Quantum Chemistry
Quantum chemistry is usually taught as equations to be trusted. This book starts with the experiments that broke classical physics, derives the machinery from them, solves every exactly solvable system by hand, and then does the approximations — variation, perturbation, many-electron atoms, Born–Oppenheimer, basis sets — that the rest of chemistry is built on.
- 9 parts
- 89 sections
- ~213,074 words
- 9 free extracts — one per part
- CSIR-NET · GATE · IIT-JAM
What you can read without paying
Every one of the 9 part pages below reproduces its opening section in full — the real text, the real figures — before the paywall. That is 9 complete sections of Quantum Chemistry, free, with no sign-in.
Foundations — Why Quantum Mechanics Exists
Quantum mechanics is usually taught as a set of equations to be trusted. This part does the opposite: it starts with the five experiments that broke classical physics, shows exactly what each one broke, and only then introduces the machinery built to replace it. By the end you should understand not just what the postulates say but why…
- Blackbody radiation and the ultraviolet catastrophe
- The photoelectric effect and Einstein's photon
- The Compton effect
- Atomic line spectra and the Rydberg formula
- The Bohr model and the four things it cannot explain
- The de Broglie relation, electron diffraction and wave packets
- The wavefunction and the Born interpretation
- Acceptable wavefunctions, normalisation and orthogonality
- The postulates of quantum mechanics
Operators, Eigenvalues & the Schrödinger Equation
This is the grammar of the subject. Every quantum calculation you will ever do is an operator acting on a function, and almost every exam question reduces to recognising which operator, which function, and whether the two commute. This part builds that machinery slowly and then uses it to derive the uncertainty principle rather than…
- Operators, operator algebra and linearity
- Hermitian operators: real eigenvalues and orthogonal eigenfunctions
- The eigenvalue equation, the correspondence rules and the Schrödinger equation
- Expectation values
- Superposition and the meaning of the expansion coefficients
- The measurement postulate, collapse, and the Ehrenfest theorem
- Commutators and their algebra
- [x, p] = iℏ and the angular-momentum commutators
- Compatible observables and the generalised uncertainty relation
Exactly Solvable Systems I — Boxes, Steps & Barriers
The particle in a box is the first system anyone solves, and the one most students learn to compute without understanding. This part treats it properly — where the quantisation actually comes from, why the zero-point energy cannot be removed, what the nodes mean — and then extends it to the cases the exam prefers: degeneracy in three…
- The infinite square well: solving it from the boundary conditions
- Normalisation, nodes, orthogonality and zero-point energy
- Expectation values and the uncertainty product
- Boxes in two and three dimensions: separation of variables
- Degeneracy, symmetry, and the free-electron model of conjugated molecules
- The free particle, the continuum, and the finite well
- The potential step
- The rectangular barrier and the tunnelling probability
- What tunnelling explains: isotope effects, STM, α-decay and NH3 inversion
Exactly Solvable Systems II — Oscillator & Rotor
Two systems carry most of molecular spectroscopy: the oscillator behind every vibrational band, and the rotor behind every microwave line. This part solves both — the oscillator twice, once by series and once by the far more elegant ladder-operator method — and then builds the general theory of angular momentum that both depend on…
- The classical oscillator, the parabolic approximation, and the Schrödinger equation
- The series solution, Hermite polynomials, the energy ladder and the wavefunctions
- Ladder operators, selection rules and anharmonicity
- Rotation in two dimensions: the particle on a ring
- Rotation in three dimensions: the particle on a sphere and the spherical harmonics
- The rigid rotor as a molecule: B, the spectrum, and centrifugal distortion
- The operators and their commutation relations
- The eigenvalue spectrum from the algebra alone, and the vector model
- Spin, and the addition of angular momenta
The Hydrogen Atom
The hydrogen atom is the only atom quantum mechanics solves exactly, and every orbital picture in chemistry descends from it. This part does the full solution — the separation, the radial equation, the three quantum numbers falling out as conditions rather than assumptions — and then spends as much time on what the answers mean, because…
