# 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 |

## References

- Choueiri, E. Plasma Propulsion-McGraw-Hill Encyclopedia of Science and Technology; McGraw-Hill: New York, NY, USA, 2007. [Google Scholar]
- Goebel, D.M.; Katz, I. Fundamentals of Electric Propulsion: Ion and Hall Thrusters; JPL: Pasadena, CA, USA, 2008. [Google Scholar]
- Kieckhafer, A.; King, L.B. Energetics of Propellant Options for High-Power Hall Thrusters. J. Propuls. Power
**2007**, 23, 21. [Google Scholar] [CrossRef] - Dressler, R.A.; Chiu, Y.H.; Levandier, D. Propellant alternatives for ion and Hall effect thrusters. In Proceedings of the 38th Aerospace Sciences Meeting and Exhibit, Reno, NV, USA, 10–13 January 2000. [Google Scholar]
- Smith, T.D.; Kamhawi, H.; Hickman, T.; Haag, T.; Dankanich, J.; Polzin, K.; Byrne, L.; Szabo, J. Overview of NASA Iodine Hall Thruster Propulsion System Development; Technical Report; NASA: Washington, DC, USA, 2016.
- Kaganovich, I.D.; Smolyakov, A.; Raitses, Y.; Ahedo, E.; Mikellides, I.G.; Jorns, B.; Taccogna, F.; Gueroult, R.; Tsikata, S.; Bourdon, A.; et al. Physics of E × B discharges relevant to plasma propulsion and similar technologies. Phys. Plasmas
**2020**, 27, 120601. [Google Scholar] [CrossRef] - Bartschat, K.; Fischer, C.F.; Grum-Grzhimailo, A.N. A Tribute to Oleg Zatsarinny (1953–2021): His Life in Science. Atoms
**2021**, 9, 53. [Google Scholar] [CrossRef] - Carr, J.M.; Galiatsatos, P.G.; Gorfinkiel, J.D.; Harvey, A.G.; Lysaght, M.A.; Madden, D.; Mašín, Z.; Plummer, M.; Tennyson, J.; Varambhia, H.N. UKRmol: A low-energy electron- and positron-molecule scattering suite. Eur. Phys. J. D
**2012**, 66, 58. [Google Scholar] [CrossRef] - Mašín, Z.; Benda, J.; Gorfinkiel, J.D.; Harvey, A.G.; Tennyson, J. UKRmol+: A suite for modelling electronic processes in molecules interacting with electrons, positrons and photons using the R-matrix method. Comp. Sci. Commun.
**2019**, 249, 107092. [Google Scholar] [CrossRef][Green Version] - Tennyson, J.; Brown, D.B.; Munroy, J.J.; Rozum, I.; Varambhia, H.N.; Vinci, N. Quantemol-N: An expert system for performing electron molecule collision calculations using the R-matrix method. J. Phys. Conf. Ser.
**2007**, 86, 012001. [Google Scholar] [CrossRef] - Cooper, B.; Tudorovskaya, M.; Mohr, S.; O’Hare, A.; Hanicinec, M.; Dzarasova, A.; Gorfinkiel, J.D.; Benda, J.; Mašín, Z.; Al-Refaie, A.F.; et al. Quantemol Electron Collisions (QEC): An Enhanced Expert System for Performing Electron Molecule Collision Calculations Using the R-Matrix Method. Atoms
**2019**, 7, 97. [Google Scholar] [CrossRef][Green Version] - Zatsarinny, O. BSR: B-spline atomic R-matrix codes. Comp. Phys. Commun.
**2006**, 174, 273. [Google Scholar] [CrossRef] - NIST Chemistry WebBook. Available online: https://webbook.nist.gov/chemistry/ (accessed on 21 September 2021).
- Tennyson, J. Electron–molecule collision calculations using the R-matrix method. Phys. Rep.
**2010**, 491, 29. [Google Scholar] [CrossRef] - Werner, H.J.; Knowles, P.J.; Knizia, G.; Manby, F.R.; Schütz, M. Molpro: A general-purpose quantum chemistry program package. Rev. Comp. Mol. Sci.
**2011**, 2, 242. [Google Scholar] [CrossRef] - Schuchardt, K.L.; Didier, B.T.; Elsethagen, T.; Sun, L.; Gurumoorthi, V.; Chase, J.; Li, J.; Windus, T.L. Basis Set Exchange: A Community Database for Computational Sciences. J. Chem. Inf. Model.
**2007**, 47, 1045. [Google Scholar] [CrossRef][Green Version] - Glukhovtsev, M.N.; Pross, A.; McGrath, M.P.; Radom, L. Extension of Gaussian-2 (G2) theory to bromine- and iodine-containing molecules: Use of effective core potentials. J. Chem. Phys.
**1995**, 103, 1878. [Google Scholar] [CrossRef] - Bardsley, J.N.; Mandle, F. Resonant scattering of electrons by molecules. Rep. Prog. Phys.
