State-resolved Differential Cross Sections Research Articles

Quantum state-resolved differential cross sections for complex-forming chemical reactions: Asymmetry is the rule, symmetry the exception.

We argue that statistical theories are generally unable to accurately predict state-resolved differential cross sections for triatomic bimolecular reactions studied in beam experiments, even in the idealized limit where the dynamics are fully chaotic. The basic reason is that quenching of interferences between partial waves is less efficient than intuitively expected, especially around the poles.

Rotational Orientation Effects in NO(X) + Ar Inelastic Collisions.

Rotational angular momentum orientation effects in the rotationally inelastic collisions of NO(X) with Ar have been investigated both experimentally and theoretically at a collision energy of 530 cm(-1). The collision-induced orientation has been determined experimentally using a hexapole electric field to select the ϵ = -1 Λ-doublet level of the NO(X) j = 1/2 initial state. Fully quantum state resolved polarization-dependent differential cross sections were recorded experimentally using a crossed molecular beam apparatus coupled with a (1 + 1') resonance-enhanced multiphoton ionization detection scheme and subsequent velocity-map imaging. To determine the NO sense of rotation, the probe radiation was circularly polarized. Experimental orientation polarization-dependent differential cross sections are compared with those obtained from quantum mechanical scattering calculations and are found to be in good agreement. The origin of the collision-induced orientation has been investigated by means of close-coupled quantum mechanical, quantum mechanical hard shell, quasi-classical trajectory (QCT), and classical hard shell calculations at the same collision energy. Although there is evidence for the operation of limiting classical mechanisms, the rotational orientation cannot be accounted for by QCT calculations and is found to be strongly influenced by quantum mechanical effects.

Effect of Reagent Vibrational Excitation on the Dynamics of F + H2(v = 1, j = 0) → HF(v', j') + H Reaction.

The reaction of fluorine atom with vibrationally excited H2 at v = 1 has been studied using a high resolution crossed molecular beam apparatus at collision energies of 0.52 and 0.90 kcal/mol. Product HF rotational state-resolved differential cross sections (DCSs) were measured at v' = 2, 3, 4 levels. The product angular distributions are predominantly backward scattered except for a small forward signal of HF(v' = 4) at 0.90 kcal/mol. At the collision energy of 0.52 kcal/mol, the forward scattering peak of the HF(v' = 2) product, which arises in F + H2(v = 0) reaction from the Feshbach resonances, disappears in F + H2(v = 1) reaction. Oscillatory structures do not appear in the backward direction of the scattering as the collision energy increases from 0.4 to 2.0 kcal/mol, indicating there are no explicit reaction resonances in the F + H2(v = 1, j = 0) → HF + H reaction in the studied energy range. Quantum dynamics calculations on a highly accurate potential energy surface are in good agreement with the experimental results and reveal that the reaction occurs via likely a direct abstraction mechanism, not via long-lived reactive resonances.

Effect of Reagent Rotational Excitation on Dynamics of F+H2→HF+H

The dynamics of the F+H2(v=0, j=0, 1) reactions have been studied at the collision energy of 1.27 kcal/mol using a high-resolution crossed molecular beam apparatus. HF product rotational state resolved differential cross sections have been obtained at the v′=1, 2, 3 levels. The product HF(v′=2) angular distributions are predominantly backward scattered for both H2 (j=0, 1) reagents. However, the distributions of product HF(v′=2) rotational states for the F+H2(v=0, j=0) reaction are significantly different from those for the F+H2(v=0, j=1) reaction. Experimental results show that the rotational excitation of H2 produces rotationally ‘hotter' HF(v′=2) product. In addition, the HF(v′=3) product is more likely scattered into the forward direction when the H2 reagent is populated at j=0 state, which could be attributed to a slow-down mechanism.

State-to-State Quantum Dynamics of Reactions O((3)P) + HD (v = 0-1, j = 0) → OH+D and OD+H: Reaction Mechanism and Vibrational Excitation.

