Towards first principles calculation of electron impact mass spectra of molecules.

The ability of modern quantum chemistry (QC) to compute or even predict molecular properties and in particular the spectroscopic signatures of molecules has advanced extraordinarily in the past decade. Kohn–Sham density functional theory (DFT) is used routinely to aid interpretation of NMR, IR, UV, and chirality-based spectroscopic data. However, a blank spot on this map of success is represented by electron impact mass spectrometry (EI-MS). This important experimental method is used routinely in chemistry and related fields for various analytical purposes. In a typical EI-MS experiment, molecules are bombarded with high-kineticenergy electrons (typically 70 eV) leading to decomposition as well as more complex chemical rearrangements (often induced by hydrogen-atom transfer). The basic difficulty in the QC treatment of EI-MS is that the recorded intensity for the fragment mass-to-charge (m/z) ratio used for interpretation results from complex chemical kinetics and not from quantized energy levels. According to Ref. [4], the theoretical simulation of EI mass spectra is extremely challenging. While the QC calculation of energy levels is straightforward, the computation of reaction rates of ionized, highly excited (hot) molecules seems to be very complicated even when one disregards the complexities in describing the primary ionization process. Hence, only qualitative and empirical estimates for simple bond-breaking events in organic radical cations have been proposed to date based on computed static properties of the molecules like bond orders, bond energies, and fragment energies to aid in the interpretation of EI-MS data. (For ab initio (mostly DFT) computed energies of stationary points on potential energy surfaces (PESs) in special EI-MS-related reactions see Ref. [6]. ) The most sophisticated theoretical approach to date is based on RRKM theory and “master equations” which, however, require computed data (e.g. transition states) for a priori defined decomposition channels (which are often not known) and some further approximations (e.g. harmonic vibrations). To the best of our knowledge, no attempt to provide a more general, dynamic, quantitative, and widely applicable theory of EI-MS was published so far. The present work aims to close this gap. It presents the conceptual and technical ideas accompanied by a few representative spectra showing that the theoretical approach indeed works in practice. All important technical details and further in-depth explanations of various theoretical aspects can be found in the Supporting Information. A “black-box” type, more or less ab initio based brute force approach is used to compute the decomposition and reaction probabilities of singly ionized molecules with large amounts of internal energy. Only valence ionization and organic molecules are considered here although these restrictions are not due to the theory but just imposed by the majority of applications. The conceptual framework is the combination of standard QC methods, molecular dynamics (MD), and stochastic methods as exemplified in Scheme 1. It includes all basic physical effects except the quantum dynamics of the nuclei and non-Born–Oppenheimer (BO) effects.