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.

Copper doping of small gold cluster cations: Influence on geometric and electronic structure

“…31 To prove that this process is possible to occur on the time-scale of the present experiment after absorption of one photon, the unimolecular dissociation rate constants k d of the investigated Au n Cu m + (n + m = 4) are calculated according to statistical RRKM (Rice, Ramsperger, Kassel, Marcus) theory 32,33 by employing the software package MASS KINETICS. 34 The required vibrational frequencies and the bond dissociation energies of Au 4 + , Au 3 Cu + , and Au 2 Cu 2 + are taken from our theoretical computations performed for the minimum energy structures. For modeling the transition state, the vibrational frequencies are taken to be the same as for the ground state structures minus the middle frequency that is treated as internal translation along the reaction coordinate, and two neighboring frequencies are scaled by a factor of 0.5.…”

Microcanonical analysis of the kinetic method. The meaning of the “apparent entropy”

“…The primary difference between their model and the present simulation is that they ignored the exponential kinetic terms in eq 16 (effectively using t 1 ϭ 0 and t 2 ϭ ϱ) and instead replaced P 0 (E) with a displaced Boltzmann distribution (internal energies shifted up by an arbitrary amount) as an ad hoc method of selecting the internal energy distribution for the dissociating ions. The present work, as well as two previous simulations using classical RRK theory by Bojesen and Breindahl [6] and by Ervin [10] and the RRKM treatment by Drahos and Vékey [11,12], properly uses the kinetic expression in eq 16 to select the energy distribution that would be observed in an experiment. In the RRKM and finite heat bath theory treatments of Laskin and Futrell [9], the integration over the distribution of the internal energies of the dissociating ions represented by eq 17 is replaced by evaluation at the single most-probable value of the internal energy.…”

“…By measuring the product intensity ratios for proton-bound dimers composed of partners with known acidity, the slope of the correlation is found and then the acidity of an unknown can be measured versus a reference acid. Theoretical formulations of varying levels of sophistication have been given that justify the correlation given by eq 3 [1,2,[5][6][7][8][9][10][11][12], but its use and the meaning of the effective temperature parameter are points of active discussion [4,10,11,[13][14][15].…”

CE50: Quantifying collision induced dissociation energy for small molecule characterization and identification

“…The amount of energy available for conversion to internal energy is proportional to the sum of the initial internal energy of the precursor ion (E=), the internal energy of the collision gas (E G ), and the E com . The fraction of this energy that is partitioned between the energy levels in the precursor ion (E) is given by eq 2; where D i is the number of degrees of freedom of the sample molecule, D G is the number of degrees of freedom of the collision gas, and D T is the translational degrees of freedom [3]. …”

“…In CID, transferring a portion of the kinetic energy of the accelerated precursor ion to internal energy by collisions with relatively stationary gas atoms increases the internal energy of a sample ion. The maximum energy available for absorption (E com ) by the precursor ion in the collision process is described by eq 1 [3]:…”