner. Good qualitative agreement is found for the observed trend of the vf, jf state-resolved DCSs. In particular, the behavior of the vf = 4 product state is well accounted for by the QCT calculation. The results are discussed in terms of the quasiclassical state-to-state reaction probabilities as a function of the total angular momentum (opacity functions).

An Experimental Study of the Dynamics of the Reaction H + CO2 → OH(v‘, j‘, f) + CO: Product State-Resolved Differential Cross Sections and Translational Energy Release Distributions

Angular distributions and pair-correlated translational energy distributions have been measured for OH(v‘ = 0, N‘ = 1), produced through the reactive scattering of hot H atoms by CO2 at 300 K and mean collision energies of 1.8 eV and 2.5 eV. The new measurements, together with those reported previously for the OH(v‘ = 0, N‘ = 5, A‘/A‘‘) products of the reaction at 2.5 eV, reveal that the differential cross sections depend strongly on collision energy and product quantum state. For the OH(v‘ = 0, N‘ = 1) channel, the angular distribution changes from broad forward scattering to pronounced backward scattering as the collision energy is raised from 1.8 to 2.5 eV. The angular distributions at the higher collision energy shift from being backward to nearly isotropic, with forward−backward peaks, as the OH angular momentum is increased from N‘ = 1 to N‘ = 5. Although somewhat less dramatic changes are evident in the pair-correlated kinetic energy release data, the measurements confirm that the CO internal energy distributions are considerably colder than those predicted by statistical phase space theory. The results are discussed in light of earlier theoretical and experimental studies, particularly the results of femtochemical kinetic measurements.

State-to-state differential cross sections for rotationally inelastic collisions of NO(2Π1/2,j⩽2.5) with CO(1Σ+) and O2(3Σg−) at a kinetic energy of 442 cm−1

Crossed molecular beam measurements of state-resolved differential cross sections for NO+O2 and NO+CO inelastic collisions at a relative kinetic energy of 442 cm−1 are reported. The initial states (NO 2Π1/2, ν=0, j⩽2.5, CO 1Σ+, ν=0, O2 3Σg−, ν=0) were prepared by pulsed supersonic expansions of pure NO, O2, and CO gas. Scattered NO products were detected by resonance enhanced two-photon ionization. Product distributions were measured in both center-of-mass scattering angle and final rotational state (j′). Intensity maxima were found in both types of scans and comparable populations were found in both of the spin–orbit manifolds (2Π1/2 and 2Π3/2). The results are compared to previous inelastic scattering experiments of NO collisions with NO, Ar, CO, and O2.

Total differential cross sections and differential energy loss spectra for He–C2H2 from an ab initio potential

State-to-state elastic and rotationally inelastic differential cross sections for He +C2H2 scattering were obtained from an ab initio potential computed by symmetry-adapted perturbation theory (SAPT) by means of converged close-coupling calculations. From these state-resolved data total differential cross sections at Ecm=71.3 meV and energy loss spectra at Ecm=62.0 and 102.9 meV were determined by transformation to the laboratory frame, and accounting for the experimental conditions via a Monte-Carlo averaging procedure. The results are in excellent agreement with experiment [U. Buck et al., J. Chem. Phys. 99, 3494 (1993)], which proves that the SAPT potential is indeed very accurate.

Experimental determination of quantum state resolved differential cross sections for the hydrogen exchange reaction H+D2→HD+D

We have carried out a systematic crossed molecular beam study of the hydrogen exchange reaction in the H+D2→HD+D isotopic form at two collision energies: 0.53 and 1.28 eV. The Rydberg atom time-of-flight method was used to measure the D-atom product angle-velocity distribution. For the first time ro-vibrational quantum state resolved differential cross sections for the title reaction were measured, which can directly be compared to theoretical predictions at this detailed level. Experimental results are compared to theoretical predictions from both quasi classical and quantum mechanical calculations on different potential energy surfaces as well as to earlier experiments. A general good agreement is found for the converged quantum mechanical calculations with indications that the Boothroyd-Keogh-Martin-Peterson potential energy surface is better suited to describe the dynamics of the reaction. For the higher collision energy the quasi classical trajectory calculations reproduce the experimental data quite well, whereas they fail to describe the situation at the lower collision energy especially with respect to angular resolved differential cross sections.

