Some molecular orbital calculations of the potential energy surfaces of organic molecules

In this thesis, molecular orbital calculations are used to study a variety of organic reactions, most of which involve molecules containing a large number of atoms. The purpose of the investigation is to elucidate the factors which bring about the stereospecificity found in certain acyclic reactions and to try and relate these factors, if possible, to those that operate in stereospecific pericyclic reactions.
Chapter 1. Molecular Orbital Theory and Organic Reactions.
The application of molecular orbital theory to organic chemistry is a relatively recent phenomenon. One area in particular that has been studied is that class of reactions known as pericyclic reactions. The various concepts and theories that have been used to explain the preferred modes of reactions are reported in this Chapter. The few calculations and simple theories that have been put forward to describe aspects of the complementary field of acyclic reactions are then enunciated. Finally a simple theory based on the use of Hückel molecular orbital theory is proposed, which seeks to explain the known confomnational preferences of a large number of acyclic reactions.
Chapter 2. Theoretical Methods.
In this Chapter, a summary of molecular orbital procedures is given, including descriptions of both ab initio and semiempirical methods. The relative advantages and disadvantages of the various approaches are discussed, especially in relation to the type of problems that are involved. The MINDO/2 semiempirical program is described in detail, as is the particular version used (OPTMO) for a large proportion of the work in thesis. Further details of the molecular orbital programs are given in an Appendix.
Chapter 3. Stereospecificity in Organic Reactions.
As a first step in testing the validity of the proposed simple Hückel theory of acyclic reactions, ab initio perturbational calculations are performed on allyl and butadiene species containing varying numbers of electrons. However difficulties are encountered in interpreting the results of the sophisticated calculations and relating them to the simple model. A variety of bonding indices are considered and used. It is decided that the only reliable method of analysis must first partition the total energy into uni- and multicentre terms, in order to discover the precise origin(s) of increased stability in a particular intermediate/transition state(T.S.) A means of carrying this out, within the context of the MINDO approximation, is described.
With this as the basis for investigation, simple models for the SN2 and SE2 reactions are studied. It is found that although certain 2-centre energy terms (i.e. bonding terms between 'non-bonded' atoms) stabilise the preferred geometry-optimised intermediate, as predicted by the simple theory, the decisive terms are several 1-centre energy terms. The origin of these terms cannot be explained by the simple theory.
In order to discover how these terms might arise, symmetrical models are examined, with geometries in between those of the two intermediates/T.S.s. These models are distorted by small amounts, towards the two intermediates, and the resulting changes are analysed in terms of perturbation theory. It was observed that inter-molecular orbital mixing is greater for the distortion towards the preferred intermediate and that this increased mixing can account completely for the difference in the energy changes of the two distortions. This differential mixing is also found to persist in the intermediates themselves. In particular, HOMOπ - LUMOσ* electron transfer is paramount.
Similarly, geometry-optimised models and symmetrical 'intermediate' models are studied for the SN2′ and SE2′ reactions. Again the symmetrical models are distorted towards the final intermediates. Now both HOMOπ - LUMOσ* and, to a lesser extent, HOMOσ - LUMOπ* electron transfer are of decisive importance in the distortions towards the preferred intermediates. (MB. There were no π* orbitals for the previous models). The qualitative magnitude of HOMO-LUMO, σ/π, mixings can be predicted from the symmetrical 'intermediate' models, simply by con- sideration of the symmetries of the borderline MOs with respect to the symmetry elements maintained during the distortions.
These conclusions provide the basis for the study of a variety of stereospecific reactions. Elimination reactions and the backbone rearrangement are examined using symmetrical 'intermediate' models. In all cases HOMO-LUMO, σ/π, considerations lead to the correct prediction for reaction preference, even when the incoming and leaving groups are not identical. Pericyclic reactions are also considered in the same manner and again the allowed modes of reaction are correctly predicted by HOMO/LUMO considerations.
The dangers of indiscriminate use of simple theories are shown in the study of the 'SN2 type' reaction of hydroxide ion with ethylene oxide (to give ethylene glycoxide). The energy partitioning method shows that this is not a simple 'SN2 type reaction' and hence it comes as no surprise to find that HOMO/LUMO considerations are not applicable here. This in fact underlines the inadequacies of the simple Hückel theory for the explanation and prediction of conformational preference. However it might still be applicable in order to differentiate between configurational isomers. This possibility is briefly examined and ideas for further study in this direction are suggested.
Finally several points of general interest are discussed, including the relevance of calculations on isolated molecules to chemical reactions in solution and the factors which determine the extent of orbital mixing. A simple perturbational model applicable to many acyclic organic reactions is then advanced, which leads to the same predictions and similar explanations as the more detailed calculations had produced. It also has the advantage of being closely related to the previous treatments of pericyclic reactions. The determining factor in both cases is found to be the total number of mobile electrons involved in the 'decisive' parts of the transition states/intermediates.