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5.1.1 The corpus of articles on experimental molecular
dynamics

The full corpus contains a core of 28 full length articles on original research done at the FOM-Institute for Atomic and Molecular Physics in Amsterdam (AMOLF). It also contains seven articles published in Letter journals for the rapid publication of short messages, five review articles that summarise the main stages in the research project and nine PhD theses issued from the project, as well as three additional articles and two theses on directly related work carried out by a collaborating group at the same laboratory. These publications have been selected and compiled by the senior author and leader of the research project we analyse. The complete list of all publications included in the corpus is given in appendix B.

The subject of the publications in the corpus can be summarised in hindsight as `vibronic coupling at intersections of covalent and ionic states', in the domain of experimental molecular dynamics. Here, we briefly sketch the physics of the corpus, referring for a more detailed description to some modules created in the analysis of the corpus.

According to the tutorial survey of the field [Levine and Bernstein, 1974, p.1], ``the subject of molecular dynamics deals with the study of elementary physical and chemical rate processes. It is concerned with both intramolecular motions and intermolecular motions, which together constitute the underlying `microscopic' basis of all bulk rate phenomena.'' Research in this domain addresses the forces acting between atoms or groups of atoms in such reactions, the intramolecular and intermolecular motions of the constituent particles, the energy flow between the different degrees of freedom during the interaction, and the mechanisms of bond-breaking and bond-making. In these mechanisms the interplay between valence electrons and nuclei is crucial. The systems that are studied cover uni-molecular systems, bi-molecular systems, clusters and molecule-surface systems.

The type of process addressed in the corpus5.1 is a one-electron transition in bi-molecular collisions that constitutes the first step of the chemical reaction

\begin{displaymath}{\rm M + XY \to M^+ + (X...Y)^- \to MX^{\dagger} + Y},
\end{displaymath} (5.1)
where M is some electropositive atom (in practice an alkali atom, ${\rm K}$, ${\rm Na}$ or ${\rm Li}$) colliding with a vibrationally excited electronegative molecule ${\rm XY}^{\dagger}$ (a halogen molecule ${\rm Br_2}$, ${\rm I_2}$ or ${\rm Cl_2}$, for example, or ${\rm O_2}$ or ${\rm NO}$).

This reaction has a relatively large cross section (meaning that the reaction takes place very efficiently), which can be explained by assuming the following reaction dynamics described in the `harpoon model'. Herschbach has given a comprehensive overview of this model in [Herschbach, 1966]. The valence electron of the electropositive atom jumps at a relatively large distance to the electronegative molecule. The resulting attractive Coulomb force creates an ionic bond. Since the ion molecule ${\rm XY^-}^{\dagger}$ is vibrationally excited, it either immediately dissociates, or is easily dissociated by the Coulomb force, so that ${\rm MX}$ can be formed. The metaphor of the harpoon model is that of the small alkali atom catching a big halogen atom, by throwing its valence electron serving as a harpoon and hauling it in with the Coulomb force.

The focal point of the corpus is the first step of the harpoon reaction: the transfer of the valence electron of the alkali atom to the electronegative molecule. By isolating the charge transfer initiating the harpoon reaction, the ion-pair formation process

 \begin{displaymath}{\rm M + XY \to M^+ + (X...Y)^- }
\end{displaymath} (5.2)
can be considered. The term used in the first part of the corpus for this charge transfer process is `chemi-ionisation'.

According to the atom-atom model for ion-pair formation in molecular collisons5.2 the charge transfer takes place via the crossing of the potential energy curves of the covalent state of the system ${\rm M+XY}$ and of the ionic state ${\rm M^+ + XY^-}$. At the crossing distance Rc both states have equal potential energy, so that the system can transform from the one state to the other through an electron jump between M and XY. The electron can jump at two moments: when the particles arrive at the crossing distance of each other during their first approach and when they are again at that distance Rc when they move away from each other. The transition probability of the electron is given by the Landau-Zener formula [Herschbach, 1966].

The ion-pair formation is examined in the corpus by means of scattering: by measuring and calculating the total and differential cross sections of these reactions, using a molecular beam set-up. Scattering is well suited as a method for the study of molecular dynamics, and a molecular beam set-up in particular offers a way to specify the input parameters of the chemical reaction very precisely.

Collision physics is a major scientific discipline in its own right. The subject of atomic and molecular scattering deals with the behaviour of ions, atoms and molecules either in binary collisions or in a potential field. Experiments are designed in such a way that the initial and final state of the system are defined as accurately as possible, preferably in terms of a set of quantum numbers. A scattering event is described in terms of cross sections of different kinds: total, differential, double differential. These physical quantities contain all the information about momentum, energy (electronic, vibrational and rotational) and angular momentum transfer. Especially the earlier corpus articles are written in terms of scattering, rather than in the terminology of molecular dynamics.