Differential cross sections for rotationally inelastic collisions of NO(2Π1/2, j′⩽2.5) with NO(2Π1/2, j′⩽2.5) at a kinetic energy of 442 cm−1

We report crossed molecular beam measurements of state-resolved differential cross sections for NO+NO collisions at relative kinetic energy of 442 cm−1. The initial state (NO 2Π1/2v=0,j⩽2.5) was prepared in both beams by pulsed supersonic expansion of pure NO gas. Scattered products were detected by resonance enhanced two-photon ionization. NO product distributions were measured in both scattering angle and final rotational state. Intensity maxima were found in both types of scans, and comparable populations were found in both of the spin-orbit manifolds (2Π1/2 and 2Π3/2). The results obtained here are compared to previous NO+Ar scattering experiments and theory, NO dimer studies, and NO+NO bulb kinetics experiments.

High resolution study of the H+D 2 → HD+D reaction dynamics at a collision energy of 2.2 eV

The reactivity of H + D 2( v = 0, j = 0) → HD( v′, j′) + D has been investigated in a high resolution crossed molecular beam experiment at a collision energy of 2.2 eV. Time-of-flight (TOF) spectra of D atoms at different laboratory (LAB) scattering angles and their total angular distribution were measured using the technique of Rydberg atom TOF spectroscopy. The resolution of this technique allows the identification of individual rovibrational states of the corresponding HD product molecule at the different LAB angles. A detailed simulation of the experimental measurements has been performed by using state resolved differential cross sections from quasiclassical trajectory (QCT) calculations on the Liu-Siegbahn-Truhlar-Horowitz (LSTH) and on the double-many-body-expansion (DMBE) potential energy surfaces (PES). A general good agreement between experiment and theory is found, although there are some discrepancies which are discussed.

Product state-resolved stereodynamics: quasiclassical study of the reaction [formula omitted

State-resolved integral and differential cross sections and product energy partitioning have been calculated for the reaction O( 1 D)+ HD(ν = 0, j = 0–1) → OH(OD) + D(H) by means of quasi-classical trajectory (QCT) calculations at a collision energy of 0.197 eV (19 kJ mol −1) using the potential energy surface of Schinke and Lester. The results indicate the dominance of an insertion mechanism producing HOD intermediates and reveal a strong dependence of the differential scattering cross section on the product quantum state. This dependence has been related to the product state-resolved opacity functions and the estimated lifetimes of the reactive collisional trajectories.

Product state resolved stereodynamics.

Abstract A first study of the stereodynamics of the reaction, O( 1 D 2 ) + HCl → OH(X; v , N ) + Cl( 2 P J ) is described. Polarised, Doppler resolved laser induced fluorescence is used to probe the product state resolved differential cross section, translational energy disposal, excitation function and rotational polarisation of the OH products, specifically OH ( X 2 Π 1 2 ; v = 4, N = 6). The new results are discussed in the context of earlier studies of the pattern of energy disposal in the above reaction and crossed beam studies of the competing reaction channel O( 1 D 2 ) + HCl → ClO(X) + H. Although the reactive trajectories may access a deeply bound well on the potential surface, the dynamics cannot simply be described solely in terms of an insertion mechanism proceeding through the intermediacy of a long-lived, persistent collision complex.

Core extraction for measuring state-to-state differential cross sections of bimolecular reactions

We describe a method we call core extraction for measuring the speed distributions of products from photoinitiated bimolecular reactions for the purpose of determining state-to-state differential cross sections. Core extraction is demonstrated by determination of the state-to-state differential cross section for the reaction Cl+CH4(υ3=1)→HCl(υ=1, J=1)+CH3. The method of core extraction measures three-dimensional projections of the velocity distribution using a time-of-flight mass spectrometer equipped with a mask to reject off-axis scattered products. This three-dimensional projection is then converted to a state-to-state differential cross section via simple transformations. Competition between instrumental resolution and signal in core extraction is discussed, and the behavior of our system is checked with simple velocity distributions that result from photodissociation of Cl2. Core extraction is compared with other methods for the measurement of state-resolved differential cross sections.