^{1}and James J. Valentini

^{1,a)}

### Abstract

A selective review of state-to-state reactiondynamics experiments is presented. The review focuses on three classes of reactions that exemplify the rich history and illustrate the current state of the art in such work. These three reactions are (1) the hydrogen exchange reaction, and its isotopomers; (2) the reactions, where is an alkane, beginning with and extending to much larger alkanes; and (3) the reactions, principally . We describe the experiments, discuss their results, present comparisons with theory, and introduce heuristic models.

This work is supported by a grant from the U.S. Department of Energy, Office of Basic Energy Sciences. The authors gratefully acknowledge the assistance of Christen Currie in the preparation of this review.

I. INTRODUCTION

II. ANALYZING STATE-TO-STATE DATA: THE SURPRISAL ANALYSIS

III. ANALYZING STATE-TO-STATE DATA: THE KINEMATIC CONSTRAINT

IV. THE HYDROGEN EXCHANGE REACTION:

V. REACTIONS OF HYDROGEN WITH ALKANES:

VI. REACTIONS OF CHLORINE WITH ALKANES:

VII. CONCLUSION

### Key Topics

- Hydrogen reactions
- 163.0
- Chemical reaction cross sections
- 44.0
- Excited state reaction dynamics
- 44.0
- Collision induced chemical reactions
- 35.0
- Atom transfer reactions
- 27.0

## Figures

Comparison of the surprisal distributions for the reaction, calculated with the total energy (dashed line) and with the kinematically constrained energy (solid line). (Reprinted with permission from Ref. 1.)

Comparison of the surprisal distributions for the reaction, calculated with the total energy (dashed line) and with the kinematically constrained energy (solid line). (Reprinted with permission from Ref. 1.)

Comparison of the surprisal distributions for the reaction, calculated with the total energy (dashed line) and with the reduced energy (solid line). (Reprinted with permission from Ref. 1.)

Comparison of the surprisal distributions for the reaction, calculated with the total energy (dashed line) and with the reduced energy (solid line). (Reprinted with permission from Ref. 1.)

Comparison of experimental (symbols with error bars) and QCT theoretical (solid lines) product quantum state distributions for the reaction. (Reprinted with permission from Ref. 31.)

Comparison of experimental (symbols with error bars) and QCT theoretical (solid lines) product quantum state distributions for the reaction. (Reprinted with permission from Ref. 31.)

Linear vibrational and rotational surprisal descriptions of the product quantum state number density distribution in the reaction. (Reprinted with permission from Ref. 31.)

Linear vibrational and rotational surprisal descriptions of the product quantum state number density distribution in the reaction. (Reprinted with permission from Ref. 31.)

vibrational state distributions in the and reactions. The solid markers represent data for the reaction and the open markers represent data for the reaction. For each reaction the distributions have been normalized so that the total cross section for product in is set to 1.00. (Reprinted with permission from Ref. 44.)

vibrational state distributions in the and reactions. The solid markers represent data for the reaction and the open markers represent data for the reaction. For each reaction the distributions have been normalized so that the total cross section for product in is set to 1.00. (Reprinted with permission from Ref. 44.)

absolute partial cross sections for the reactions vs the fraction of total energy in rotation. The solid circles represent data for and the open circles represent data for . The solid and dashed lines are linear surprisal fits for the and data, respectively, and correspond to and 3.8. (Reprinted with permission from Ref. 44.)

absolute partial cross sections for the reactions vs the fraction of total energy in rotation. The solid circles represent data for and the open circles represent data for . The solid and dashed lines are linear surprisal fits for the and data, respectively, and correspond to and 3.8. (Reprinted with permission from Ref. 44.)

absolute partial cross sections for the reactions vs the fraction of available energy in rotation. The solid squares represent data for and the open squares represent data for . The solid and dashed lines are linear surprisal fits for the and data, respectively, and correspond to and 3.8. (Reprinted with permission from Ref. 44.)

absolute partial cross sections for the reactions vs the fraction of available energy in rotation. The solid squares represent data for and the open squares represent data for . The solid and dashed lines are linear surprisal fits for the and data, respectively, and correspond to and 3.8. (Reprinted with permission from Ref. 44.)

Experimental (solid square with error bars) and theoretical (solid line) product rotational state distributions for at different collision energies. (Reprinted with permission from Ref. 50.)

Experimental (solid square with error bars) and theoretical (solid line) product rotational state distributions for at different collision energies. (Reprinted with permission from Ref. 50.)

Experimental and theoretical rotational state distributions for over a range of collision energies. The closed squares with error bars represent experimental data. The dashed lines represent results of time-independent quantum mechanical calculations, the dotted lines represent results of time-dependent quantum mechanical calculations, and the dashed-dotted lines represent results of time-dependent quantum mechanical calculations including the experimental spread in collision energy. (Reprinted with permission from Ref. 52.)

