--- title: "Chemistry and materials · Simulations · Simulation Hypothesis" url: https://simulation-hypothesis.com/simulations/chemistry-materials description: "Electrons, bonds, liquids, crystals and fracture: the behaviour of matter before it is synthesised. Part of a taxonomy of the simulations people actually run." license: https://creativecommons.org/licenses/by/4.0/ credit: "Ross Allan Dahl, Simulation Hypothesis (simulation-hypothesis.com)" --- [Simulations](https://simulation-hypothesis.com/simulations)domain 4 of 18 # Chemistry and materials Electrons, bonds, liquids, crystals and fracture: the behaviour of matter before it is synthesised. Materials and reactions can be simulated before they are made: electrons for chemistry, atoms for mechanics, grains for microstructure. Computational chemistry is one of the largest consumers of supercomputer time. ## Electrons and bonds ### 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 10^15 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. [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ### 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 10^15 FLOPS rough a university cluster, days per reaction studied. Since: 1976 Warshel and Levitt's first combined quantum and classical reaction model. [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Atoms ### 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 10^16 FLOPS rough a large cluster, running thousands of calculations in parallel. Since: 2006 early high-throughput calculations screening candidate materials. [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Atoms ### 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 10^15 FLOPS rough a university cluster, hours to days per molecule. Since: 1984 early time-dependent quantum chemistry calculations of excited molecules. [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ### 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 10^14 FLOPS rough a workstation or small cluster, hours per molecule. Since: 1974 early computed nuclear magnetic resonance shifts compared against measured spectra. [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ### 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 10^14 FLOPS rough a workstation or small cluster, minutes to hours per molecule. Since: 1981 early continuum solvation models added to quantum chemistry calculations. [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ### 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 10^17 FLOPS rough Training on thousands of quantum calculations, then large MD Since: 2007 Generalized neural-network representation of high-dimensional potential-energy surfaces (2007) [source](https://doi.org/10.1103/PhysRevLett.98.146401) In the simulations tree: [Learned surrogate models](https://simulation-hypothesis.com/trees/simulations?n=m-learned) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Atoms ### 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 10^17 FLOPS rough Training on millions of structures, cheap inference Since: 2022 A universal graph deep learning interatomic potential for the periodic table (2022) [source](https://arxiv.org/abs/2202.02450) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)floor: Atoms ### 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 small Since: 2014 A variational eigenvalue solver on a photonic quantum processor (2014) [source](https://doi.org/10.1038/ncomms5213) [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Molecules ### 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 10^16 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. [source](https://doi.org/10.1103/physrevlett.55.2471) In the simulations tree: [Ab initio molecular dynamics](https://simulation-hypothesis.com/trees/simulations?n=mat-abinitio) [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Atoms ### 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 10^15 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](https://doi.org/10.1063/1.446740) [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Atoms ### 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 10^16 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](https://doi.org/10.1103/physrevb.54.4484) [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Atoms ### 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 10^13 FLOPS rough multiconfigurational propagation for tens of degrees of freedom. Since: 1990 Meyer, Manthe and Cederbaum's multiconfigurational time-dependent Hartree approach. [source](https://doi.org/10.1016/0009-2614%2890%2987014-i) [Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Molecules ### 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 10^14 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](https://doi.org/10.1142/9789812839664%5F0016) [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Atoms ### 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 10^8 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](https://doi.org/10.1021/ie00028a003) [Rules and states](https://simulation-hypothesis.com/simulations/methods#m-rules)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Molecules ### 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 10^17 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](https://doi.org/10.1103/physrevlett.45.566) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ### 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 10^16 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](https://doi.org/10.1103/physrevlett.108.253002) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ### 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 10^18 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](https://arxiv.org/abs/1909.02487) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ## Molecules in motion ### 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 10^14 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 [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Molecules ### 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 10^14 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. [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Molecules ### 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 10^16 FLOPS rough a large cluster, days for a full engine cycle. Since: 1955 early numerical solutions of the laminar flame equations. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### 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 10^13 FLOPS rough a workstation or desktop GPU, hours per assembly run. Since: 1986 early Brownian dynamics simulations of colloidal particles in suspension. [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Molecules ### 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 10^14 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. [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Molecules ### 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 10^14 FLOPS rough a desktop GPU or small cluster, hours per liquid studied. Since: 1983 early molecular dynamics simulations of a molten salt. [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Molecules ### 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 10^16 FLOPS rough Millions of atoms for nanoseconds Since: 2001 ReaxFF: a reactive force field for hydrocarbons (2001) [source](https://doi.org/10.1021/jp004368u) [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Atoms ### 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 10^17 FLOPS rough Many biased trajectories on a few chosen variables Since: 2002 Escaping free-energy minima (2002) [source](https://doi.org/10.1073/pnas.202427399) [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Atoms ### 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 10^16 FLOPS rough Training plus reweighting Since: 2018 Boltzmann Generators: sampling equilibrium states of many-body systems with deep learning (2018) [source](https://arxiv.org/abs/1812.01729) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Molecules ### 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 10^11 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](https://doi.org/10.1016/0021-9991%2875%2990060-1) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)floor: Atoms ### 