The chemistry, physics, mathematics and computing words these notes use, each in one sentence. Molecules have their own pages in the Spectrum Atlas. Every term has an anchor, so a post can link straight to it (for example /glossary/#hessian).

Analytic derivative
A derivative of the energy computed from an exact formula instead of by nudging the atoms and comparing results, which makes it faster and free of step-size noise.
Anchor
In this project, a molecule whose vibrations have been computed with the expensive coupled-cluster method, so that cheaper predictions can be checked and corrected against it.
Anharmonicity
The ways a real molecular vibration departs from an ideal spring, which shift every infrared band by a few to tens of wavenumbers and create extra, weaker bands.
Aromatic infrared bands
The family of broad emission features at wavelengths of about 3 to 20 micrometres, seen across the universe and attributed to PAHs heated by starlight.
Atomic polar tensor (APT)
For each atom, how much the molecule's dipole moment changes when that atom moves a little in each direction — the quantity that sets how bright each infrared band is.
B3LYP
A widely used recipe (functional) for density functional theory that mixes a share of exact exchange with approximate terms and gives good vibrational frequencies at modest cost.
Band
A peak in an infrared spectrum, produced when the molecule absorbs or emits light at the frequency of one of its vibrations.
Band family
In this project, a group of vibrations of the same kind — carbon–hydrogen stretches, carbon–hydrogen out-of-plane bends, in-plane ring motions, and the rest — whose errors are measured separately because they behave differently.
Basis set
The collection of mathematical functions used to describe where the electrons can be, where a larger set gives more accurate answers at a steeply higher cost.
Bohr
The atomic unit of length, about 0.053 nanometre.
Bootstrap
A way to estimate how uncertain a fitted number is by repeating the fit many times on random resamples of the data and looking at the spread of the results.
Cation
A molecule that has lost an electron and so carries a positive charge, as many PAHs in space are thought to have.
CCSD(T)
Coupled cluster with single, double and perturbative triple excitations, often called the "gold standard" of quantum chemistry for molecules like these: accurate, but very expensive.
Combination band
A weak infrared band in which one photon excites two different vibrations at once, so that it appears near the sum of their frequencies.
Commit
A recorded snapshot of the project's files in the version-control system git, to which every number in these notes can be traced.
Coriolis coupling
The interaction between a molecule's rotation and its vibrations, a small term that enters the anharmonic corrections.
Corpus
The project's own collection of molecules whose vibrations have been computed with the cheaper density-functional methods, used to train and test the network.
Correction
In this project, the difference between a cheap and an accurate description of a molecule's force constants, which the network learns to predict instead of the whole answer.
Coupled cluster
A family of quantum-chemistry methods that include electron correlation systematically, giving highly accurate energies at a cost that grows very fast with molecule size.
CPHF (coupled-perturbed equations)
The set of linear equations that tells how the electrons rearrange when the atoms move or an electric field is applied, needed for analytic Hessians and intensities.
Degenerate modes
Two or more vibrations that have exactly the same frequency because of the molecule's symmetry.
Delta learning (Δ-learning)
Training a model to predict the difference between a cheap and an expensive calculation rather than the expensive result itself, which is usually easier to learn and needs less data.
Density functional theory (DFT)
A quantum-chemistry approach that computes a molecule's energy from its electron density, cheap enough for large molecules, with good but not perfect accuracy.
Dipole moment
The separation of positive and negative charge in a molecule; a vibration shows up in the infrared only if it makes this dipole change.
Early stopping
Ending a network's training at the point where its error on held-aside validation data stops improving, so that it does not merely memorise its training examples.
Eigenvalue and eigenvector
For a matrix such as the mass-weighted Hessian, the special directions that are only stretched and not turned (eigenvectors) and their stretch factors (eigenvalues), which give the vibrations and their frequencies.
Electron correlation
The way electrons avoid one another beyond what a simple averaged picture captures; quantum-chemistry methods differ mainly in how much of it they include.
Epoch
One full pass of a network through all of its training examples.
Equilibrium geometry
The arrangement of atoms with the lowest energy, where every force vanishes and around which vibrations are described as small motions.
Equivariant network
A neural network built so that rotating the input molecule rotates its output in exactly the same way, which builds the rules of geometry in instead of having to learn them.
Extrapolation
Using a trend measured on the available data to predict values beyond it — useful for planning, but always less certain than a measurement.
Fermi resonance
An accidental near-coincidence between a fundamental and an overtone or combination band of the same symmetry, which makes the two mix, shift and share intensity.
Finite differences
Estimating a derivative by moving the atoms a small step in each direction and comparing the results, simple but sensitive to the step size and to numerical noise.
Force constant
The stiffness of the "spring" behind an atomic motion: the second derivative of the energy with respect to the atoms' displacements.
Frozen core
Leaving each atom's tightly bound inner electrons out of the expensive correlation treatment, which saves much time at a small, controlled cost in accuracy.
Functional
In density functional theory, the formula that turns the electron density into an energy; different functionals, such as B3LYP and ωB97X, give slightly different answers.
Fundamental
The infrared band in which a vibration is raised by one quantum from the ground state, usually the strongest band of each vibration.
Geometry optimisation
The search for the equilibrium geometry by moving the atoms downhill in energy until the remaining forces fall below a set threshold.
GVPT2
Generalised second-order vibrational perturbation theory, the variant of VPT2 that takes resonances out of the perturbative sums and treats them separately.
Harmonic approximation
Treating every vibration as an ideal spring, which gives frequencies from the Hessian alone and is the starting point that anharmonic corrections improve on.
Hartree
The atomic unit of energy, about 27.2 electronvolts or 219,475 wavenumbers.
