We present an overview of the current status of transition-state theory and its generalizations. We emphasize (i) recent improvements in available methodology for calculations on complex systems, including the interface with electronic structure theory, (ii) progress in the theory and application of transition-state theory to condensed-phase reactions, and (iii) insight into the relation of transition-state theory to accurate quantum dynamics and tests of its accuracy via comparisons with both experimental and other theoretical dynamical approximations.

Current status of transition-state theory

A review of the theoretical and computational modeling of bimolecular reactions is given. The review is divided into several sections which are as follows: gas-phase thermal reactions; gas-phase state-selected reactions and product state distributions; and condensed-phase bimolecular reactions. The section on gas-phase thermal reactions covers the enthalpies and free energies of reaction, kinetics, saddle points and potential energy surfaces, rate theory for simple barrier reactions and bimolecular reactions over potential wells. The section on gas-phase state-selected reactions focuses on electronically adiabatic reactions and electronically nonadiabatic reactions. Finally, the section on condensed-phase bimolecular reactions covers reactions in liquids, reactions on surfaces and in solids and tunneling at low temperature.

Modeling the Kinetics of Bimolecular Reactions

The rate of unimolecular processes is calculated by means of a statistical adiabatic channel model. The rates are mainly determined by the maxima of the channel energies. The channels are constructed by correlating reactant and product states; the channel energies are computed by a simple interpolation procedure. The coupling between the various vibrational-rotational motions is taken into account. The influence of parameters of the potential surface on channel energies and on rate constants is studied. Numerical results for the NO2, CH4, CD4, C2H6 and C2D6 dissociation – recombination kinetics are compared to experimental data. The statistical adiabatic channel model gives similar results as minimum local entropy models. Both these approaches lead to stronger curvatures of k(E) and smaller activation energies for the thermal rate constant k∞ than the corresponding RRKM calculations.



Die Geschwindigkeit unimolekularer Zerfallsreaktionen wird mit Hilfe eines Modells adiabatischer Kanale statistisch berechnet. Wesentlich fur die Reaktionsgeschwindigkeiten sind die Maximalenergien der Kanale, die durch Korrelation von Zustanden der Reaktanten und Produkte und einfache Interpolation bestimmt werden. Die Kopplung der Schwingungs-Rotationsbewegungen wird beachtet. Der Einflus von Potentialflachenparametern auf Kanalenergien und Geschwindigkeitskonstanten wird studiert. Numerische Ergebnisse fur die Dissoziations-Rekombinationskinetik von NO2, CH4, CD4, C2H6 und C2D6 werden mit experimentellen Daten verglichen. Das Modell adiabatischer Kanale ergibt ahnliche Ergebnisse wie Modelle mit aktivierten Komplexen, die an Stellen minimaler Zustandsdichte lokalisiert werden. Beide Ansatze fuhren zu einer starkeren Krummung der k(E)-Kurven und zu geringeren Arrhenius-Aktivierungsenergien fur die thermischen Geschwindigkeitskonstanten k∞ als entsprechende RRKM Rechnungen.

Specific Rate Constants of Unimolecular Processes II. Adiabatic Channel Model

This tutorial presents the most common ion activation techniques employed in tandem mass spectrometry. In-source fragmentation and metastable ion decompositions, as well as the general theory of unimolecular dissociations of ions, are initially discussed. This is followed by tandem mass spectrometry, which implies that the activation of ions is distinct from the ionization step, and that the precursor and product ions are both characterized independently by their mass/charge ratios. In collision-induced dissociation (CID), activation of the selected ions occurs by collision(s) with neutral gas molecules in a collision cell. This experiment can be done at high (keV) collision energies, using tandem sector and time-of-flight instruments, or at low (eV range) energies, in tandem quadrupole and ion trapping instruments. It can be performed using either single or multiple collisions with a selected gas and each of these factors influences the distribution of internal energy that the activated ion will possess. While CID remains the most common ion activation technique employed in analytical laboratories today, several new methods have become increasingly useful for specific applications. More recent techniques are examined and their differences, advantages and disadvantages are described in comparison with CID. Collisional activation upon impact of precursor ions on solid surfaces, surface-induced dissociation (SID), is gaining importance as an alternative to gas targets and has been implemented in several different types of mass spectrometers. Furthermore, unique fragmentation mechanisms of multiply-charged species can be studied by electron-capture dissociation (ECD). The ECD technique has been recognized as an efficient means to study non-covalent interactions and to gain sequence information in proteomics applications. Trapping instruments, such as quadrupole ion traps and Fourier transform ion cyclotron resonance instruments, are particularly useful for the photoactivation of ions, specifically for fragmentation of precursor ions by infrared multiphoton dissociation (IRMPD). IRMPD is a non-selective activation method and usually yields rich fragmentation spectra. Lastly, blackbody infrared radiative dissociation is presented with a focus on determining activation energies and other important parameters for the characterization of fragmentation pathways. The individual methods are presented so as to facilitate the understanding of each mechanism of activation and their particular advantages and representative applications.

http://aether.cmi.ua.ac.be/artikels/MB_31643.pdf

Ion activation methods for tandem mass spectrometry.

Mass Spectrometric Analysis. Molecular Rearrangements

been of fundamental importance in the development of present-day physical theories. As has been stated so many times, the general problem is now solved "in principle" by the quantum mechanics, but the application of the theory to only the simplest systems has been practicable.l, 2 In recent years a very large amount of data has been accumulated on the "mass spectra" resulting from the bombardment of molecules by electrons of energy 50 and 70 volts.3 There is also a significant amount of data on special aspects of the mass spectra of a few polyatomic molecules. A reasonably exact analysis of a mass spectrum would require detailed knowledge of all the electronic states both of the molecule and of all the ions formed from it by removal of electrons and by removal and rearrangement of nuclei. In this paper we present a statistical approach to the problem. Necessarily, assumptions and approximations are required. 'While this theory is in no way complete, we believe it permits the discussion and coordination of a large amount of the available data in terms of the structure of molecules and ions. Knowledge of the effect of low-voltage electron bombardment on molecules, besides being of interest in its own right, has varied applications. It has bearing on the relation of molecular structure to chemical reactivity. It is well known that the major fraction of the effect of high energy radiation on matter, including living systems, is due to the low energy secondary electrons.4 The rate theory presented here should also be applicable to other problems involving isolated systems having a large but finite number of degrees of freedom. The ionization and dissociation of diatomic molecules by electron impact has by now become quite well understood. Hagstrum5 has recently discussed in great detail the mass spectra of a number of diatomic molecules, explaining the formation of the several ions and their kinetic energies in terms of Franck-Condon transitions to the various electronic states of the diatomic ions. Another discussion is that of Stevenson6 who calculated the relative abundance ratios H+/H2+ and D+/D2+ in the mass spectra of hydrogen and deuterium, again using the picture of Franck-Condon transitions to known electronic states. While any discussion of large polyatomic molecules mass spectra must be in accord with these discussions, the direct application of the same methods is impossible.

https://www.pnas.org/content/pnas/38/8/667.full.pdf

M. B. Wallenstein

Papers

Absolute Rate Theory for Isolated Systems and the Mass Spectra of Polyatomic Molecules.