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 10^16 FLOPS rough millions of beads over microseconds. Since: 2007 Marrink and colleagues' coarse-grained force field for biomolecular simulations. [source](https://doi.org/10.1021/jp071097f) [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Molecules ### 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 10^14 FLOPS rough millions of beads over long times. Since: 1992 Hoogerbrugge and Koelman's simulation of microscopic hydrodynamic phenomena with dissipative particle dynamics. [source](https://doi.org/10.1209/0295-5075/19/3/001) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)floor: Molecules ### 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 10^16 FLOPS rough long biased runs along chosen variables. Since: 2002 Laio and Parrinello's escaping free-energy minima by metadynamics. [source](https://doi.org/10.1073/pnas.202427399) [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Atoms ### 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 10^13 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](https://doi.org/10.1080/00268977500100221) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Molecules ### 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 10^12 FLOPS rough solving diffusion equations on a grid in three dimensions. Since: 1965 Edwards's statistical mechanics of polymers with excluded volume. [source](https://doi.org/10.1088/0370-1328/85/4/301) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Molecules ### 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 10^9 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](https://doi.org/10.1063/1.1741967) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Molecules ## Solids ### 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 10^12 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 [source](https://zhanggroup.org/teaching/literature/Metropolis1953.pdf) In the simulations tree: [Metropolis algorithm](https://simulation-hypothesis.com/trees/simulations?n=m-mcmc) [Run the interactive model](https://simulation-hypothesis.com/simulations/run#toy-ising) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Atoms ### 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 10^14 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. [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)floor: Atoms ### 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 10^14 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. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Fields ### 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 10^14 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](https://simulation-hypothesis.com/simulations/run#toy-sand) [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Bodies ### 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 10^14 FLOPS rough a workstation or small cluster, hours to days per run. Since: 1990 early discrete dislocation dynamics simulations of crystal plasticity. [Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Atoms ### 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 10^13 FLOPS rough a workstation; hours per simulated film. Since: 1966 early kinetic Monte Carlo models of atoms arriving on a growing surface. [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Atoms ### 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 10^13 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](https://doi.org/10.1103/physrev.120.1229) [Molecular dynamics](https://simulation-hypothesis.com/simulations/methods#m-molecular-dynamics)[Particles and N-body](https://simulation-hypothesis.com/simulations/methods#m-particles)floor: Atoms ### 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 10^12 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](https://doi.org/10.1016/0378-4371%2884%2990096-7) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Lattice field theory](https://simulation-hypothesis.com/simulations/methods#m-lattice)floor: Atoms ### 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 10^12 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](https://doi.org/10.1016/0001-6160%2882%2990005-0) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### 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 10^12 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](https://doi.org/10.1063/1.341858) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### 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 10^11 FLOPS rough Monte Carlo hops on large lattices. Since: 1993 Bassler's Monte Carlo simulation of charge transport in disordered organic photoconductors. [source](https://doi.org/10.1002/pssb.2221750102) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)floor: Molecules ### 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 10^15 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](https://doi.org/10.1063/1.2822891) [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Atoms ### 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 10^8 FLOPS rough millions of walkers on a lattice. Since: 1981 Witten and Sander's diffusion-limited aggregation, a kinetic critical phenomenon. [source](https://doi.org/10.1103/physrevlett.47.1400) [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)floor: Rules ### 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 10^18 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](https://arxiv.org/abs/2110.06197) [Learned emulators](https://simulation-hypothesis.com/simulations/methods#m-learned)[First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ## Reactions, catalysis and electrochemistry ### 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 10^15 FLOPS rough a university cluster, days per candidate catalyst surface. Since: 1995 early quantum calculations mapping a reaction path across a catalyst surface. [First principles](https://simulation-hypothesis.com/simulations/methods#m-first-principles)floor: Atoms ### 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 10^14 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. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### 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 10^13 FLOPS rough a workstation; hours per corrosion scenario. Since: 1970 early computer models of pitting and electrochemical corrosion. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)floor: Fields ### 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 10^13 FLOPS rough a workstation or small cluster, hours per batch simulated. Since: 1988 early computed models of nucleation and growth from a supersaturated solution. [Monte Carlo](https://simulation-hypothesis.com/simulations/methods#m-monte-carlo)[Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Molecules ### 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 10^15 FLOPS rough a university or industrial cluster, days per design studied. Since: 1970 early computational fluid dynamics models of an industrial chemical reactor. [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)floor: Fields ### 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 10^12 FLOPS rough a laptop; a full batch simulation takes minutes. Since: 1968 early computed kinetic models of a chain-growth polymerisation. [Stochastic processes](https://simulation-hypothesis.com/simulations/methods#m-stochastic)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Molecules ### 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 10^10 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](https://doi.org/10.1149/1.2085971) [Continuum fields](https://simulation-hypothesis.com/simulations/methods#m-continuum)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields ### 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 10^10 FLOPS rough networks of up to millions of pores, cheap compared with direct flow. Since: 1956 Fatt's network model of porous media. [source](https://doi.org/10.2118/574-g) [Network models](https://simulation-hypothesis.com/simulations/methods#m-network)[Differential equations](https://simulation-hypothesis.com/simulations/methods#m-equations)floor: Fields [◂ Earth and climate](https://simulation-hypothesis.com/simulations/earth-climate)[Life and medicine ▸](https://simulation-hypothesis.com/simulations/life-medicine)