Endohedral CH(4)@(H(2)O)(n) (n = 16, 18, 20, 22, 24) clusters with standard and nonstandard cage configurations containing four-, five-, six-, seven-membered rings were generated by spiral algorithm and were systematically explored using DFT-D methods. The geometries of all isomers were optimized in vacuum and aqueous solution. In vacuum, encapsulation of methane molecules can stabilize the hollow (H(2)O)(n) cage by 2.31~5.44 kcal/mol; but the endohedral CH(4)@(H(2)O)(n) cages are still less stable than the pure (H(2)O)(n) clusters. Aqueous environment could promote the stabilities of the hollow (H(2)O)(n) cages as well as the CH(4)@(H(2)O)(n) clusters, and the CH(4)@(H(2)O)(n) clusters possess larger stabilization energies with regard to the pure (H(2)O)(n) clusters except for n = 24. The lowest energy structures of the CH(4)@(H(2)O)(20) and CH(4)@(H(2)O)(24) cages are identical to the building units in the crystalline sI clathrate hydrate. All of the low-energy cages (including both regular and irregular ones) have large structural similarity and can be connected by "dimer-insertion" operation and Stone-Wales transformation. Our calculation also showed that in the range of cluster size n = 16-24, the relative energies of cage isomers tend to decrease with increasing number of the adjacent pentagons in the oxygen skeleton structures. In addition to the regular endohedral CH(4)@(H(2)O)(20) and CH(4)@(H(2)O)(24) cage structures, some nonstandard CH(4)@(H(2)O)(n) (n = 18, 20, 22, 24) cages have lower energies and might appear during nucleation process of methane hydrate. For the methane molecules in these low-energy cage isomers, we found that the C-H symmetric stretching frequencies show a red-shift trend and the (13)C NMR chemical shifts generally move toward negative values as the cavity size increases. These theoretical results are comparable to the available experimental data and might help experimental identification of the endohedral water cages during nucleation.

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.

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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.