Quantum mechanics

Crystal (programming language)

Pure mathematics

Materials science

Group theory

Graph theory

Random graph

Operating system

Crystal structure

Computer science

Acoustics

Lattice (music)

Physics

Crystal structure prediction

Graphite

Graph

Mathematics

Composite material

Combinatorics

Crystallography

Chemistry

Programming language

Quotient

Group (periodic table)

Space (punctuation)

Physical review. B./Physical review. B

A method is introduced to stochastically generate crystal structures with defined structural characteristics. Reasonable quotient graphs for symmetric crystals are constructed using a random strategy combined with space group and graph theory. Our algorithm enables the search for large-size and complex crystal structures with a specified connectivity, such as threefold ${\mathrm{sp}}^{2}$ carbons, fourfold ${\mathrm{sp}}^{3}$ carbons, as well as mixed ${\mathrm{sp}}^{2}\text{\ensuremath{-}}{\mathrm{sp}}^{3}$ carbons. To demonstrate the method, we randomly construct initial structures adhering to space groups from 75 to 230 and a range of lattice constants, and we identify 281 new ${\mathrm{sp}}^{3}$ carbon crystals. First-principles optimization of these structures show that most of them are dynamically and mechanically stable and are energetically comparable to those previously proposed. Some of the new structures can be considered as candidates to explain the experimental cold compression of graphite.

Stochastic generation of complex crystal structures combining group and graph theory with application to carbon