Theory and Energetics of Mass Spectrometry

BY T. BAER

1 Introduction

A review of the theory and energetics in mass spectrometry is a formidable task because the field is so broad. Consistent with the theory and energetics chapters of previous volumes, I have tried to limit the review to those aspects of the literature during the past two years which are relevant to the fundamental understanding of ion dynamics. Particular emphasis has been given to those developments which will help us in our ultimate quest, the ability to predict qualitatively or quantitatively the behaviour of energized ions.

2 Ion Thermochemistry

As dynamical experiments and theories are becoming more sophisticated and precise, the need for accurate thermochemical data on molecules, ions, and fragments continues to grow. During the past few years the experimental effort has been supported by numerous calculations, most of which are of the ab initio type. With the advent of readily available high-level programs, numerous groups are now performing calculations. In combination with good experimental information, these results are of great value in extending our chemical knowledge because accompanying the calculated energy is an assumed structure. Although some of the theoretical work will be treated under a separate subheading, a large portion of it will be mixed in with the review of experimental results.

Molecular Orbital Calculations. — Ab initio calculations have decreased in cost to such an extent that few calculations are now being done with semiempirical programs. This is also partly as a result of the fact that the semiempirical programs are usually parametrized to do one job well, but at the expense of their predictive ability for other properties.

The most commonly used ab initio program is the STO-3G (Slater-type orbitals with 3 gaussian functions). This uses a minimal, split-valence set of basis functions. The split valence means that two basis functions are used for each valence atomic orbital. More sophisticated basis sets are ones belonging to the K-LMG family, in which K is the number of gaussians used to describe the inner-shell s-type functions, L is the number of gaussians for the s- and p-type valence functions, and M is the number of gaussians for the outer sp-type functions. A commonly used basis set has been the 4-31G which is available through the Quantum Chemistry Program Exchange (QCPE) of the University of Indiana. This and the other K-LMG programs have been developed by Pople and his co-workers.

Some new K-LMG programs have been developed and are, or will soon be, available through the QCPE. Two of these are ones which use the 6-21G and 3-21G basis sets. Either of these is claimed to be as good as the 4-31G or the PFPB 4-21G basis set. The K-21G split-valence basis sets are definitely superior to the STO-3G minimal basis set. Equilibrium geometries are about as good as those of the 4-31G but superior with regard to the description of the bond angles involving heteroatoms. Vibrational frequencies are also equal to, or better than, those of the 4-31G. Similarly, electric dipole moments are better with either the 6- or the 3-21G than with the 4-31G. Happily, because the 3-21G has fewer primitive gaussian functions it is faster than the 4-31G set. It appears to be inferior to the 4-31G only in the calculation of reaction energies. Comparisons for over 20 molecules are given.

Halgren et al.4 have compared the speed and accuracy of a number of semiempirical and ab initio programs for calculations of various properties. The overall effectiveness versus speed curve is shown in Figure 1. This paper also introduces a new semiempirical program, the PRDDO (partial retention of diatomic differential overlap). It is 16 times faster than one of the simplest ab initio programs, the STO-3G, yet it agrees very well with this program in relative energies, atomic charges, and dipole moments. In a follow-up to this paper, Dewar and Ford have added their MNDO program to this comparison. They compared seven MO methods by listing the root mean square (r.m.s.) error of the energy, ionization energy (Koopmans' theory), and dipole moment with respect to experimental results. These are listed in Table 1 and should serve as a guide to experimentalists. Although impressive, the calculations must be used with care. Furthermore it is doubtful that single configuration calculations will reach experimental accuracies of say 1 kJ mol-1. For such precision elaborate configuration interaction (CI) calculations must be carried out. These are still the domain of the theoreticians.

The most studied molecular ion during the past two years has been CN+. No less than four separate investigations were reported dealing primarily with the identity of the ground state. As with the isoelectronic C2, the two states 1Σ+ and 3Π are very close in energy. Wu did an SCF calculation and concluded that the 3Πis lower in energy by 0.33 eV. The fact that this was a single configuration calculation makes it somewhat suspect. Yet Ha using CI also found that the 3Π is lower than the 1Σ+ state by 0.41 eV. Murrell et al. would not commit themselves, stating that the two states are extremely close. This caution is certainly justified because Hirst using the ATMOL SCF calculation with CI found that either state could be made the ground state depending on the number of configurations used. Yet the bond distances are quite different (1.20 Å and 1.28 Å). Other diatomics studied are the mixed alkali metals and alkali salts such as NaK+, NaRb+, NaCs+, KBr+, KCs+, RbCs+, Na2+, K2+, Rb2+, and Cs2+. A number of stable excited electronic states were found.

Often the most stable structure for an ion is not the same as the most stable neutral structure. These situations are sometimes difficult to establish experimentally, but they are quite amenable to calculations. In fact the calculation of energies of isomers is one of the most fruitful uses...