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 is the collection of AOs.

Basis set

The finite set of functions the molecular orbitals are expanded in (basis chapter).

BSSE (basis-set superposition error)

An artificial stabilization when fragments borrow each other’s basis functions; corrected with ghost atoms.

Born–Oppenheimer approximation

Clamping the nuclei to solve the electronic problem, because nuclei are much heavier than electrons (foundations).

Correlation energy

\(E_{\text{corr}} = E_{\text{exact}} - E_{\text{HF}}\) — the electron-avoidance energy Hartree–Fock misses (post-SCF).

CGTO (contracted Gaussian-type orbital)

A fixed linear combination of primitive Gaussians used as a basis function (basis chapter).

DFT (density functional theory)

An electronic-structure method based on the electron density; in practice Kohn–Sham DFT (foundations).

DIIS

Direct inversion of the iterative subspace — the default SCF convergence accelerator (SCF).

ECP (effective core potential)

A potential replacing the core electrons of a heavy atom (cuts cost, adds scalar relativity; basis chapter).

ELF (electron localization function)

A real-space field revealing electron pairs — cores, bonds, lone pairs (QTAIM & ELF).

ERI (electron repulsion integral)

A two-electron integral \((\mu\nu|\lambda\sigma)\); how they are handled is the eri= strategy (ERI strategies).

Fock / Kohn–Sham matrix

The effective one-electron operator whose eigenvectors are the molecular orbitals (SCF).

Functional (xc)

The exchange–correlation approximation in DFT (LDA/GGA/meta-GGA/hybrid; foundations).

HOMO / LUMO

The highest occupied / lowest unoccupied molecular orbital; their gap gauges reactivity (spectra & DOS).

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).

MP2 (second-order Møller–Plesset)

The cheapest post-HF estimate of the correlation energy (post-SCF).

Multiplicity (2S+1)

The spin state — 1 = singlet, 2 = doublet, 3 = triplet (molecular input).

QTAIM (quantum theory of atoms in molecules)

Bader’s analysis of the density topology — atoms, bonds, basins (QTAIM & ELF).

RHF / UHF / ROHF

Restricted / unrestricted / restricted-open-shell Hartree–Fock — the three references (SCF).

RI (resolution of identity / density fitting)

Approximating four-index integrals through an auxiliary basis (post-SCF, ERI strategies).

SCF (self-consistent field)

The iterative solution of the Fock/Kohn–Sham equations (SCF).

Spin contamination

A UHF wavefunction’s admixture of higher-spin states, measured by ⟨S²⟩ (SCF).

High-performance computing

Amdahl’s law

The serial fraction of a program limits the maximum parallel speedup (primer).

BLAS / LAPACK

Tuned libraries for dense linear algebra (MKL or OpenBLAS; threads chapter).

GPU / CUDA

A massively-parallel accelerator and NVIDIA’s platform for it (GPU chapter).

InfiniBand

A high-performance cluster interconnect (~35× Ethernet; MPI chapter).

MPI (message passing interface)

The distributed-memory model for many machines (MPI chapter).

Oversubscription

Asking for more threads than cores, which slows a run down (threads chapter).

Process / thread

A program with private memory / a stream of execution sharing a process’s memory (primer).

Rank

One MPI process (MPI chapter).

qc-rs concepts

Checkpoint

qc-rs’s central object — a molecule you build, extend, run, and query (checkpoints).

IOP

The iop={...} channel for fine-grained numerical knobs (IOP reference).

Sentinel

A qc.*_ENABLED boolean reporting a compiled-in feature (API reference).