CALYPSO Crystal And Cluster Structure Prediction: Method And Applications

The structure of a material is the basic information for understanding its variousphysical and chemical properties. Currently, there still exist problems and challengesconcerning the sole use of experimental measurement to determine the structure of amaterial, such as purity of the sample, quality of the signal and external conditions.Here, theoretical structure prediction is crucial. It not only can assist experiment todetermine the structures, but also can predict structure with novel physical andchemical properties, having profound guiding significance for experiment. There aretwo main methodologies on theoretical structure prediction:（i） the method toovercome the energy barrier based on the guessed initial structures and （ii） geneticalgorithm based on the group searches. The first kind of methods heavily depends onthe initial structures and is not able to overcome the very large energy barrier, whilegenetic algorithm may allow structures trapped in the local minimum and has theproblem of structural diversity and the difficulty in handling the large systems. Thusthe developing of reliable and efficient structure prediction method is an urgent issue.Particle swarm optimization （PSO） algorithm is a global optimization algorithmbased on the group search, which was proposed by Eberhart and Kennedy at1995, Asa high efficient multiple target algorithm, it has been applied to system identificationand training of neural network. Recently, we have developed a CALYPSO （Crystalstructure AnaLYsis by Particle Swarm Optimization） methodology, which is the firstapplication of PSO algorithm into extended systems. The CALYPSO method canefficiently explore the multidimensional potential energy surfaces of a periodic system at given external conditions （e.g., pressure） and requires only known information ofchemical compositions to predict the stable structure. It has been successfully appliedto the prediction of many systems （e.g., elemental, binary and ternary compounds）with various chemical-bonding environments （e.g., metallic, ionic, and covalentbonding）. Clusters are non-periodic systems and can be regarded as zero-dimensionalmaterials. They possess various structural motifs and usually exhibit geometricalfrustration due to the competition between surface and bulk. Thus the directapplication of CALYPSO method, which was earlier designed for periodic systems,into the prediction of cluster structures is not feasible. There, both the structuralgeneration and characterization techniques are inefficient when dealing with clusters.The main algorithm of PSO should also be properly revised to allow the structuralevolution of clusters. In this thesis, based on the accumulation of early experiencewe,we have developed CALYPSO cluster structure prediction method and programed thederived formula into the CALYPSO software. Then, we have investigated the crystalstructures of lithium under high pressure and the cluster structure of boron. The mainresults of the thesis are as follows:1. We have developed the CALYPSO methodology for cluster structureprediction based on the PSO algorithm. The key elements of the proposed methodsare random structural generation based on the symmetry constraints, structuralcharacterization based on the bond characterization matrix （BCM） and structuralevolution based on the PSO algorithm. We find that the introduction of point groupsymmetries into generation of cluster structures enables structural diversity, reducesthe search space and apparently avoids the generation of liquid-like （disordered）structures. We have specifically devised a technique of so-called bondcharacterization matrix to allow the proper measure on the structural similarity. TheBCM technique was then employed to eliminate similar structures and define thedesirable local search spaces. We have introduced two versions （global and local） ofPSO algorithm into the CALYPSO method. While the global PSO is powerful forglobal structural convergence, the local PSO allows a fine exploration of the potential energy surface, suitable for difficult system. Our method has been extensivelybenchmarked on Lennard-Jones （LJ） clusters with different sizes up to150atoms andapplied into prediction of new structures of medium-sized Lin（n=20,40,58） clusters.High search efficiency was achieved, demonstrating the reliability of the currentmethodology and its promise as a major method on cluster structure prediction.2. The light alkali elements lithium （Li） and sodium （Na） are often consideredto be “simple” metals as their electronic properties are well described by the nearlyfree-electron model at ambient conditions. However, there are growing evidences thatthese materials exhibit unexpectedly complex behavior under compression. Especially,pressure-induced metal-to-semiconductor/insulator transitions were observed in bothLi and Na. While the insulating phase of Na has been determined to adopt the c-axishighly compressed double hexagonal-close-packed structure, the structure of thesemiconducting phase of Li is still in mystery. In this thesis, we have systematicallyinvestigated the high-pressure phases of Li based on the CALYPSO crystal structureprediction method and proposed a complex base-centered orthorhombic structure,Aba2-40（40atoms per cell, stable at60-80GPa）. Our calculations reveal that aninsulating electronic state emerges in the Aba2-40phase because core exclusion andthe localization of valence electrons in the voids of crystal. Here, compression causesthe2p bands to rapidly drop in energy relative to the2s bands, resulting in theincreased transformation from s to p electrons. Currently, the Aba2-40structure hasbeen confirmed by independent experimental work.We also targeted on the high-pressure structures in the range of100-500GPa. Inthis pressure range, as the localization energy cost becomes larger. Li shows severalother phase transitions. We unraveled an intriguing orthorhombic structure ofCmca-56（56atoms per cell, stable at185-269GPa）. This structure is in fact athreefold coordinated structure, where each Li atom and its three nearest neighborsform a trigonal plane. We predict that the local trigonal planar structural motif adoptedby Cmca-56exists in a wide pressure range of85-434GPa, favorable for the weakmetallic feature. The present results inevitably stimulate future experimental and theoretical study of Li at high pressure.3Much effort has been devoted to the synthesis of fullerene-like structures thatformed by elements other than carbon, in order to find possible building block fornonasciences. However, since the discovery of C₆₀ buckyball in1985, no other bareelemental fullerene structures have been synthesized. Boron is the first element topossess a p electron in the periodic table. The unique characters of boron, such aselectron deficiency, short covalent radius and flexibility to adopt sp2and three-centerbonds, endow boron clusters various structural motif and intriguing chemical bonding.By means of the CALYPSO cluster structure prediction method and first-principlescalculations, we propose a hollow cage with D_2h symmetry as the ground-statestructure for B38clusters. The structure is composed of boron triangles and fourhexagonal holes, which can be seen as a hexagonal hole-doped icosahedron. It isenergetically superior to the double-ring structure by about1.32eV and has a largeenergy gap of1.11eV. Chemical bonding analysis reveals that the B₃₈hollow cagepossesses an intriguing doubly aromaticity. It is even more aromatic than the knownmost aromatic quasi-planar B₁₂and double-ring B₂₀clusters. The large energy gap andthe high aromaticity indicate that the B₃₈hollow cage can be seen as an all-boronfullerene, which possesses a close-shell electronic structure and should be chemicallyinert. The present results inevitably simulate further experimental and theoreticalstudies of medium-sized boron clusters.