# Electron Scattering Cross-Section Calculations for Atomic and Molecular Iodine

^{1}

^{2}

^{3}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Method

#### 2.1. Breit-Pauli B-spline R-matrix (BPBSR)

#### 2.2. Molecular R-matrix Method

#### 2.3. Local Complex Potential Approximation

## 3. Results

#### 3.1. Atomic Iodine

#### 3.2. Molecular Iodine

#### 3.2.1. Dissociative Electron Attachment

#### 3.2.2. Vibrational Excitation

#### 3.2.3. Electron-Impact Excitation

#### 3.2.4. Ionization

#### 3.2.5. Elastic Scattering

## 4. Conclusions and Outlook

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

BEB | Binar Encounter Bethe |

BPBSR | Breit-Pauli B-Spline R-matrix |

CASSCF | Complete Active Space Self-Consistent Field |

DEA | Dissociative Electron Attachment |

ECP | Effective core potential |

EP | Electric Propulsion |

LCP | Local Complex Potential |

QEC | Quantemol Electron Collisions |

QN | Quantemol-N |

VE | Vibrational Excitation |

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**Figure 1.**Elastic scattering cross section as a function of the electron energy. Cross sections for the ground state obtained in the BPBSR-10 and BPBSR-29 models are shown, as well the BPBSR-29 prediction for the first excited state and the result from the DBSR calculation reported by Zatsarinny et al. [25]. The experimental data at 40 eV and 50 eV are taken from ref. [25].

**Figure 2.**Electron-impact excitation cross section from (

**a**) the ground state and (

**b**) the first excited state of atomic iodine. The total cross sections shown are obtained by summing the partial cross sections into 10, 20, and 25 final states as shown in the legend.

**Figure 3.**Ab initio calculations of the neutral and anion (resonance) potential energy curves. MOLPRO results are shown for the four resonant symmetries ${}^{2}{\mathsf{\Sigma}}_{g}^{+},{}^{2}{\mathsf{\Pi}}_{u},{}^{2}{\mathsf{\Sigma}}_{u}^{+}$, and ${}^{2}{\mathsf{\Pi}}_{g}$. The ${}^{2}{\mathsf{\Pi}}_{g}$ and ${}^{2}{\mathsf{\Pi}}_{u}$ resonance positions calculated with the R-matrix method agree well with the bound-state results.

**Figure 4.**(

**a**) Eigenphase sum for the ${}^{2}{\mathsf{\Pi}}_{g}$ symmetry evaluated at several internuclear separations R. (

**b**) Resonance widths $\mathsf{\Gamma}\left(R\right)$ for the two scattering symmetries considered in the present calculations.

**Figure 5.**DEA cross section of I${}_{2}$. In the LCP framework (solid and dashed lines), the cross section shows maxima at 0.6 and 2 eV similar to Buchdal et al. [28]. The results from Healy et al. [29] agree with the ${}^{2}{\mathsf{\Pi}}_{u}$ resonance position. QN’s SEP calculations (dashed-dotted line) exhibit the same structures with shifted peaks compared to the present results.

**Figure 6.**VE cross sections obtained for the ${}^{2}{\mathsf{\Pi}}_{g}$ and ${}^{2}{\mathsf{\Pi}}_{u}$ symmetries. Dashed and dashed-dotted lines show the $\nu =0\to 1,10$ results and the solid line shows total VE cross section, respectively.

**Figure 7.**Cross sections for excitation to the ${}^{3}{\mathsf{\Pi}}_{u}$, ${}^{1}{\mathsf{\Pi}}_{u}$, ${}^{3}{\mathsf{\Sigma}}_{g}^{-}$, and ${}^{1}{\mathsf{\Sigma}}_{g}^{+}$ states from the ground state.

**Figure 8.**Electron-impact ionization cross section obtained for I and I${}_{2}$. Also shown are the partial ionization cross sections for I${}_{2}$ leading to products I${}_{2}^{+}$ (dashed line) and I${}^{+}$ (dashed-dotted line).