Time-dependent quantum wave packet dynamics calculations have been performed in order to characterize the dynamics and mechanism of O((3)P) + HD (v = 0-1, j = 0) → OH+D and OD+H reactive collisions using the adiabatic potential energy surface by Rogers et al. [J. Phys. Chem. A 2000, 104, 2308] Special attention has been paid to the calculations and discussion of the state resolved integral and differential cross sections and the product state distributions. In addition, the intramolecular isotopic branching ratio has been determined. The results revealed that the OD + H is the favored product channel and the product OH has the same quantum number v as the reactant HD. For low collision energy, the product angular distributions concentrate in the backward region being consistent with a rebounding mechanism. In the case of higher collision energy, the stripping collisions with larger impact parameters tend to produce sideways and forward scatterings, especially for the HD vibrationally excited state. The cross section and intramolecular isotopic branching ratio are in agreement with the previous theoretical results. A cartoon depiction collision model is built and works well for our calculation results.

Quantum State-to-State Dynamics of the H + LiH → H2 + Li Reaction.

State-to-state quantum dynamics calculations for the H + LiH (v = 0-1, j = 0) → H2 + Li reactions are performed based on an ab initio ground electronic state potential energy surface (PES). Total and product state-resolved integral and differential cross sections and rate constants are calculated. The present total integral cross sections and rate constants for the H + LiH (v = 0, j = 0) reaction are found to be in agreement with previous literature results. Product state-resolved integral cross sections and rate constants reveal that the H2 products are preferred to be formed in their rovibrational excited states. The differential cross sections show that the intensity of forward scattering for the H2 products in their rovibrational excited states is stronger than other states. The mechanisms for the v = 0 and v = 1 reactions are found to be highly consistent with each other. Further, the influence of the stripping mechanism on the H + LiH reaction is studied. It is found that the stripping mechanism could be responsible for the decrease of the reactivity, the product state distribution, and scattering direction of the H2 products. It is related to the "attractive" feature of the underlying PES.

Atom-diatom scattering dynamics of spinning molecules.

We present full quantum mechanical scattering calculations using spinning molecules as target states for nuclear spin selective atom-diatom scattering of reactive D+H2 and F+H2 collisions. Molecules can be forced to rotate uni-directionally by chiral trains of short, non-resonant laser pulses, with different nuclear spin isomers rotating in opposite directions. The calculations we present are based on rotational wavepackets that can be created in this manner. As our simulations show, target molecules with opposite sense of rotation are predominantly scattered in opposite directions, opening routes for spatially and quantum state selective scattering of close chemical species. Moreover, two-dimensional state resolved differential cross sections reveal detailed information about the scattering mechanisms, which can be explained to a large degree by a classical vector model for scattering with spinning molecules.

Correlation functions for fully or partially state-resolved reactive scattering calculations.

Flux correlation functions and the quantum transition state concept are important tools for the accurate description of polyatomic reaction processes. Combined with the multi-configurational time-dependent Hartree approach, they facilitate rigorous full-dimensional calculations of cumulative and initial-state selected reaction probabilities for six atom reactions. In recent work [R. Welsch, F. Huarte-Larrañaga, and U. Manthe, J. Chem. Phys. 136, 064117 (2012)], an approach which allows one to calculate also state-to-state reaction probabilities within the quantum transition state concept has been introduced. This article presents further developments. Alternative generalized flux correlation functions are introduced and discussed. Equations for the calculation of fully state-resolved differential cross section using arbitrary definitions of the body fixed frame are derived. An approach for the efficient calculation of partially state-resolved observables as a function of the collision energy is introduced. Finally, numerical test studying the D + H2 reaction illustrate important aspects of the formalism.

Influence of collision energy on the dynamics of the reaction H (2S) + NH (X3Σ−) → N (4S) + H2 (X1Σ g + ) by the state-to-state quantum mechanical study

State-to-state time-dependent quantum dynamics calculations have been carried out to study the abstraction processes in the title reaction for the first time. The ab initio potential energy surface of the lowest quartet electronic state of the system recently reported by Zhai et al. (J Chem Phys 135:104314/1–104314/7, 2011) is employed in this investigation. Influences of the collision energy on the product state-resolved differential cross sections (DCSs) are calculated and discussed. For low collision energies, we find that reactive collisions along the collinear pathway result in the H2 product backward scattering. In the case of high collision energy, the stripping collisions with larger impact parameters tend to produce sideways scattering and furnish a high internal excitation of the H2. The product H2 is found to have an inverted rotational distribution and no inversion in vibrational distributions. Moreover, the state-to-state DCSs provide a global perspective of the reaction mechanisms and their contribution to the final H2 internal energy states. A reaction model is built and works well for our calculated results.

