Quantum Chemistry

An Introduction

Michael Springborg, Meijuan Zhou

• Publisher: De Gruyter
• Year: 2021
• Print ISBN: 9783110742190
• eBook ISBN: 9783110742237
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Chemistry
• Index: Chemistry

This textbook introduces the reader to quantum theory and quantum chemistry. The textbook is meant for 2 nd – 3 rd year bachelor students of chemistry or physics, but also for students of related disciplines like materials science, pharmacy, and bioinformatics.

At first, quantum theory is introduced, starting with experimental results that made it inevitable to go beyond classical physics. Subsequently, the Schrödinger equation is discussed in some detail. Some few examples for which the Schrödinger equation can be solved exactly are treated with special emphasis on relating the results to real systems and interpreting the mathematical results in terms of experimental observations.

Ultimately, approximate methods are presented that are used when applying quantum theory in the field of quantum chemistry for the study of real systems like atoms, molecules, and crystals. Both the foundations for the different methods and a broader range of examples of their applications are presented.

The textbook assumes no prior knowledge in quantum theory. Moreover, special emphasis is put on interpreting the mathematical results and less on an exact mathematical derivations of those. Finally, each chapter closes with a number of questions and exercises that help in focusing on the main results of the chapter. Many of the exercises include answers.

1 What is quantum theory?

1.1 Classical physics

The quantum theory, together with the theory of relativity, is one of the two most important developments in physics during the 20th century. The quantum theory is important when considering objects that are very small (e. g., electrons and atoms), while the relativity theory becomes important when the objects move very fast. In both cases, phenomena occur that are different from what we are experiencing in our everyday life. The book of George Gamow, Mr. Tompkins in Wonderland can be recommended for the interested readers. This book describes what the world would look if either quantum effects or relativistic effects were noticeable in our everyday life. The book is written as an entertainment, and the author who also was a very capable scientist, has been able to present science to the educated layman.

Before these two theories were developed, the situation in the second half-part of the 19th century has often been compared with our present situation. One was largely convinced that all important physical laws were understood, and one needed “only” to apply these on all sorts of issues. That everything would change within few years was not considered possible. Whether we will soon experience another, similar revolution in the natural sciences is an open question.

Here, we shall briefly discuss some concepts of classical physics, which are not always valid with the introduction of quantum theory. “Not always” means that classical physics must be regarded as sufficiently accurate when it comes to macroscopic objects, e. g., when sending a rocket to the moon.

According to classical physics:

• Position and momentum coordinates are independent of each other and can have arbitrary values.
• If one knows the position and momentum of an object at a certain point in time, as well as all forces acting on the object, the position and momentum coordinates at any later time, in principle, can be computed with any precision.
• The energy of an object can take any value.
• A part of physics deals with bodies, while another part deals with waves. The two parts have little to do with each other.

We shall now see how experimental and theoretical results led to questioning these statements.

1.2 Black-body radiation

A black body with a certain temperature emits electromagnetic radiation (see Figure 1.1). This radiation is composed of radiation with all possible wavelengths λ and the whole spectrum depends on the temperature of the body, as shown in Figure 1.2. This effect is already known from everyday life. When you turn on a hearth, it becomes increasingly hot, and thereby its color changes from black to red, and even later to orange and yellow.

Figure 1.1 Schematic representation of the radiation of a black body. From the surface of the internal cavity of the body, radiation (photons) is emitted, which is brought into thermal equilibrium with the black body through multiple reflections at the surface before it emerges through a small opening. Ultimately, the intensity of the emitted radiation can be measured as a function of the wavelength.

Figure 1.2 The radiation of a black body as measured experimentally at two different temperatures. Adapted from the book of Peter W. Atkins, Kurzlehrbuch Physikalische Chemie, Wiley-VCH, 2001.

According to Wilhelm Wien, the wavelength ${\mathit{\lambda }}_{\max }$, at which the spectrum h...

Table of contents

• Title Page
• Copyright
• Contents
• 1 What is quantum theory?
• 2 Basics of quantum theory
• 3 Operators and quantum theory
• 4 Particle in a box
• 5 More or less free particles
• 6 Vibrations
• 7 Rotations
• 8 The hydrogen atom
• 9 Foundations of the approximate methods
• 10 The orbital model
• 11 Atoms
• 12 The smallest molecules
• 13 Other diatomic molecules
• 14 Larger systems: methods
• 15 Larger systems: applications
• 16 Supporting information
• 17 Mathematical formulas
• Subject Index