- The two-body problem and the reduced mass
- The Coulomb potential and separation in spherical polars
- The radial equation, the Laguerre polynomials, and where n comes from
- The three quantum numbers and the constraints among them
- Radial wavefunctions and radial nodes
- Angular functions, real orbitals and the shapes you draw
- The radial distribution function, and why its maximum is not where ψ² peaks
- Expectation values, the size of the atom, and the virial theorem
- The spectrum, selection rules, hydrogen-like ions and fine structure
- Where this leads — a pointer to Part 6
Approximation Methods
Beyond hydrogen, nothing is exactly solvable — so everything else in quantum chemistry is approximation. Two methods do almost all the work, and the exam reliably asks you to choose between them and to execute one by hand. This part derives both from scratch, applies them to the same problems so the comparison is concrete, and is honest…
- The variation theorem, stated and proved
- Trial functions, variational parameters, and the minimisation
- The linear variation method, secular equations and the secular determinant
- Rayleigh–Schrödinger theory: first-order energy and wavefunction
- The second-order energy, its sign, and where the series fails
- Degenerate perturbation theory and the Stark effect
- Time-dependent perturbation theory, Fermi's golden rule and selection rules
- The helium atom: both methods on the same problem
- The WKB approximation
- Born–Oppenheimer as an approximation, and how CSIR-NET tests all this
Many-Electron Atoms
The moment a second electron appears, the Schrödinger equation stops being solvable and quantum chemistry becomes the art of good approximations. This part explains what actually goes wrong, why antisymmetry is forced on us rather than assumed, and how the orbital picture every chemist uses is recovered from a problem that strictly has…
- Electron spin: what forced it on us, and how it is handled
- Indistinguishability and the antisymmetry principle
- Slater determinants, exchange energy, singlets and triplets
- The helium problem and the orbital approximation
- The Hartree and Hartree–Fock methods, and the SCF procedure
- Screening, Slater's rules, the aufbau principle and correlation
- Russell–Saunders coupling and the term symbol
- Microstates, the derivation of terms, and Hund's three rules
- Spin–orbit coupling, j–j coupling, the Zeeman effect and selection rules
Molecular Quantum Mechanics
Molecules introduce a second problem on top of the many-electron one: nuclei that move. The Born–Oppenheimer approximation separates the two, and everything chemists mean by a potential-energy surface, a bond length or a reaction path depends on it. This part builds molecular orbital theory from the one molecule that can be solved…
- The molecular Hamiltonian, the BO separation and potential-energy surfaces
- H2+: the molecule that can be solved
- LCAO in general, and where Born–Oppenheimer breaks down
- Homonuclear diatomics: the correlation diagram, s–p mixing and the N2/O2 crossover
- Heteronuclear diatomics, valence bond theory, and a fair comparison
- Hybridisation as algebra, and MO theory for polyatomics by symmetry
- The approximations, the secular determinant, and ethene
- Allyl, butadiene and benzene; delocalisation energy, charge densities and bond orders
- Cyclic systems, the Frost circle, (4n + 2), heteroatoms and extended Hückel
Computation, Spectroscopy & the Quantum Toolkit
The last part connects the machinery to the two places a chemist actually meets it: the computer and the spectrometer. It explains what a basis set is and what the acronyms on a paper's methods line mean, derives the transition-moment integral that every selection rule in spectroscopy comes from, shows how symmetry decides whether an…
- Basis sets — the vocabulary the molecule is described in
- Past Hartree–Fock — the correlation energy and how to get it back
- Density functional theory
- Semi-empirical methods, geometry optimisation, and reading an output file
- The transition dipole moment — where every selection rule comes from
- Rotational and vibrational spectra — the rules derived
- Electronic spectra and the Franck–Condon principle
- Raman, magnetic resonance and photoelectron spectroscopy
- The master formula sheet
- Every exactly solvable system, side by side
- Units, constants and conversions
- Which method for which problem
- The top exam traps, Parts 1–9
- Section-by-section index
- The argument, from Part 1 to Part 9
Read all 89 sections
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