The fully quantum state-resolved inelastic scattering of NO(X) + Ne: experiment and theory

Fully Λ-doublet quantum state-resolved differential cross-sections for collisions of NO(X) with neon at a collision energy of 540 cm−1 are presented. Initial state selection of the Ω = 0.5, j = 0.5, f Λ-doublet level of the NO(X) was achieved using hexapole focussing. Both spin-orbit level conserving and spin-orbit level changing transitions have been studied. The experimental results are compared with those obtained from quantum scattering calculations and are shown to be in excellent agreement. Quantum scattering calculations have also been performed on a modified potential energy surface with the attractive region removed, to determine the effects this has on the differential cross-sections. Comparisons are also made with the inelastic scattering of NO(X) with He and Ar.

Disagreement between theory and experiment grows with increasing rotational excitation of HD(v′, j ′) product for the H + D2 reaction

The Photoloc technique has been employed to measure the state-resolved differential cross sections of the HD(v', j(')) product in the reaction H + D2 over a wide range of collision energies and internal states. The experimental results were compared with fully dimensional, time-dependent quantum mechanical calculations on the refined Boothroyd-Keogh-Martin-Peterson potential energy surface. We find nearly perfect agreement between theory and experiment for HD(v', j(')) product states with low to medium rotational excitation, e.g., HD(v' = 1, j(') = 3) at a collision energy, Ecoll, of 1.72 eV, HD(v' = 1, j(') = 3, 5) at Ecoll = 1.97 eV, and HD(v' = 3, j(') = 3) at Ecoll = 1.97 eV. As the rotational angular momentum, j('), of HD(v', j(')) increases, the agreement between theoretical predictions and experimental measurements worsens but not in a simple fashion. A moderate disagreement between theory and experiment has been found for HD(v' = 0, j(') = 12) at Ecoll = 1.76 eV and increased monotonically for HD(v' = 0, j(') = 13) at Ecoll = 1.74 eV, HD(v' = 0, j(') = 14) at Ecoll = 1.72 eV, and HD(v' = 0, j(') = 15) at Ecoll = 1.70 eV. Disagreement was not limited to vibrationless HD(v', j(')) product states: HD(v' = 1, j(') = 12) at Ecoll = 1.60 eV and HD(v' = 3, j(') = 8, 10) at Ecoll = 1.97 eV followed a similar trend. Theoretical calculations suggest more sideways∕forward scattering than has been observed experimentally for high j(') HD(v', j(')) states. The source of this discrepancy is presently unknown but might be the result of inaccuracy in the potential energy surface.

Observation of Extremely High Vibrational Excitation in O2 from Inelastic Scattering of Rydberg H Atom with O2.

The state-resolved differential cross sections for the Rydberg-atom (RA) inelastic scattering process H*(n = 46) + O2(v = 0, j = 1,3) → H*(n') + O2(v', j') have been measured by using the H-atom Rydberg tagging time-of-flight (HRTOF) technique. Extensive vibrational excitation of O2 products has been observed at the two collision energies of 0.64 and 1.55 eV. Experimental results show that the O2 products in the low vibrationally excited states are clearly forward-scattered, whereas those in the highly vibrationally excited states are mainly backward-scattered. Partially resolved rotational structures were also observed and assigned. The striking observation of extremely high energy transfer from translational to vibrational excitation at the backward direction could be explained involving charge transfer between proton and O2 molecule and possibly complex formation during the scattering process.