**1968**, 31, 471. [Google Scholar] [CrossRef] - Domcke, W. Theory of resonance and threshold effects in electron-molecule collisions: The projection-operator approach. Phys. Rep.
**1991**, 208, 97. [Google Scholar] [CrossRef] - Bardsley, J.N. Configuration interaction in the continuum states of molecules. J. Phys. B At. Mol. Phys.
**1968**, 1, 349. [Google Scholar] [CrossRef] - Bardsley, J.N. Molecular resonance phenomena. In Electron-Molecule and Photon-Molecule Collisions; Rescigno, T., McKoy, V., Schneider, B., Eds.; Plenum: New York, NY, USA, 1979. [Google Scholar]
- Wigner, E.P. On the Behavior of Cross Sections Near Thresholds. Phys. Rev.
**1948**, 73, 1002. [Google Scholar] [CrossRef] - Fabrikant, I.I.; Hotop, H. Low-energy behavior of exothermic dissociative electron attachment. Phys. Rev. A
**2001**, 63, 022706. [Google Scholar] [CrossRef] - Zatsarinny, O.; Bartschat, K. Relativistic B-spline R-matrix method for electron collisions with atoms and ions: Application to low-energy electron scattering from Cs. Phys. Rev. A
**2008**, 77, 062701. [Google Scholar] [CrossRef] - Zatsarinny, O.; Bartschat, K.; Garcia, G.; Blanco, F.; Hargreaves, L.R.; Jones, D.B.; Murrie, R.; Brunton, J.R.; Brunger, M.J.; Hoshino, M.; et al. Electron-collision cross sections for iodine. Phys. Rev. A
**2011**, 83, 042702. [Google Scholar] [CrossRef][Green Version] - Computational Chemistry Comparison and Benchmark Database. Available online: https://cccbdb.nist.gov/ (accessed on 21 September 2021).
- Tennyson, J.; Noble, C.J. RESON—A program for the detection and fitting of Breit-Wigner resonances. Comp. Phys. Commun.
**1984**, 33, 421. [Google Scholar] [CrossRef] - Buchdal, R.J. Negative Ion Formation in Iodine Vapor by Electron Impacts. J. Chem. Phys.
**1941**, 9, 146. [Google Scholar] [CrossRef] - Healy, R.H. The behaviour of electrons in iodine vapour. Philos. Mag. J. Sci.
**1938**, 26, 940. [Google Scholar] [CrossRef] - Munro, J.J.; Harrison, S.; Fujimoto, M.M.; Tennyson, J. A dissociative electron attachment cross-section estimator. Phys. Conf. Ser.
**2012**, 388, 012013. [Google Scholar] [CrossRef] - Mulliken, R.S. Iodine Revisited. J. Chem. Phys.
**1971**, 55, 288. [Google Scholar] [CrossRef] - Kim, Y.K.; Rudd, M.E. Binary-encounter-dipole model for electron-impact ionization. Phys. Rev. A
**1994**, 50, 3954. [Google Scholar] [CrossRef] [PubMed][Green Version] - Graves, V.; Cooper, B.; Tennyson, J. The efficient calculation of electron impact ionization cross sections with effective core potentials. J. Chem. Phys.
**2021**, 154, 114104. [Google Scholar] [CrossRef] [PubMed] - Yadav, H.; Vinodhkumar, M.; Limbachiya, C.; Vinodhkumar, P.C.; Mason, N.J. Low energy electron interactions with Iodine molecule (I
_{2}). J. Quant. Spectrosc. Radiat. Transf.**2020**, 250, 107035. [Google Scholar] [CrossRef] - Tam, W.C.; Wong, S.F. Dissociative attachment of halogen molecules by 0–8 eV electrons. J. Chem. Phys.
**1978**, 68, 5626. [Google Scholar] [CrossRef] - Fabrikant, I.I.; Eden, S.; Mason, N.J.; Fedor, J. Recent Progress in Dissociative Electron Attachment: From Diatomics to Biomolecules. Adv. At. Mol. Opt. Phys.
**2017**, 66, 545. [Google Scholar] - Ruf, M.W.; Barsotti, S.; Braun, M.; Hotop, H.; Fabrikant, I.I. Dissociative attachment and vibrational excitation in low-energy electron collisions with chlorine molecules. J. Phys. B At. Mol. Opt. Phys.
**2003**, 37, 41. [Google Scholar] [CrossRef] - Braun, M.; Ruf, M.W.; Fabrikant, I.I.; Hotop, H. Observation of p-Wave Threshold Behavior in Electron Attachment to F
_{2}Molecules. Phys. Rev. Lett.**2007**, 99, 253202. [Google Scholar] [CrossRef] [PubMed] - Kurepa, M.V.; Babic, D.S.; Belic, D.S. Electron-bromine-molecule total ionisation and electron attachment cross sections. J. Phys. B. At. Mol. Phys.
**1981**, 14, 375. [Google Scholar] [CrossRef]

**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