Quantum Chemistry

The following sections are included:

• Contents

• Preface to the Second Edition

• Preface

• Acknowledgments¹

The theory of the electronic structure of molecules is like many problems in science; the basic laws underlying the problem are very well known, but the way in which these laws are to be applied to yield results which are meaningful in a particular context is not obvious. This situation is, perhaps, most familiar in the application of Newton’s mechanics to the motions of the solar system. Just as it is not possible to predict the number of satellites which actually orbit Jupiter, we cannot obtain a description of the electronic structures of molecules solely from the basic laws; we must supply additional ideas from a knowledge of the chemistry involved. The main idea used here is the breakdown of the overall system into a series of interacting sub-systems.

The last chapter showed that we need to know something of the electron distributions in atoms and something of the way in which atoms are joined by chemical bonds before we can make a start on any theory of the electronic structure of molecules. This chapter lists what we should know and how that knowledge can be put to use in a theory of chemical bonding.

Now is the time to put together the general ideas from Chapter 1 about choosing the most appropriate overall structure for a molecule and the ideas we have reviewed in the previous chapter about atomic and molecular electronic structure.

The effect of the Pauli principle, which has been given in its simplest form on page 41:

When a many-electron system is described by

electrons occupying orbitals, no more than two

electrons may occupy any one orbital,

is important throughout the theory of molecular electronic structure. The Pauli principle is a decisive factor in the theory of the electronic structure of molecules and needs more careful consideration than this simple statement. What needs to be done is to explain how and why the Pauli principle causes the saturation of bonding: why the valence of an atom is not the same as its atomic number, i.e. why the valence of carbon is generally four, not six, and of helium is zero, not two.

Rather than proceed to considerations of the bonding in other diatomic molecules which have more complex bonding patterns, this chapter looks at perhaps the most important generalisation of the ideas developed so far: the electronic structure and bonding in polyatomic molecules. The simplest of these is the ‘fundamental’ organic molecule methane, CH₄. The theory of the bonding in homonuclear and heteronuclear diatomics — which involve new types of bond — is deferred until Chapter 9.

The theory developed so far explains only the bonding pattern and shapes of molecules whose electronic structure consists of just two types of substructure: atomic cores and single bonds. This is not enough. The idea of a ‘lone pair’ of electrons is all-pervasive as a factor in the theory of the shapes and reactivities of molecules. It proves to be just as necessary to understand the effect that bond formation has on the ‘non-bonding’ electrons of atoms as it is to have a theory of how chemical bonds form.

So far, we have looked at only three types of electronic substructure occurring in molecules: atomic cores, single bonds and lone pairs. There are a lot more to be investigated. We must, therefore, continue our investigation of the different types of environment-insensitive electronic substructures in molecules. In some ways, a consideration of the presence of multiple bonds in polyatomic molecules is easier and more direct than the approach of the problem through diatomics. The rather exceptional high (cylindrical) symmetry of diatomic molecules complicates matters rather than simplifying them. There is, for example, no diatomic molecule in which there is a typical double bond of the type found in thousands of organic molecules: two bond pairs. Also, of course, along with lone pairs, it is the existence of multiple bonds in organic molecules which gives them their interesting and valuable chemical properties. We must, therefore, take a careful look at double and triple bonds in organic molecules.

Many of the simple molecules that we have discussed so far are symmetrical in the sense that, in the molecule, there are atoms which are in identical environments: the H atoms in CH₄, the H atoms in NH₃, the C atoms in C₂H₄, for example. In the ethene and methanal molecules of the last chapter, in both cases as well as the H atoms in the molecules having identical environments, the molecules are planar; this is another type of symmetry in the molecule (the molecule N₂H₄, for example, is not planar). Some accounts of the electronic structure of molecules make much use of elements of molecular symmetry. We need to make at least a short examination of symmetry in the molecular context.

A discussion of the electronic structure of ‘simple’ diatomic molecules — those composed of the atoms H through F — has been put off for long enough by saying that their structure is not typical. This chapter considers the possible molecules of the type X₂, where X is one of Be, B, C, N and O, and a slight diversion into the structure of the CO molecule. Some comparisons are made with the considerations of Chapter 7, where multiple bonds in organic compounds were discussed, and Chapter 8, where some of the implications of molecular symmetry were introduced. There is an important lesson to be learned from this excursion outside the domain of ‘typical’ polyatomic molecules.

