^{1,a)}, Thomas M. Miller

^{2}and Albert A. Viggiano

^{2}

### Abstract

Detailed statistical rate calculations combined with electron capturetheory and kinetic modeling for the electron attachment to and detachment from [Troe *et al.*, J. Chem. Phys.127, 244303 (2007)] are used to test thermionic electron emission models. A new method to calculate the specific detachment rate constants and the electron energy distributions as functions of the total energy of the anion and the energy of the emitted electrons is presented, which is computationally simple but neglects fine structures in the detailed . Reduced electron energy distributions were found to be of the form with , whose shape corresponds to thermal distributions only to a limited extent. In contrast, the average energies can be roughly estimated within thermionic emission and finite heat bath concepts. An effective temperature is determined from the relation , where denotes the thermal internal energy of the detachment product at the temperature and EA is the electron affinity of . The average electron energy is then approximately given by , but dynamical details of the process are not accounted for by this approach. Simplified representations of in terms of from the literature are shown to lead to only semiquantitative agreement with the equally simple but more accurate calculations presented here. An effective “isokinetic” electron emission temperature does not appear to be useful for the electron detachment system considered because it neither provides advantages over a representation of as a function of , nor are recommended relations between and of sufficient accuracy.

This work was supported by the European Office of Aerospace Research and Development (Award No. FA8655-09-1-3001). One of the authors (T.M.M.) is under contract with Boston College. Continuing encouragement by M. Berman and technical assistance by A. I. Maergoiz are gratefully acknowledged.

I. INTRODUCTION

II. STATISTICAL RATE THEORY

III. DETACHMENT RATES AND ELECTRON ENERGY DISTRIBUTIONS FROM

IV. EFFECTIVE TEMPERATURES

V. CONCLUSIONS

### Key Topics

- Electron capture
- 20.0
- Statistical analysis
- 13.0
- Electron emission
- 12.0
- Reaction rate constants
- 12.0
- Electron densities of states
- 10.0

## Figures

Discrete distributions of electron energies in the detachment from at the energies (a), (b), and [(c) and (d)]. (d) shows with bins ; the continuous curve is from Eq. (2.12), see text.

Discrete distributions of electron energies in the detachment from at the energies (a), (b), and [(c) and (d)]. (d) shows with bins ; the continuous curve is from Eq. (2.12), see text.

Specific rate constants for electron detachment from . Curves from top to bottom: (i) RRKM-type model without electron capture contributions, i.e., for ; (ii) pure electron capture model, i.e., ; (iii) electron capture with IVR contribution, i.e., ; (iv) electron capture with IVR and VEX contributions, i.e., . Full curves: Detailed calculations from Ref. 15; dashed curves for the upper three models: Simplified calculations with Eq. (3.9) from the present work, see text.

Specific rate constants for electron detachment from . Curves from top to bottom: (i) RRKM-type model without electron capture contributions, i.e., for ; (ii) pure electron capture model, i.e., ; (iii) electron capture with IVR contribution, i.e., ; (iv) electron capture with IVR and VEX contributions, i.e., . Full curves: Detailed calculations from Ref. 15; dashed curves for the upper three models: Simplified calculations with Eq. (3.9) from the present work, see text.

Energy distribution of electrons from the detachment from ; full line: RRKM-type model; dashed line: electron capture VW model; dotted line: electron capture with IVR model; dash-dotted line with peak near : electron capture with IVR and VEX model, see text.

Energy distribution of electrons from the detachment from ; full line: RRKM-type model; dashed line: electron capture VW model; dotted line: electron capture with IVR model; dash-dotted line with peak near : electron capture with IVR and VEX model, see text.

Energy distribution of electrons from the detachment from ; full calculations: (a) RRKM-type model with , (b) electron capture VW-model with , and (c) -model with ; dashed functions (3.10) with exponents (d), 0.5 (e), and 1.0 (f).

Energy distribution of electrons from the detachment from ; full calculations: (a) RRKM-type model with , (b) electron capture VW-model with , and (c) -model with ; dashed functions (3.10) with exponents (d), 0.5 (e), and 1.0 (f).

Average energy of electrons detached from at total energy . Full calculations; (a) RRKM-type model; (b) electron capture VW-model; (c) electron capture with model. Dashed emission results; (d) putting in Eq. (4.1); (e) including finite from Eqs. (4.1), (4.2), and (4.4); see text.

Average energy of electrons detached from at total energy . Full calculations; (a) RRKM-type model; (b) electron capture VW-model; (c) electron capture with model. Dashed emission results; (d) putting in Eq. (4.1); (e) including finite from Eqs. (4.1), (4.2), and (4.4); see text.

Specific rate constants for electron detachment from [full curves: Detailed calculations identified in Fig. 2; dashed curves: Simplified thermionic emission approximations to the upper three detailed cases: The highest dashed curve is from Eqs. (4.5)–(4.8), the next uses (slightly corrected) Whitten–Rabinovitch densities of states for , and the lowest curve uses from Eqs. (4.1), (4.2), and (4.4), see text].

Specific rate constants for electron detachment from [full curves: Detailed calculations identified in Fig. 2; dashed curves: Simplified thermionic emission approximations to the upper three detailed cases: The highest dashed curve is from Eqs. (4.5)–(4.8), the next uses (slightly corrected) Whitten–Rabinovitch densities of states for , and the lowest curve uses from Eqs. (4.1), (4.2), and (4.4), see text].

Comparison of the daughter temperature , based on Eq. (4.1), and an effective or isokinetic temperature , from Eq. (4.9), in thermionic emission models of electron detachment from (detailed calculations of this work, see text).

Comparison of the daughter temperature , based on Eq. (4.1), and an effective or isokinetic temperature , from Eq. (4.9), in thermionic emission models of electron detachment from (detailed calculations of this work, see text).

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