Chemistry and materials

Electronic structure

The electrons of a molecule or crystal, solved from quantum mechanics to get shapes, energies and colours.

Question it answers: Is this molecule stable, and what colour is it?

Leaves out: The exact quantum many-electron problem is unsolvable, so every method leans on an approximation somewhere.

Runs on: about 10¹⁵ FLOPS rough a university cluster, hours to days per molecule or crystal.Since: 1953 early Hartree-Fock calculations run on some of the first computers.

Reaction dynamics

Bonds breaking and forming during a chemical reaction, often with the reacting core treated quantum mechanically and the surroundings classically.

Question it answers: Which path does the reaction take, and how fast?

Leaves out: The boundary between the quantum core and the classical surroundings is a modelling choice, not a real line.

Runs on: about 10¹⁵ FLOPS rough a university cluster, days per reaction studied.Since: 1976 Warshel and Levitt's first combined quantum and classical reaction model.

Computational materials screening

Thousands of candidate compounds calculated automatically, sometimes with learned shortcuts, to find ones with useful properties.

Question it answers: Which of these ten thousand candidates would make a better battery or solar cell?

Leaves out: Filters candidates by easy-to-compute properties, which are not always those that matter for making the material.

Runs on: about 10¹⁶ FLOPS rough a large cluster, running thousands of calculations in parallel.Since: 2006 early high-throughput calculations screening candidate materials.

Excited states and photochemistry

A molecule after it absorbs a photon, computed as it relaxes, twists or breaks apart on a different energy surface than its ground state.

Question it answers: What does this molecule do in the instant after it absorbs light?

Leaves out: Excited-state methods are less reliable than ground-state ones, and the cheapest ones can get it entirely wrong.

Runs on: about 10¹⁵ FLOPS rough a university cluster, hours to days per molecule.Since: 1984 early time-dependent quantum chemistry calculations of excited molecules.

Spectroscopy prediction

A molecule's nuclei and electrons computed to predict where its magnetic resonance, infrared or other spectral lines will fall, checked against a measured spectrum.

Question it answers: Does this computed spectrum match what the instrument actually recorded, confirming the structure?

Leaves out: Gets noticeably worse for the heavier atoms and more flexible molecules that matter most in practice.

Runs on: about 10¹⁴ FLOPS rough a workstation or small cluster, hours per molecule.Since: 1974 early computed nuclear magnetic resonance shifts compared against measured spectra.

Solvation free energy

A molecule's electrons recomputed as if sitting inside a continuous approximation of a solvent, to get how much energy dissolving it costs or releases.

Question it answers: How readily will this molecule dissolve, and does the solvent change how it reacts?

Leaves out: Replaces the solvent with a smooth average field, omitting specific interactions such as a hydrogen bond to an individual water molecule at a critical site.

Runs on: about 10¹⁴ FLOPS rough a workstation or small cluster, minutes to hours per molecule.Since: 1981 early continuum solvation models added to quantum chemistry calculations.

Machine-learned interatomic potentials

A neural network is fit to electronic-structure energies and then drives molecular dynamics with near-quantum accuracy at classical cost.

Question it answers: Can quantum-level forces be had for millions of atoms over nanoseconds?

Leaves out: Accuracy is limited to the chemistries and geometries in the training set.

Runs on: about 10¹⁷ FLOPS rough Training on thousands of quantum calculations, then large MDSince: 2007 Generalized neural-network representation of high-dimensional potential-energy surfaces (2007) sourceIn the simulations tree: Learned surrogate models

Universal interatomic potentials

A single graph neural network trained on a large materials database predicts energies and forces for most of the periodic table.

Question it answers: Can one learned model replace a separate fitted potential for each material?

Leaves out: Accuracy varies by element and often softens the potential-energy surface.

Runs on: about 10¹⁷ FLOPS rough Training on millions of structures, cheap inferenceSince: 2022 A universal graph deep learning interatomic potential for the periodic table (2022) source

Quantum chemistry on quantum computers

A variational quantum algorithm prepares and measures a molecule's electronic state on a real device, with a classical optimiser tuning the circuit.

