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Theoretical Studies of Charge Recombination Reactions

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Theoretical Studies of Charge Recombination Reactions Theoretical studies of charge recombination reactions Sifiso Musa Nkambule Akademisk avhandling f¨oravl¨aggandeav licentiatexamen vid Stockholms universitet, Fysikum. January, 2015. Abstract This thesis is based on theoretical studies that have been done for low-energy reactions involving small molecular systems. It is mainly focusing on mutual neutralization of oppositely charged ions and dissociative recombination of molecular ions. Both reactions involve highly excited electronic states that are coupled to each other. Employing electronic structure meth- ods, the electronic states relevant to the reactions are computed. It is necessary to go beyond the Born-Oppenheimer approximation and include non-adiabatic effects. This non-adiabatic behaviour plays a crucial role in driving the reactions. Schemes on how to go about and include these coupling elements are discussed in the thesis, which include computations of non-adiabatic and electronic couplings of the resonant states to the ionisation continuum. The nuclear dynamics are studied either semi-classically, using the Landau-Zener method or quantum mechanically, employing the time-independent and time-dependant Schr¨odinger + equations. Reactions studied here are mutual neutralization in collision of H + H−, where both the semi-classical and quantum mechanical methods are employed. Total and differential cross sections are computed for all hydrogen isotopes. We also perform quantum mechanical + studies of mutual neutralization in the collision of He + H−. For this system not only the non-adiabatic couplings among the neutral states have to be considered, but also the electronic coupling to the ionization continuum. Worth noting in the two systems is that reactants and the final products belong to different electronic states, which a coupled together, hence for the reaction to take place there must be non-adiabatic transition. + Lastly, the direct mechanism of dissociative recombination of H2O is studied. Here time- dependant quantum mechanical methods are employed and the dissociation cross section is computed. Acknowledgements I am most grateful to my supervisor Asa˚ Larson who has supported and encouraged me in both scientific and less scientific issues since I began my doctoral studies. I am also sincerely grateful, for the same reason to Nils Elander. I am also very thankful to Ann Orel for the valuable discussion we have had and her patience when I commit the many errors in handling the data. I wish to thank my friends and colleagues at the Stockholm University, Department of Physics. List of papers This work is based on the following papers; I Differential and total cross sections of mutual neutralization in low-energy + collisions isotopes of H + H−. Sifiso M. Nkambule, Nils Elander and Asa˚ Larson, in manuscript. + II Landau-Zener studies of mutual neutralization in collisions of H + H− and + Be + H−. Hanae Miyano Hedberg, Sifiso Nkambule and Asa˚ Larson, Journal of Physics B: Atomic, Molecular and Optical Physics, 47 (22), 2014 III Studies of HeH: DR, RIP, VE, DE, PI, MN,.... Asa˚ Larson, Sifiso Nkambule, Ermelie Ertan, Josefin S¨oderand Ann E. Orel, EPJ web of Conferences accepted for publication, 2015. + IV Theoretical study of the mechanism of H2O dissociative recombination. Sifiso M. Nkambule, Asa˚ Larson, S. Fonseca dos Santos and Ann E. Orel, in manuscript. Reprints made with permission from publishers. i Contributions from author Paper I. I participated in deriving the formulas for calculating the cross section, carried out the nuclear scattering calculations and analysed the results. I also wrote the first draft of the article. Paper II. I calculated the electronic couplings that enter the Landau-Zener formula from previous structure calculations. I also performed the two-by-two adiabatic-diabatic transformation transformation and I also participated in the discussions about the computations of the other set of electronic couplings and on the discussions about the paper. Papers III. I performed the diabatization of HeH resonant states. I also participated in deriving the formulas relevant for the adiabatic-diabatic states transformation and I carried out the nuclear scattering calculations and analysis of results. Paper IV. I participated in carrying out the quasidiabatization scheme, extracted some resonance energies and autoinization widths from the eigenphase sum data and performed the one- dimensional wave packet calculations and analysis. I also participated on the discussions about the paper. ii Contents 1 Introduction 1 1.1 Mutual Neutralization . 2 1.2 Dissociative Recombination . 3 1.3 Overview of computation scheme . 5 2 Computational details 6 2.1 Molecular Schr¨odingerequation . 6 2.1.1 Born-Oppenheimer approximation and potential energy surfaces . 7 2.2 Quantum chemistry calculations . 9 2.2.1 The Hatree-Fock method . 9 2.2.2 Configuration interaction method . 11 2.3 Electronic scattering calculations . 12 2.3.1 Basic scattering theory and resonance . 