# Foundations of quantum chemistry

Part I showed you how to *drive* qc-rs. This part explains **what it is actually computing**. It is the
theoretical heart of the manual — written to be read like a short textbook, from the physical problem down
to the equations a program like qc-rs solves. You do not need it to run a calculation, but you *do* need it
to understand your results, choose sensible methods, and know when to trust a number.

We build the story in four steps, each its own chapter:

1. **[The many-electron problem & Born–Oppenheimer](many-electron-and-bo.md)** — the molecular Schrödinger
   equation, why it cannot be solved exactly, and the first great simplification (freezing the nuclei).
2. **[Variational principle, LCAO & basis sets](variational-lcao-basis.md)** — how we turn an
   impossible differential equation into a finite matrix problem: expand the unknown orbitals in a basis and
   minimize the energy.
3. **[Hartree–Fock](hartree-fock.md)** — the foundational approximation: one Slater determinant, the
   self-consistent-field equations, and what it gets right and wrong.
4. **[Density functional theory & Kohn–Sham](dft-kohn-sham.md)** — recasting the problem in terms of the
   electron density, and the workhorse of modern quantum chemistry.

:::{note} How to read this part
Each chapter states the theory with its equations, then connects it back to what you *do* in qc-rs (the
`ao=` basis, `ref="r"`, `xc="b3lyp"`, and so on). Read it straight through the first time; later, come back
to a single chapter when a term in the [User guide](../20-guide/molecular-input.md) needs unpacking. We use
**atomic units** throughout — introduced in the next chapter.
:::

Ready? Start with [the many-electron problem](many-electron-and-bo.md).