Introduction to Computational Chemistry

Citation

Jensen, F. (2017). Introduction to Computational Chemistry (3rd ed.). John Wiley & Sons.

Chapter Summary

The third edition has 18 chapters, a short concluding chapter and five appendices in about 670 pages. Wiley describes it as a comprehensive account of the fundamental principles behind the different computational methods. The opening chapter states the book's aim: to put the variety of modern methods in perspective so that a reader can judge which problems benefit from calculation, choose a suitable level of theory and assess the quality of the result.

Chapter 1: Introduction

Surveys the fundamental issues (describing a system, the fundamental forces, the dynamical equation and how to solve it, separation of variables) and sets classical mechanics, quantum mechanics and chemistry side by side.

Chapters 2–3: Force Field Methods; Hartree–Fock Theory

Chapter 2 covers the force field energy, parameterization, differences among atomistic force fields, water models, coarse-grained force fields, validation, transition structure modeling and hybrid force field/electronic structure methods. Chapter 3 begins the quantum treatment with the adiabatic and Born–Oppenheimer approximations, the energy of a Slater determinant, Koopmans' theorem, the basis set approximation, restricted and unrestricted Hartree–Fock, SCF techniques and periodic systems.

Chapters 4–6: Electron Correlation Methods; Basis Sets; Density Functional Methods

Chapter 4 covers configuration interaction, multiconfiguration SCF, many-body perturbation theory, coupled cluster, methods using the interelectronic distance, efficiency techniques, excited states and quantum Monte Carlo. Chapter 5 treats Slater- and Gaussian-type orbitals, the classification and construction of basis sets, plane waves, effective core potentials, basis set extrapolation and basis set superposition error. Chapter 6 covers Kohn–Sham theory, exchange–correlation holes and functionals, their performance, differences from Hartree–Fock, time-dependent DFT and known DFT problems.

Chapters 7–9: Semi-empirical Methods; Valence Bond Methods; Relativistic Methods

Chapter 7 covers NDDO, INDO and CNDO approximations, parameterization, Hückel theory and tight-binding DFT. Chapter 8 treats classical, spin-coupled and generalized valence bond theory. Chapter 9 introduces the Dirac equation, relativistic many-particle treatments and four- and two-component calculations.

Chapters 10–12: Wave Function Analysis; Molecular Properties; Illustrating the Concepts

Chapter 10 covers population analyses (based on basis functions, electrostatic potential and electron density), localized and natural orbitals. Chapter 11 covers molecular properties and the methods for obtaining them: perturbation and derivative techniques, response methods, electric and magnetic field perturbations, geometry and time-dependent perturbations. Chapter 12 illustrates the concepts through convergence of geometry, energy, dipole moment and vibrational frequency, bond dissociation and angle bending curves, problematic systems and the relative energies of C4H6 isomers.

Chapters 13–15: Optimization Techniques; Statistical Mechanics and Transition State Theory; Simulation Techniques

Chapter 13 covers optimizing functions to find minima and saddle points, choice of coordinates, constrained and global optimization, molecular docking and intrinsic reaction coordinates. Chapter 14 treats transition state theory, RRKM theory, statistical mechanics, the rigid-rotor harmonic-oscillator approximation and condensed phases. Chapter 15 covers Monte Carlo and time-dependent methods, periodic boundary conditions, extracting information from simulations, free energy methods and solvation models.

Chapters 16–18 and Concluding Remarks: Qualitative Theories; Mathematical Methods; Statistics and QSAR

Chapter 16 covers frontier molecular orbital theory, density-functional-based concepts, energy decomposition analysis, the Woodward–Hoffmann rules, the Bell–Evans–Polanyi principle and More O'Ferrall–Jencks diagrams. Chapter 17 reviews the mathematics used: vectors, matrices and tensors, coordinate changes, operators, differential equations, function approximation and Fourier and Laplace transforms. Chapter 18 covers statistical measures, correlation, QSAR, non-linear correlation and clustering. A short concluding chapter and appendices on notation, the variational principle and Hohenberg–Kohn theorems, atomic units, Z-matrix construction, and first and second quantization follow.

