Global optimization for inorganic crystals Inorganic solids | Elemental composition; optionally pressure, symmetry constraints, or cell-size limits. | Candidate unit cells and atomic coordinates, typically ranked by calculated energy or enthalpy. | Interatomic potentials for broad searches, followed by density functional theory (DFT) relaxation and ranking. | Can explore structures without requiring a known prototype; evolutionary, random-search, and swarm-based strategies can sample different regions of structure space. | Search cost grows with system size and complexity. Results depend on the energy model and search settings; a search may miss relevant structures. | Discovering plausible structures of inorganic compounds, including systems with unknown or unexpected crystal frameworks. |
Molecular-crystal structure prediction Molecular solids | Molecular identity and geometry, composition, and any known experimental or computational constraints. | Possible crystal packings, molecular orientations, unit cells, and relative lattice-energy rankings. | Molecular mechanics or force-field screening, often followed by periodic DFT or another higher-accuracy energy calculation. | Targets packing and polymorphism, where the same molecule can form multiple distinct crystal structures. | Small energy differences between polymorphs can be difficult to rank reliably; molecular flexibility, thermal effects, and disorder add complexity. | Assessing possible polymorphs of molecular compounds and generating candidate packings for experimental follow-up. |
Random-structure search Broad exploration | Composition, allowed cell sizes, and constraints such as minimum interatomic distances or pressure. | A population of independently generated candidate structures that are relaxed and compared. | Fast empirical or machine-learned potentials for initial screening; DFT for refinement and final comparisons. | Conceptually simple and able to sample diverse structures without relying on a single structural prototype. | Efficiency can be low in large search spaces, and outcomes may vary with constraints, sampling strategy, and the number of trials. | Initial exploration when little is known about likely structure families or symmetry. |
Evolutionary or population-based search Iterative search | Composition and a starting population of structures; optional symmetry, pressure, or chemical constraints. | Successive generations of candidate structures produced through selection and variation operations. | Structure relaxation and fitness ranking using interatomic potentials, machine-learned potentials, or DFT. | Uses information from better-performing candidates to guide later search steps and can efficiently explore complex landscapes. | Search diversity can diminish prematurely; performance depends on population design, variation operators, and energy evaluations. | Searching for low-energy structures when many candidate arrangements must be explored iteratively. |
Machine-learning-potential-assisted search Accelerated screening | Composition and candidate structures, plus a suitable trained interatomic model or reference data for model development. | Rapid approximate energies and forces that can guide structural searches and pre-screen candidates. | Machine-learned interatomic potentials, with selected candidates checked using DFT or experimental data. | Can reduce the cost per structure evaluation compared with performing DFT on every candidate. | Reliability depends on training coverage and transferability. Unfamiliar chemistries, phases, or pressure conditions require careful validation. | Large searches where a validated model is available and expensive first-principles evaluations need to be prioritized. |
First-principles structure relaxation and ranking High-accuracy refinement | Candidate crystal structures, composition, and computational settings such as exchange-correlation treatment and pressure. | Relaxed cell and atomic positions, electronic energies, forces, and related properties for supplied candidates. | Periodic DFT; higher-level electronic-structure methods may be used for selected systems when computationally practical. | Provides a physics-based refinement and comparison step for candidates generated by a separate search. | Usually too computationally expensive to exhaustively explore a large structure space by itself; energy differences depend on the chosen approximations. | Validating, relaxing, and ranking a shortlist of structures rather than generating all candidates from scratch. |
Prototype- and symmetry-guided search Constrained exploration | Composition plus candidate structural prototypes, space groups, or symmetry constraints. | Structures consistent with selected frameworks or symmetry choices, followed by relaxation and comparison. | Empirical potentials, machine-learned models, or DFT, depending on the screening stage. | Can focus computational effort when experimental analogues, chemical rules, or likely structural families are known. | May overlook structures outside the chosen prototypes or symmetry assumptions. | Testing plausible structure families or investigating materials related to known compounds. |