Question it answers: Can a quantum processor find the ground-state energy of a small molecule?

Leaves out: Only very small molecules so far, with noise dominating the error.

Runs on: no computer. Quantum hardware; classical checks smallSince: 2014 A variational eigenvalue solver on a photonic quantum processor (2014) source

Ab initio molecular dynamics

Atoms moving in time with the forces recomputed from the electrons at every step, so bonds break and form without a pre-set force field.

Question it answers: How do atoms move and bond when their forces come directly from quantum mechanics?

Leaves out: Only hundreds of atoms for picoseconds can be followed, and density-functional errors enter every force.

Runs on: about 10¹⁶ FLOPS rough hundreds of atoms for tens of picoseconds on a large allocation.Since: 1985 Car and Parrinello's unified approach for molecular dynamics and density-functional theory. sourceIn the simulations tree: Ab initio molecular dynamics

Path-integral molecular dynamics

Atomic nuclei treated as quantum objects by representing each as a ring of linked copies, so tunnelling and zero-point motion shift hydrogen bonds and diffusion.

Question it answers: How much do the quantum effects of hydrogen change the behaviour of water and ice?

Leaves out: Real-time quantum behaviour is not recovered, only equilibrium and approximate dynamical properties.

Runs on: about 10¹⁵ FLOPS rough tens of copies per atom multiply the cost of classical dynamics.Since: 1984 Parrinello and Rahman's path-integral simulation of an electron trapped in molten salt. source

Real-time electron dynamics

The electron cloud of a molecule or crystal followed in time as a light pulse hits it, to find absorption spectra and ultrafast response.

Question it answers: How do electrons respond in the first femtoseconds after light arrives?

Leaves out: The approximate exchange-correlation functional misses some excitations, and ions are usually frozen.

Runs on: about 10¹⁶ FLOPS rough a time-stepped density-functional run over many thousand steps.Since: 1996 Yabana and Bertsch's time-dependent local-density approximation in real time. source

Quantum wavepacket dynamics

The nuclei of a small molecule treated as a quantum wave moving across the energy surface, to follow reaction, tunnelling and vibration exactly.

Question it answers: How does a molecule vibrate and react when its nuclei obey quantum mechanics?

Leaves out: Cost grows steeply with the number of atoms, so only small molecules are tractable.

Runs on: about 10¹³ FLOPS rough multiconfigurational propagation for tens of degrees of freedom.Since: 1990 Meyer, Manthe and Cederbaum's multiconfigurational time-dependent Hartree approach. source

Transition-state and reaction-path search

The lowest-energy route between two arrangements of atoms found by relaxing a chain of intermediate images, to get reaction barriers and rates.

Question it answers: What barrier must atoms cross when a molecule or defect changes shape?

Leaves out: It finds routes that exist near the guess and can miss the true lowest barrier.

Runs on: about 10¹⁴ FLOPS rough each image needs an electronic-structure calculation, repeated across the chain.Since: 1998 Jonsson, Mills and Jacobsen's nudged elastic band method for minimum energy paths. source

Automated reaction-mechanism generation

Rules generate every reaction a set of molecules could undergo, then a rate model prunes them to a mechanism for combustion or pyrolysis.

Question it answers: Which reactions matter when a fuel burns or breaks down?

Leaves out: Rate coefficients are estimated from group rules, and uncommon pathways are sparsely tested.

Runs on: about 10⁸ FLOPS rough network growth over thousands of species, plus kinetic runs.Since: 1994 Broadbelt, Stark and Klein's computer generated pyrolysis modelling with on-the-fly species and reaction generation. source

Quantum Monte Carlo for electrons

Random walkers sample the many-electron wavefunction directly, giving near-exact energies of molecules and solids without the density-functional approximation.

Question it answers: What is the accurate energy of this electron system, as a benchmark for cheaper methods?

Leaves out: The fermion sign problem is avoided by fixing the nodes of the wavefunction, which makes the answer depend on that guess.