Key Concepts

Chapters 1–9: Methods

• Force fields: classical energy expressions with fitted parameters for large systems.
• Hartree–Fock and electron correlation: the mean-field reference and the post-Hartree–Fock methods that recover correlation.
• Basis sets and density functionals: the two main sources of approximation in electronic structure calculations.
• Semi-empirical, valence bond and relativistic methods: simplified methods, a bonding-focused alternative and the treatment of relativistic effects.

Chapters 10–15: Using the methods

• Population and wave function analysis: ways to extract chemical interpretation from a calculation.
• Geometry optimization and saddle points: locating minima and transition structures.
• Monte Carlo, time-dependent simulation and free energies: simulating condensed phases and solvation.

Chapters 16–18: Interpretation and tools

• Qualitative theories: orbital-based rules for predicting reactivity.
• Statistics and QSAR: correlating computed and experimental data.

Critical Analysis

Strengths

• Breadth of methods in one volume. The contents run from force fields and Hartree–Fock through correlation methods, DFT, semi-empirical and valence bond methods to simulation, optimization and statistics, which allows a reader to compare approaches rather than learn one in isolation.
• Method choice and error assessment. The opening chapter makes choice of level of theory and evaluation of results central, and Chapter 12 shows convergence and failure cases on concrete examples.
• Updated third edition. Wiley lists new or extended coverage of polarizable force fields, tight-binding DFT, more DFT functionals, excited states and time-dependent molecular properties, accelerated molecular dynamics, tensor decomposition, cluster analysis and reduced-scaling methods.
• Reference apparatus. Each chapter ends with references, and the mathematical chapter, notation appendix, atomic-units appendix and Z-matrix appendix serve as lookup material.

Limitations

• No exercises in the contents. The chapter endings listed in the table of contents are reference lists, not problem sets, so the book does not itself provide drill; practice has to come from running calculations.
• Not a program manual. The contents describe methods, not the use of particular software packages.
• Mathematically demanding. Slater determinants, second quantization, response theory and the Dirac equation appear, and a Chapter 17 on mathematical methods is provided to support readers.

Where It Fits in the Course

In the quantum chemistry and spectroscopy course, Jensen is the book on computation. Thakkar's Quantum Chemistry: A Concise Introduction is a short, idea-centred text for readers who will use electronic-structure calculations rather than develop the theory, and it ends with an introduction to computational quantum chemistry; Engel and Reid's Physical Chemistry: Quantum Chemistry and Spectroscopy is a physical chemistry volume that develops quantum theory and molecular spectroscopy; and McQuarrie's Quantum Chemistry is a more rigorous treatment of quantum-mechanical ideas. Any of these is a sensible preparation for Chapters 3 to 6, which start from Hartree–Fock theory.

Pavia's Introduction to Spectroscopy and Silverstein's Spectrometric Identification of Organic Compounds concern interpreting experimental spectra to identify organic molecules; Jensen is the complementary route, computing molecular structures, energies and properties, including those that appear in spectra.

How to Use This Book

The book is aimed at graduate students and researchers, and at advanced undergraduates with a quantum chemistry background who want to know what computational methods do and how to choose among them.

A practical plan:

• Orientation: Chapter 1, then Chapters 2 and 3.
• Core electronic structure: Chapters 4, 5 and 6 on correlation, basis sets and DFT, with Chapter 12 as a check on how the choices behave in practice.
• By need: Chapter 7 for semi-empirical methods, Chapters 10 and 11 for analysis and properties, Chapters 13 to 15 for reactions, optimization and simulation, and Chapter 16 for qualitative chemical reasoning.
• Support: Chapter 17 and Appendices A to E when notation or mathematics gets in the way.

Pair the reading with a program that can run calculations, and repeat the benchmarks of Chapter 12 on small molecules to build a feeling for how results change with method and basis set.