Structure of atoms as chemistry's computational substrate: nucleons and electrons, the historical sequence of atomic models (Thomson plum-pudding, Rutherford nuclear, Bohr, quantum-mechanical), and electron-configuration rules (Aufbau,…
atomic-structure
Proton
Positively-charged composite baryon (uud) forming part of every atomic nucleus; charge +e, mass ≈ 1.6726e-27 kg.
Neutron
Electrically-neutral composite baryon (udd) forming part of most atomic nuclei; charge 0, mass ≈ 1.6749e-27 kg. Beta-decays to a proton +…
Electron
Fundamental lepton with charge -e and mass ≈ 9.109e-31 kg. Fermion (spin-1/2) obeying Pauli exclusion — the origin of the shell structure…
Atom
Smallest unit of a chemical element that retains its identity: a dense nucleus (Z protons + N neutrons) surrounded by Z electrons in…
Thomson plum-pudding model
J.J. Thomson's 1904 atomic model: atoms are diffuse positively-charged 'puddings' with negatively-charged electrons embedded like plums.…
Rutherford nuclear model
Rutherford's 1911 atomic model: nearly all mass and positive charge concentrated in a tiny central nucleus; electrons orbit at a much…
Bohr atomic model
Bohr's 1913 semi-classical atomic model: electrons occupy quantised circular orbits with angular momentum L = nℏ; transitions between…
Quantum-mechanical atomic model
The canonical modern atomic model: electrons are described by wavefunctions ψ(r) that are eigenstates of the atomic Hamiltonian, giving…
Electron configuration (Aufbau)
Ground-state electronic structure of an atom built up by filling orbitals in order of increasing energy (Aufbau), subject to the Pauli…
Geiger–Marsden gold-foil scattering
1909–13 experiment firing α-particles at a thin gold foil and finding a small fraction backscattered. The large-angle scattering rate is…
Hydrogen line spectrum
Discrete emission/absorption lines of atomic hydrogen (Lyman, Balmer, Paschen series) accurately described by the Rydberg formula. The…
Atomic number (Z)
The number of protons in the nucleus of an atom, labelled Z. Uniquely identifies the chemical element — all atoms with Z = 6 are carbon…
Mass number (A)
The total number of nucleons (protons + neutrons) in an atomic nucleus, labelled A. A = Z + N where N is the neutron count. Distinguishes…
Isotope
Atoms of the same element (same Z) but different neutron counts (different A). All isotopes of an element have (nearly) identical chemistry…
Quantum numbers (n, ℓ, mₗ, mₛ)
The four quantum numbers that uniquely identify each electronic state in an atom: principal (n = 1, 2, 3, …) sets energy/shell; azimuthal…
Atomic orbital
A one-electron wavefunction ψ(r, θ, φ) solving the single-electron Schrödinger equation in a central Coulomb potential; its squared modulus…
Aufbau principle
Electrons fill atomic orbitals in order of increasing energy (lowest first). The canonical filling order — 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p,…
Hund's rule of maximum multiplicity
Within a degenerate subshell (p, d, f), electrons occupy separate orbitals with parallel spins before pairing up. Consequence: the…
Slater's rules for Z_eff
Z_eff = Z - σ with shielding contributions (n',ℓ') by group; estimate orbital energies; explains periodicity in IE, χ.
Koopmans' theorem
First ionization energy ≈ -ε_HOMO in Hartree–Fock; relaxation and correlation corrections partially cancel; PES interpretation.
Hund's rules
(1) Max S, (2) max L at given S, (3) J = |L-S| if shell <½ full, J = L+S if ≥ ½; minimizes electron-electron repulsion.
Russell–Saunders term symbols
^(2S+1)L_J with L in S,P,D,F,...; classifies multi-electron atomic states; Slater determinant construction.
j-j coupling (heavy atoms)
Dominates for Z>~40 where spin-orbit > electron-electron; couple individual j_i first; intermediate coupling mostly in between.
Configuration interaction (CI)
Linear combination of Slater determinants; captures correlation beyond HF; CISD, CISDT, full-CI (exponential cost).
Multi-reference CASSCF/CASPT2
Active space with variationally-optimized MO + CI coefficients; CASPT2 adds dynamic correlation; photodynamics, transition metals.
Dirac–Hartree–Fock (relativistic)
4-component relativistic SCF; large spin-orbit in heavy atoms; ZORA, DKH approximations for efficiency; essential for 5d/5f.
Natural orbitals and occupation numbers
Eigenfunctions of 1-RDM with eigenvalues n_i ∈ [0,2]; most compact representation of correlated wavefunction.
Atomic form factor f(Q)
Fourier transform of electron density; X-ray scattering amplitude; anomalous dispersion f' + if'' near absorption edges.
Auger effect & XPS
Inner-shell hole filled by outer electron with ejection of second (Auger) electron; KE independent of exciting source; surface analysis.
XANES and EXAFS
X-ray absorption fine structure near (XANES) and extended (EXAFS) absorption edge; probes oxidation state, local coordination.
Photoelectron spectroscopy (XPS/UPS)
KE = hν - BE - φ; core-level chemical shifts; XPS surface-sensitive; UPS probes valence band; ESCA by Siegbahn (1981 Nobel).
QED corrections in atoms
Lamb shift, self-energy, vacuum polarization corrections at α(Zα)⁴ level; precision H, He⁺, muonic atoms test QED.