Runs on: about 10¹⁷ FLOPS rough millions of core-hours for a molecular crystal.Since: 1980 Ceperley and Alder's stochastic calculation of the ground state of the electron gas. source

Learned density functionals

A machine-learning model maps the electron density to the energy, replacing the hand-built approximations in density-functional theory.

Question it answers: Can a fitted functional beat the hand-designed ones that chemists have used for decades?

Leaves out: The fitted functional is reliable only for the kinds of molecules and conditions represented in its training data.

Runs on: about 10¹⁶ FLOPS rough training on high-accuracy reference energies, then a standard-cost electronic-structure run.Since: 2012 Snyder, Rupp, Hansen, Müller and Burke's machine-learned density functionals for a model system. source

Neural-network wavefunctions for molecules

A neural network is used as the many-electron wavefunction of a molecule and trained by variational Monte Carlo to reach near-exact energies.

Question it answers: How accurately can a learned wavefunction describe the electrons of a small molecule?

Leaves out: Cost climbs steeply with the number of electrons, so only small molecules have been reached.

Runs on: about 10¹⁸ FLOPS rough days on tens of GPUs for one molecule.Since: 2019 Pfau and colleagues' FermiNet, a deep neural network solution of the many-electron Schrödinger equation. source

Liquids and solutions

Water and other liquids as millions of interacting molecules, with solutes dissolved in them.

Question it answers: Why does water show anomalous properties, and how does salt dissolve?

Leaves out: The force field between atoms is fitted to a small set of properties and is not guaranteed to reproduce the rest.

Runs on: about 10¹⁴ FLOPS rough a desktop GPU; billions of molecule-steps per second.Since: 1964 Rahman’s molecular dynamics of liquid argon; water followed with Rahman and Stillinger in 1971

Polymers and soft matter

Long-chain molecules, gels, foams and liquid crystals, usually coarse-grained into beads.

Question it answers: How does a plastic stretch, and how does a gel set?

Leaves out: Coarse-graining throws away the fast atomic motion, so the timing of some processes is only approximate.

Runs on: about 10¹⁴ FLOPS rough a desktop GPU or small cluster, hours per system.Since: 1962 Verdier and Stockmayer's early lattice Monte Carlo model of a polymer chain.

Combustion

Flames as fluid flow coupled to hundreds of chemical reactions.

Question it answers: How do we burn fuel cleaner, or stop an engine knocking?

Leaves out: Hundreds of real reactions are simplified to the dozens a computer can afford to track each step.

Runs on: about 10¹⁶ FLOPS rough a large cluster, days for a full engine cycle.Since: 1955 early numerical solutions of the laminar flame equations.

Colloids and nanoparticle assembly

Thousands of nanoparticles or colloidal grains driven by thermal fluctuations of the surrounding fluid, adhering, ordering or aggregating as they collide.

Question it answers: Will these particles self-assemble into an ordered structure, or aggregate disordered?

Leaves out: The details of a particle's surface coating strongly affect the outcome and are usually reduced to a single adhesion parameter.

Runs on: about 10¹³ FLOPS rough a workstation or desktop GPU, hours per assembly run.Since: 1986 early Brownian dynamics simulations of colloidal particles in suspension.

Glass formation

A liquid cooled so fast in simulation that its molecules jam into a disordered solid before they can crystallise.

Question it answers: Why does this liquid freeze into a disordered glass instead of an ordered crystal?

Leaves out: Simulated cooling is always far faster than any real glass has ever been cooled, by many orders of magnitude.

Runs on: about 10¹⁴ FLOPS rough a desktop GPU or small cluster, hours to days per run.Since: 1976 early molecular dynamics simulations of a liquid quenched into a glass.

Molten salts and ionic liquids

Ions rather than neutral molecules, interacting through strong Coulomb forces in a liquid with no solvent at all.

Question it answers: How well does this liquid conduct charge, and how do its ions move?

Leaves out: The strong electrostatic forces between ions are harder to capture in a force field than those of neutral molecules and are often only approximated.