Experimental and theoretical rotational state distributions for over a range of collision energies. The closed squares with error bars represent experimental data. The dashed lines represent results of time-independent quantum mechanical calculations, the dotted lines represent results of time-dependent quantum mechanical calculations, and the dashed-dotted lines represent results of time-dependent quantum mechanical calculations including the experimental spread in collision energy. (Reprinted with permission from Ref. 52.)

center-of-mass differential cross sections for . The symbols give the experimental results; the solid lines show the results of quantum mechanical calculations. (Reprinted with permission from Ref. 63.)

center-of-mass differential cross sections for . The symbols give the experimental results; the solid lines show the results of quantum mechanical calculations. (Reprinted with permission from Ref. 63.)

angular distributions derived from the core-extracted time-of-flight profiles. The solid lines are guides to the eyes. (Reprinted with permission from Ref. 21.)

angular distributions derived from the core-extracted time-of-flight profiles. The solid lines are guides to the eyes. (Reprinted with permission from Ref. 21.)

(a) Correlation between the most probable scattering angle and product rotational angular momentum . The circles correspond to and the triangles to . (b) Relationship between the most probable scattering angle and the reduced impact parameter deduced from the correlation shown in (a). The solid line represents the hard-sphere limit, given by . (Reprinted with permission from Ref. 54.)

(a) Correlation between the most probable scattering angle and product rotational angular momentum . The circles correspond to and the triangles to . (b) Relationship between the most probable scattering angle and the reduced impact parameter deduced from the correlation shown in (a). The solid line represents the hard-sphere limit, given by . (Reprinted with permission from Ref. 54.)

Differential cross sections for products as a function of collision energy. The filled circles with error bars are experimental points; the solid line represents the theory of Althorpe blurred with the experimental instrument function. (Reprinted with permission from Ref. 57.)

Differential cross sections for products as a function of collision energy. The filled circles with error bars are experimental points; the solid line represents the theory of Althorpe blurred with the experimental instrument function. (Reprinted with permission from Ref. 57.)

Plot of population vs fraction of energy contained in rotation for the , products of the reactions at collision energy. The dashed line represents the products of the reaction. The solid line represents the products of the reaction. The two data sets have been scaled so that the sum of the product populations over all is the same for both. (Reprinted with permission from Ref. 70.)

Plot of population vs fraction of energy contained in rotation for the , products of the reactions at collision energy. The dashed line represents the products of the reaction. The solid line represents the products of the reaction. The two data sets have been scaled so that the sum of the product populations over all is the same for both. (Reprinted with permission from Ref. 70.)

Differential cross section for the product of the reaction as a function of the cosine of the center-of-mass scattering angle . The uncertainty in the experimental measurements is indicated by the shaded region. (Reprinted with permission from Ref. 83.)

Differential cross section for the product of the reaction as a function of the cosine of the center-of-mass scattering angle . The uncertainty in the experimental measurements is indicated by the shaded region. (Reprinted with permission from Ref. 83.)

absolute partial cross sections for the reactions plotted vs rotational quantum number, . The solid squares show data for , and the open squares are data for . The solid and dashed lines are linear surprisal fits for the and data, respectively, and are characterized by and 6.4. (Reprinted with permission from Ref. 79.)

absolute partial cross sections for the reactions plotted vs rotational quantum number, . The solid squares show data for , and the open squares are data for . The solid and dashed lines are linear surprisal fits for the and data, respectively, and are characterized by and 6.4. (Reprinted with permission from Ref. 79.)

absolute partial cross sections for the reactions plotted vs rotational quantum number, . The solid circles show data for , and the open circles are data for . The solid and dashed lines are linear surprisal fits for the and data, respectively, and are characterized by and 4.4. (Reprinted with permission from Ref. 79.)

absolute partial cross sections for the reactions plotted vs rotational quantum number, . The solid circles show data for , and the open circles are data for . The solid and dashed lines are linear surprisal fits for the and data, respectively, and are characterized by and 4.4. (Reprinted with permission from Ref. 79.)

product rotational state distributions for the reactions , , , and , plotted as a function of reduced rotational energy. Top panel for , bottom panel for . The lines give the best-fit linear surprisal description of the data. (Reprinted with permission from Ref. 3.)

product rotational state distributions for the reactions , , , and , plotted as a function of reduced rotational energy. Top panel for , bottom panel for . The lines give the best-fit linear surprisal description of the data. (Reprinted with permission from Ref. 3.)