I | Reaction |
---|---|

Elastic scattering | ${\mathrm{e}}^{-}+\mathrm{I}\left({}^{2}{\mathrm{P}}_{3/2}\right)\to {\mathrm{e}}^{-}+\mathrm{I}\left({}^{2}{\mathrm{P}}_{3/2}\right)$ ${\mathrm{e}}^{-}+\mathrm{I}\left({}^{2}{\mathrm{P}}_{1/2}\right)\to {\mathrm{e}}^{-}+\mathrm{I}\left({}^{2}{\mathrm{P}}_{1/2}\right)$ |

Excitation | ${\mathrm{e}}^{-}+\mathrm{I}\left({}^{2}{\mathrm{P}}_{3/2}\right)\to {\mathrm{e}}^{-}+{\mathrm{I}}^{*}$ ${\mathrm{e}}^{-}+\mathrm{I}\left({}^{2}{\mathrm{P}}_{1/2}\right)\to {\mathrm{e}}^{-}+{\mathrm{I}}^{*}$ |

Ionization | ${\mathrm{e}}^{-}+\mathrm{I}\left({}^{2}{\mathrm{P}}_{3/2}\right)\to 2{\mathrm{e}}^{-}+{\mathrm{I}}^{+}$ |

I${}_{2}$ | Reaction |

Elastic scattering | ${\mathrm{e}}^{-}$ + I${}_{2}\left(X\phantom{\rule{3.33333pt}{0ex}}{}^{1}{\mathsf{\Sigma}}_{g}^{+}\right)\to {\mathrm{e}}^{-}$ + I${}_{2}\left(X\phantom{\rule{3.33333pt}{0ex}}{}^{1}{\mathsf{\Sigma}}_{g}^{+}\right)$ |

Excitation | ${\mathrm{e}}^{-}$ + I${}_{2}\left(X\phantom{\rule{3.33333pt}{0ex}}{}^{1}{\mathsf{\Sigma}}_{g}^{+}\right)\to {\mathrm{e}}^{-}$ + I${}_{2}^{*}$ |

Dissociative Electron attachment | ${\mathrm{e}}^{-}$ + I${}_{2}\left(X\phantom{\rule{3.33333pt}{0ex}}{}^{1}{\mathsf{\Sigma}}_{g}^{+}\right)$ → I(${}^{2}{\mathrm{P}}_{1/2}$) + I${}^{-}\left({}^{1}\mathrm{S}\right)$ |

Vibrational excitation | ${\mathrm{e}}^{-}$ + I${}_{2}(X\phantom{\rule{3.33333pt}{0ex}}{}^{1}{\mathsf{\Sigma}}_{g}^{+},\nu =0)$ → ${\mathrm{e}}^{-}$ + I${}_{2}(X\phantom{\rule{3.33333pt}{0ex}}{}^{1}{\mathsf{\Sigma}}_{g}^{+},\nu ={\nu}_{f})$ |

Ionization | ${\mathrm{e}}^{-}$ + I${}_{2}\left(X\phantom{\rule{3.33333pt}{0ex}}{}^{1}{\mathsf{\Sigma}}_{g}^{+}\right)$ → $2{\mathrm{e}}^{-}$ + I${}_{2}^{+}$ |

Dissociative ionization | ${\mathrm{e}}^{-}$ + I${}_{2}\left(X\phantom{\rule{3.33333pt}{0ex}}{}^{1}{\mathsf{\Sigma}}_{g}^{+}\right)$ → $2{\mathrm{e}}^{-}$ + I + I${}^{+}$ |

**Table 2.**Configurations and excitation energies (eV) for the lowest ten states of I in the BPBSR calculations.

Configuration | BPBSR-29 | NIST [13] |
---|---|---|

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{5}\phantom{\rule{3.33333pt}{0ex}}\left({}^{2}{\mathrm{P}}_{3/2}\right)$ | 0.0000 | 0.0000 |

