#symmetry
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Forbidden and allowed: what symmetry does to a spectrum
Dissolve cobalt chloride in water and the solution is pale pink; add hydrochloric acid and it turns an intense blue — same ion, same kind of transition, a hundredfold jump in intensity. The gap didn't change; the symmetry did. This post pays the pigment series' oldest promissory note and explains what "forbidden" and "allowed" actually mean — one integral, one parity argument, one character table — and why forbidden bands show up anyway.
Hartree–Fock and the correlation gap: where the orbital energies come from
A water molecular-orbital diagram quotes orbital energies as if they were just there to be read off. This post derives the ground-state machinery — the Hartree–Fock equations, their self-consistent solution, Koopmans' theorem, and the correlation energy that the mean field leaves behind — that actually computes them.
Reading water off the page: geometry, orbitals, acidity, and spectra
Water is the most familiar molecule and one of the strangest. This post builds it up from the bottom — where the atoms sit, what the electrons do, why it is both an acid and a base, and how it talks to light.