# Glossary

A quick reference for the quantum-chemistry and HPC terms used in this manual. Each entry links to the
chapter where it is explained in full.

## Quantum chemistry

**AO (atomic orbital)**
: A basis function centred on an atom. The [basis set](../20-guide/basis-and-ao.md) is the collection of AOs.

**Basis set**
: The finite set of functions the molecular orbitals are expanded in ([basis chapter](../20-guide/basis-and-ao.md)).

**BSSE (basis-set superposition error)**
: An artificial stabilization when fragments borrow each other's basis functions; corrected with
  [ghost atoms](../40-reference/mol-spec.md).

**Born–Oppenheimer approximation**
: Clamping the nuclei to solve the electronic problem, because nuclei are much heavier than electrons
  ([foundations](../10-foundations/many-electron-and-bo.md)).

**Correlation energy**
: $E_{\text{corr}} = E_{\text{exact}} - E_{\text{HF}}$ — the electron-avoidance energy Hartree–Fock misses
  ([post-SCF](../20-guide/post-scf.md)).

**CGTO (contracted Gaussian-type orbital)**
: A fixed linear combination of primitive Gaussians used as a basis function
  ([basis chapter](../20-guide/basis-and-ao.md)).

**DFT (density functional theory)**
: An electronic-structure method based on the electron density; in practice Kohn–Sham DFT
  ([foundations](../10-foundations/dft-kohn-sham.md)).

**DIIS**
: Direct inversion of the iterative subspace — the default SCF convergence accelerator
  ([SCF](../20-guide/scf.md)).

**ECP (effective core potential)**
: A potential replacing the core electrons of a heavy atom (cuts cost, adds scalar relativity;
  [basis chapter](../20-guide/basis-and-ao.md)).

**ELF (electron localization function)**
: A real-space field revealing electron pairs — cores, bonds, lone pairs ([QTAIM & ELF](../20-guide/properties/qtaim-elf.md)).

**ERI (electron repulsion integral)**
: A two-electron integral $(\mu\nu|\lambda\sigma)$; how they are handled is the `eri=` strategy
  ([ERI strategies](../30-hpc/eri-jk-strategies.md)).

**Fock / Kohn–Sham matrix**
: The effective one-electron operator whose eigenvectors are the molecular orbitals ([SCF](../20-guide/scf.md)).

**Functional (`xc`)**
: The exchange–correlation approximation in DFT (LDA/GGA/meta-GGA/hybrid; [foundations](../10-foundations/dft-kohn-sham.md)).

**HOMO / LUMO**
: The highest occupied / lowest unoccupied molecular orbital; their gap gauges reactivity
  ([spectra & DOS](../20-guide/properties/spectra-dos.md)).

**J / K (Coulomb / exchange)**
: The two-electron parts of the Fock matrix — classical repulsion (J) and the exchange term (K).

**LCAO**
: Linear combination of atomic orbitals — how molecular orbitals are built ([foundations](../10-foundations/variational-lcao-basis.md)).

**MP2 (second-order Møller–Plesset)**
: The cheapest post-HF estimate of the correlation energy ([post-SCF](../20-guide/post-scf.md)).

**Multiplicity (2S+1)**
: The spin state — 1 = singlet, 2 = doublet, 3 = triplet ([molecular input](../20-guide/molecular-input.md)).

**QTAIM (quantum theory of atoms in molecules)**
: Bader's analysis of the density topology — atoms, bonds, basins ([QTAIM & ELF](../20-guide/properties/qtaim-elf.md)).

**RHF / UHF / ROHF**
: Restricted / unrestricted / restricted-open-shell Hartree–Fock — the three references ([SCF](../20-guide/scf.md)).

**RI (resolution of identity / density fitting)**
: Approximating four-index integrals through an auxiliary basis ([post-SCF](../20-guide/post-scf.md),
  [ERI strategies](../30-hpc/eri-jk-strategies.md)).

**SCF (self-consistent field)**
: The iterative solution of the Fock/Kohn–Sham equations ([SCF](../20-guide/scf.md)).

**Spin contamination**
: A UHF wavefunction's admixture of higher-spin states, measured by ⟨S²⟩ ([SCF](../20-guide/scf.md)).

## High-performance computing

**Amdahl's law**
: The serial fraction of a program limits the maximum parallel speedup ([primer](../30-hpc/parallel-computing-primer.md)).

**BLAS / LAPACK**
: Tuned libraries for dense linear algebra (MKL or OpenBLAS; [threads chapter](../30-hpc/threads-and-blas.md)).

**GPU / CUDA**
: A massively-parallel accelerator and NVIDIA's platform for it ([GPU chapter](../30-hpc/gpu-cuda.md)).

**InfiniBand**
: A high-performance cluster interconnect (~35× Ethernet; [MPI chapter](../30-hpc/mpi-and-interconnects.md)).

**MPI (message passing interface)**
: The distributed-memory model for many machines ([MPI chapter](../30-hpc/mpi-and-interconnects.md)).

**Oversubscription**
: Asking for more threads than cores, which slows a run down ([threads chapter](../30-hpc/threads-and-blas.md)).

**Process / thread**
: A program with private memory / a stream of execution sharing a process's memory
  ([primer](../30-hpc/parallel-computing-primer.md)).

**Rank**
: One MPI process ([MPI chapter](../30-hpc/mpi-and-interconnects.md)).

## qc-rs concepts

**Checkpoint**
: qc-rs's central object — a molecule you build, extend, run, and query ([checkpoints](../40-reference/checkpoints.md)).

**IOP**
: The `iop={...}` channel for fine-grained numerical knobs ([IOP reference](../40-reference/iop.md)).

**Sentinel**
: A `qc.*_ENABLED` boolean reporting a compiled-in feature ([API reference](../90-api/qc.md)).