product rotational state distributions for the reactions , , , and , plotted as a function of reduced rotational energy. Top panel for , bottom panel for . The lines give the best-fit linear surprisal description of the data. (Reprinted with permission from Ref. 3.)

rotational state distributions from the reaction . The filled squares are the data of Murray *et al.*, the open squares are from Varley and Dagdigian (Ref. 120), and the open circles are from Simpson *et al.* (Ref. 99). The distributions have been normalized such that the populations each sum to unity over the levels shown. (Reprinted with permission from Ref. 98.)

rotational state distributions from the reaction . The filled squares are the data of Murray *et al.*, the open squares are from Varley and Dagdigian (Ref. 120), and the open circles are from Simpson *et al.* (Ref. 99). The distributions have been normalized such that the populations each sum to unity over the levels shown. (Reprinted with permission from Ref. 98.)

product speed distribution and differential cross section from the reaction. Panel (a) shows the product speed distribution. The scale bars on the top show the laboratory-frame speed limits for both the reaction of spin-orbit excited and ground state chlorine atoms. Panel (b) shows the differential cross section derived from this speed distribution. (Reprinted with permission from Ref. 99.) (Original figure to be supplied prior to publication.)

product speed distribution and differential cross section from the reaction. Panel (a) shows the product speed distribution. The scale bars on the top show the laboratory-frame speed limits for both the reaction of spin-orbit excited and ground state chlorine atoms. Panel (b) shows the differential cross section derived from this speed distribution. (Reprinted with permission from Ref. 99.) (Original figure to be supplied prior to publication.)

rotational state distributions for the reaction. The populations are represented by the dotted lines and open symbols, and the populations by the solid lines and filled symbols. (Reprinted with permission from Ref. 105.)

rotational state distributions for the reaction. The populations are represented by the dotted lines and open symbols, and the populations by the solid lines and filled symbols. (Reprinted with permission from Ref. 105.)

Rotational state distribution of the product for the reaction of Cl with (a) ∣1100⟩ and (b) . (Reprinted with permission from Ref. 110.)

Rotational state distribution of the product for the reaction of Cl with (a) ∣1100⟩ and (b) . (Reprinted with permission from Ref. 110.)

State-to-state differential cross sections for the (a) products, (b) the products, (c) the products, and (d) the products from the reaction of atomic chlorine with vibrationally excited methane. The results for the reaction are represented by the open squares and solid lines, and for the reaction by the closed circles and dotted lines. (Reprinted with permission from Ref. 106.)

State-to-state differential cross sections for the (a) products, (b) the products, (c) the products, and (d) the products from the reaction of atomic chlorine with vibrationally excited methane. The results for the reaction are represented by the open squares and solid lines, and for the reaction by the closed circles and dotted lines. (Reprinted with permission from Ref. 106.)

Schematic model of the observed scattering behavior from the reaction and the reaction. The products result from glancing collisions (a) that cause side scattering and rotational excitation. The products are formed via two competing mechanisms: stripping (b) and rebound (c). The stripping mechanism leads to forward-scattered products with little rotational excitation, and the rebound mechanism leads to backward-scattered products that have more rotational excitation. (Reprinted with permission from Ref. 106.)

Schematic model of the observed scattering behavior from the reaction and the reaction. The products result from glancing collisions (a) that cause side scattering and rotational excitation. The products are formed via two competing mechanisms: stripping (b) and rebound (c). The stripping mechanism leads to forward-scattered products with little rotational excitation, and the rebound mechanism leads to backward-scattered products that have more rotational excitation. (Reprinted with permission from Ref. 106.)

(a) Comparison of product differential cross sections for the reaction (solid circles) and the reaction (open squares). (b) Comparison of the product differential cross sections for the reaction (solid circles) and the reaction (open squares). (Reprinted with permission from Ref. 110.)

(a) Comparison of product differential cross sections for the reaction (solid circles) and the reaction (open squares). (b) Comparison of the product differential cross sections for the reaction (solid circles) and the reaction (open squares). (Reprinted with permission from Ref. 110.)

Measured rotational state distributions for (a) and (b) products from the reaction . The distributions have been normalized so that the sum of the rotational populations is unity. (Reprinted with permission from Ref. 120.)

Measured rotational state distributions for (a) and (b) products from the reaction . The distributions have been normalized so that the sum of the rotational populations is unity. (Reprinted with permission from Ref. 120.)

Translational energy release for different center-of-mass scattering angles: solid line, 5°–50°; dashed line, 55°–115°; and dotted-dashed line, 124°–175°, in the reaction . (Reprinted with permission from Ref. 124.)

Translational energy release for different center-of-mass scattering angles: solid line, 5°–50°; dashed line, 55°–115°; and dotted-dashed line, 124°–175°, in the reaction . (Reprinted with permission from Ref. 124.)

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