Theory and Energetics of Mass Spectra

BY B. N. McMaster

1 Introduction

The quasi-equilibrium theory remains the cornerstone of discussions of mass spectral fragmentations in the literature, and has been well reviewed by Wahraftig. However, very significant advances have been made in the theoretical treatments of chemical dynamics in closely related fields. More sophisticated experimental methods are now being applied to studies of ion decompositions and promise to fill some of the wide gaps in our knowledge. Most emphasis has been therefore placed on these aspects and a review style has been adopted, since this is felt to be more useful in the midst of such developments. Where clarification of concepts or methods seems necessary, criticism has been made in a spirit of stimulating further work and discussion.

The topics reviewed follow a logical development. Theoretical calculations of ion structures and energies are briefly discussed, followed by ionization processes and their important relationship to energy deposition functions. Current developments in theories of unimolecular rate processes are reviewed and their relevance to ion decompositions is stressed. Results from photoelectron-photoion coincidence, charge-transfer mass spectra, field ionization kinetics, and meta-stable ion kinetic energy measurements are discussed with particular emphasis on fundamental aspects. Finally, methods of determining appearance potentials are critically evaluated, and their uses in thermochemical calculations are reported.

Although the literature coverage is as comprehensive as possible, some degree of selection has been necessary. Numerous reviews on specific topics are cited in the appropriate sections, but more general coverage of related work in mass spectrometry can be found in Vol. 2 of this series and in a very comprehensive literature survey covering 1972 — 73.

2 Calculations of Ion Structures and Energies

Ab initio Self-consistent Field Calculations including Electron Correlation. — An important distinction must be drawn between ab initio SCF calculations using extended basis sets and those using minimal basis sets. Only the former are expected to give results of Hartree–Fock accuracy in the single-particle approximation (which ignores electron correlation). These calculations are very expensive for polyatomic molecules, and minimal basis set calculations are therefore more generally performed. With judicious choice of basis functions for particular systems, results within a few kcal mol-1 of the Hartree-Fock limit can be obtained using minimal basis sets. But even with results of this accuracy erroneous conclusions may be drawn because electron correlation is ignored in the Hartree–Fock treatment. Theoretical calculations of electronic energies are generally used to determine the energy difference between species. If the correlation energy of each species is the same, then comparisons at the Hartree–Fock level will be quite accurate. However if it differs, even slightly, the relative energies may be drastically changed because the correlation energy is of a similar order of magnitude to the total chemical binding energy.

A number of techniques for estimating the correlation energy, or at least that part which differs between related species, have recently been developed to correct the Hartree–Fock energies. Some of these methods and their application to diatomic molecules have been reviewed by Wahl, including the molecular orbital configuration interaction (MO-CI), multiconfiguration self-consistent field (MCSCF), and independent electron-pair approximation (IEPA) treatments. The calculations of electron correlation effects reported below have used extended basis sets, unless stated otherwise.

Kutzelnigg et al. have calculated correlation energy corrections for vinyl and ethyl ions with classical and non-classical (H-bridged) structures (1), (2) and (3), (4) respectively using the IEPA method. They used the geometries corresponding to local energy minima obtained by slightly-extended basis set calculations, and found that the non-classical structures were more stable by ca. 8 kcal mol-1. Although the quantitative magnitude of the stability is uncertain because of the remaining small errors, its qualitative validity is assured and contrasts with calculations ignoring electron correlation which predicted the classical structure to be more stable in the case of the C2H3+ ions, and about equally stable in the case of the C2H5+ ion. These important differences in predictions have been attributed to the overestimation of electron repulsion in the Hartree–Fock approximation.

Similar calculations for the CH5+ ion indicated that the CS (5) and C2v (6) structures have almost identical energies, while the C4v (7) and D3h (8) structures were less stable by about 6 and 20 kcal mol-1 respectively. Minimal basis set calculations which ignored the correlation energy predicted all these structures to have very similar energies, although later calculations with extended basis sets predicted significant differences. A dissociation energy of 40 kcal mol-1 was obtained for the reaction CH5+ -> CH3+ H2 when the correlation energy was treated. The importance of correlation energy has also been noted in the derivation of accurate potential energy curves for proton transfer in H5O2+, and electrocyclic transformations of cyclopropyl and allyl cations, radicals, and anions.

The π-electron states of benzene have been extensively studied by Hay and Shavitt using an MO–CI method with a frozen σ-core. Excitation energies were obtained for many singlet, triplet, quintet, and Rydberg states of the molecule and several doublet states of the molecular ion. Good agreement with experiment was observed over all and the molecular ion states were well discussed. Very accurate calculations of correlation effects in the ground and ionized states of methane have been reported by Meyer using a pseudo-natural orbital (PNO–CI) treatment, and an interesting discussion of the energy surface of CH4+ has been given. Other CI calculations have been reported for neutral and ionic states of the silyl radical using a minimal basis set.

For some particular cases, which include the dissociation of a doublet molecular ion to a doublet and a singlet state...