Dynamics of the D+ + H2 and H+ + D2 reactions: a detailed comparison between theory and experiment

An extensive set of experimental measurements on the dynamics of the H(+) + D(2) and D(+) + H(2) ion-molecule reactions is compared with the results of quantum mechanical (QM), quasiclassical trajectory (QCT), and statistical quasiclassical trajectory (SQCT) calculations. The dynamical observables considered include specific rate coefficients as a function of the translational energy, E(T), thermal rate coefficients in the 100-500 K temperature range. In addition, kinetic energy spectra (KES) of the D(+) ions reactively scattered in H(+) + D(2) collisions are also presented for translational energies between 0.4 eV and 2.0 eV. For the two reactions, the best global agreement between experiment and theory over the whole energy range corresponds to the QCT calculations using a gaussian binning (GB) procedure, which gives more weight to trajectories whose product vibrational action is closer to the actual integer QM values. The QM calculations also perform well, although somewhat worse over the more limited range of translational energies where they are available (E(T) < 0.6 eV and E(T) < 0.2 eV for the H(+) + D(2) and D(+) + H(2) reactions, respectively). The worst agreement is obtained with the SQCT method, which is only adequate for low translational energies. The comparison between theory and experiment also suggests that the most reliable rate coefficient measurements are those obtained with the merged beams technique. It is worth noting that none of the theoretical approaches can account satisfactorily for the experimental specific rate coefficients of H(+) + D(2) for E(T)≤ 0.2 eV although there is a considerable scatter in the existing measurements. On the whole, the best agreement with the experimental laboratory KES is obtained with the simulations carried out using the state resolved differential cross sections (DCSs) calculated with the QCT-GB method, which seems to account for most of the observed features. In contrast, the simulations with the SQCT data predict kinetic energy spectra (KES) considerably cooler than those experimentally determined.

High Resolution Crossed Molecular Beams Study on the F+HD→DF+H Reaction at Collision Energy of 8.19–18.98 kJ/mol

The crossed beams scattering dynamics of the F+HD→DF+H reaction have been studied at collision energies ranging from 8.19 kJ/mol to 18.98 kJ/mol using the high resolution H-atom Rydberg tagging time-of-flight method. Product rotational state-resolved differential cross sections have been measured. Most of the DF products are backward scattered at low collision energies and then gradually shift to the sideway as the collision energy increases. In addition to the backward and sideway scatterings, we have also observed the DF(v′ = 4) product in the forward direction for the first time for this reaction. The forward scattering DF(v = 4) product also increases with the collision energy. Angular and collision energy dependence of the product energy disposals in different degrees of freedom have been determined. Collision energy dependence of the vibrational branching ratios has also been examined. Possible dynamical origins of the forward scattering DF(v′=4) products were discussed.

High Resolution Crossed Molecular Beams Study on the F+HD→HF+D Reaction at Collision Energy of 5.43–18.73 kJ/mol

The dynamics of F+HD→HF+D reaction has been studied at ten collision energies ranging from 5.43 kJ/mol to 18.73 kJ/mol using high-resolution H/D atom Rydberg tagging time-of-flight method. Product vibrational and rotational state-resolved differential cross sections have been determined. The intensity of the HF(v′ = 2) forward products decreases as the collision energy increases, suggesting that the resonance contribution is reduced as the collision energy increases. The forward peak of HF(v′=3) product has also been observed above the threshold of this product channel. Product energy disposals in different degrees of freedom have been analyzed. The collision energy dependence of the HF vibrational product branching was also determined. This work presents a comprehensive dynamic picture of this resonance mediated reaction in a wide collision energy regime, providing a good test ground for theoretical understandings of this interesting reaction at higher collision energies.

Energy dependent dynamics of the O(1D) + HCl reaction: A quantum, quasiclassical and statistical study

The dynamics of the reaction O((1)D) + HCl → ClO + H, OH + Cl has been investigated in detail by means of a time-dependent wave packet (TDWP) method in comparison with quasiclassical trajectory (QCT) and statistical approaches on the ground potential energy surface by Martínez et al. [Phys. Chem. Chem. Phys., 2000, 2, 589]. Fully coupled quantum mechanical (QM) reaction probabilities for high values of the total angular momentum (J≤ 50) are reported for the first time. At the low collision energy regime (E(c)≤ 0.4 eV) the TDWP probabilities are well reproduced by the QCT and statistical results for the ClO forming product channel, but for the OH + Cl arrangement, only QCT probabilities are found to agree with the QM values. The good accordance found between the rigorous statistical models and the dynamical QM and QCT calculations for the O + HCl → ClO + H process underpins the assumption that the reaction pathway leading to ClO is predominantly governed by a complex-forming mechanism. In addition, to further test the statistical character of this reaction channel, the laboratory angular distribution and time-of-flight spectra obtained in a crossed molecular beam study by Balucani et al. [Chem. Phys. Lett. 1991, 180, 34] at a collision energy as high as 0.53 eV have been simulated using the state resolved differential cross section obtained with the statistical approaches yielding a satisfactory agreement with the experimental results. For the other channel, O + HCl → OH + Cl, noticeable differences between the statistical results and those found with the QCT calculation suggest that the dynamics of the reaction are controlled by a direct mechanism. The comparison between the QCT and QM-TDWP results in the whole range of collision energies lends credence to the QCT description of the dynamics of this reaction.

