Ab initio Calculations on Molecules containing Five or Six Atoms

BY C. THOMSON

1 Introduction

The present Report attempts to survey calculations carried out during the past few years by ab initio methods which were not covered in Volume 2 of the present series. In the latter, the Report by Thomson dealt with molecules containing up to four atoms, and the article by Duke dealt with large molecules. Since the completion of Volume 2, the literature on ab initio calculations has continued to grow rapidly and it was soon clear that space limitations would preclude any comprehensive coverage of the literature dealing with medium-sized molecules. Therefore this Report is restricted to calculations on molecules containing five or six atoms, and even within this group it is not possible to refer to all such calculations which have been published. Those studies which seem of particular interest to the Reporter have therefore been surveyed so that the selection is somewhat subjective.

During the past five years there have been no spectacular advances in fundamental theory; rather there has been a consolidation of earlier experience in ab initio methodology and a more widespread use of existing methods in tackling problems of interest to more chemists in general, i.e. there have been many more applications to medium sized polyatomic molecules, usually employing minimal basis sets (MBS).

There have also been many more calculations in which geometry optimizations are carried out, and in which the basis sets in SCF calculations have been extended to DZ or DZ+ P quality, and more recently one sees an increasing use of methods which include at least some electron correlation, especially via configuration interaction (CI). Examples of the latter calculation were until recently restricted to molecules containing up to three atoms, but the recent development of efficient CI programmes had enabled these calculations to be carried out without too great expense on a variety of larger molecules, and this work is referred to later on in this Report.

In order that this Report be useful to non-specialists interested in earlier ab initio work in this area, it is useful to cite several reviews and books relevant to the subject matter of this chapter. The bibliography by Richards and co-workers has been updated to 1973, and contains a list of all the earlier ab initio calculations. The proceedings of the First International Congress on Quantum Chemistry, and that of a conference on 'Quantum Chemistry: The State of the Art', contain many review papers and survey many of the currently interesting areas in quantum chemistry. A volume devoted to theoretical chemistry has appeared in Series Two of the MTP International Review of Science, and an excellent survey of recent developments in molecular electronic structure theory by Schaefer has recently appeared. This review gives a more comprehensive list of books and reviews than is possible here. We should, however, mention that a comprehensive series of eight volumes on 'Modern Theoretical Chemistry' is starting to appear and this series in particular should give an up to date and comprehensive survey of ab initio calculations. We have also not attempted in this Report to survey the individual molecules containing five and six atoms which are studied usually together with the larger molecules in the series of papers from Pople's group. Recent reviews of this work have appeared and the reader is referred to these for further details and references. The general availability of the Gaussian 70 programme developed by Pople and co-workers (via the Quantum Chemistry Program Exchange has encouraged many non-specialists to venture into this field and to extend their investigations to larger molecules. However, it is important that such packages are not used in an uncritical way, and the limitations of the SCF procedure, and of minimal basis set calculations in certain instances, should be borne in mind. A recent book by Csizmadia is useful in this light, dealing with applications to organic molecules.

As in the previous Report, developments in theoretical and computational methods as such will not be dealt with. The results of calculations will usually be quoted in atomic units (distances/Bohr, energies[Hartree) but occasionally electron volts (eV) or kilojoules (kJ) for energies are used. A list of commonly used abbreviations is given at the beginning of this volume.

The calculations described are organized into sections defined by the general formulae of the species. This is to some extent an arbitrary division but serves to group together those molecules of similar geometrical structure. As mentioned above, discussion will be restricted usually to work carried out during the period 1973–6.

2 Molecules containing Five Atoms

These are divided into the following classes, where in a particular class we also consider the relevant charged species: H5, AH4, AB4, HAB3, H2NX, H2CNX, Nitrenes, Diazomethane, H2CXY, Carbonium ions, Miscellaneous penta-atomic molecules.

A. H5, H5+, and H5-. — The simplest penta-atomic molecule is H5+ and it has been the subject of several recent studies. The mass spectrum is well known and earlier work on the stability of this molecule is referred to in a paper by Huang et al.

These authors investigated several geometrical structures by either carrying out a VB calculation with CI, or by obtaining SCF wave functions using a flexible basis set. The VB-CI calculations showed no stability for H5+ in a D2a configuration (in contrast to previous predictions by Poshusta et al. and the authors concluded that the method is unreliable for this type of ionic system. However, the SCF calculations predict a binding energy of 0.007 Hartree (17.8 kJ mol-1) with an overall C2v symmetry. A more recent VB-CI study by Salmon and Poshusta used a more flexible basis set and gave similar results to the SCF calculations, and it is clear that polarization of the basis orbitals is very important in improving the VB results. Other calculations on H5+ and Hn+ (n < 15) have been reported, but the most extensive work to date is that of Ahlrichs, who used the PNO-CI and CEPA methods. Reviews of these methods have been given elsewhere, but essentially they go beyond the SCF–type wave function and include electron correlation. In the PNO-CI method, all doubly excited configurations in addition to the HF function are included, and the CEPA method also accounts for the effects of higher than doubly substituted configurations in an approximate way. For H5+ the two methods give very similar results.

In Ahlrichs' work, a large CGTO basis of lobe functions was used and the orbital exponents were carefully optimized so that the various different kinds of interaction such as ion-dipole,...