Hartree–Fock
The simplest quantum-chemistry method, in which each electron moves in the averaged field of all the others — the starting point of more accurate methods.
Hessian
The table of second derivatives of a molecule's energy with respect to the positions of its atoms, which holds all its harmonic force constants and hence its vibrational frequencies.
Hindered rotor
A group of atoms that can twist around a bond but meets an energy barrier as it does, whose motion is too large for small-vibration theories and is often treated on its own.
Hold-out set
Molecules deliberately kept out of training so that a network can be tested on examples it has never seen.
Infrared spectrum
The pattern of infrared light that a molecule absorbs or emits, a fingerprint of how its atoms vibrate.
Integration grid
The set of points in space at which density functional theory evaluates its formulas numerically; a coarser grid is faster but adds small numerical errors.
Intensity
How strongly a vibration absorbs or emits infrared light, set by how much the dipole moment changes during the motion.
Interstellar medium
The gas and dust between the stars, where PAHs are thought to be common.
Lane
In this project, one independent stream of calculations on a server, given a fixed number of processor threads.
Large-amplitude motion
A movement, such as the twisting of a side group, that carries the atoms far from the equilibrium geometry and so breaks the small-displacement assumption of standard vibrational theories.
Learning curve
A plot of a model's test error against the amount of training data, used to decide whether more data would still help.
Least squares
Choosing a model's parameters so that the sum of the squared differences between its predictions and the data is as small as possible.
Local correlation (LNO)
A way to make coupled-cluster calculations of large molecules affordable by correlating each electron pair only with its surroundings, with controlled approximations.
Loss function
The number that a network's training tries to make small, measuring how far its predictions are from the targets.
Mass-weighted coordinates
Atomic displacements scaled by the square root of each atom's mass, the natural coordinates in which a molecule's vibrations separate into independent normal modes.
Neural network
A flexible mathematical model made of many simple connected units whose parameters are adjusted on examples until it predicts well.
Noise guard
In this project, an automatic check that computes the same constant in two independent ways and refuses a result when the two disagree by more than a set limit.
Normal mode
One of the independent patterns in which all of a molecule's atoms vibrate together at a single frequency; a non-linear molecule of N atoms has 3N − 6 of them.
Out-of-plane bend
A vibration in which atoms of a flat molecule move above and below its plane, such as the carbon–hydrogen wags behind the strong PAH bands near 11 to 14 micrometres.
Overfitting
When a model learns the quirks of its training examples instead of the general pattern, so that it does well on them and badly on new molecules.
Overtone
A weak infrared band in which a single vibration is raised by two or more quanta at once, appearing near a multiple of its frequency.
PAH (polycyclic aromatic hydrocarbon)
A flat molecule of fused carbon rings with hydrogen atoms around the rim, the kind of molecule believed to cause the aromatic infrared bands seen in space.
PAHdb
The NASA Ames PAH IR Spectroscopic Database, the main public library of computed and measured PAH spectra that astronomers use.
Perturbation theory
Calculating a small correction to a problem that is already solved — here, the anharmonic effects added on top of the harmonic vibrations.
Point group
The set of symmetry operations — rotations, reflections and inversion — that leave a molecule unchanged, used to classify and simplify its vibrations.
Polarisation functions
Basis functions of higher angular momentum, such as d functions on carbon, that let the electron cloud deform in a molecule and matter for accurate force constants.
Pre-registration
Writing down, before a computation runs, what will be measured, how it will be read and what result is expected, so that the outcome cannot be reinterpreted afterwards.
Proxy
In this project, a cheap stand-in for the expensive correction — the difference between two density functionals — used to study what a network can learn before coupled-cluster data exist.
Psi4
An open-source quantum-chemistry program, used in this project to build the first density-functional corpus.
PySCF
An open-source quantum-chemistry program written in Python, used in this project for analytic Hessians, coupled-cluster gradients and intensities.
Quartic force field (QFF)
A description of a molecule's energy around its equilibrium geometry up to the fourth power of the atomic displacements, the input that VPT2 needs.
Ridge regression
Least squares with a small penalty on large parameters, which keeps a fitted model stable when the data are few.
Ring coupling
The force constants that link the motions of neighbouring rings, the part of the correction that becomes hardest to predict as molecules grow.
Rung
In this project, one step of the size ladder: the largest affordable set of molecules of a given size, tested before the next step is taken.
Scaffold
The ring skeleton of a molecule without its side groups, used here to group molecules into families.
Seed
The starting number of a random-number generator; repeating a training run with different seeds shows how much of a result is luck.
Size ladder
The project's plan to learn step by step from small molecules to large ones, checking at each rung that what was learned carries over to the next.
Spectral shape
The full profile of a spectrum — where its bands lie, how strong and how wide they are — rather than a list of separate peak positions.
Standard error
The uncertainty of an average, roughly the spread of the individual values divided by the square root of their number.
Substituent
A small group of atoms, such as a methyl or a cyano group, attached to a ring in place of a hydrogen atom.
Transfer learning
Reusing what a model learned on one task, such as cheap density-functional data, to do better on another, such as coupled-cluster data.
Translation sum rule
The requirement that moving a whole neutral molecule does not change its dipole moment, so that its atomic polar tensors add up to zero — a free check on their accuracy.
Validation set
Data held aside during training to decide when to stop and which settings to keep, separate from the final test.
VPT2
Second-order vibrational perturbation theory, the standard way to compute anharmonic band positions from a quartic force field.
Wavenumber (cm⁻¹)
The unit spectroscopists use for vibrational frequencies, the number of wavelengths per centimetre; molecular vibrations lie between roughly 100 and 3,200 cm⁻¹.
ωB97X
A density functional that treats the long-range interaction between electrons differently from B3LYP; in this project the difference between the two serves as the proxy correction.