For an explicit study of the ion-pair formation initiating the harpoon reaction, the relative velocity of the colliding particles has to correspond to a kinetic energy in the electronvolt range. At lower energies only an investigation of the reaction as a whole is possible. At AMOLF, methods and techniques were developed to generate well-defined electronvolt beams of neutral atoms and molecules and to detect the products of the chemical reaction. Later, other groups have studied these reactions using femtosecond lasers instead of scattering experiments.5.3

At first, the aim of the research project at AMOLF was closely related to the molecular beam experiments on harpoon reactions of Herschbach and co-workers, whose experiments had inspired the AMOLF group to consider the initiation of the harpoon reaction. The research had a strong emphasis on scattering. In the course of the project, it evolved into a more general interest in molecular reaction dynamics between atoms and molecules. The main review paper, in which a thorough overview is given of the whole research project, is Vibronic coupling at intersections of covalent an ionic states (Kleyn, Los and Gislason, 1982; R45.4).

In retrospect, three sub-projects can be distinguished in the project. The program was initiated by the measurement of the total cross section in the electronvolt range of ion-pair formation in collisions between halogen molecules and other electronegative molecules on the one hand, and alkali atoms ${\rm K}$, ${\rm Na}$ and ${\rm Li}$ on the other hand. These measurements were interpreted qualitatively by reducing the atom-molecule problem to an atom-atom problem; for the electron transfer the Landau-Zener approximation is used. It was soon realised that this case was too complicated to be described as a simple binary collision.

The rest of this first part therefore consists of a detailed quantitative experimental study of the electron transfer in atom-atom collisions between a sodium atom Na and an iodine atom I

\begin{displaymath}{\rm Na + I \to Na^+ + I^-},
\end{displaymath} (5.3)
to test the Landau-Zener approximation in the domain in which it is supposed to be valid. In terms of scattering, both the total and the differential cross sections of this process were measured, and it was found that the Landau-Zener approximation for the transition probability indeed provides a very satisfactory explanation of the measurements of the total (Moutinho et al., 1971; A04) and the differential cross section (Delvigne & Los, 1973; A08). Thus, a solid foundation was created, on which further research and descriptions could be based.

The first part of this research project resulted in three Ph.D. theses: (Moutinho, 1971; T2) and (Baede, 1972; T3) with respect to the total cross sections, and (Delvigne, 1973; T4) with respect to the differential cross sections. It has been briefly summarised in (Los, 1976; R2) and more extensively in the conference contribution Chemi-ionisation by dynamic coupling (Los, 1973; R1). Our analysis concentrates on this first subset of the corpus.

After the satisfactory conclusion of the first part, research proceeded at AMOLF to the much more complicated case of atom-molecule collision. The subject of the second part of the research project published in the corpus is the correlation between the transfer of the electron and the inter- and intramolecular motions of the nuclei in reaction (5.2)

The electron transfer itself can be considered instantaneous, compared to the other velocities involved. However, the time between the two passages of the crossing between the atom M and the molecule XY is long enough for the bond of the ${\rm XY}^-$ molecule which is formed at the first crossing to stretch. The influence of vibration on the electron transfer, i.e. the vibronic coupling at intersections of covalent and ionic states, was studied classically in the second part of the research project. In terms of scattering, the relation was studied between total and differential ion-pair cross sections on the one hand and the intramolecular motion of the halogen molecule during the collision on the other hand. This study of the reaction was executed systematically. The total cross section was measured, with variation in the initial energy and the internal energy of the ${\rm XY}$ molecule, along with the degree of dissociation of the ${\rm (X...Y)^-}$ anion. From these data the adiabatic and vertical electron affinity of the electronegative molecule were determined. The differential cross section was also measured.

The second part of the corpus is summarised in a conference progress report: The dynamics of ion pair forming collisions (Los, 1978; R3). The Ph.D. theses (Hubers, 1976; T5), (Aten, 1977; T6) and (Kleyn, 1980; T7) issued from this sub-project.

The same phenomena were studied from a theoretical point of view in a collaborating group at AMOLF. Evers worked on numerical studies, based upon the surface hopping trajectory model introduced by Tully [Tully and Preston, 1971], for collisions between alkali atoms and halogen molecules, especially ${\rm K + Br_2}$. This collaboration resulted among other things in the joined publications Energy transfer and differential scattering for ion pair formation in ${\rm Na}$, ${\rm K}$, ${\rm Cs +I_2}$ collisions (Aten, Evers, de Vries and Los, 1977; A19) and Non reactive scattering of ${\rm K}$ by ${\rm Br_2}$ in the energy range of 0-10 eV (Evers, de Vries and Los, 1978; A21).

The third and last part of the project consisted of the quantum mechanical treatment of the same problem of vibronic coupling at intersections. The subject of this part can be summarised as the study of the vibrational wave packets in one-electron transfer collisions. It has been set out in the theses (U.C. Klomp,1982; T8) and (M.R.Spalburg,1985; T9), and its outline is given in the conference progress report Non-Franck-Condon behaviour in inelastic atom-molecule collisions (Los and Spalburg, 1984; R5).



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