Runs on: about 10¹⁴ FLOPS rough a desktop GPU or small cluster, hours per liquid studied.Since: 1983 early molecular dynamics simulations of a molten salt.

Reactive force-field dynamics

Molecular dynamics with bond-order potentials that let bonds form and break during the run, at far lower cost than quantum methods.

Question it answers: How do bonds break and form in thousands of atoms over nanoseconds?

Leaves out: Parameters are fitted per chemistry, and electrons are not treated explicitly.

Runs on: about 10¹⁶ FLOPS rough Millions of atoms for nanosecondsSince: 2001 ReaxFF: a reactive force field for hydrocarbons (2001) source

Metadynamics and enhanced sampling

Molecular dynamics in which a history-dependent bias pushes the system out of local minima to map rare events and free-energy surfaces.

Question it answers: How high are the barriers between states that plain dynamics never crosses?

Leaves out: The result depends on picking good collective variables.

Runs on: about 10¹⁷ FLOPS rough Many biased trajectories on a few chosen variablesSince: 2002 Escaping free-energy minima (2002) source

Learned equilibrium samplers

A generative network is trained to draw independent molecular configurations from the Boltzmann distribution, avoiding long trajectories.

Question it answers: Can rare states of a molecule be sampled directly instead of waiting for them?

Leaves out: Dynamics and kinetics are lost, and training is hard for large systems.

Runs on: about 10¹⁶ FLOPS rough Training plus reweightingSince: 2018 Boltzmann Generators: sampling equilibrium states of many-body systems with deep learning (2018) source

Kinetic Monte Carlo

Atoms hopping on a surface or in a crystal chosen at random with probabilities set by their rates, so processes that take seconds or hours are reached.

Question it answers: How does a surface or crystal change over the long times between atomic jumps?

Leaves out: Every possible event and its rate must be listed in advance, so surprising mechanisms are missed.

Runs on: about 10¹¹ FLOPS rough millions of events, with rates computed beforehand from first principles.Since: 1975 Bortz, Kalos and Lebowitz's event-driven Monte Carlo algorithm for Ising spin systems. source

Coarse-grained molecular dynamics

Groups of several atoms merged into single beads so membranes, polymers and self-assembling lipids can be followed for microseconds over larger boxes.

Question it answers: How do large molecular assemblies form over microseconds?

Leaves out: Merging atoms discards detail such as hydrogen-bond directionality, and time is not strictly physical.

Runs on: about 10¹⁶ FLOPS rough millions of beads over microseconds.Since: 2007 Marrink and colleagues' coarse-grained force field for biomolecular simulations. source

Dissipative particle dynamics

Soft beads that stand for clumps of fluid interact with friction and random kicks, giving correct hydrodynamics for polymers and colloids at large scales.

Question it answers: How do polymer and surfactant fluids flow and self-organise at mesoscopic scales?

Leaves out: Soft potentials allow chains to cross unphysically unless corrected.

Runs on: about 10¹⁴ FLOPS rough millions of beads over long times.Since: 1992 Hoogerbrugge and Koelman's simulation of microscopic hydrodynamic phenomena with dissipative particle dynamics. source

Enhanced-sampling free-energy methods

Simulations nudged to cross high barriers, such as adding history-dependent bias, so rare events and free-energy landscapes can be computed.

Question it answers: What is the free-energy cost of a rare change, such as nucleation or binding?

Leaves out: The answer depends on the choice of collective variables, and a missing one gives a wrong landscape.

Runs on: about 10¹⁶ FLOPS rough long biased runs along chosen variables.Since: 2002 Laio and Parrinello's escaping free-energy minima by metadynamics. source

Adsorption in porous materials

Gas molecules inserted and removed at random in a model of a porous solid, to predict how much a zeolite or framework material will adsorb.

Question it answers: How much gas does a porous material hold at a given pressure?

Leaves out: Rigid-framework and fixed-charge approximations misjudge flexible materials.

