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.
Our ab initio global searches reveal the lowest-energy cage for B28, which is built from two B12 units and prevails over the competing structural isomers such as planar, bowl, and tube. This smallest boron cage extends the scope of all-boron fullerene and provides a new structural motif of boron clusters and nanostructures.
Clathrate hydrates of natural gases
are important backup energy
sources. It is thus of great significance to explore the nucleation
process of hydrates. Hydrate clusters are building blocks of crystalline
hydrates and represent the initial stage of hydrate nucleation. Using
dispersion-corrected density functional theory (DFT-D) combined with
machine learning, herein, we systematically investigate the evolution
of stabilities and nuclear magnetic resonance (NMR) chemical shifts
of amorphous precursors from monocage clusters CH4(H2O)
n
(n = 16–24)
to decacage clusters (CH4)10(H2O)
n
(n = 121–125). Compared
with planelike configurations, the close-packed structures formed
by the water-cage clusters are energetically favorable. The 512 cages are dominant, and the emerging amorphous precursors
may be part of sII hydrates at the initial stage of nucleation. Based
on our data set, the possible initial fusion pathways for water-cage
clusters are proposed. In addition, the 13C NMR chemical
shifts for encapsulated methane molecules also showed regular changes
during the fusion of water-cage clusters. Machine learning can reproduce
the DFT-D results well, providing a structure–energy-property
landscape that could be used to predict the energy and NMR chemical
shifts of such multicages with more water molecules. These theoretical
results present vital insights into the hydrate nucleation from a
unique perspective.
Protonated water cluster is one of the most important hydrogen-bond network systems. Finding an appropriate DFT method to study the properties of protonated water clusters can substantially improve the economy in computational resources without sacrificing the accuracy compared to high-level methods. Using high-level MP2 and CCSD(T) methods as well as experimental results as benchmark, we systematically examined the effect of seven exchange-correlation GGA functionals (with BLYP, B3LYP, X3LYP, PBE0, PBE1W, M05-2X, and B97-D parametrizations) in describing the geometric parameters, interaction energies, dipole moments, and vibrational properties of protonated water clusters H(HO). The overall performance of all these functionals is acceptable, and each of them has its advantage in certain aspects. X3LYP is the best to describe the interaction energies, and PBE0 and M05-2X are also recommended to investigate interaction energies. PBE0 gives the best anharmonic frequencies, followed by PBE1W, B97-D and BLYP methods. PBE1W, B3LYP, B97-D, and X3LYP can yield better geometries. The capability of B97-D to distinguish the relative energies between isomers is the best among all the seven methods, followed by M05-2X and PBE0.
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