Inelastic x-ray scattering study of the state-resolved differential cross section of Compton excitations in helium atoms

The state-resolved differential cross sections for both the $1{s}^{2}$ ${}^{1}{S}_{0}\ensuremath{\rightarrow}1s2s$ ${}^{1}{S}_{0}$ monopolar transition and the $1{s}^{2}$ ${}^{1}{S}_{0}\ensuremath{\rightarrow}1s2p$ ${}^{1}{P}_{1}$ dipolar transition of atomic helium had been measured over a large momentum transfer region by high-resolution inelastic x-ray scattering (IXS). The almost-perfect match of the present measurement with the theoretical calculations gives a stringent test of the theoretical method and the calculated wave functions. Our results demonstrate that high-resolution IXS is a powerful tool for studying the excitations in atoms and molecules.

High Resolution Crossed Beams Scattering Study of the F+HDDF+H Reaction

Crossed beams scattering study was carried out on the F+HDDF+H reaction using high-resolution H-atom Rydberg tagging time-of-flight technique. Vibrational state-resolved differential cross sections were measured, with partial rotational state resolution, at eight collision energies in the range of 2.515.60 kJ/mol. Experimental results indicated that the product angular distributions are predominantly backward scattered. As the collision energy increases, the backward scattered peak becomes broader gradually. Dependence of product vibration branching ratios on the collision energy was also determined. The experimental results show that the DF products are highly inverted in the vibrational state distribution and the DF (v = 3) product is the most populated state. Furthermore, the DF (v = 1) product has also been observed at collision energy above 3.97 kJ/mol.

Quantum dynamics of vibrational excitations and vibrational charge transfer processes in H+ + O2 collisions at collision energy 23 eV

Quantum mechanical study of vibrational state-resolved differential cross sections and transition probabilities for both the elastic/inelastic and the charge transfer processes have been carried out in the H+ + O2 collisions at the experimental collision energy of 23 eV. The quantum dynamics has been performed within the vibrational close-coupling rotational infinite-order sudden approximation framework employing our newly obtained quasi-diabatic potential energy surfaces corresponding to the ground and the first excited electronic states which have been computed using ab initio procedures and Dunning’s correlation consistent-polarized valence triple zeta basis set at the multireference configuration interaction level of accuracy. The present theoretical results for elastic/inelastic processes provide an overall agreement with the available state-selected experimental data, whereas the results for the charge transfer channel show some variance in comparison with those of experiments and are similar to the earlier theoretical results obtained using model effective potential based on projected valence bond method and using semi-empirical diatomics-in-molecules potential. The possible reason for discrepancies and the likely ways to improve the results are discussed in terms of the inclusion of higher excited electronic states into the dynamics calculation.

Energy dependence of differential and integral cross sections for O(D1)+H2(υi=,ji=)→OH(υf,jf)+H reaction

State-to-state differential and integral cross sections for the title reaction have been calculated using a dynamically exact quantum mechanical wave packet method on the ab initio ground H(2)O(X (1)A(')) electronic state potential energy surface of Dobbyn and Knowles. We focus on the energy dependence of the cross sections up to 0.15 eV. The total integral cross section and rate constant, obtained by summing the state-to-state integral cross sections over all open product rovibrational channels, are in excellent agreement with experimental measurements. Also in agreement with experimental data, the OH product is found to have highly inverted rotational state distributions and monotonically decaying vibrational state distributions. The calculated total differential cross section is roughly forward-backward symmetric, consistent with experimental data. The vibrational state-resolved differential cross sections are found to depend on the collision energy. The calculated results confirm the dominance of the insertion mechanism and provide a stringent test of the potential energy surface.