12 2.3.2 Complex Kohn variational method . 14 2.4 Adiabatic to diabatic transformation . 19 3 Nuclear Dynamics 23 3.1 Time-dependant wave propagation . 23 3.1.1 1D wave dynamics . 23 3.1.2 The MCTDH method . 25 3.2 Time-independent nuclear scattering . 26 3.3 Semi-classical Landau-Zener studies . 27 4 Discussion of attached papers 29 + 4.1 Paper I: Differential cross section for mutual neutralization of H + H− ..... 29 4.1.1 Scattering of nuclei species . 29 + 4.2 Paper II: Landau-Zener studies of mutual neutralization in collisions of H + H− + and Be + H−..................................... 34 4.3 Studies of HeH: DR, RIP, VE, DE, PI, MN,... 36 + 4.4 Paper IV: Theoretical study of the mechanism of H2O dissociative recombination 38 5 Conclusion and outlook 42 A Deriving spin multiplicity factors for bosons and fermions i iii List of Figures 1.1 The Mutual neutralization process . 3 1.2 Direct dissociative recombination . 4 1.3 Indirect dissociative recombination . 5 2.1 Resonance features . 14 2.2 Elastic electron scattering . 18 2.3 Adiabatic and Diabatic potential energy curves . 19 2.4 Quasidibatization of the water molecule . 20 3.1 1D Wave Propagation . 25 4.1 Differential cross section for all isotopes . 31 4.2 Differential cross section for hydrogen at different energies . 31 4.3 Total cross section . 32 4.4 Landau-Zener cross section . 33 4.5 Branching ratios . 33 4.6 Radial couplings . 34 4.7 Rotational angle . 35 4.8 Adiabatic and Diabatic states . 35 4.9 Electronic couplings . 35 4.10 HeH MN cross section . 37 4.11 HeH MN branching ratios . 38 4.12 Asymetric streth Widths . 39 4.13 Symetric strecth Potential energy curves . 40 4.14 Symetric streth Cross sections . 40 4.15 1D total cross section . 41 iv List of Tables 4.1 Cross section ratios . 32 v Chapter 1 Introduction This thesis is based on a theoretical study of low energy (< 10 eV) molecular collision processes, occurring in low temperature ionized environments, namely; mutual neutralization (MN) and dissociative recombination (DR). Such processes are of significance in many fields of research, such as primordial and pre galactic gas reactions, interstellar gas clouds chemistry, planetary ionosphere chemistry and plasma physics. In the divetor section of a fusion plasma facility, like the ITER [1] project, undesirable rest products that can be harmful to the environment are created and it is important to understand the processes taking place in this region of the plasma [2–4]. Molecular H2 gas is also believed to play a crucial role in the formation of the first stars and galaxies, and as such the chemical evolution of gases at the early epochs are crucial if one needs to understand the competing process in the formation of H2 [5–12]. A strong motivation for this research has been to get a better understanding of how molecular ions involved in these reactions are destroyed and the kind of new fragments that are formed. The theoretical framework for studying microscopic phenomena involving molecules is a quantum mechanical picture, using the Schr¨odingerequation. The fundamental property of molecules is the large ratio of the mass of nuclei to electron mass, which is about 3680 even + for the lightest molecule of H2 . This property thus implies that the electronic motion and nuclear motions are viewed as uncoupled from each other, or the electrons can instantaneously adjust to the slower motion of the nuclei. This enables a description based on the so-called Born-Oppenheimer approximation [13], which takes advantage of this mass difference between the particles and makes great ease in describing and studying the molecular reaction based on a quantum mechanical description. It enables us to view the system in the adiabatic picture, (to be further described in Chapter 2) and it means the electrons stay in the same quantum state while the nuclei position are changing. In this model, the wavefunction of the molecule is divided into electronic and nuclear components and in solving the Schr¨odingerequation involving only the latter, at a fixed nuclear positions, the eigenvalues are obtained, and if obtained for a range of internuclear positions, the so-called potential energy surface (potential energy curve in the case of diatomic molecules) can be computed. This model forms the basis of most chemistry models aimed at describing chemical phenomena at microscopic model [14]. However, this approach of the molecular phenomena is applicable, to a good approximation, for processes that involve electronic states well separated in energy. This usually includes reac- tions occurring in the ground electronic state [15, 16]. On the other hand, reactions involving excited electronic states do not fall in this category. For processes driven by the dynamics on highly excited electronic states, the Born-Oppenheimer approximation can often not be applied. These electronic states can lie close to each other, and as a result, non-adiabatic transitions from one electronic state to another may occur [17]. When studying non-adiabatic processes, a change of electronic state basis is usually advan- tageous [18].
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