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

Quantum Chemistry III — Density Functional Theory

Courses

Trade the 3N-dimensional wavefunction for the 3-dimensional density. Derive both Hohenberg-Kohn theorems, build the Kohn-Sham machinery as a mirror of your Hartree-Fock code, derive LDA from the electron gas, climb Jacob’s ladder — and map the failure modes (self-interaction, dispersion) every practitioner must know cold.

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Quantum Chemistry III — Density Functional TheoryCourse cleared — every checkpoint passed 🎉0/0 units cleared · 0/0 questions · 19 planned · ~7h
Unit 1

The density idea

planned

From 3N coordinates to 3: Thomas-Fermi as the brave, wrong first try.

  • lessonWhy the density might be enoughplanned
  • projectProject — Thomas-Fermi energy of an atomplanned
Unit 2

Hohenberg-Kohn

planned

Both theorems, derived — proof by contradiction as an exercise format.

  • lessonHK I: the density determines everythingplanned
  • exercisesExercises — Derive the Hohenberg-Kohn theoremsplanned
  • lessonHK II: the variational principle for densitiesplanned
Unit 3

Kohn-Sham

planned

The fictitious system trick — your Fock derivation, mirrored.

  • lessonKohn-Sham: exact in principle, practical in formplanned
  • exercisesExercises — Derive the Kohn-Sham equationsplanned
  • lessonEverything unknown in one corner: the exchange-correlation functionalplanned
Unit 4

LDA from the electron gas

planned

Derive ε_x ∝ ρ^(4/3), then run your own DFT next to your own HF.

  • lessonThe homogeneous electron gas pays for everythingplanned
  • exercisesExercises — Derive the LDA exchange energyplanned
  • projectProject — Slater-Xα SCF for H₂ on a gridplanned
Unit 5

Jacob's ladder

planned

GGA, hybrids, meta-GGA, range separation — what B3LYP literally is.

  • lessonGradients enter: GGA and PBE mechanicsplanned
  • lessonHybrids: why exact exchange, how much, and the B3LYP recipeplanned
  • lessonThe rest of the ladder, honestly pricedplanned
Unit 6

Where DFT lies

planned

Self-interaction, dispersion, gaps — the failure modes every user must know cold.

  • projectProject — H₂⁺ in HF vs LDA: one electron, two verdictsplanned
  • lessonSelf-interaction and delocalization errorplanned
  • lessonDispersion: the missing force and the +D patchesplanned
Unit 7

Time-dependent DFT

planned

Excited states from response: the Casida machinery, bridged to the existing pages.

  • lessonLinear response and the Casida equationsplanned
  • readingReading — Casida's Equationplanned