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

Quantum Chemistry I — Hartree-Fock from Nothing

Courses

The complete Hartree-Fock arc, problem-first: derive the machinery, write every piece of a working SCF program in your browser, break it where it must break, and transfer it to a molecule the textbook uses as its own worked example.

15 skills 51 questions ← whole tech tree
The spine Work the problem set → Every pencil-and-paper problem in the course, one numbered list. Solve them all. Assess yourself Take the final exam → Comprehensive, timed, closed-book — score + full review at the end.
Quantum Chemistry I — Hartree-Fock from NothingUnit 1 · Start here — the whole story, by swipe0/11 units cleared · 0/52 questions · ~18h
Unit 1

Start here — the whole story, by swipe

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See the entire arc before deriving any of it: scroll the Hartree-Fock story end to end, swiping each idea for a second explanation. The map before the territory.

Unit 2

The variational game

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Rigorous guessing: every method downstream is this idea with more parameters.

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Basis sets

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Many-electron wavefunctions

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Spin

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Integrals

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The Fock problem

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Self-consistency

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Beyond the mean field

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Stress tests

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Reading the density

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The course as a map

The same course, drawn as a prerequisite graph — each node is a skill the units above teach; green means its questions are done.

Atomic Basis Functions0%

Gaussian primitives and contracted basis sets.

Variational Principle0%

Energy minimization over trial wavefunctions.

Slater Determinants🔒

Antisymmetric many-electron wavefunctions.

▶ Locked — finish prerequisites▶ Locked — finish prerequisites
One-Electron Integrals🔒

Overlap, kinetic, and nuclear-attraction matrices.

▶ Locked — finish prerequisites▶ Locked — finish prerequisites
Spin & Determinants🔒

S² eigenfunctions, the 2K singlet-triplet split, and the ⟨S²⟩ contamination diagnostic.

▶ Locked — finish prerequisites
Two-Electron Integrals🔒

The four-index electron-repulsion tensor.

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The Fock Matrix🔒

Coulomb and exchange as a mean-field operator.

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deep dive ↓Hartree-Fock Method
Roothaan-Hall🔒

The generalized eigenproblem for molecular orbitals.

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SCF Iteration🔒

The self-consistent field convergence loop.

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Density Matrices & Populations🔒

P as the one-electron oracle: Mulliken charges, dipoles, and what is (and is not) observable.

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Orbital Energies & Koopmans🔒

What the ε's mean: ionization potentials from frozen orbitals, and why the errors cancel.

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deep dive ↓Hartree-Fock Method
Correlation & Where HF Fails🔒

Dynamic vs static correlation, the stretched-H₂ failure, and the UHF trade.

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UHF & Broken Symmetry🔒

Pople-Nesbet, the Coulson-Fischer point, and the spin-contamination trade.

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MP2🔒

Correlation as a perturbation: the workhorse second-order correction.

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Full Configuration Interaction🔒

Exact correlation in a basis: diagonalize all determinants.

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