Quantum Chemistry: A Concise Introduction for Students of Physics, Chemistry, Biochemistry and Materials Science

Citation

Thakkar, A. J. (2021). Quantum Chemistry: A Concise Introduction for Students of Physics, Chemistry, Biochemistry and Materials Science (3rd ed.). IOP Publishing.

Chapter Summary

This is a short book: retail listings give about 165–172 pages for eleven chapters and six appendices, preceded by "A note to the student", a preface and the author's biography. The publisher presents it both as a text for second- or third-year undergraduates and as a quick introduction or refresher for researchers, and says its emphasis is on explaining ideas rather than enumerating facts or procedural detail. The third edition grew from ten chapters to eleven: the publisher lists new material on the time-dependent Schrödinger equation, correlated wave-function methods and density functional theory (DFT), more problems, an introduction to computational quantum chemistry and lists of resources. Section headings below that are quoted from the second edition (2017) indicate what the chapters covered then; the third edition's sections may differ.

Chapter 1: Molecular symmetry

The book opens with symmetry rather than quantum mechanics. In the second edition the chapter covered symmetry operations and elements, the classification of molecular symmetry and the implications of symmetry. The publisher calls the first two chapters the keystone of the book.

Chapter 2: Basic quantum mechanics

The postulates: in the second edition, wave functions as descriptions of a system's state, operators for observables, Schrödinger's equation, and measured and average values. The time-dependent Schrödinger equation is among the material the publisher lists as new in the third edition.

Chapters 3–5: Translation and vibration; Symmetry and degeneracy; Rotational motion

Three chapters of simple models that, in the publisher's words, underlie molecular spectroscopy and statistical thermodynamics, with symmetry woven through them. In the second edition they covered a particle in a wire and the harmonic oscillator; a particle in a rectangular plate, how symmetry leads to degeneracy and the symmetry of wave functions; and a particle on a ring, a particle on a sphere and the rigid rotor.

Chapter 6: Electronic motion: the hydrogen atom

The electronic structure of the hydrogen atom. The second-edition version began with the Born–Oppenheimer approximation and the electronic Hamiltonian before solving the hydrogen atom and hydrogen-like ions.

Chapter 7: A molecular prototype: the hydrogen molecular-ion

The simplest molecule. The second edition used it to introduce the LCAO model and potential energy curves, the variation method, force constants and dissociation energy, and excited states.

Chapter 8: A mean field model for many-electron systems

Having studied the one-electron prototypes, the reader turns to the ideas used for many-electron atoms and molecules. The second-edition chapter, then called "Many-electron systems", moved from the helium atom through spin and the Pauli postulate, electron densities and the Hartree–Fock model to atoms, diatomic molecules and the Kohn–Sham model.

Chapter 9: The Hückel model

Qualitative molecular orbital theory for conjugated hydrocarbons. In the second edition this covered cumulenes, annulenes and other planar conjugated hydrocarbons, charges, bond orders and reactivity, and closed with a section on why the Hückel model is not quantitative.

Chapter 10: Handling electron correlation

A chapter new to the third edition, consistent with the publisher's note on new material on correlated wave-function methods and DFT; its contents are not published in section-level detail.

Chapter 11: Computational quantum chemistry

The publisher describes the final part as an introduction to computational methods and the "bare minimum" of technical choices needed to run meaningful electronic-structure calculations with quantum chemistry software. In the second edition the corresponding chapter covered practical calculations, post-Hartree–Fock methods, Kohn–Sham DFT calculations and choosing a basis set.

Appendices A–F

Systems with time-independent potentials; perturbation theory; solving the matrix Hartree–Fock equations; reference material; problem hints and solutions; and resources for study and exploration.

Key Concepts

Chapters 1–2: Symmetry and the postulates

• Symmetry operations and point groups: the operations that leave a molecule unchanged and the classification of molecules by them, used throughout the book.
• Wave functions and operators: the state of a system and the operators that represent observable quantities.
• Schrödinger's equation: the equation whose solutions give the allowed states and energies.

