“Know how to solve every problem that has been solved.” “What I cannot create, I do not understand.” — Richard Feynman

Quantum Chemistry IV — The Machinery

Courses

Everything between a minimal-basis toy and a production code: integral recurrences past s-type (McMurchie-Davidson, Obara-Saika), SCF convergence technology, analytic gradients, optimization on potential energy surfaces, and response properties — with live wasm demonstrations compiled from the Knot DSL.

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Quantum Chemistry IV — The MachineryCourse cleared — every checkpoint passed 🎉0/0 units cleared · 0/0 questions · 20 planned · ~9h
Unit 1

Integrals past s-type

planned

Angular momentum enters: Hermite Gaussians and the recurrences production codes run.

  • lessonHermite Gaussians and the McMurchie-Davidson ideaplanned
  • readingReading — McMurchie-Davidsonplanned
  • readingReading — Obara-Saikaplanned
  • exercisesExercises — Run the recurrences by hand for p-functionsplanned
  • projectProject — p-orbital overlap & kinetic via MD recurrenceplanned
  • live demoLive — Water in 6-31G(d), compiled from Knot to wasmplanned
Unit 2

SCF technology

planned

DIIS, damping, level shifts, guesses — convergence as an engineering discipline.

  • lessonDIIS: extrapolating in error spaceplanned
  • projectProject — Add DIIS to your SCF; count the iterations it savesplanned
  • lessonConvergence pathologies and the fixes that actually workplanned
Unit 3

Gradients

planned

Hellmann-Feynman, Pulay forces, and why atom-centered bases make derivatives subtle.

  • lessonHellmann-Feynman and its fine printplanned
  • exercisesExercises — Derive the Pulay termsplanned
  • projectProject — Analytic vs finite-difference gradient of E(R)planned
Unit 4

Geometry optimization

planned

Newton on the PES, internal coordinates, transition states.

  • lessonWalking the surface: quasi-Newton and coordinates that helpplanned
  • projectProject — Optimize the H₂ bond length with your own gradientplanned
  • live demoLive — Watch water relax (Knot → wasm)planned
Unit 5

Properties & response

planned

Polarizability, vibrational frequencies, and the road to spectra.

  • projectProject — Polarizability by finite fieldplanned
  • projectProject — Harmonic frequency of H₂ vs the experimental 4401 cm⁻¹planned
  • lessonResponse theory in one lessonplanned
Unit 6

Symmetry

planned

Point groups and how codes exploit them.

  • lessonPoint groups for quantum chemistryplanned
  • exercisesExercises — Symmetry-block a small Hamiltonianplanned