Runs on: about 10¹³ FLOPS rough millions of insertions per state point, thousands of structures.Since: 1975 Adams's grand canonical ensemble Monte Carlo for a Lennard-Jones fluid. source

Polymer self-consistent field theory

Chains replaced by a density field that feels its own average pull, so block copolymers and blends can be solved for their ordered patterns without tracking individual chains.

Question it answers: What pattern will a block copolymer self-assemble into?

Leaves out: Mean-field theory ignores fluctuations, which matter near phase boundaries.

Runs on: about 10¹² FLOPS rough solving diffusion equations on a grid in three dimensions.Since: 1965 Edwards's statistical mechanics of polymers with excluded volume. source

Chain-growth Monte Carlo for polymers

Long molecular chains built one bond at a time with weights, to measure their size, entropy and excluded-volume behaviour.

Question it answers: How big is a long flexible chain, and why does it not cross itself?

Leaves out: Weights grow unevenly with chain length, so very long ones need resampling tricks.

Runs on: about 10⁹ FLOPS rough millions of chains, far cheaper than dynamics.Since: 1955 Rosenbluth and Rosenbluth's Monte Carlo calculation of the average extension of molecular chains. source

Magnetism and phase transitions

Spins on a lattice flipping at random, the classic Ising model and its descendants, used to study how order appears at a critical temperature.

Question it answers: Why does a magnet lose its magnetism at exactly one temperature?

Leaves out: A real magnet has details of shape and impurity that the idealised lattice omits by construction.

Runs on: about 10¹² FLOPS rough a laptop; billions of spin flips per second.Since: 1953 the Metropolis accept–reject Monte Carlo method, later the standard tool for spin models; the 1953 paper itself simulated hard disks sourceIn the simulations tree: Metropolis algorithm

Run the interactive model

Fracture and defects

Atoms at the tip of a crack, and the defects that let metals bend instead of shattering.

Question it answers: Why does this material crack instead of bending?

Leaves out: A crack tip only a few atoms wide still has to stand in for one that runs through a whole beam.

Runs on: about 10¹⁴ FLOPS rough a desktop GPU or small cluster, hours per crack run.Since: 1976 Ashurst and Hoover's early molecular dynamics simulation of a crack tip.

Microstructure

Crystal grains forming and growing as a metal solidifies or is heat-treated, often with the phase-field method.

Question it answers: Which heat treatment gives the strongest alloy?

Leaves out: Grain boundaries are treated as smooth mathematical surfaces, not the messy defects they really are.

Runs on: about 10¹⁴ FLOPS rough a workstation or small cluster, hours per solidifying alloy.Since: 1991 Chen and Khachaturyan's early phase-field model of a growing microstructure.

Granular materials

Sand, grain, powders and pills as millions of individual particles colliding and jamming.

Question it answers: Why does the silo jam, and how does an avalanche start?

Leaves out: Real grains are rough and irregular; simulated ones are almost always idealised spheres.

Runs on: about 10¹⁴ FLOPS rough a desktop GPU or small cluster, millions of grains at once.Since: 1979 Cundall and Strack's first discrete element model of granular particles.

Run the interactive model

Dislocation dynamics

Line defects threading through a crystal's lattice, tracked as they move, multiply and tangle to produce permanent bending or stretching.

Question it answers: Why does this metal bend rather than snap, and how strong is it really?

Leaves out: Treats dislocations as clean lines in an otherwise perfect crystal, when real metals are full of other defects they interact with.

Runs on: about 10¹⁴ FLOPS rough a workstation or small cluster, hours to days per run.Since: 1990 early discrete dislocation dynamics simulations of crystal plasticity.

Thin film growth

Atoms arriving one by one on a surface and sticking, hopping or burying each other as a film builds up layer by layer.

Question it answers: Will this film grow smooth, or rough and full of defects?

Leaves out: Real deposition chambers have contamination and uneven flow that an idealised flux of atoms does not include.

Runs on: about 10¹³ FLOPS rough a workstation; hours per simulated film.Since: 1966 early kinetic Monte Carlo models of atoms arriving on a growing surface.