Chapters 3–5: Model systems

• Particle in a box, harmonic oscillator, rigid rotor: the simple models behind translational, vibrational and rotational energy levels.
• Degeneracy: equal energies for different states, which the book connects directly to symmetry.

Chapters 6–9: Atoms, molecules and orbitals

• Born–Oppenheimer approximation: separating electronic from nuclear motion, which makes potential energy curves possible.
• LCAO and the variation method: building molecular orbitals from atomic orbitals and optimizing them by minimizing the energy.
• Hartree–Fock (mean field) model: treating each electron as moving in the average field of the others.
• Hückel model: a simple, qualitative molecular-orbital method for conjugated π systems.

Chapters 10–11: Beyond mean field and computation

• Electron correlation: what the mean-field model leaves out, addressed by correlated wave-function methods and DFT.
• Basis sets and method choice: the technical choices needed to run a meaningful calculation with standard software.

Critical Analysis

Strengths

• Short and focused on ideas. At under two hundred pages, the book can be read alongside a course rather than instead of one. The publisher's stated emphasis is on concepts, not procedural detail, for "novice users" of spectroscopy and electronic-structure software.
• Symmetry first. Starting with molecular symmetry and linking it to degeneracy and wave-function symmetry in Chapter 4 gives chemists a framework that the later chapters keep using, from degenerate energy levels to molecular orbitals.
• Leads to practice. The final chapter is aimed at people who will actually run quantum chemistry programs, explaining the choices of method and basis set rather than the algorithms, and the new resources appendix points to further print and online material.
• Supports self-study. Appendix E gives hints and solutions to the problems, which the third edition expanded.

Limitations

• Concise means selective. Each chapter is short (in the first and second editions the chapters ran from about seven to fourteen pages), so derivations and worked examples are limited; students who need full mathematical development will need a longer text.
• Little spectroscopy as such. The models underlying spectroscopy are covered, and perturbation theory is relegated to an appendix, but the table of contents has no chapters on spectroscopic techniques or selection rules; it does not replace a spectroscopy text.
• No published review found. No independent review of the third edition was located, so the publisher's description is the main evidence for the book's approach.

Where It Fits in the Course

Within this course Thakkar serves as the compact conceptual introduction. Engel and Reid's Physical Chemistry: Quantum Chemistry and Spectroscopy is a full physical chemistry textbook on the same subjects with extensive spectroscopy; McQuarrie's Quantum Chemistry is a longer, mathematically detailed treatment for students who want derivations. Thakkar can be read before either as a map of the subject, or alongside them as a short summary of the ideas.

Frank Jensen's Introduction to Computational Chemistry is a graduate-level account of the methods that Thakkar's last two chapters introduce, and a natural next step for anyone who will run calculations. Pavia and co-authors' Introduction to Spectroscopy and Silverstein and co-authors' Spectrometric Identification of Organic Compounds are practical texts on interpreting spectra for structure determination; they use spectroscopy rather than explain its quantum basis, so they pair with Thakkar's Chapters 3–5 rather than overlapping.

How to Use This Book

The book suits second- or third-year undergraduates in chemistry, biochemistry, materials science and physics, and researchers who use spectroscopy or electronic-structure software and want the underlying concepts. It assumes calculus and some comfort with vectors and matrices; Appendix D collects reference material.

A practical plan:

• Core: Chapters 1–2, then Chapters 3–5 as one block on model systems, then Chapters 6–8 on atoms, the hydrogen molecular-ion and the mean-field model. These chapters carry the book's argument and should be read in order, because symmetry from Chapter 1 returns throughout.
• Organic and qualitative bonding: Chapter 9 on the Hückel model for students who mainly need π-orbital reasoning.
• Toward computation: Chapters 10–11 for anyone who will run calculations, followed by Jensen or software documentation; Appendix C shows how the matrix Hartree–Fock equations are solved.
• Supporting material: Appendices A and B on time-independent potentials and perturbation theory for students taking a course that uses them.

Work the problems before checking the hints and solutions in Appendix E. Because the book is concise, keep a longer textbook at hand for derivations, and use the resources listed in Appendix F to explore further.