Theory and Energetics in Mass Spectrometry

BY B. N. McMASTER

1 Introduction

The previous Report in this series essayed a fairly critical discussion of the fundamental concepts underlying some of the newer theoretical and experimental approaches being used in mass spectrometry. The past two years have witnessed further application of these techniques, rather than any major new developments. This report therefore focuses more on the results obtained by these methods, and is intended to complement the previous Report which provides the relevant background material. The literature coverage is accordingly more selective, but gives a representative illustration of the current capabilities of reported techniques.

Ab initio calculations of the structures of ions and energy barriers for their rearrangements are reviewed. Accurate appearance potential measurements, and other experimental methods of determining the energetics of ion decompositions are also discussed. A brief review of some recent theoretical studies of unimolecular dissociation reactions then leads on to an examination of results from experimental studies which have provided important information about the rate constants and translational energy disposal in unimolecular ion decompositions.

2 Ab initio Calculations of Ion Structures

In view of the rapidly growing dissemination and use of ab initio quantum chemistry programs, such as GAUSSIAN 70, it may be wise to inject a blunt note of caution. At their lowest minimal basis set level (e.g. STO-3G), which is the most widely used level because it is cheapest, the results are not of predictive value with respect to their implicitly stated aims of determining reliable geometries and relative energies of ion structures. Such calculations represent a false economy, particularly when the cheaper MINDO/3 method gives more reliable predictions (see Chapter 2, Section 5). More expensive ab initio calculations using larger basis sets are necessary to achieve results which are of chemically useful predictive value. Because of its practical importance, this question of basis set quality is emphasized in the following discussion. But before proceeding, it is useful to clarify briefly some of the shorthand jargon commonly used to describe the basis sets.

For reasons of computational efficiency, the basis sets used for ab initio calculations on polyatomic species are almost invariably composed of contracted Gaussian-type orbitals (CGTO), which are simply fixed linear combinations of one or more GTOs. These may be derived from atomic calculations in which a primitive GTO basis set is first optimized and then broken into the required number of CGTOs. Alternatively the CGTOs may be derived by determining the best least squares fit of appropriate numbers of GTOs to optimized Slater-type orbitals (STO) from atomic calculations. The quality of the basis set may be roughly ranked in a convenient fashion according to how many CGTOs are used to represent each canonical atomic orbital. A single-zeta (SZ), or minimal, basis set uses only one CGTO per atomic orbital, whereas a double-zeta (DZ) basis uses two, and so on. One particular intermediate case is also commonly encountered, where the valence atomic orbitals are represented by two CGTOs and the core orbitals by only one CGTO. Examples of this type of basis set include the GAUSSIAN 70 4–31G and 6-31G sets, which may be regarded as roughly '1½-zeta' on this relative scale. All these basis sets may also be augmented by polarization functions consisting of a single GTO of the appropriate type for each atom (e.g. p for H, d for C), and this is often indicated by superscript asterisks (see below).

Most ab initio calculations on ionic species have so far been performed at the Hartree–Fock (HF) SCF level, which neglects electron correlation effects. Such neglect is likely to render unreliable the conclusions regarding the relative stabilities of different structures where small energy differences are involved. Furthermore, the wide disparity in the quality of the basis sets used can make it difficult to assess the reliability of the results obtained by different workers, particularly for those who are not closely familiar with these calculations. At the end of this section, an attempt has therefore been made to summarize the more important criteria of quality, and to suggest standards which should be met in reliable calculations of various properties (e.g. geometries, energy differences of stable structures, and potential energy surfaces).

Pople has recently reviewed ab initio calculations on small organic ions and second-period hydride cations performed at the HF-SCF level with various basis sets. The geometries of several AH+n species (A = C, N, O, or F) have been optimized under appropriate symmetry constraints with 6-31G* basis sets, which contain d-type polarization functions on the central atom. In the few cases where comparison is possible, the calculated bond lengths were within 0.1 — 0.2 Å of experimental values, and bond angles were within 1 — 2°. Other calculations on NH2[??], NH2[??], and H2O[??] using larger double-zeta plus polarization (DZ + P) basis sets were primarily concerned with the electronic reorganization upon ionization, although the structures of some excited states of H2O[??] have also been investigated.

The species H3+, LiH2+, BeH3+, BH4+, CH5+ may be regarded as complexes of H2 with the corresponding simple Lewis acids, and have recently been studied by Collins et al. using several basis sets. The geometries of these cations were first determined using an STO-3G basis, and then reoptimized for a 4-31G basis set. Single SCF calculations at these geometries were then done with 6-31G* and 6-31G** basis sets; the latter includes p-type polarization functions on hydrogen, as well as d-type on the second-period atoms. This inclusion of polarization functions gave a modest increase in the binding energies between H2 and the Lewis acids. Finally, unrestricted Moller–Plesset second-order perturbation theory (UMP2) was applied to these calculations to obtain an approximate estimate of the correlation energy. The...