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{5}\phantom{\rule{3.33333pt}{0ex}}\left({}^{2}{\mathrm{P}}_{1/2}\right)$ | 0.9529 | 0.9426 |

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{4}6\mathrm{s}\phantom{\rule{3.33333pt}{0ex}}\left({}^{4}{\mathrm{P}}_{5/2}\right)$ | 7.2015 | 6.7736 |

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{4}6\mathrm{s}\phantom{\rule{3.33333pt}{0ex}}\left({}^{4}{\mathrm{P}}_{3/2}\right)$ | 7.3939 | 6.9546 |

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{4}6\mathrm{s}\phantom{\rule{3.33333pt}{0ex}}\left({}^{2}{\mathrm{P}}_{3/2}\right)$ | 7.9452 | 7.6646 |

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{4}6\mathrm{s}\phantom{\rule{3.33333pt}{0ex}}\left({}^{2}{\mathrm{P}}_{1/2}\right)$ | 8.0447 | 7.8341 |

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{4}6\mathrm{p}\phantom{\rule{3.33333pt}{0ex}}\left({}^{4}{\mathrm{P}}_{5/2}\right)$ | 8.1850 | 8.0473 |

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{4}6\mathrm{s}\phantom{\rule{3.33333pt}{0ex}}\left({}^{4}{\mathrm{P}}_{1/2}\right)$ | 8.1898 | 7.5501 |

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{4}6\mathrm{p}\phantom{\rule{3.33333pt}{0ex}}\left({}^{4}{\mathrm{P}}_{3/2}\right)$ | 8.2217 | 8.0577 |

$4{\mathrm{d}}^{10}5{\mathrm{p}}^{4}6\mathrm{p}\phantom{\rule{3.33333pt}{0ex}}\left({}^{4}{\mathrm{D}}_{7/2}\right)$ | 8.3228 | 8.1420 |

Property | Present Value | Value in [26] |
---|---|---|

Ground state energy (Hartree) | −13,833.5045 | −13,834.05986 |

Bond length (Å) | 2.8102 | 2.6655 |

Vibrational frequency (cm${}^{-1}$) | 207.71 | 214.502 |

Symmetry | D${}_{2h}$ | D${}_{2h}$ |

State | Energy | Ref. [31] |
---|---|---|

${}^{3}{\mathsf{\Pi}}_{u}$ | 2.18 | 2.37 |

${}^{1}{\mathsf{\Pi}}_{u}$ | 3.00 | 2.38 |

${}^{3}{\mathsf{\Sigma}}_{g}^{-}$ | 5.18 | 3.9 |

${}^{1}{\mathsf{\Sigma}}_{g}^{+}$ | 5.7 | − |

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**MDPI and ACS Style**

Ambalampitiya, H.B.; Hamilton, K.R.; Zatsarinny, O.; Bartschat, K.; Turner, M.A.P.; Dzarasova, A.; Tennyson, J.
Electron Scattering Cross-Section Calculations for Atomic and Molecular Iodine. *Atoms* **2021**, *9*, 103.
https://doi.org/10.3390/atoms9040103

**AMA Style**

Ambalampitiya HB, Hamilton KR, Zatsarinny O, Bartschat K, Turner MAP, Dzarasova A, Tennyson J.
Electron Scattering Cross-Section Calculations for Atomic and Molecular Iodine. *Atoms*. 2021; 9(4):103.
https://doi.org/10.3390/atoms9040103

**Chicago/Turabian Style**

Ambalampitiya, Harindranath B., Kathryn R. Hamilton, Oleg Zatsarinny, Klaus Bartschat, Matt A. P. Turner, Anna Dzarasova, and Jonathan Tennyson.
2021. "Electron Scattering Cross-Section Calculations for Atomic and Molecular Iodine" *Atoms* 9, no. 4: 103.
https://doi.org/10.3390/atoms9040103