Molecular Orbitals and Organic Chemical Reactions

Ian Fleming

• Publisher: Wiley
• Year: 2011
• ISBN:
  9781119964650
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Physical & Theoretical Chemistry

Winner of the PROSE Award for Chemistry & Physics 2010

Acknowledging the very best in professional and scholarly publishing, the annual PROSE Awards recognise publishers' and authors' commitment to pioneering works of research and for contributing to the conception, production, and design of landmark works in their fields. Judged by peer publishers, librarians, and medical professionals, Wiley are pleased to congratulate Professor Ian Fleming, winner of the PROSE Award in Chemistry and Physics for Molecular Orbitals and Organic Chemical Reactions.

Molecular orbital theory is used by chemists to describe the arrangement of electrons in chemical structures. It is also a theory capable of giving some insight into the forces involved in the making and breaking of chemical bonds—the chemical reactions that are often the focus of an organic chemist's interest. Organic chemists with a serious interest in understanding and explaining their work usually express their ideas in molecular orbital terms, so much so that it is now an essential component of every organic chemist's skills to have some acquaintance with molecular orbital theory.

Molecular Orbitals and Organic Chemical Reactions is both a simplified account of molecular orbital theory and a review of its applications in organic chemistry; it provides a basic introduction to the subject and a wealth of illustrative examples. In this book molecular orbital theory is presented in a much simplified, and entirely non-mathematical language, accessible to every organic chemist, whether student or research worker, whether mathematically competent or not. Topics covered include:

• Molecular Orbital Theory
• Molecular Orbitals and the Structures of Organic Molecules
• Chemical Reactions — How Far and How Fast
• Ionic Reactions — Reactivity
• Ionic Reactions — Stereochemistry
• Pericyclic Reactions
• Radical Reactions
• Photochemical Reactions

Slides for lectures and presentations are available onthesupplementary website: www.wiley.com/go/fleming_student

Molecular Orbitals and Organic Chemical Reactions: Student Edition is an invaluable first textbook on this important subject for students of organic, physical organic and computational chemistry.

The Reference Edition edition takes the content and the same non-mathematical approach of the Student Edition, and adds extensive extra subject coverage, detail and over 1500 references. The additional material adds a deeper understanding of the models used, and includes a broader range of applications and case studies. Providing a complete in-depth reference for a more advanced audience, this edition will find a place on the bookshelves of researchers and advanced students of organic, physical organic and computational chemistry. Further information can be viewed here.

"These books are the result of years of work, which began as an attempt to write a second edition of my 1976 book Frontier Orbitals and Organic Chemical Reactions. I wanted to give a rather more thorough introduction to molecular orbitals, while maintaining my focus on the organic chemist who did not want a mathematical account, but still wanted to understand organic chemistry at a physical level. I'm delighted to win this prize, and hope a new generation of chemists will benefit from these books."
- Professor Ian Fleming

1

Molecular Orbital Theory

1.1 The Atomic Orbitals of a Hydrogen Atom

The spatial distribution of the electron in a hydrogen atom is usually expressed as a wave function ø where ø²dτ is the probability of finding the electron in the volume dτ, and the integral of ø²dτ over the whole of space is 1. The wave function is the underlying mathematical description, and it may be positive or negative. Only when squared does it correspond to anything with physical reality—the probability of finding an electron in any given space. Quantum theory gives us a number of permitted wave equations, but the one that matters here is the lowest in energy, in which the electron is in a 1s orbital. This is spherically symmetrical about the nucleus, with a maximum at the centre, and falling off rapidly, so that the probability of finding the electron within a sphere of radius 1.4 Å is 90% and within 2 Å better than 99%. This orbital is calculated to be 13.60 eV lower in energy than a completely separated electron and proton.

