Quantum Chemistry

Citation

McQuarrie, D. A. (2007). Quantum Chemistry (2nd ed.). University Science Books.

Chapter Summary

The book runs to about 690 pages. It has twelve chapters, eight short "MathChapters" (A to H) placed between them, an answers section for numerical problems and an index. Each chapter carries a broad range of problems and exercises.

Chapter 1: The Dawn of the Quantum Theory

The opening chapter introduces the quantum theory through its historical beginnings, setting up the need for a new mechanics before any wave equation appears. MathChapter A (Complex Numbers) follows immediately.

Chapter 2: The Classical Wave Equation

A classical wave equation is treated first, as preparation for the Schrödinger equation. MathChapter B (Probability and Statistics) follows.

Chapter 3: The Schrödinger Equation and a Particle in a Box

The Schrödinger equation is introduced and applied to the particle in a box, the first exactly solvable model. MathChapter C (Vectors) follows.

Chapter 4: The Postulates and General Principles of Quantum Mechanics

The formal framework is stated as postulates, together with the general principles that govern operators and measurements. MathChapter D (Series and Limits) follows.

Chapters 5–6: The Harmonic Oscillator and Vibrational Spectroscopy; The Rigid Rotator and Rotational Spectroscopy

These two chapters pair a model system with the spectroscopy it explains: vibration with the harmonic oscillator, rotation with the rigid rotator. The publisher notes that molecular spectroscopy is now discussed throughout these chapters. MathChapter E (Spherical Coordinates) sits between them and MathChapter F (Determinants) follows Chapter 6.

Chapter 7: The Hydrogen Atom

The hydrogen atom has its own chapter, with its electronic spectroscopy discussed there according to the publisher. MathChapter G (Matrices) follows.

Chapter 8: Approximation Methods

Approximation methods are presented as the route to systems that cannot be solved exactly. MathChapter H (Matrix Eigenvalue Problems) follows.

Chapter 9: Many-Electron Atoms

A chapter devoted entirely to atoms with more than one electron. The publisher describes a step-by-step self-consistent-field calculation for the helium atom here, and a website of Hartree-Fock atomic orbitals that is used to calculate properties of multielectron atoms.

Chapters 10–11: The Chemical Bond: One- and Two-Electron Molecules; Qualitative Theory of Chemical Bonding

Chapter 10 moves from atoms to molecules, with a step-by-step self-consistent-field calculation for the hydrogen molecule. Chapter 11 turns to a qualitative theory of bonding.

Chapter 12: The Hartree–Fock–Roothaan Method

The final chapter is devoted to the Hartree-Fock method and post-Hartree-Fock methods for calculating molecular properties. According to the publisher it introduces Gaussian orbitals and the notation used to label calculations (such as HF/STO-6G and HF/6-31G**), and its closing sections treat configuration interaction, coupled-cluster theory and density functional theory at a semi-quantitative level.

Key Concepts

Chapters 1–4: Foundations

• Quantum theory's origins: the experimental and historical reasons classical mechanics had to be replaced.
• Schrödinger equation: the wave equation whose solutions describe a quantum system, first applied to the particle in a box.
• Postulates of quantum mechanics: the formal rules relating states, operators and measured values.

Chapters 5–8: Model systems and approximation

• Harmonic oscillator and rigid rotator: the model systems for vibration and rotation, tied to vibrational and rotational spectroscopy.
• Hydrogen atom: the exactly solvable atom and its electronic spectroscopy.
• Approximation methods: techniques for systems without an exact solution.

Chapters 9–12: Atoms, bonds and computation

• Many-electron atoms: atomic structure beyond hydrogen, with self-consistent-field calculation.
• Chemical bond: the treatment of one- and two-electron molecules, then qualitative bonding theory.
• Hartree–Fock–Roothaan method: the basis of modern molecular calculations, with Gaussian orbitals and the post-Hartree-Fock methods that build on it.

Critical Analysis

Strengths

• Mathematics is handled separately. The MathChapters are short interchapters placed through the book so that students can concentrate on the physical principles. They cover complex numbers, probability and statistics, vectors, series and limits, spherical coordinates, determinants, matrices and matrix eigenvalue problems, each at the point where it is first needed.
• Low stated prerequisite. The publisher's description states a prerequisite of one year of calculus and no required knowledge of differential equations, which makes the text reachable from a standard chemistry background.
• Modern computation is built in. The second edition adds worked self-consistent-field calculations for helium and hydrogen, a chapter on Hartree-Fock and beyond, and problems that use computational chemistry programs and the NIST website of experimental and ab initio data.
• Spectroscopy is tied to the models. Vibrational and rotational spectroscopy are developed in the same chapters as the harmonic oscillator and rigid rotator, and hydrogen's electronic spectrum is treated in its own chapter.

Limitations

• Scope is the core of quantum chemistry only. The chapter list ends with the Hartree-Fock-Roothaan method; configuration interaction, coupled-cluster theory and density functional theory are covered only "at least semi-quantitatively" in the closing sections, so computational practice needs another source.
• No chapter on molecular symmetry or group theory appears in the contents. Readers whose course covers these must look elsewhere.
• Length. At about 690 pages with twelve chapters plus eight MathChapters, a single semester is unlikely to cover all of it.

Where It Fits in the Course

Among the course's books, McQuarrie is the full, self-contained development of quantum mechanics for chemists. Engel and Reid's Physical Chemistry: Quantum Chemistry and Spectroscopy is one volume of an undergraduate physical chemistry course that goes from quantum theory's origins through atoms and molecules to spectroscopy, which makes it the comparable alternative inside a physical chemistry sequence. Thakkar's Quantum Chemistry: A Concise Introduction is a short, idea-centred text for readers who will use spectroscopy and calculations rather than develop the theory, and is a lighter first pass before McQuarrie.

Jensen's Introduction to Computational Chemistry continues where McQuarrie's last chapter stops, and is the natural follow-on for the calculation methods McQuarrie only introduces. Pavia's Introduction to Spectroscopy and Silverstein's Spectrometric Identification of Organic Compounds address a different job, identifying organic structures from spectra, and complement McQuarrie's theory of why molecules have the spectra they do.

How to Use This Book

The text suits students who have completed a year of calculus and want a full treatment of quantum mechanics as used in chemistry, whether in an advanced undergraduate or a first graduate course. Differential equations are not required beforehand.

A practical plan:

• Core: Chapters 1 to 4 in order, then Chapters 5 to 7 for the three standard exactly solvable systems.
• Mathematics on demand: read each MathChapter when the chapter it follows needs it, and skip those that are already familiar.
• Atoms and molecules: Chapters 8 to 11 give the approximation methods and the first applications to atoms and bonds.
• Computation: Chapter 12 is the entry point to molecular calculations; pair it with the book's problems that use a computational chemistry program and the NIST data website.

Work the problems as the course proceeds, since each chapter has a wide range, and check numerical results against the answers section at the back of the book.