Radiation-damage cascades in materials

A fast atom knocked into a crystal, followed as it displaces neighbours and leaves vacancies, to predict how irradiated metals degrade.

Question it answers: How many atoms does a single impact knock out of a crystal?

Leaves out: Defects then evolve for years, far beyond the cascade, and need other methods to bridge the gap.

Runs on: about 10¹³ FLOPS rough millions of atoms for tens of picoseconds, repeated for many impact directions.Since: 1960 Gibson, Goland, Milgram and Vineyard's dynamics of radiation damage in a copper lattice. source

Alloy cluster expansion

The energy of an alloy written as a sum over small clusters of neighbouring atoms, so the order and phase diagram can be sampled with Monte Carlo.

Question it answers: Which arrangements of atoms does an alloy prefer, and when does it order?

Leaves out: The expansion is fixed to a given lattice and can miss vibrational and magnetic contributions.

Runs on: about 10¹² FLOPS rough hundreds of first-principles energies, then cheap lattice Monte Carlo.Since: 1984 Sanchez, Ducastelle and Gratias's generalised cluster description of multicomponent systems. source

Crystal plasticity finite-element modelling

Metal grains deforming by slip on specific crystal planes, with their individual orientations, to predict strength, texture and forming behaviour.

Question it answers: How do crystal orientations decide how a metal bends and hardens?

Leaves out: Hardening laws are fitted to tests and carry no memory of individual dislocations.

Runs on: about 10¹² FLOPS rough finite-element models of thousands of grains.Since: 1982 Peirce, Asaro and Needleman's analysis of nonuniform and localised deformation in ductile single crystals. source

Micromagnetic simulation

The direction of magnetisation in a magnet, discretised into cells, with exchange, anisotropy and stray fields, to follow how domains form and switch.

Question it answers: How does the magnetisation of a nanomagnet switch?

Leaves out: Temperature is treated crudely, and cells larger than the exchange length lose detail.

Runs on: about 10¹² FLOPS rough finite-difference runs with millions of cells.Since: 1988 Schabes and Bertram's three-dimensional micromagnetic study of magnetisation processes in ferromagnetic cubes. source

Organic semiconductor charge transport

Electrons or holes hopping between disordered molecules, simulated with random walks to predict mobility in plastic electronics.

Question it answers: How fast do charges move through a disordered organic material?

Leaves out: Hop rates are assumed forms and the morphology is idealised.

Runs on: about 10¹¹ FLOPS rough Monte Carlo hops on large lattices.Since: 1993 Bassler's Monte Carlo simulation of charge transport in disordered organic photoconductors. source

Lattice thermal-conductivity calculation

Heat carried by lattice vibrations, with their scattering rates from first principles, to predict thermal conductivity of a crystal without fitting.

Question it answers: How well does a crystal carry heat, from atoms alone?

Leaves out: Strongly anharmonic and disordered materials need extra treatment.

Runs on: about 10¹⁵ FLOPS rough thousands of force calculations in a supercell.Since: 2007 Broido, Malorny, Birner, Mingo and Stewart's intrinsic lattice thermal conductivity of semiconductors from first principles. source

Diffusion-limited aggregation

Particles wandering at random until they stick to a growing cluster, producing branching fractals like dendrites and mineral deposits.

Question it answers: Why do random walkers grow branching fractal clusters?

Leaves out: It models only one idealised growth rule, with no surface energy or chemistry.

Runs on: about 10⁸ FLOPS rough millions of walkers on a lattice.Since: 1981 Witten and Sander's diffusion-limited aggregation, a kinetic critical phenomenon. source

Generative models of crystals

A diffusion or variational model trained on known crystals proposes new periodic structures, which are then checked and relaxed with quantum-mechanical calculations.

Question it answers: Can a model dream up stable new materials rather than screening known ones?

Leaves out: Most proposed structures are unstable or unmakeable, and the model does not know how to synthesise any of them.

