Theory of Computational Quantum Chemistry: From the Schrödinger Equation to Electronic-Structure Theory

The quantum chemistry book that leaves nothing as an exercise for the reader.

Open almost any quantum chemistry textbook and you will meet the same two sentences: The derivation is left as an exercise for the reader. For details, see the references. One line of text, one lost evening — and often, in the end, one abandoned chapter.

This book omits none of it. Starting from the Schrödinger equation, it builds a single continuous argument through Hartree–Fock theory, electron correlation (configuration interaction, perturbation theory, coupled cluster), and excited-state methods (CIS/TDHF, ADC, EOM-CC), without skipping a line of algebra anywhere along the way.

The only prerequisite is high-school mathematics. The linear algebra, calculus, and variational methods you need are developed from scratch in the text, so no prior quantum mechanics or physical chemistry is assumed. It was written by a computer scientist who went looking for a textbook with nothing hidden between the lines, could not find one, and wrote it — for self-learners and students who want to follow every step themselves.

What sets this book apart

Every intermediate step written out, from the Schrödinger equation all the way to EOM-CCSD Begins at high-school level: linear algebra, the variational principle, and Lagrange multipliers are built up before they are used Carries the derivations down to implementation level — CCSD residual equations, the Davidson algorithm, Obara–Saika and McMurchie–Davidson integral recursions, Schwarz screening An algorithmic viewpoint runs through the whole book: the O(Mⁿ) cost of each method, and where that exponent comes from Real numbers from real calculations — H₂ dissociation, SCF convergence, basis-set convergence — computed with PySCF and reported throughout Appendices bridge to density functional theory (Kohn–Sham) and QM/MM Contents (34 chapters + Appendices A–G)

Mathematical preliminaries (linear algebra, variational methods) · foundations of quantum mechanics · many-electron systems and second quantization · Hartree–Fock theory (RHF, UHF, ROHF) · basis sets and the Roothaan–Hall equations · molecular integral algorithms · SCF convergence acceleration (DIIS) · energy gradients and geometry optimization · electron correlation (CI, MP, CCSD(T), multireference methods) · excited states (CIS, TDHF, ADC, EOM-CC) · a closing survey of accuracy versus computational cost

If the companion volume, Inside Quantum Chemistry Calculations , is the book that gives you the concepts and the intuition, this is the one that derives every equation standing behind them — for everyone who wants to work through the theory with a pencil in hand and make it their own.