MassKinetics: a theoretical model of mass spectra incorporating physical processes, reaction kinetics and mathematical descriptions

Abstract

A theoretical framework and an accompanying computer program (MassKinetics, www.chemres.hu/ms/ masskinetics) is developed for describing reaction kinetics under statistical, but non-equilibrium, conditions, i.e. those applying to mass spectrometry. In this model all the important physical processes influencing product distributions are considered: reactions, including the effects of acceleration, collisions and photon exchange. These processes occur simultaneously and are taken into account by the master equation approach. The system is described by (independent) product, kinetic energy and internal energy distributions, and the time development of these distributions is studied using transition probability functions. The product distribution at the end of the experiment corresponds to the mass spectrum. Individual elements in this scheme are mostly well known: internal energy-dependent reaction rates are calculated by transition state theory (RRK or RRKM formalisms). In the course of collisions, energy transfer and other processes may occur (the latter usually resulting in the 'loss' of ion signal). Collisions are characterized by their probability and by energy transfer in a single collision. To describe single collisions, three collision models are used: long-lived collision complexes, partially inelastic collisions and partially inelastic collisions with cooling. The latter type has been developed here, and is capable of accounting for cooling effects occurring in collision cascades. Descriptions of photon absorption and emission are well known in principle, and these are also taken into account, in addition to changes in kinetic energy due to external (electric) fields. These changes in the system occur simultaneously, and are described by master equations (a set of differential equations). The usual form of the master equation (taking into account reactions and collisional excitation) was extended to consider also radiative energy transfer, kinetic energy changes, energy partitioning and ion loss collisions. Initial results show that close to experimental accuracy can be obtained with MassKinetics, using few or no adjustable parameters. The model/program can be used to model almost all types of mass spectrometric experiments (e.g. MIKE, CID, SORI and resonant excitation). Note that it was designed for mass spectrometric applications, but can also be used to study reaction kinetics in other non-equilibrium systems.