Runs on: about 10¹⁸ FLOPS rough weeks of GPU training, then a pipeline of electronic-structure checks.Since: 2021 Xie and colleagues' crystal diffusion variational autoencoder for periodic material generation. source

Catalysis

A reacting molecule sticking to a catalyst's surface, computed step by step to find the path that lowers the energy needed for the reaction.

Question it answers: Which surface, and which arrangement of atoms on it, speeds up this reaction the most?

Leaves out: Real catalysts have defects, poisons and ageing that a clean, perfect model surface never has to deal with.

Runs on: about 10¹⁵ FLOPS rough a university cluster, days per candidate catalyst surface.Since: 1995 early quantum calculations mapping a reaction path across a catalyst surface.

Battery and electrochemical cell modelling

A whole battery or fuel cell, its electrodes, electrolyte and interfaces, modelled together through charge, discharge and heating over many cycles.

Question it answers: How many cycles will this cell survive before it degrades, and how hot will it get?

Leaves out: Degradation over years of real use is still mostly extrapolated from short accelerated tests, not directly simulated.

Runs on: about 10¹⁴ FLOPS rough a workstation or small cluster, hours per simulated cycling test.Since: 1975 early mathematical models of a battery electrode's charge and discharge.

Corrosion

A metal surface losing atoms to an electrochemical reaction with its environment, tracked as it pits, thins or forms a protective layer.

Question it answers: How long will this metal last before it corrodes through?

Leaves out: Real corrosion depends strongly on local contamination, surface scratches and stray currents that an ideal model omits.

Runs on: about 10¹³ FLOPS rough a workstation; hours per corrosion scenario.Since: 1970 early computer models of pitting and electrochemical corrosion.

Crystallisation

Molecules or ions in a supersaturated solution finding each other and locking into a growing crystal lattice, used to predict how a compound will crystallise.

Question it answers: What shape and size of crystals will this process actually produce?

Leaves out: Nucleation, the very first cluster forming, happens on a scale and speed still too fast to observe or fully compute directly.

Runs on: about 10¹³ FLOPS rough a workstation or small cluster, hours per batch simulated.Since: 1988 early computed models of nucleation and growth from a supersaturated solution.

Chemical reactor engineering

Fluid flow, mixing, heat and hundreds of reaction steps inside an industrial vessel, modelled together to predict how much product comes out.

Question it answers: Will this reactor design mix and cool fast enough to get a clean, safe reaction?

Leaves out: Scaling up from a small test reactor to a full industrial one still loses accuracy in ways engineers correct for by experience.

Runs on: about 10¹⁵ FLOPS rough a university or industrial cluster, days per design studied.Since: 1970 early computational fluid dynamics models of an industrial chemical reactor.

Polymerisation kinetics

Small molecules linking up one reaction step at a time into long chains, tracked to predict how long they grow and how uniform they end up.

Question it answers: How long will the polymer chains be, and how much will that vary?

Leaves out: Side reactions that branch or terminate chains early are usually simplified into a few average rates.

Runs on: about 10¹² FLOPS rough a laptop; a full batch simulation takes minutes.Since: 1968 early computed kinetic models of a chain-growth polymerisation.

Fuel-cell membrane and transport modelling

Water, protons and gas moving through the membrane and electrodes of a fuel cell, to predict performance and when it dries out or floods.

Question it answers: How do water and charge move through a fuel cell membrane?

Leaves out: Membrane transport relies on fitted laws, and liquid water in pores is hard to model.

Runs on: about 10¹⁰ FLOPS rough two- or three-dimensional cell models, light on a workstation.Since: 1991 Springer, Zawodzinski and Gottesfeld's polymer electrolyte fuel cell model. source

Pore-network modelling

A porous rock or electrode reduced to a network of pores and throats, through which fluid invades step by step, to predict flow and capillary behaviour.

Question it answers: How does fluid fill and move through a porous material?

Leaves out: Real pore shapes are simplified to tubes and spheres.

Runs on: about 10¹⁰ FLOPS rough networks of up to millions of pores, cheap compared with direct flow.Since: 1956 Fatt's network model of porous media. source