We need pictures to illustrate the electron distribution, and the most common is simply to draw a circle, Fig. 1.1a, which can be thought of as a section through a spherical contour, within which the electron would be found, say, 90% of the time. Fig. 1.1b is a section showing more contours and Fig. 1.1c is a section through a cloud, where one imagines blinking one’s eyes a very large number of times, and plotting the points at which the electron was at each blink. This picture contributes to the language often used, in which the electron population in a given volume of space is referred to as the electron density. Taking advantage of the spherical symmetry, we can also plot the fraction of the electron population outside a radius r against r, as in Fig. 1.2a, showing the rapid fall off of electron population with distance. The van der Waals radius at 1.2 Å has no theoretical significance—it is an empirical measurement from solid-state structures, being one-half of the distance apart of the hydrogen atoms in the C—H bonds of adjacent molecules. It is an average of several measurements. Yet another way to appreciate the electron distribution is to look at the radial density, where we plot the probability of finding the electron between one sphere of radius r and another of radius r + dr. This has the form, Fig. 1.2b, with a maximum 0.529 Å from the nucleus, showing that, in spite of the wave function being at a maximum at the nucleus, the chance of finding an electron precisely there is very small. The distance 0.529 Å proves to be the same as the radius calculated for the orbit of an electron in the early but untenable planetary model of a hydrogen atom. It is called the Bohr radius a₀, and is often used as a unit of length in molecular orbital calculations.

Fig. 1.1 The 1s atomic orbital of a hydrogen atom

Fig. 1.2 Radial probability plots for the 1s orbital of a hydrogen atom

1.2 Molecules made from Hydrogen Atoms

1.2.1 The H₂ Molecule

To understand the bonding in a hydrogen molecule, we have to see what happens when the atoms are close enough for their atomic orbitals to interact. We need a description of the electron distribution over the whole molecule. We accept that a first approximation has the two atoms remaining more or less unchanged, so that the description of the molecule will resemble the sum of the two isolated atoms. Thus we combine the two atomic orbitals in a linear combination expressed in Equation 1.1, where the function which describes the new electron distribution, the molecular orbital, is called σ and ø₁ and ø₂ are the atomic 1s wave functions on atoms 1 and 2.

1.1

The coefficients, c₁ and c₂, are a measure of the contribution which the atomic orbital is making to the molecular orbital. They are of course equal in magnitude in this case, since the two atoms are the same, but they may be positive or negative. To obtain the electron distribution, we square the function in Equation 1.1, which is written in two ways in Equation 1.2.

1.2

Taking the expanded version, we can see that the molecular orbital σ² differs from the superposition of the two atomic orbitals (c₁ø₁)² + (c₂ø₂)² by the term 2c₁ø₁c2ø₂. Thus we have two solutions (Fig. 1.3). In the first, both c₁ and c₂ are positive, with orbitals of the same sign placed next to each other; the electron population between the two atoms is increased (shaded area), and hence the negative charge which these electrons carry attracts the two positively charged nuclei. This results in a lowering in energy and is illustrated in Fig. 1.3, where the bold horizontal line next to the drawing of this orbital is placed low on the diagram. Alternatively, c₁ and c₂ are of opposite sign, and we represent the sign change by shading one of the orbitals, calling the plane which divides the function at the sign change a node. If there were any electrons in this orbital, the reduced electron population between the nuclei would lead to repulsion between them and a raised energy for this orbital. In summary, by making a bond between two hydrogen atoms, we create two new orbitals, σ and σ*, which we call the molecular orbitals; the former is bonding and the latter antibonding (an asterisk generally signifies an antibonding orbital). In the ground state of the molecule, the two electrons will be in the orbital labelled σ. There is, therefore, when we make a bond, a lowering of energy equal to twice the value of E_σ in Fig. 1.3 (twice the value, because there are two electrons in the bonding orbital).

Fig. 1.3 The molecular orbitals of the hydrogen molecule

The force holding the two atoms together is obviously dependent upon the extent of the overlap in the bonding orbital. If we bring the two 1s orbitals from a position where there is essentially no overlap at 2.5 Å through the bonding arrangement to superimposition, the extent ...

Table of contents

• Cover
• Title
• Copyright
• Preface
• 1: Molecular Orbital Theory
• 2: The Structures of Organic Molecules
• 3: Chemical Reactions—How Far and How Fast
• 4: Ionic Reactions—Reactivity
• 5: Ionic Reactions—Stereochemistry
• 6: Thermal Pericyclic Reactions
• 7: Radical Reactions
• 8: Photochemical Reactions
• References
• Index