Cluster, as the aggregate of a few to thousands of atoms or molecules, bridges the microscopic world of atoms and molecules and the macroscopic world of condensed matters. The physical and chemical properties of a cluster are determined by its ground state structure, which is significantly different from its bulk structure and sensitively relies on the cluster size. As a well-known nondeterministic polynomial-time hard problem, determining the ground state structure of a cluster is a challenging task due to the extreme complexity of high-dimensional potential energy surface (PES). Genetic algorithm (GA) is an efficient global optimisation method to explore the PES of clusters. Recently, we have developed a GA-based programme, namely comprehensive genetic algorithm (CGA), and incorporated it with ab initio calculations. Using this programme, the lowest energy structures of a variety of elemental and compound clusters with different types of chemical bonding have been determined, and their physical properties have been investigated and compared with experimental data. In this article, we will describe the technique details of CGA programme and present an overview of its successful applications.

Using a genetic algorithm combined with density functional theory calculations, we perform a global search for the lowest-energy structures of B clusters with n = 46, 48, 50. Competition among different structural motifs including a hollow cage, core-shell, bilayer, and quasi-planar, is investigated. For B, a core-shell B@B structure resembling the larger B clusters with n ≥ 68 is found to compete with a quasi-planar structure with a central hexagonal hole. A quasi-planar configuration with two connected hexagonal holes is most favorable for B. More interestingly, an unprecedented bilayer structure is unveiled at B, which can be extended to a two-dimensional bilayer phase exhibiting appreciable stability. Our results suggest alternatives to the cage motif as lower-energy B cluster structures with n > 50.

Vanadium-doped silicon cluster anions, V 3 Si n − (n = 3−14), have been generated by laser vaporization and investigated by anion photoelectron spectroscopy. The vertical detachment energies (VDEs) and adiabatic detachment energies (ADEs) of these clusters were obtained. Meanwhile, genetic algorithm (GA) combined with density functional theory (DFT) calculations are employed to determine their groundstate structures systematically. Excellent agreement is found between theory and experiment. Among the V 3 Si n − clusters, V 3 Si 5 − , V 3 Si 9 − , and V 3 Si 12 − are relatively more stable. Generally speaking, three V atoms prefer to stay close with others and form strong V−V bonds. Starting from V 3 Si 11 − , cage configurations with one interior V atom emerge.

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The ground state structures of neutral and anionic clusters of Na(n)Si(m) (1 ≤ n ≤ 3, 1 ≤ m ≤ 11) have been determined using genetic algorithm incorporated in first principles total energy code. The size dependence of the structural and electronic properties is discussed in detail. It is found that the lowest-energy structures of Na(n)Si(m) clusters resemble those of the pure Si clusters. Interestingly, Na atoms in neutral Na(n)Si(m) clusters are usually well separated by the Si(m) skeleton, whereas Na atoms can form Na-Na bonds in some anionic clusters. The ionization potentials, adiabatic electron affinities, and photoelectron spectra are also calculated and the results compare well with the experimental data.

Stimulated by the early theoretical prediction of B80 fullerene and the experimental finding of the B40 cage, the structures of medium-sized boron clusters have attracted intensive research interest during the last decade, but a complete picture of their size-dependent structural evolution remains a puzzle.

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A complete core-shell and highly symmetric B96 was designed. The core-shell B96 of Th symmetry is energy-favorable to the bilayer motif, and the core-shell structure can be well maintained during...