We saw at the end of Chapter 6 that lone pairs of electrons will be expected to undergo changes when given the chance to be attracted to positive ions or regions of positive potential. In this chapter we look at the consequences of this simple fact. We shall see that some of the simplest and most familiar chemical reactions — the ‘everyday’ ones, so familiar that we forget that they are chemical reactions — involve the formation of dative bonds.

So far all the environment-insensitive electronic substructures we have met have been groups of electron pairs of various types: inner shells, bond pairs and lone pairs. A closer look at some organic molecules reveals that we must broaden our outlook and admit substructures with more than two electrons to our collection.

The concepts and methods developed so far provide most of the tools required to understand the environment-insensitive substructures to be found in the vast majority of organic molecules. The question is: ‘can these methods be relied upon to explain the complexities found in the world of inorganic chemistry?’ Organic and inorganic chemistry both deal with complicated molecules, but these molecules are complicated in very different ways: organic molecules are complicated because of the vast number of combinations and permutations of a relatively simple set of electronic substructures; inorganic molecules tend to contain more complicated individual electronic structures.

All the discussion so far has concentrated on trying to explain the chemical bonds in molecules formed from the atoms H through F, the very ‘top’ of the periodic table. It should be the case that the same or similar arguments will apply to molecules containing atoms from ‘lower down’ the table, since we have concentrated on explanations involving the physical laws underlying the processes occurring on bonding, rather than rules involving the manipulation of orbitals. However, there are important differences between the electronic structures of atoms in the progression down any column of the periodic table. These differences are principally due to the fact that as the atomic number increases going down a column, the valence electrons are less tightly bound, and this has some important effects on their valence properties, since the valence of an atom is determined by how easy it is to polarise and share its electrons.

The last two chapters have shown that the first of the simple rules developed to describe the valence of atoms — the octet rule — has only a limited application and cannot, therefore, be considered as a guide to likely molecular structures. Of course, the octet rule was proposed long before there was any clear understanding of the laws which govern the distribution of electrons. This chapter addresses some of the problems with this type of empirical rule revealed by the phenomenon of hypervalence and variable valence.

No-one should ever imagine that the behaviour of nature can be explained by means of a few simple rules. All science is ‘abstract’, in the sense that it can only deal with typical cases, and nature provides us with constant surprises with brand new ‘typical cases’ all the time as well as exceptions to the typical cases. The most important exception to the ‘electron-pair’ model is, of course, the delocalised π system of Chapter 11. Here are a few which we did not think about earlier.

The ‘transition’ metals are so called because they interrupt the sedate progression in the periodic table through groups of just eight elements. They are a different type of atom from both the non-metals and the metals of the rest of the periodic table. In the case of the typical¹ elements there is an abrupt change in chemical properties with atomic number, i.e. each additional electron. In the transition elements this sudden change in properties is replaced by a gradual change from metal to metal, reflecting their different type of atomic electronic structure. Naturally, this means that molecules containing the transition metals will exhibit some properties which we have not met so far and the relationship among the properties of these elements will be different from those of the typical elements. It is important to emphasise, however, that, at the moment, there is no coherent qualitative theory of the bonding in transition-metal molecules.

The electronic structure of matter is a very complex subject, and what has been attempted in this work is basically an approach in which the physical interpretation of the results of the application of Schröodinger’s mechanics (quantum theory) is at the forefront. There is much work still to be done, particularly in the inorganic chemistry area where, as yet, only the barest outline is possible. This chapter describes some areas which have been deliberately omitted so far, and tries to draw together the ideas which have proved fruitful in the study.

The following sections are included:

• Appendix H The Pauli Principle, ‘Spin’ and Electron Repulsion
  • Pauli and Electron Interactions
  • Effects of Electron ‘Spin’
  • Three Types of Spin Alignment

• Appendix I A Note About ‘Unoccupied’ MOs

• Help with the Assignments

• Index